laser pointer slit experiment

December 12, 2013

Double-Slit Science: How Light Can Be Both a Particle and a Wave

Learn how light can be two things at once with this illuminating experiment

By Education.com & Mack Levine

Key Concepts Light Wave Particle Lasers

Introduction You may have heard that light consists of particles called photons. How could something as simple as light be made of particles? Physicists describe light as both a particle and a wave. In fact, light's wavelike behavior is responsible for a lot of its cool effects, such as the iridescent colors produced on the surface of bubbles. To see a dramatic and mind-bending example of how light behaves like a wave, all you need is three pieces of mechanical pencil lead, a laser pointer and a dark room.

Background Sound is a great example of a wave that propagates, or travels, much like ripples in a pond do. In both cases kinetic energy flows through matter without permanently displacing the molecules in the matter itself—instead, it puts the matter through phases of compression (where the molecules get pushed together) and rarefaction (where the molecules spread apart). Think of the inside of a speaker vibrating with the music.

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When waves come into contact with one another, they exhibit interference: waves that are all in phase (rarefying or compressing the same particles at the same time) add together to become stronger, and waves that are out of phase with one another (for example, one wave attempts to rarefy particles in a medium while another attempts to compress those same particles) cancel out. This is how noise-canceling headphones work—they produce a sound wave that resembles the wave responsible for the unwanted sound, but with the original phases of rarefaction and compression flipped. This has the effect of dampening the offending sound wave's effect on the air molecules. So that by the time its energy reaches your ear, the sound you perceive is more of a whisper than a shout—or an airplane engine's roar is more like a quiet hum.

Diffraction is another important feature of waves: When waves encounter small openings, they spread out after they pass through. In the following experiment we'll set up two slits to give waves of light the opportunity to diffract as they travel through them. The different points at which the diffracted waves overlap should demonstrate some cool patterns of constructive and destructive interference, and you'll get to witness the puzzling effect of light "canceling itself out."

Materials • Three or more pieces of mechanical pencil lead (either 0.5 or 0.7 millimeter) • Laser pointer (Red will work just fine, but green produces a more dramatic effect.) • Dark room

Procedure • Darken the room. • Stand about four feet from a wall. • Hold the three pieces of pencil lead between your thumb and forefinger of your nondominant hand (your left hand if you are right-handed). Spread them apart very slightly so that you create two tiny gaps between the leads. These will act as your diffraction slits. • Shine your laser through the slits you created, and look at the pattern of light emitted on the wall. What do you see? • Play around with the positioning of your pencil leads, your laser and the width of the slits you created. When you get everything right, you should see a distinct pattern of dots appear on the wall behind the pencil lead. • Extra : Try using more pencil leads to create more diffraction slits. How does adding more slits change the pattern of light projected on the wall? Results and observations Laser light is emitted in the form of parallel waves that are coherent, or in phase with one another: all of the peaks and valleys line up. This is quite different than the light emitted from a flashlight—the rays are neither parallel nor in phase with each other. The laser's waves diffract as they pass through the slits you made, fanning out in a shotgunlike pattern from each slit. This allows them to interfere with one another as they overlap. In some places the waves will interfere constructively, creating bright spots on the wall. In other places the waves cancel themselves out, leading to the dark spaces you see between the spots.

If light demonstrated particlelike behavior exclusively, you would see only two dots on the wall corresponding to the locations of the slits. Oddly enough, Isaac Newton understood light this way: as a stream of particles, like a series of baseballs being thrown in a straight line. The problem posed by the double-slit experiment is that "baseballs" thrown through one hole seem to care about what the baseballs thrown through the other hole do! In the 19th century scientists decided that light must be a wave, but after witnessing light demonstrating particlelike behavior, Albert Einstein proposed that light can indeed be described as a particle (called a photon). The physicist Max Planck panicked, claiming, "the theory of light would be thrown back not by decades, but by centuries" if the scientific community were to accept Einstein's theory! But scientists ultimately arrived at the conclusion that light is both a particle (photon) and a wave.

Think of light's wave function as corresponding to the likelihood of a photon being in a certain place at a certain time. This makes it a little easier to understand how photons are forced to arrive at certain positions on the wall when their waves interfere with one another. What's less intuitive is the fact that photons fired one at a time toward two slits still demonstrate the same wavelike interference behavior after they pass through—it's as though individual photons are able to travel through two slits at once while still arriving at one location!

More to Explore The Original Double-Slit Experiment , from Veritasium Double-Slit Experiment Explained! By Jim Al-Khalili , from The Royal Institution Wave–Particle Duality of Light , from Education.com Young's Double-Slit Experiment , from YouTube Bubble Colors , from The Exploratorium

This activity brought to you in partnership with  Education.com

What is the double-slit experiment, and why is it so important?

Reality will surprise you..

John Loeffler

Timm Weitkamp/Wikimedia Commons

Few science experiments are as strange and compelling as the double-slit experiment. 

Few experiments, if any, in modern physics are capable of conveying such a simple idea—that light and matter can act as both waves and discrete particles depending on whether they are being observed—but which is nonetheless one of the great mysteries of quantum mechanics.

It’s the kind of experiment that despite its simplicity is difficult to wrap your mind around because what it shows is incredibly counter-intuitive.

But not only has the double-slit experiment been repeated countless times in physics labs around the world, but it has also even spawned many derivative experiments that further reinforce its ultimate result, that particles can be waves or discrete objects and that it is as if they “know” when you are watching them.

What does the double-slit experiment demonstrate?

To understand what the double-slit experiment demonstrates, we need to lay out some key ideas from quantum mechanics.

In 1925, Werner Heisenberg presented his mentor, the eminent German physicist Max Born, with a paper to review that showed how the properties of subatomic particles, like position, momentum, and energy, could be measured. 

Born saw that these properties could be represented through mathematical matrices, with definite figures and descriptions of individual particles, and this laid the foundation for the matrix description of quantum mechanics .

Meanwhile, in 1926,  Edwin Schrödinger  published his wave theory of quantum mechanics which showed that particles could be described by an equation that defined their waveform; that is, it determined that particles were actually waves.

This gave rise to the concept of wave-particle duality, which is one of the defining features of quantum mechanics. According to this concept, subatomic entities can be described as both waves and particles, and it is up to the observer to decide how to measure them.

That last part is important since it will determine how quantum entities will manifest. If you try to measure a particle’s position, you will measure a particle’s position, and it will cease to be a wave at all.

If you try to define its momentum, you will find that behaves like a wave and you can’t know anything definitive about its position beyond the probability that it exists at any given point within that wave.

Essentially, you will measure it as a particle or a wave, and doing so decides what form it will take.

The double-slit experiment is one of the simplest demonstrations of this wave-particle duality as well as a central defining weirdness of quantum mechanics, one that makes the observer an active participant in the fundamental behavior of particles.

How does the double-slit experiment work?

The easiest way to describe the double-slit experiment is by using light. First, take a source of coherent light, such as a laser beam, that shines in a single wavelength, like purely blue visible light at 460nm, and aim it at a wall with two slits in it.  The distance between the slits should be roughly the same as the light’s wavelength  so that they will both sit inside that beam of light.

Behind that wall, place a screen that can detect and record the light that impacts it. If you fire the laser beam at the two slits, on the recording screen behind the wall you will see a stripey pattern like this:

This is probably not what you might have been expecting, and that’s perfectly rational if you treat light as if it were a wave. If the light was a wave, then when the single wave of light from the laser hit both slits, each slit would become a new “source” of light on the other side of the wall, and so you would have a new wave originating from each slit producing two waves.

Where those two waves intersect causes something known as interference, and it can be either constructive or destructive. When the amplitude of the waves overlaps at either a peak or a trough, it acts to boost the wavelength in either direction by adding its energy together. This is constructive interference, and it produces these brighter bars in this pattern.

When the waves cancel each other out, as when a peak hits a trough, the effect neutralizes the wavelength and diminishes or even eliminates the light, producing the blacked-out spaces in between the blue bars.

But in the case of quantum entities like photons of light or electrons, they are also individual particles. So what happens when you shoot a single photon through the double slits?

One photon alone reacting to the screen might leave a tiny dot behind, which might not mean much in isolation, but if you shoot many single photons at the double slits, those tiny dots that the photon leaves behind on our screen actually show up in that same stripey interference pattern produced by the laser beam hitting the double slits.

In other words, the individual photon behaves as if it passed through both slits like it was a wave.

Now, here’s where things get really weird.

We can set up a detector in front of one of the slits that can watch for photons and light up whenever it detects one passing through. When we do this, the detector will light up 50% of the time, and the pattern left behind on the screen changes, giving us something that looks like this:

And to make things even wilder, we can set up a detector behind the wall that only detects a photon after it has passed through the slit and we get the same result. That means that even if the photon passes through both slits as a wave, the moment it is detected, it is no longer a wave but a particle. And not just that, that second wave emerging from the other slit also collapses back into the particle that was detected passing through the other slit.

In practice, this means that somehow the universe “knows” that someone is watching and flips the metaphorical quantum coin to see which slit the particle passed through. The more individual photons you shoot through the double slit, the closer that photon detector comes to detecting photons 50% of the time, just as flipping a coin 10 times might give you heads 70% of the time while flipping it 100 times might give you tails 55% of the time, and flipping it 1 billion times gives you heads 50.0003% of the time.

This seems to show that not only is the universe watching the observer as well, but that the quantum states of entities passing through the double slits are governed by the laws of probability, making it impossible to ever predict with certainty what the quantum state of an entity will be.

Who invented the double-slit experiment?

The double-slit experiment actually predates quantum mechanics by a little more than a century.

During the Scientific Revolution, the nature of light was a particularly contentious topic, with many—like Isaac Newton himself—arguing in favor of a corpuscular theory of light that held that light was transmitted through particles.

Others believed that light was a wave that was transmitted through “aether” or some other medium, the way sound travels through air and water, but Newton’s reputation and a lack of an effective means to demonstrate the wave theory of light solidified the corpuscular view for just shy of a century after Newton published his  Opticks in 1704 .

The definitive demonstration came from the British polymath Thomas Young, who presented a paper to the Royal Society of London in 1803 that described a pair of simple experiments that anyone could perform to see for themselves that light was in fact a wave.

First, Young established that a pair of waves were subject to interference when they overlapped, producing a distinctive interference pattern.

He initially demonstrated this interference pattern using a ripple tank of water, showing that such a pattern is characteristic of wave propagation.

Young then introduced the precursor to the modern double-slit experiment, though instead of using a laser beam to produce the required light source, Young used reflected sunlight striking two slits in a card as its target.

The resulting light diffraction showed the expected interference pattern, and the wave theory of light gained considerable support. It would take another decade and a half before further experimentation conclusively refuted corpuscles in favor of waves, but the double-slit experiment that Young developed proved to be a fatal blow to Newton’s theory.

How to do the double-slit experiment

Young wasn’t lying when he said , “The experiments I am about to relate…may be repeated with great ease, whenever the sun shines, and without any other apparatus than is at hand to everyone.”

While it might be a stretch to say that you can use the double-slit experiment to demonstrate some of the more counterintuitive features of quantum mechanics (unless you have a photon detector handy and a laser that shoots individual photons), you can still use it to demonstrate the wave nature of light.

If you want to replicate Young’s experiment, you only need as large a box as is practical with a hole cut in it a little smaller than an index card. Then, take an Exacto knife or similar blade for fine cutting work and cut two slits into a piece of cardboard larger than the hole in your box. The slits should be between 0.1mm and 0.4mm apart, as the closer together they are, the more distinct the interference pattern will be. It’s better to create cards for this rather than cut directly into the box since you might need to make adjustments to the spacing of the slits.

Once you’re satisfied with the spacing, affix the card with the double-slit in it over the hole and secure it in place with tape. Just make sure sunlight isn’t leaking around the card.

You’ll also need to create some eye-holes in the box so you can look inside without getting in the way of the light hitting the double-slit card, but once you figure that out, you’re all set.

To accurately diffract sunlight using this box, you will need to have the sunlight more or less hitting the double-slit card dead on, so it might take some maneuvering to get it properly positioned.

Once it is, look through the eye holes and you can see the interference pattern forming on the inside wall, as well as different colors emerging as the different wavelengths interfering with each other change the color of the light being created.

If you wanted to try it out with something fancier, get yourself a laser pointer from an office supply store. Just like you’d do with a viewing box, create cards with slits in them, and when properly spaced, set up a shielded area for the card to rest on.

You’ll want to make sure that only the light from the laser pointer is hitting the double-slit, so shield the card however you need to. Then, set the laser pointer on a surface level with the slits and shine the laser at them. On the wall behind the card, the interference pattern from the slits should be clearly visible.

If you don’t want to go through all that trouble, you can also use Photoshop or similar software to recreate the effect.

First, create a template of evenly spaced concentric circles. Using different layers for each source, as well as a background later, position the center of the concentric rings near to one another. On a 1200 pixel wide canvas, a distance of 100 pixels between the two centers should do nicely.

Then, fill in the color of each concentric ring, alternating light and dark, with an opacity set to about 33%. You may need to hide one of the concentric circle layers while you work on the other. When you’re done, reveal the two overlapping layers of circles and the interference pattern should jump out at you immediately, looking something like this:

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Of course, if you want to dig into the quantum mechanics side of things, you’ll need to work in a pretty advanced physics lab at a university or science institute, since photon detectors aren’t the kind of thing you can pick up at the hobby store.

Still, if you’re compelled to try the heavier stuff out for yourself, you wouldn’t be the first person to get drawn into a career in physics because of the weirdness of quantum mechanics, and there are definitely worse ways to make a living.

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ABOUT THE EDITOR

John Loeffler John is a writer and programmer living in New York City. He writes about computers, gadgetry, gaming, VR/AR, and related consumer technologies. You can find him on Twitter @thisdotjohn

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Collection of Physics Experiments

Double-slit experiment, experiment number : 1703, goal of experiment.

This experiment should help students grasp the term interference and familiarize them with Young’s historically important experiment.

The principle of interference is that two waves coming from different sources to one point superpose in that point. Interference is used for demonstration of the wave nature of the investigated physical phenomenon.

If we want to observe the interference phenomenon, the superposing light waves must be coherent. Light waves are coherent if they have the same frequency and their phase difference is at a considered point of space constant. At the points of interference minima, where waves with opposite phase meet, the light intensity decreases. On the contrary, at the points of interference maxima, where the waves with the same phase meet, the light intensity increases.

If we illuminate a pair of slits with a monochromatic light, an interference pattern with parallel, equidistant dark and light stripes is created on a screen. The distance y between two adjacent maxima (or minima) is directly proportional to the distance l between the screen and the slits and the wavelength λ of the monochromatic light; it is inversely proportional to the distance d between the slits. Thus

Laser pointer, three micro pencil graphite refills with a diameter of 0.5 mm, screen.

We hold the three refills between the thumb and the forefinger of one hand so that they are parallel, side by side, and from a greater part visible.

We point the laser pointer at them against the screen.

An interference pattern appears on the screen (see photo below).

Sample result

During this experiment a laser pointer with given wavelength λ  = 532 nm was used. The distance between the screen and the refills was set as l  =1.5 m. The distance between two interference maxima was measured as y  = 1 mm. The distance of the slits can then be calculated from the relation (1).

After substituting into the adjusted equation (1) we obtain an approximate distance of the slits

With respect to the diameter of the refills this result is within the errors, committed in this measurement, considered to be realistic.

Technical Notes

When working with a laser, it is necessary to follow safety rules.

A classroom wall can be used as a screen.

It is convenient to fasten the laser pointer and the refills into holders.

It is possible to use holders with clamps; one for the laser pointer, the other for the refills tied with a duct tape. The duct tape is used to prevent the refills from breaking and falling apart during the experiment.

For clearer interference pattern, it is good to darken the class, but this is not essential.

Pedagogical notes

If we know the distance of the slits, we should be able to determine the wavelength of the laser used or the distance between the slits and the screen using the equation (1).

Students should realize that the two slits represent two coherent light sources.

The laser and one refill can also be used to illustrate the bending phenomenon of light on a thin obstacle.

Links to tasks dealing with a double-slit experiment

This experiment can be linked to numerous tasks that deal with the same issue – Young’s (double-slit) experiment. On the secondary-school level, it is the task Position of First–Order Maxima When Two Coherent Rays Interfere , on the college level it is the tasks Young’s Interference Experiment (neglecting the diffraction at the slits) and Young’s Experiment including Impact of Diffraction (without this neglect).

Picture This: The Double Slit Test

“One can, damn it, not reduce the whole of philosophy to a screen with two holes."

That was Danish philosopher Jørgen Jørgensen’s exasperated retort in 1936, when confronted with the double-slit experiment and the questions it posed about the nature of quantum reality. The experiment, disarming in its simplicity and confounding in its implications, caused Richard Feynman to claim that it embodied the “central mystery” of the quantum world. A version of the experiment that laid bare this mystery was realized in the 1970s and 1980s, a tortuous path that started with serendipitous double vision, spider silk, and gold.

The double-slit experiment was first done in the early 1800s by English physicist and polymath Thomas Young. He used regular, classical, not quantum light—unsurprisingly, since the quantum world was yet to be discovered. The light of our everyday experience is classical. It can be mathematically described as a wave and it indeed behaves like one. Young’s experimental setup was sinfully simple. You can perform it at home with a little do-it-yourself chops: Shine light of one frequency (say, using a red laser pointer) at an opaque sheet with two fine openings or “slits.” The light can only pass through those slits. On a screen on the other side, you’d intuitively expect to see two strips of light right behind the slits. Instead, you see alternating bands of light and dark.

The light acts like a wave passing through the two slits, not unlike an ocean wave encountering a coastal breakwall with two openings. Waves emerge on the other sides of the slits, propagate, and interfere, creating bright bands where the crest of one wave lines up with the crest of the other (constructive interference), and dark bands where a crest coincides with a trough, canceling out the light (destructive interference). We get an interference pattern—one which can only be explained if something wavelike goes through both slits at once. A beam of red laser light does indeed act like a wave.

But quantum physics says that light, at its feeblest, comes in quanta, or particles, which are small, indivisible packets of energy called photons. Imagine dialing down the intensity of your laser pointer, such that it starts emitting one photon at a time (easier said than done; and you certainly can’t do this at home).

Now, imagine the single photons going through the two slits, one at a time and landing on a photographic plate on the other side. Our intuition screams: surely, the photons will go through one slit or the other, since each photon cannot be divided any further, and the photons over time will form two strips of light on the photographic plate?

Quantum theory says otherwise. It predicts that we will get the same interference pattern as before, only that it will form slowly over time, as most photons will land only in certain regions on the photographic plate, forming bright bands, and fewer or no photons strike the regions that make up the dark bands. The interference pattern builds up photon by photon. Crucially, this is possible only if each photon acts like a wave that goes through both slits. And that’s the mystery: something that is regarded as an indivisible particle somehow acts like a wave and goes through both openings at once.

Theorists understood this in the 1920s, but experimental verification remained a distant dream. Any such experiment would have to guarantee that there was only one photon going through the experimental setup at any moment. Even in the 1960s, when Feynman began lecturing about the experiment, no one had a clue how to do this experiment with single photons.

Feynman, however, talked up the same experiment done with single electrons, which are particles of matter. While some minds may—mistakenly—allow for photons of light to somehow magically go through two slits at once, they tend to recoil at the idea of an indivisible lump of matter doing the same. Surely, matter cannot indulge in such shenanigans. Well, again, quantum theory tells us otherwise: matter is no different. According to the theory, a fundamental particle is a quantum—the smallest unit of energy—of some field. A photon, for example, is a quantum of an electromagnetic field, a type of force-carrying field. An electron is a quantum of another type of field, broadly classified as a matter field. Quantum mechanics treats all fields and their quanta the same. That’s why even electrons fired one-by-one at a double slit should form an interference pattern on the far screen.

What Feynman didn’t know in the early 1960s is that German scientists had already begun assembling some of the basic paraphernalia needed for doing the double-slit experiment with electrons. It began with a chance observation. In the 1950s, Gottfried Möllenstedt at the University of Tübingen was looking through an electron microscope. There was a thin tungsten wire stretched across the microscope’s objective lens. Sometimes the microscope was creating two images, where there should be one. It turned out that two images formed when the tungsten wire was electrically charged. Möllenstedt figured that the charged wire was causing the electron beam to split into two, giving the microscope its double vision. The finding triggered a question: Could such a charged wire be used to split a fine beam of electrons and then recombined to create an interference pattern, à la the double-slit experiment? It’d be as if the electrons had gone through two slits and interfered on the other side.

Such an experiment required some pretty thin wire. Möllenstedt and his student Heinrich Düker had the brilliant idea of using gold-plated spider silk. Historian of science, Robert Crease, in The Prism and the Pendulum: The Ten Most Beautiful Experiments in Science, writes that Möllenstedt “kept a collection of spiders around the laboratory for this purpose.” After ostensibly experimenting with spider silk, Möllenstedt and Düker settled on gold-plated quartz wire (three microns in diameter, about 30 times thinner than human hair). They showed that electrons aimed at such a suitably-thin charged wire would split into two beams, which would recombine downstream, giving rise to an interference pattern. The duo had invented what’s called an electron biprism.

The interference pattern couldn’t be seen with the naked eye. Möllenstedt and Düker had to first image the electrons on a photographic plate, and then magnify the photograph under an optical microscope to see fine interference fringes. The electrons were demonstrating a duality: The indivisible particles of matter were behaving as waves, interfering and forming their own wave pattern.

Still, this wasn’t quite the double-slit experiment that Feynman envisaged. It showed that a beam of electrons was acting like a wave. Feynman was interested in the wave-like properties of a single electron. Such a quantum version of the experiment would require individual electrons going through the apparatus one at a time, and still form an interference pattern. Just like an electron would have the choice of going through one slit or the other, in the case of a biprism the electron would have the option of taking one path or the other around the thin wire. An interference pattern would imply that a single electron—an indivisible particle—was somehow acting like a wave and taking two paths at once.

It’d take two teams—an Italian team of Pier Giorgio Merli, GianFranco Missiroli, and Giulio Pozzi in Bologna, Italy, in 1974 and Akira Tonomura and colleagues at Hitachi in Japan in 1989—to demonstrate such a double-slit experiment with single electrons, using sophisticated versions of Möllenstedt and Düker’s electron biprism and more elaborate detectors. The Japanese team differentiated itself by claiming to show that the interference pattern formed even though there was indisputably only one electron traversing the equipment at a time.

The series of images shown above reveal the interference pattern forming over time. In the beginning (panels a and b ), the dots appear seemingly at random, but as more electrons land on the plate, the dots clearly begin to accumulate in regions of constructive interference, while avoiding regions of destructive interference (panels c and d ).

As Feynman said, the experiment encapsulates one of the central mysteries at the heart of quantum physics. At any instant, only a single electron approaches the charged wire. But something splits, takes both paths around the charged wire and eventually recombines. What is that something? In the formalism of quantum physics, that something is a mathematical entity called the wavefunction , which represents the electron’s quantum state. It’s this wavefunction that takes both paths and later interferes with itself. But is the wavefunction real? Or is it a figment of our mathematical machinery, a way to represent our knowledge—or lack thereof—of the quantum underworld?

Differing answers to that question can lead one to fundamentally different views of reality, from those indicating that reality—the electron, in this case—doesn’t exist until it’s measured to those suggesting a multitude of worlds in which every eventuality exists independent of measurement—in one world, the electron goes one way; in another, it goes the other way.

About a century since the invention of quantum physics, we are still in the dark about such questions. Despite Jørgen Jørgensen’s protestations, philosophical questions about the nature of reality can indeed be reduced to a screen with two holes. ♦

Simple Laser Diffraction Experiment at Home

Introduction: Simple Laser Diffraction Experiment at Home

Long story short : You will learn how to observe interference patterns at home (using the cheapest laser point you got). I will also teach you how to use your laser to measure tiny objects, like the width of your hair !! It's super easy!

* This instructable can seem a bit technical, so feel free to ask me stuff!

If you find physics interesting I suggest you read through (at least the introduction part!) before you skip to the pictures and videos and how-to's!

Long story starts here:

So interference patterns look cool, but so are many other things!! why should we study them??

As a physicist you get to study how things work. You start with the basics - mechanics (Newton and his buddies from the 18th century), and gradually move towards the 19th century where you learn about electro-magnetism (Maxwell and such) and eventually you get to Quantum Mechanics and Einsteins relativity. There are many universalities to these theories, but my favorite is that they can all describe waves.

Whether it's the waves on the surface of a pond or a vibrating string which are usually described by Newtons laws, light, which is an electromagnetic wave, gravity waves described by Einsteins theory, or miniature particles described by wave mechanics (aka Quantum Mechanics) - they all share many similar properties.

This makes the study of waves an extremely important part of the education of physicists. In my opinion, it helps you develop intuition and see the world differently. Once you study what waves are, you begin to see them everywhere.. and it's beautiful! One of my favorite wave phenomena are related to wave interference, which lead to interference patterns.

To perform the single-slit experiment at home, you'll need:

1) 2 old credit-cards (or some more plastic cards). I painted mine with a dark permanent marker

2) A piece of plywood (about 1/2 inch thick).

3) 2 short flat-end screws (about 1/2 inch long).

4) 2 longer flat-end screws (about 2 inches long) and suitable nuts.

5) Rubber bands

6) 6 small right-angle joints (see picture)

7) a laser pointer

Step 1: What Are Interference Patterns?

We all know what waves are from our everyday lives, but what are they, really?

Waves are disturbances to a "field". In the case of sound waves, for example, this "field" is the air-pressure around us - sound waves are simply disturbances to the air pressure that travel through space. For our purposes, we should consider a simple case where these waves are periodic in time.

I added a video from Veritasium's channel that talks about waves. It's a nice video that should teach you the basics of waves.

Now, imagine two identical waves travelling through space. When these two wave collide with, they add up to form a single disturbance. Many waves are even simpler than that - the magnitude of the combined oscillation is simply the sum of both waves.

There are two interesting cases to talk about. If both waves happen to meet at a point in space while both oscillations are at their maximum, the wave we would see when we look at it would be a single wave, with twice the magnitude of each one separately. This is called constructive interference . Alternatively, if the two waves meet at a point in space while one is pointing 'upwards', while the other is pointing 'downwards' (one is positive and the other is negative), they completely cancel each other out! This is called destructive interference .

An interference pattern is what you get when you look at more than one point in space. For example, if you throw two rocks into a pond, their ripples would interfere with each other in many places - in some points they would interfere constructively and in others they would interfere destructively.

Step 2: The Single Slit Experiment

Light, as it turns out, is also a wave (it is a disturbance in the electromagnetic field). This means that light beams can also interfere with each other! There are many ways to see this, but one of the simplest experiments is the single-slit experiment.

When a light-beam (a wave) hits a narrow slit, it shatters in many directions. Each point of the slit would behave a source for new waves, which could interfere with each other. If we now place a piece of paper a few feet away from it, we would see the resulting interference pattern!

This pattern can be predicted from the physics theory of waves. In our case, it is only interesting to quote the final results, which is called a "sinc" function (see the image I attached). The cool part is that this pattern can tell us stuff! For example, if we know the width of the slit, and the distance from the slit to our piece of paper, we can calculate the wavelength (~the period) of the light-wave we used! If, on the other hand, we know the type of laser we used, we can measure the width of tiny objects using the simplest laser-point we got!

But more about this later, for now, let's first see how to observe this pattern using a cheap laser-pointer.

Step 3: Assemble the Experiment

First, attach two short flat-head screws and a right-angle joint to one of the plastic cards (see first picture). On the other side, attach another right-angle joint (see 2nd and 3rd picture). Notice their orientation. Similarly, attach right-angle joints to the other plastic card so that they face each other (see 4th image).

Next, fix one of the plastic cards to the plywood. Now use two more right-angle joints such that they form a track pointing at the previous (fixed) card. This will allow the 2nd card to slide towards the first (fixed) one. Attach these joints to the plywood (see picture 4).

You should now have one fixed plastic card and another that can slide towards it.

Finally, screw in a long screw to the plywood next to the sliding card (pointing upwards), and connect it with rubber bands (see pictures 4-5). Connect the two cards using long flat-head screws. When you screw the them in, the cards should come closer to each other, and when you unscrew them, the cards should move apart.

I also added a small stand for the laser-pointer with rubber bands holding it to place (see last image). When I turn the laser on, the beam hits the slit formed between the two cards (see last picture). When I move the cards close to each other, a diffraction patter is formed!

Step 4: Single-Slit Experiment

Safety First

Laser pointers, of any kind, can damage your sight! do not point them at anyone's eyes or at any reflective surfaces. The cheapest lasers often have a much higher potential for damaging your eyes!

Performing the Experiment

Place your laser + slit at a given distance away from a white wall. About 2-4 feet away should be fine.

Turn on the laser and displace the move-able card such that the laser beam passes through without hitting the plastic cards.

Now, using a screwdriver, slowly bring the two plastic cards closer together such that a narrow slit is formed between them. Notice what happens on the wall! As you bring the cards closer to each other, the interference pattern on the wall becomes larger and larger!!

In the video you can see what it should look like when you change the width of the slit back in forth. I also took a picture with my phone and analysed the light intensity (gray-scale) using a free software called imageJ . Notice how it very much resembles the 'sinc' function I mentioned earlier!

Step 5: Using Laser to Measure Tiny (microscopic) Objects

How can we use this interference patter to measure microscopic objects?

When sizes are larger than, say, a millimetre, you can use ordinary tools such as a ruler or a caliber to measure them. But when you reach the micrometer scale, things get more complicated (at least at home!). For example, a human hair is about 100 micro-meter thick, and it's not that easy to measure it using everyday tools!

We can overcome this using a cheap laser pointer! It turns out that if you know the wavelength of the laser you're using (red lasers are usually ~630-670 nano-meters, 650nm would be a good approximation) and the distance between your object (in our case, the slit) to the wall, you can calculate the size of that object!

All we need to do is measure the distance between the central lobe (the bright spot in the middle) to the next bright spot. Let's denote this distance by the letter 'y'.

The image is taken from hyperphysics . Let's use their notation. If we denote the size of the object we're measuring by the letter 'a', the distance from that object to the wall by 'D' and the wavelength by the Greek letter 'lambda'. Using these notations, the size of the object is given by:

a = 3/2 * lambda * D / y

In the image they have decided to measure the distance from the first lobe to the following dark spots - you can can even use their calculator to plug in the measurements you took in order to calculate the size of the object you've measured.

But this is just a slit, how can we use this to measure other objects?

It turns out that if you take other objects which are narrow enough, such as a human hair, the resulting diffraction pattern will be very similar (and often identical) to the single-slit experiment! This means that the same formula I showed you earlier works just as well!

So.. if you want to measure tiny objects, just shine a laser beam at them, and analyse their diffraction pattern!

If you want to see this happens, just t ake a single human hair and hold it against your laser pointer. This will create a diffraction pattern which you can use to measure the width of your hair ! I used this and found that my hair is about 100 micrometers thick!

That's all for today! see you soon :)

Two-Slit Wave Model

By experimenting with this model of light-wave addition, you can understand the behavior of light as it passes through two narrow slits. Why do two sources of light sometimes combine to make bright spots and sometimes dark? It’s all a matter of phases.

• Twenty-five 3 x 5 index cards (approximately 75 x 125 millimeters)—we’ll call these “smaller cards”
• Seventeen 5 x 7 index cards (approximately 125 x 175 millimeters)—we’ll call these “larger cards”
• Masking tape that is 1/2 in (1 cm) wide; the narrower the better
• Transparent tape
• Blue and red marker pens
• Pencil (not shown)
• Optional: String (not shown)

Note: Prior to doing this activity, we recommend you try Two-Slit Experiment to observe an interference pattern. Together, these two Snacks will help you move from observing the two-slit interference phenomenon to understanding the science behind it.

For this activity, you'll need to first make a sine-wave template, and then use the template to create a set of cards with sine waves drawn across both sides.

Use this trick to draw more accurate sine waves:

• Take one of the small index cards and fold it in half lengthwise (hot dog fold). Unfold the card. Now fold the card in half along its width (hamburger fold). Leaving that fold in place, fold the card in half again. Unfold the card. You should see a long fold mark lengthwise across the middle, and three shorter fold marks across the width of the card. The card should be divided into eighths.
• Mark a point on the crosswise fold mark nearest the left edge, about 1/2 in (1.25 cm) down from the top of the card—your maximum.
• Along the bottom of the card, mark a point on the right crosswise fold mark, about 1/2 in (1.25 cm) up from the bottom—your minimum.
• Using scissors, cleanly cut along the sine wave that you’ve drawn. The top half and the bottom half produce two sine-wave templates—give one to a friend.
• To use this template, line up the bottom of the template with the bottom of a new card and, using a blue marker, draw along the wave edge. Repeat until you have created twenty-four cards with matching blue sine-waves drawn on them.
• Using transparent tape, tape the smaller cards together into two straight rows of twelve cards each, making sure that all the sine waves move upwards from the left side (following the original pattern of the template before you flipped the cards over). It’s important that the sides of the cards touch but don’t overlap.
• Once you've finished making your two sets of blue sine-wave cards, follow all of the steps above again with the larger cards to make two sets of red sine-wave cards with eight cards each.

Make a model of two slits:

• Tear off several long strips of masking tape. Tape them in a line on the floor, leaving two small slits that are approximately two "blue" wavelengths (10 inches or 25 centimeters) apart.
• Tear off another long strip of masking tape, about two meters in length. Tape this down so it is parallel to and about five “blue” wavelengths (25 in or 55 cm) away from the other tape. This strip represents your screen.

Compare the blue and red sine-wave cards. Notice the difference in length between the blue and red waves. The red light waves will be longer than the blue. You have made a good model of red and blue light waves.

Look at any sine-wave card and notice three important points: the maximum (highest point), the zero crossings (where the wave crosses the middle line of the card, including at the leading and trailing edges), and the minimum (lowest point). Scientists describe these points using the term phase. When two waves add up “out of phase,” this means the highest point of one wave lines up with the lowest point of the other, canceling out the light. When waves add up “in phase,” this means the highest point of one wave lines up with the highest point of the other, strengthening the light.

Consider a light source like a laser shining into the two slits. The waves come into the slits in phase, oscillating together.

Take one strip of blue sine-wave cards and line it up with the center of one slit. Take the other strip of blue sine-wave cards and line it up with the center of the other slit. Make sure the two strips begin in phase at the slits. Unfurl both card strips towards the “screen” (second tape line), angling them so they cross the screen together at a point opposite the midway point between the two slits. Notice that both waves have the same phase at the screen. They add together in phase, producing a bright spot where they meet on the screen. Make a blue mark at this point on the tape (see photo below).

Investigate other points on the screen, by stretching the strips from each slit to intersect at different places along the screen. Try to find a point where the two strips arrive out of phase. Here the light will be canceled, creating a dark spot. Make a black mark at the intersection point on the tape and draw a blue circle around it to note this is where blue light cancels out (click to enlarge the photos below).

Repeat the experiment using the red sine-wave cards. Notice and mark the locations of the bright regions and the dark regions (see below).

After you’re done investigating both the blue and red sine-wave cards, change the distance between the slits, and repeat the experiment with fresh pieces of tape.

Both waves start out together with the same phase and travel the same distance to the center of the screen (the halfway point between the two slits), so they have the same phase when they add together. There is thus a bright spot in the middle of the screen. When one wave travels one‐half of a wavelength further than the other, the lights cancel and create a dark region.

There are additional bright and dark regions that stretch out in both directions from the center. When the two light paths differ by an integer number of wavelengths, the waves arrive in phase and make a bright spot. When they travel an odd integer multiple of a half-wavelength, they add up out of phase and create a dark spot.

Since red and blue lights have different wavelengths, the distance between adjacent red maxima is different than the distance between adjacent blue maxima. The spacing between adjacent maxima is usually measured as an angle with its vertex halfway between the two slits. If the wavelength of the light is L , and the distance between the slits is d , then maxima occur when the angle, T , is an integer multiple of L/d . 

Related Snacks

Double-slit experiment that proved the wave nature of light explored in time

by Thomas Angus [Photographer] , Hayley Dunning 03 April 2023

Imperial physicists have recreated the famous double-slit experiment, which showed light behaving as particles and a wave, in time rather than space.

The experiment relies on materials that can change their optical properties in fractions of a second, which could be used in new technologies or to explore fundamental questions in physics.

Our experiment reveals more about the fundamental nature of light while serving as a stepping-stone to creating the ultimate materials that can minutely control light in both space and time. Professor Riccardo Sapienza

The original double-slit experiment, performed in 1801 by Thomas Young at the Royal Institution, showed that light acts as a wave. Further experiments, however, showed that light actually behaves as both a wave and as particles – revealing its quantum nature.

These experiments had a profound impact on quantum physics, revealing the dual particle and wave nature of not just light, but other ‘particles’ including electrons, neutrons, and whole atoms.

Now, a team led by Imperial College London physicists has performed the experiment using ‘slits’ in time rather than space. They achieved this by firing light through a material that changes its properties in femtoseconds (quadrillionths of a second), only allowing light to pass through at specific times in quick succession.

Lead researcher Professor Riccardo Sapienza , from the Department of Physics at Imperial, said: “Our experiment reveals more about the fundamental nature of light while serving as a stepping-stone to creating the ultimate materials that can minutely control light in both space and time.”

Details of the experiment are published today in Nature Physics .

Patterns of interference

The original double-slit setup involved directing light at an opaque screen with two thin parallel slits in it. Behind the screen was a detector for the light that passed through.

To travel through the slits as a wave, light splits into two waves that go through each slit. When these waves cross over again on the other side, they ‘interfere’ with each other. Where peaks of the wave meet, they enhance each other, but where a peak and a trough meet, they cancel each other out. This creates a striped pattern on the detector of regions of more light and less light.

Light can also be parcelled up into ‘particles’ called photons, which can be recorded hitting the detector one at a time, gradually building up the striped interference pattern. Even when researchers fired just one photon at a time, the interference pattern still emerged, as if the photon split in two and travelled through both slits.

In the classic version of the experiment, light emerging from the physical slits changes its direction, so the interference pattern is written in the angular profile of the light.

Instead, the time slits in the new experiment change the frequency of the light, which alters its colour. This created colours of light that interfere with each other, enhancing and cancelling out certain colours to produce an interference-type pattern.

Metamaterials and time crystals

The material the team used was a thin film of indium-tin-oxide, which forms most mobile phone screens. The material had its reflectance changed by lasers on ultrafast timescales, creating the ‘slits’ for light. The material responded much quicker than the team expected to the laser control, varying its reflectivity in a few femtoseconds.

The material is a metamaterial – one that is engineered to have properties not found in nature. Such fine control of light is one of the promises of metamaterials, and when coupled with spatial control, could create new technologies and even analogues for studying fundamental physics phenomena like black holes.

Co-author Professor Sir John Pendry said: "The double time slits experiment opens the door to a whole new spectroscopy capable of resolving the temporal structure of a light pulse on the scale of one period of the radiation."

The team next want to explore the phenomenon in a ‘time crystal’, which is analogous to an atomic crystal, but where the optical properties vary in time.

Co-author Professor Stefan Maier said: “The concept of time crystals has the potential to lead to ultrafast, parallelized optical switches.”

‘ Double-slit time diffraction at optical frequencies ’ by Romain Tirole, Stefano Vezzoli, Emanuele Galiffi, Iain Robertson, Dries Maurice, Benjamin Tilmann, Stefan A. Maier, John B. Pendry and Riccardo Sapienza is published in Nature Physics .

Article text (excluding photos or graphics) © Imperial College London.

Photos and graphics subject to third party copyright used with permission or © Imperial College London.

Thomas Angus [Photographer] Communications Division

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Hayley Dunning Communications Division

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Building and Demonstrating the Two-Slit Experiment at Home

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After a bit of experimentation, I have been able to do this in a satisfactory way. Takes about an hour if you have the parts. Purchase a 1 dollar red laser pointer. Remove the laser head by opening it up and discard everything else. Put together 3 AA batteries with a switch connected to the head and build a decent stand for it so the beam is horizontal (needs soldering to do it right). The projection screen is to be placed in a dark area, about 10 to 15 meters away from the laser. Cut a 1 square inch piece of aluminum foil for the slits/pinhole. Use pinholes instead of slits. Not only are the patterns prettier, but pinholes are easier to produce. Create the pinholes by pressing a pin on the foil placed on a paper pad. The spacing of the pinholes should be about 1 mm. The pinholes should be as small as possible. For slits, use a razor to cut the foil - slits should be 1 mm apart, 5 mm or more in length, but as narrow as possible. Now you need some kind of adjustable hand with a stand and an alligator clip - like the kind sold in Radio Shack to grab wires and things. The clip will grab the foil, and the hand will be adjusted so that the laser beam shines right through the pinholes. It is important that you be able to adjust the spatial position of the foil very finely and effortlessly. The foil will be placed about 15 cm in front of the laser head. First shoot the beam to the middle of the screen. Then while watching the foil, adjust the hand with the foil so that the beam falls ****with equal intensity**** on the two pinholes (or slits). You will see beautiful results on the screen. With pinholes, the diameter of the image is about 10 cm. With slits, up to 30 cm long. Try different patterns and dot sizes. The closer the pinholes, the more prominent the interference pattern is. The smaller the pinhole, the IP will be dimmer but sharper and nicer. This exercise is well worth it, and makes a great demo for kids. Take a look at the photo at this link. This was made with 3 pinholes arranged as an equilateral triangle. Image diameter is 10 cm. The real thing is a lot more colorful. http://www.geocities.com/zekise/TriplePinhole.JPG have fun  

Tried it too, worked like a charm! Even got a 5 slit working, thanks!  

FAQ: Building and Demonstrating the Two-Slit Experiment at Home

1. what is the two-slit experiment.

The Two-Slit Experiment is a famous physics experiment that demonstrates the wave-particle duality of light. It involves shining a beam of light through two parallel slits onto a screen, creating an interference pattern that can only be explained by the wave-like behavior of light.

2. Can the Two-Slit Experiment be performed at home?

Yes, the Two-Slit Experiment can be performed at home with basic materials such as a laser pointer, cardboard, and a paper screen. However, it may be difficult to achieve precise results without specialized equipment.

3. Is the Two-Slit Experiment only applicable to light?

No, the Two-Slit Experiment has been performed with other particles such as electrons, protons, and even large molecules. It demonstrates the wave-particle duality of all matter, not just light.

4. What is the significance of the Two-Slit Experiment?

The Two-Slit Experiment is significant because it challenges our understanding of the behavior of particles. It shows that particles can exhibit both wave-like and particle-like properties, and it has important implications in fields such as quantum mechanics and particle physics.

5. Are there any real-world applications of the Two-Slit Experiment?

Yes, the principles demonstrated in the Two-Slit Experiment have practical applications in technologies such as electron microscopy, holography, and diffraction gratings. It also helps scientists better understand the behavior of particles at the quantum level.

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Double slit experiment

What's the simplest way to describe and show the double slit experiment? I have to perform an experiment proving how it all works in my physics class.

• experimental-physics
• double-slit-experiment

• 1 $\begingroup$ I advise you to do some research and come back with a more specific question. at the moment, this is quite broad. $\endgroup$ –  innisfree Commented Mar 13, 2015 at 18:10
• $\begingroup$ A laser pointer shining at a hair will result in a diffraction pattern on a screen... not quite double slit but diffraction, and super easy. $\endgroup$ –  Floris Commented Mar 13, 2015 at 19:40

3 Answers 3

You can have a pool of water and place a cardboard or a piece of plastic with two slits in the middle. Just create a wave that goes through both slits and the waves should start interfering.

• 2 $\begingroup$ I did a demo of geometric optics in high school using a wave tank that had a clear bottom. I set it on top of an overhead projector (does anybody make those anymore?) which vividly rendered the waves on the projection screen. $\endgroup$ –  Solomon Slow Commented Mar 13, 2015 at 19:04
• $\begingroup$ Truth be known, it wasn't my own idea. I saw it in a science museum first. Don't remember where, but it was long enough ago (1970-something) that it probably doesn't matter anymore. In my version, I bent strips of sheet metal into parabolic and elliptical shapes to emulate mirror optics. In the science museum version, they had convex and concave lens shapes made from thick sheets of clear acrylic. The lenses worked by changing the depth of the water. The surface waves propagate more slowly in the shallower water above the "lens". $\endgroup$ –  Solomon Slow Commented May 12, 2015 at 13:18
• $\begingroup$ Well hey in the end you made it yours. That is pretty interesting how you had to apply different concepts to simulate the slit experiment. $\endgroup$ –  Lift God Commented May 13, 2015 at 5:07

I think that for the demonstration, a laser and double slits are probably the best way to show the interference pattern. First showing with the 1st slit only, and then the 2nd. Finally show with the 2 slits opened.

You probably want to emphasize one of the wonderful aspect of the interference-based experiments, roughly said: "You put light on light, and you get darkness"

For the explanations you can stick to an analogy based on the wave, which is probably the standard stance.

I'm personnaly fond of the explanation provided by Feynman in "Light and Matter": http://en.wikipedia.org/wiki/QED:_The_Strange_Theory_of_Light_and_Matter

I will not redo the argumentation here, but he provides a very "hand-on" explanation, you're basically putting arrows end-to-end, which in fact describe in layman terms what we call "path integrals" and "quantum electrodynamic".

I believe this can be efficiently used to explain the double slit experiment, as well as many optical effects.

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Instructional Resources and Lecture Demonstrations

6d10.10 - interference - laser and cornell plate (db. slit).

The slit plate has single, double, and multiple as well as variable slits on it.  With the laser as shown you can show a variety of diffraction and interference patterns.  Information on the plate is in the file.

Two variations of the laser and slit plate demo are as follows.  To easily see what the difference between a single and double slit diffraction pattern look like, shine the laser through the double slit pattern.  Then with a razor blade cover one of the slits.  In this way you can instantly see the difference between the two patterns.

Direct a diffuse laser beam onto the central diffraction pattern.  Using the 7 cm. lens you can focus two different images.  At the focal length you get a row of diffracted dots as if the laser beam was not expanded.  Outside the focal length you get an image of the diffraction pattern that is on the slit plate.

By using the pointer or the variable slit to block one or more of the diffraction nodes out of the transmitted image, the image will at times become more focused and at other times less focused depending on which nodes are blocked.

A simple reproduction of Thomas Young's original experiment is to place a 2 mm piece of note card edgewise into the beam of a laser pointer.  Use the variable focus laser pointer and adjust it to the narrowest beam possible.  You will get a double slit pattern on the screen that can be investigated in a variety of ways.

• Chun-Ming Chiang, Shih-Hsin Ma, Shou-Tai Lin, Wel-Hung Hsu, Pin-Jui Huang, "Application of Optical Path Drawing Technology: The Light Intensity Problem of Double-Slit Interference", TPT, Vol. 60, #6, Sept. 2022, p. 457.
• Alan DeWeerd, "Inexpensive Single and Double Slits Using a Fine-Toothed Comb", TPT, Vol. 60, #5, May 2022, p. 380.
• J. P. Sharpe, C. Yee, "Young's Two-Slit Experiment Without a Laser", TPT, Vol. 59, #6, Sept. 2021, p. 420.
• Chang-won Kang, Hyen-Jung Nam, Jung Bog Kim, "Pseudo-Double-Slit Experiment with Two Glass Plates", TPT, Vol. 58, #9, Dec. 2020, p. 649.
• Chun-Ming Chiang, Shih-Hsin Ma, Jyun-Yi Wu, and Yao-Chen Hung, "3-D Optical Path Drawing Method", TPT, Vol. 57, #3, Mar. 2019, p. 179.
• Tom Ekkens, "Two-Dimensional Light Diffraction From an EPROM Chip", TPT, Vol. 56, #2, Feb 2018, p. 70.
• Robert D. Polak, Nicolette Fudala, Jason T. Rothchild, Sam E. Weiss, and Marcin Zelek, "Easily Accessible Experiments Demonstrating Interference", TPT, Vol. 54, #2, Feb. 2016, p. 120.
• Athanasios Velentzas, "Teaching Diffraction of Light and Electrons: Classroom Analogies to Classic Experiments", TPT, Vol. 52, #8, Nov. 2014, p. 493.
• Dave Van Domelen, "Binder Clip Optics Bench for Young's Double-Slit Experiment", TPT, Vol. 50, #2, Feb. 2012, p. 116.
• Paul Hewitt, "Figuring Physics: Double Slit", TPT, Vol. 48, #5, May 2010, p. 284.
• Jim Hicks, "Laser Beams, Plastic Cassette Boxes, and the Joy of Serendipitous Discovery", TPT, Vol. 47, #3, Mar. 2009, p. 189.
• Ronald Newburgh, "Optical Path, Phase, and Interference", TPT, Vol. 43, #8, Nov. 2005, p. 496.
• Michael I. Sobel, "Correction: 'Algebraic Treatment of Two-Slit Interference' [Phys. Teach. 40 (7), 402–404 (2002)]", TPT, Vol. 41, #2, Feb. 2003, p. 69.
• Dick C. H. Poon, "How Good Is the Approximation ' Path Difference ≈ d sin θ'?", TPT, Vol. 40, #8, Nov. 2002, p. 460.
• Andrew DePino Jr., "Diffraction Patterns Using a Constant-Velocity Cart", TPT, Vol. 40, #7, Oct. 2002, p. 418.
• Michael I. Sobel, "Algebraic Treatment of Two-Slit Interference", TPT, Vol. 40, #7, Oct. 2002, p. 402.
• Rand S. Worland and Matthew J. Moelter, "Hands-On Phasors and Multiple-Slit Interference", TPT, Vol. 35, #8, Nov. 1997, p. 486.
• Kenneth Ford, "Double-Slit Experiment on Web", TPT, Vol. 35, #8, Nov. 1997, p. 474.
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• Changsug Lee, Kwangmoon Shin, Sungmuk Lee, and Jaebong Lee, "Fabrication of Slits for Young's Experiment Using Graphic Arts Films", AJP, Vol. 78, #1, Jan. 2010, p. 71.
• P. F. Hinrichsen, "A Simple Interference Scanner", AJP, Vol. 69, #8, Aug. 2001, p. 917.
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• R. D. Bahuguna, Arthur B. Western, and Sean Lee, "Young's Double-Slit Experiment Using Speckle Photography", AJP, Vol. 56, #6, June 1988, p. 531.
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• Nobuo Naba, "A Method to Vary Continuously the Slit Spacing on the Diffraction Experiments by a Laser", AJP, Vol. 40, #2, Feb. 1972, p. 341.
• Virgil B. Eligns, "A Simple Method to Vary Continuously the Effective Slitwidth and Slit Spacing on Single- and Multiple- Slit Diffraction Gratings", AJP, Vol. 38, #10, Oct. 1970, p. 1263.
• E. Fortin, "Direct Demonstration of the Fresnel-Arago Law", AJP, Vol. 38, #7, July 1970, p. 917.
• Freier and Anderson, "Ol-9", A Demonstration Handbook for Physics.
• "O-405: Double Slit with Laser", DICK and RAE Physics Demo Notebook.
• T. Kallard, "Young's Double Slit Method for Producing Interference", Exploring Laser Light, p. 112.
• T. Kallard, "Interference and Interferometers", Exploring Laser Light, p. 111.
• Borislaw Bilash II and David Maiullo, "Wave Theory of Light", A Demo a Day: A Year of Physics Demonstrations, p. 348.
• Julien Clinton Sprott, "6.2, Laser Beam", Physics Demonstrations, ISBN 0-299-21580-6, p. 235.
• Gordon McComb, "Experiments with Double Slits", Lasers, Ray Guns, & Light Cannons, p. 121 - 123.
• Seville Chapman and Harold Meese, "Effective and Inexpensive Slits for Teaching Physical Optics", Cornell Aeronautical Laboratory, Inc., Buffalo, New York, August 8, 1956.
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Disclaimer: These demonstrations are provided only for illustrative use by persons affiliated with The University of Iowa and only under the direction of a trained instructor or physicist.  The University of Iowa is not responsible for demonstrations performed by those using their own equipment or who choose to use this reference material for their own purpose.  The demonstrations included here are within the public domain and can be found in materials contained in libraries, bookstores, and through electronic sources.  Performing all or any portion of any of these demonstrations, with or without revisions not depicted here entails inherent risks.  These risks include, without limitation, bodily injury (and possibly death), including risks to health that may be temporary or permanent and that may exacerbate a pre-existing medical condition; and property loss or damage.  Anyone performing any part of these demonstrations, even with revisions, knowingly and voluntarily assumes all risks associated with them.

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• Published: 02 September 2024

Ultraviolet astronomical spectrograph calibration with laser frequency combs from nanophotonic lithium niobate waveguides

• Markus Ludwig 1   na1 ,
• Furkan Ayhan   ORCID: orcid.org/0000-0001-6606-0709 2   na1 ,
• Tobias M. Schmidt   ORCID: orcid.org/0000-0002-4833-7273 3   na1 ,
• Thibault Wildi   ORCID: orcid.org/0000-0002-0193-7132 1 ,
• Thibault Voumard 1 ,
• Roman Blum 4 ,
• Zhichao Ye   ORCID: orcid.org/0000-0002-4708-3582 5 ,
• Fuchuan Lei   ORCID: orcid.org/0000-0003-2257-7057 5 ,
• François Wildi 3 ,
• Francesco Pepe 3 ,
• Mahmoud A. Gaafar   ORCID: orcid.org/0000-0001-5887-5772 1 ,
• Ewelina Obrzud 4 ,
• Davide Grassani 4 ,
• Olivia Hefti 4 ,
• Sylvain Karlen   ORCID: orcid.org/0000-0001-8404-6521 4 ,
• Steve Lecomte 4 ,
• François Moreau 6 ,
• Bruno Chazelas 3 ,
• Rico Sottile 6 ,
• Victor Torres-Company   ORCID: orcid.org/0000-0002-3504-2118 5 ,
• Victor Brasch   ORCID: orcid.org/0000-0002-0354-2847 7 ,
• Luis G. Villanueva   ORCID: orcid.org/0000-0003-3340-2930 2 ,
• François Bouchy 3 &
• Tobias Herr   ORCID: orcid.org/0000-0002-5966-6697 1 , 8  

Nature Communications volume  15 , Article number:  7614 ( 2024 ) Cite this article

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• Frequency combs
• Integrated optics
• Nonlinear optics
• Supercontinuum generation

Astronomical precision spectroscopy underpins searches for life beyond Earth, direct observation of the expanding Universe and constraining the potential variability of physical constants on cosmological scales. Laser frequency combs can provide the required accurate and precise calibration to the astronomical spectrographs. For cosmological studies, extending the calibration with such astrocombs to the ultraviolet spectral range is desirable, however, strong material dispersion and large spectral separation from the established infrared laser oscillators have made this challenging. Here, we demonstrate astronomical spectrograph calibration with an astrocomb in the ultraviolet spectral range below 400 nm. This is accomplished via chip-integrated highly nonlinear photonics in periodically-poled, nano-fabricated lithium niobate waveguides in conjunction with a robust infrared electro-optic comb generator, as well as a chip-integrated microresonator comb. These results demonstrate a viable route towards astronomical precision spectroscopy in the ultraviolet and could contribute to unlock the full potential of next-generation ground-based and future space-based instruments.

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Continuous ultraviolet to blue-green astrocomb

Visible-to-ultraviolet frequency comb generation in lithium niobate nanophotonic waveguides

Near-ultraviolet photon-counting dual-comb spectroscopy

Introduction.

Precise astronomical spectroscopy has led to the Nobel-Prize-winning discovery of the first exo-planet via the radial velocity method 1 , which relies on the precise tracking of minute Doppler shifts in the stellar spectrum caused by an orbiting planet. The detection of Earth-like planets in the habitable zone around a Sun-like star requires measuring a radial velocity change as small as 10 cm/s (relative Doppler-frequency shift of 3 × 10 −10 ) over the time scale of 1 year. This necessitates regular wavelength calibration of the spectrograph against a suitable calibration light source. Highly stable and accurate calibration light sources hence take on a key role in astronomical precision spectroscopy.

Calibration sources with outstanding accuracy and precision can be provided by laser frequency combs 2 , 3 (LFCs). Their spectra are comprised of large sets of discrete laser lines whose frequencies can be precisely known when linked to a metrological frequency standard, on a level that exceeds the astronomical requirements. Provided their lines can be separated by the spectrograph, LFCs can serve as exquisite wavelength calibrators 4 , 5 and are then also referred to as astrocombs (Fig.  1 a). Recent years have seen significant progress in developing astrocombs 6 , 7 , 8 , 9 , 10 and extending their coverage to visible (VIS) wavelengths, where the emission of Sun-like stars peaks, and to near-infrared wavelength, where relatively cold stars can accommodate rocky planets in tight orbits.

a Precision spectroscopy of astronomical objects enabled by laser frequency combs (LFC) providing absolutely and precisely known laser frequencies, cf. main text. QSO: quasi-stellar object, H, H 2 : hydrogen, D: deuterium, P: optical power. b Atmospheric transmission (high altitude, dry), spectral ranges for different astrophysical studies. c Expected redshift drift signal for the standard Λ CDM cosmology 89 in units of cm/s per decade (Sandage test) as a function of wavelength, corresponding to the redshifted H I Ly α transition. d Concept of broadening and transferring a high-repetition-rate astrocomb from infrared (IR) to visible (VIS) and ultraviolet (UV) wavelengths based on optical χ (2) - and χ (3) -nonlinearities.

Extending astrocombs further towards the atmospheric cutoff and into the ultraviolet (UV) regime would not only be relevant to exo-planet science, but highly desirable for fundamental physics and precision cosmology (Fig.  1 b). Indeed these are also major science drivers for the upcoming ANDES high-resolution spectrograph at the extremely large telescope (ELT) 11 . For instance, by accurately determining the wavelengths of narrow metal absorption features in the spectra of quasi-stellar objects (QSOs), one can infer the value of the fine-structure constant, α , at the place and time of absorption, i.e. billions of years ago. This allows us to test whether fundamental physical constants might have varied on cosmological scales 12 , 13 . Another exciting, but extremely demanding science case is the direct observation of cosmic expansion in real time, often referred to as the Sandage test 14 , 15 , 16 . This requires detecting a drift of H I Ly α forest absorption features in QSO spectra by just a few cm/s (relative frequency shift of 3 × 10 −11 ) over several decades. As lined out in ref. 17 , observations and corresponding wavelength calibrations in the UV are needed to access low redshifts, z , in particular, the important zero-crossing of the drift at z  = 2, corresponding to 365 nm (Fig.  1 c). Achieving such an extreme level of wavelength stability will require a community effort over the next decade to develop improved spectrographs, data analysis methods, and in particular LFC-based calibration sources 18 . Furthermore, it has recently become clear that a detailed modeling of the instrumental line-spread function is crucial to further improve the accuracy and stability of spectroscopic observations 17 , 19 , 20 . This, however, requires a broadband calibration source with a spectrum of narrow lines, such as those of an LFC.

Astrocombs can be derived from high-repetition-rate ( f rep  > 10 GHz) laser sources, such as line-filtered mode-locked lasers 6 , 7 , 8 , 21 , electro-optic (EO) comb generators 22 , 23 and chip-integrated microresonators 24 , 25 , 26 , 27 , 28 . Their spectra consist of equidistant optical laser frequencies ν n  =  ν 0  +  n f rep , spaced by the laser’s pulse repetition rate f rep and with an offset frequency ν 0 , which we here define to be the central frequency of the laser ( n is an integer comb line index). To transfer the comb spectra to the desired wavelength range and to increase their spectral coverage, second- ( χ (2) ) and third-order ( χ (3) ) nonlinear optical effects are utilized. However, the high-repetition rates of  >10 GHz, that are necessary for the comb lines to be separated by the spectrograph, imply low pulse energies and hamper nonlinear optical effects. In addition, and especially at shorter wavelengths, strong material dispersion complicates the efficient nonlinear energy transfer.

So far, short-wavelength blue and green astrocombs have been achieved via second-harmonic generation of infrared mode-locked lasers 21 , 29 , 30 and of EO combs 31 in bulk χ (2) -nonlinear crystals. Spectral broadening in χ (3) -nonlinear photonic crystal fiber resulted in astrocombs spanning from infrared (IR) to VIS wavelength 32 , 33 , 34 , some extending to below 450 nm. In addition to these approaches, micro- and nanophotonic waveguides made of highly nonlinear materials can further increase the efficiency in a compact setup. In the IR, χ (3) -nonlinear silicon nitride (Si 3 N 4 ) waveguides have led to broadband astrocombs 35 , and via third-harmonic generation, a 10 GHz IR comb has been transferred to VIS wavelengths 36 . Strong nonlinear effects in waveguides, including harmonic frequency generation, may also be obtained via the quadratic χ (2) -nonlinearity. At low pulse repetition rates, spectra across multiple optical octaves have been obtained in large-mode area (~100 μm 2 ) periodically poled lithium niobate (LiNbO 3 ) waveguides with mm-long propagation distances 37 , 38 , 39 , 40 . Notably, periodically poled LiNbO 3 waveguides were utilized with a 30 GHz repetition rate line-filtered erbium-doped mode-locked laser 41 , creating harmonic spectra in VIS and UV domains for astronomical spectrograph calibration. In addition, recent work leveraged a combination of second-harmonic and sum-frequency generation based on a titanium-doped sapphire laser to obtain, in conjunction with line-filtering, a continuous green to ultraviolet 30 GHz astrocomb 42 . In nanophotonic waveguides from thin-film LiNbO 3 43 , 44 , 45 , 46 , 47 , 48 , owing to their sub-μm 2 modal confinement, highly-efficient UV spectral generation has been reported 49 , 50 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , including at 10 GHz repetition rate 59 . However, astronomical spectrograph calibration in the UV spectral range has so far not been demonstrated.

Here, we demonstrate astronomical spectrograph calibration with laser frequency combs in the UV below 400 nm. Specifically, we design chip-integrated nano-structured LiNbO 3 waveguides with sub-μm 2 mode cross-section and a tailored poling pattern to enable efficient UV astrocomb generation via cascaded harmonic generation from a robust telecommunication-wavelength 18 GHz EO comb, as well as, a 25 GHz chip-based microresonator comb. The generated astrocombs are tested in March 2023 on the high-resolution echelle spectrograph SOPHIE 60 at the Observatoire de Haute Provence (OHP, France), achieving radial-velocity precision in the range of 1 to 2 m/s.

We base our astrocombs on a robust, telecommunication-grade EO comb with a pulse repetition rate of 18 GHz, as well as, a microresonator comb with a repetition rate of 25 GHz. Both are derived from an IR continuous-wave (CW) laser of frequency ν 0 ≈192 THz (wavelength ca. 1.56 μm) and operate intrinsically at a high-repetition rate, so that filtering of unwanted comb lines is not required. To transfer the IR comb to the UV (and VIS), we utilize chip-based LiNbO 3 nanophotonic waveguides, for cascaded harmonic generation as illustrated in Fig.  1 d. The possible comb frequencies are

where m is the harmonic order. In general, each harmonic m of the comb spectrum has a different offset frequency m ν 0 . While this can facilitate the detection of the comb’s offset frequency 51 , 55 , 57 , 59 , care must be taken to avoid inconsistent frequency combs from overlapping harmonics with different offsets. Alternatively, stabilizing ν 0 to a multiple of f rep could address this point. Practically, this could be achieved, for instance, by locking the beatnote between adjacent harmonics to zero 61 , or via an auxiliary low-repetition rate frequency comb 62 .

A key difference between broadband electro-optic combs obtained via conventional self-phase modulation χ (3) -based supercontinua and spectra generated via χ (2) -based harmonics, lies in the phase noise properties of their comb lines. In χ (3) -based spectra, the phase noise, impacting linewidth and line contrast, grows quadratically with the frequency distance from the fundamental pump laser. In contrast, in χ (2) -based harmonic spectra the phase noise (approximately) depends on the frequency distance from its corresponding harmonic’s center frequency (Supplementary Information  SI , Section  1 and Supplementary Fig.  1 ). This property, along with the efficiency of the nanophotonic waveguides, permits us to directly generate comb lines in the ultraviolet from a telecom-wavelength electro-optic source, within a certain bandwidth around the harmonic’s center frequency; future extension of this bandwidth will, as we discuss in detail in the Section  1 in the  SI and show in the Supplementary Figs.  2, 3 , require the addition of a noise filtering cavity, which has been established for broadband χ (3) -based electro-optic combs 63 , but is not implemented in this initial proof-of-concept demonstration.

Waveguide design

An illustration of a nano-structured LiNbO 3 waveguide and the strong mode confinement to sub-μm 2 cross-section for efficient nonlinear conversion is shown in Fig.  2 a. The waveguides are fabricated from a commercially available undoped lithium niobate-on-insulator (LNOI) substrate with an 800-nm-thick LiNbO 3 layer via electron-beam lithography and reactive-ion etching, resulting in a sidewall angle of  ~75° (Fig.  2 c, Methods, SI Section  2 and Supplementary Figs.  4 , 5 ). The waveguides taper to a width of 2500 nm at the chip facet, for input and output coupling. In the first design step, considering the fundamental transverse electric field polarization (TE) waveguide mode, we define the waveguide geometry, which in nanophotonic waveguides enables engineering of the waveguide’s group velocity dispersion (GVD), and additional χ (3) -nonlinear spectral broadening of the input IR comb. In unpoled waveguides, top widths in the range of 800 to 1200 nm result in anomalous GVD and the most significant broadening. Spectral broadening is also possible in the normal GVD regime, typically resulting in less broad, but more uniform spectra.

a Geometry of a nanophotonic lithium niobate (LiNbO 3 ) waveguide, showing the optical mode profile for the fundamental transverse electric field polarization (TE) mode and a possible poling pattern with spatially variable poling period Λ . The extraordinary crystal axis is oriented along the x-direction to access the highest electro-optic tensor element of LiNbO 3 . b Poling periods Λ required for quasi-phase-matching of various nonlinear optical processes for waveguides of different (top) width as a function of the fundamental comb’s wavelength. SHG: second-harmonic generation, SHG+F: sum-frequency generation of second-harmonic and fundamental comb, THG+F: sum-frequency generation of third-harmonic and fundamental comb, SHG+SHG: sum-frequency generation of the second-harmonic. Respective higher-order phase matching with three-fold period Λ is indicated (the current fabrication limit only allows for Λ  > 2 μ m). c Photograph of a waveguide in operation and scanning electron microscope image of the LiNbO 3 on silica (SiO 2 ). d – g Examples of waveguide designs showing poling pattern (top), experimentally generated spectra for different input pulse energies provided by a 100 MHz, 80 fs mode-locked laser with a central wavelength of 1560 nm (waveguide cross-section are shown as insets and on chip-pulse energy is indicated by the color code) and pyChi 64 simulation results (bottom) for a pulse energy of 50 pJ. The spurious spikes observed in the traces for 4 pJ pulse energy are manifestations of the noise floor of the optical spectrum analyzer (Yokogawa AQ6374).

In a second design step, we define the waveguide’s poling pattern to transfer the broadened fundamental spectrum to shorter wavelengths. This can be achieved efficiently, when a fixed phase relation between the involved waves is maintained (phase matching). However, due to chromatic material dispersion, this cannot easily be fulfilled across the entire spectral interval of interest (regardless of the choice of waveguide geometry and GVD at the fundamental wavelength). As an alternative to natural phase matching, in ferroelectric crystals such as LiNbO 3 , quasi-phase matching (QPM) is possible. Here, the sign of the χ (2) -nonlinearity is periodically flipped within segments of length Λ (poling period), via poling of the crystal’s domains (Methods) to compensate the increasing phase-mismatch between the waves. For sum-frequency generation processes (which underlie harmonic generation), Λ is

where k 1 and k 2 are the input propagation constants, and k 3 is the output propagation constant in the waveguide. To achieve broadband QPM, Λ may be chirped (i.e., varied along the waveguide). To design Λ ( z ) ( z is the spatial coordinate in the propagation direction), we numerically compute the frequency ω dependent propagation constants k ( ω ) of the fundamental waveguide mode for waveguide top widths of 800, 1000, and 1200 nm. Based on Eq. ( 2 ), we derive the required poling period Λ for a number of sum-frequency processes that would result in second-harmonic generation (SHG = fundamental + fundamental), third-harmonic generation (THG = SHG + fundamental), and fourth-harmonic generation (FHG = SHG + SHG or THG + fundamental). These periods Λ are shown in Fig.  2 b, as a function of the fundamental comb’s wavelengths.

Prior to astrocomb generation, we tested different waveguide designs with a low-repetition rate (100 MHz), 80 fs mode-locked laser operating at a center wavelength of 1560 nm. The pulses are coupled to the chip via a high-numerical aperture lens (NA = 0.7) lens and the spectra are collected using reflective collimation optics and a fluoride multimode fiber that connects to a grating-based optical spectrum analyzer (Yokogawa AQ6374). Utilizing a lensed fiber with a calibrated coupling efficiency as a temporary output coupler, we determine the input coupling efficiency of the high-NA lens to be 13 ± 2%. To illustrate the impact of the poling structure, we compare in Fig.  2 d a waveguide poled for broadband SHG ( Λ weakly chirped as indicated) with an unpoled waveguide (Fig.  2 e), demonstrating markedly different behaviors. The poled waveguide creates a broadband SHG at ~400 THz, whereas the unpoled waveguide only creates a narrow SHG. These observations agree with numerical simulation via pyChi 64 (shown below the experimental spectra). Note that the poled waveguide also exhibits a more substantial broadening of the input spectrum (and its harmonics), which can be explained through the contributions of cascaded χ (2) -processes to the effective χ (3) -nonlinearity. In a more advanced design (Fig.  2 f) a short SHG section (supporting also broadening) is followed by a longer and strongly chirped section designed to enable FHG. Indeed, pronounced FHG is visible, although, in contrast to the simulation, it is not stronger than the THG signal. We attribute this to the very small values of Λ  < 2 μm, which are challenging to fabricate with high fidelity. To overcome the fabrication challenge for very small Λ , we also consider higher-order QPM (Fig.  2 b). In higher-order QPM, the poling period is an integer multiple q of the fundamental poling period Λ 65 , which relaxes fabrication requirements at the cost of reduced efficiency. In our design for symmetric poling (equal length for both crystal orientations), q is an odd-integer (here: q  = 3). In addition, unintentional phase-matching may occur involving higher-order waveguide modes and coupling between orthogonal polarizations. A possible design is shown in Fig.  2 g, where, after a short length of SHG poling, Λ ranges from 2 to 7 μm. This choice of Λ respects the fabrication limit and provides QPM for most processes (Fig.  2 b). The generated harmonic spectrum extends across 600 THz (ca. 350 to 1000 nm) within  ~20 dB of dynamic range, demonstrating, in agreement with previous work 59 , the potential of LiNbO 3 waveguides for generating gap-free spectra in the VIS and UV domains.

Spectrograph calibration

With the principle of efficient harmonic generation validated, we build a dedicated ultraviolet astrocomb and use it for spectrograph calibration under realistic conditions at the high-resolution echelle spectrograph SOPHIE 60 at the Observatoire de Haute Provence (OHP, France). With the help of an Echelle-grating and a prism, the spectrograph cross disperses the input spectrum on a two-dimensional charged coupled device (CCD) detector array so that the spectrum is arranged in a vertically separated set of nearly horizontal lines ( Echelle orders ), where each line represents a distinct wavelength interval. The SOPHIE spectrograph, covers the wavelengths λ from 387 to 708 nm with a resolving power of \(R=\frac{\lambda }{\Delta \lambda }\approx 75^{\prime} 000\) (i.e., frequency resolution of approximately 10 GHz at 400 nm wavelength) and its echelle-grating is enclosed in a pressure vessel to reduce externally induced drifts. Traditionally, wavelength calibration can be obtained via thorium-argon hollow-cathode lamps (ThAr) and a passively-stabilized Fabry-Pérot etalon (FP) 66 , 67 , permitting calibration on the 1 to 2 m s −1 level 68 .

As an initial IR comb generator, we utilize an 18 GHz EO comb, similar to ref. 62 (Fig.  3 a). A CW laser of wavelength 1556.2 nm is stabilized to an optical resonance frequency in rubidium (Rb), providing an absolute frequency anchor for the IR EO comb (Methods). Comb generation proceeds by sending the CW laser through two electro-optic phase- and one electro-optic intensity modulator, creating an initial IR comb spanning ~0.6 THz. The modulation frequency of 18 GHz is provided by a low-noise microwave synthesizer, referenced to a miniature Rb atomic frequency source; over the relevant time scales of our experiments, a relative frequency stability better than 10 −11 is achieved (Methods). In a waveshaper, a polynomial spectral phase up to third order is imprinted on the EO comb spectrum, to ensure short pulses after the amplification in an erbium-doped fiber amplifier (EDFA) and an additional stretch of optical fiber for nonlinear pulse compression. In this way, an 18 GHz femtosecond pulse train with 3 W of average power can be generated. The pulses are out-coupled to free space and coupled to the chip via a high-numerical aperture (NA = 0.7) lens (estimated on-chip-pulse energy  ~20 pJ). Despite the high average input power levels, we did not observe any waveguide damage.

a Setup for ultraviolet (UV) astrocomb generation. Rb rubidium-based atomic references (main text, Methods); CW continuous-wave laser, PM phase modulator, IM intensity modulator, WS waveshaper, EDFA erbium-doped fiber amplifier, Col. fiber-to-free-space collimator, M mirror, CU calibration unit splitting the comb equally into A and B fibers, CCD SOPHIE charged coupled device detector. All fibers following the lithium niobate chip and feeding the spectrograph are multimode fibers. b Composite CCD detector image, obtained with two different settings of the flux-balancing prism, showing fourth- and third-harmonic in the UV and visible (VIS) wavelength ranges. The inset indicates how wavelengths increase along the individual cross-dispersed echelle orders. The magnified CCD sub-images show the distinguishable but slightly overlapping frequency comb lines on the detector, originating from the two spectrograph fibers, which are both fed by the same comb. c Extracted 1-dimensional comb spectra of both harmonics; the insets show a magnified (linear scale) portion of the spectrum and the 18 GHz-spaced comb lines. The UV detector cutoff is marked.

For comb generation, we choose the waveguide in Fig.  2 f, as it exhibits a strong UV signal and a clear separation between the harmonics. We arrange the waveshaper and the optical fiber after the amplifier such that the driving pulses are of ca. 200 fs duration, maintaining the separation between the harmonics, so that the emergence of inconsistent frequency combs, as described above, can be excluded. As we show in the  SI , Section  3 and Supplementary Fig.  6 , shorter pulses can enable the generation of broadband and merging harmonics, which opens opportunities for future work. The generated spectra are similar to those generated at a lower repetition rate (Fig.  2 d–g). The chip’s output, including fundamental and higher-order waveguide modes, is collimated using a parabolic mirror and sent through a tunable prism for coarse wavelength filtering and balancing of flux levels as needed, before being coupled to a multimode fiber. The light is sent through a mode-scrambler (Methods) and then routed to an auxiliary input port in the spectrograph’s calibration unit, which marks the interface between our LFC setup and the existing telescope and spectrograph infrastructure at OHP 60 . The calibration unit splits the comb light equally into two optical fibers (A/B fiber), which are placed next to each other on the spectrograph entrance slit, each creating an equivalent cross-dispersed spectrum on the two-dimensional detector. Figure  3 b shows a comb spectrum as recorded on the CCD detector of the SOPHIE spectrograph. The comb structure of the LFC spectrum is clearly visible along the individual spectral orders of the cross-dispersed echelle spectrograph for both A and B fibers. Data extraction and reduction of the LFC exposures is performed using a custom code initially developed for the ESPRESSO spectrograph 69 . It extracts the spectral information from the two-dimensional detector frame using a variant of the flat-relative optimal extraction algorithm 70 , provides default wavelength calibration based on a combined ThAr/FP wavelength solution 69 , 71 , and combines the data from the individual spectral orders to a single one-dimensional spectrum (Fig.  3 c) and thus makes it accessible to subsequent analysis. The resolving power of the spectrograph is not sufficient to fully separate the comb lines. In particular, in the UV part of the spectrum, the wings of the spectrograph’s line-spread functions for adjacent comb lines overlap and imply a reduced contrast. Nevertheless, the individual comb lines are clearly discernible.

To test the stability of the LFC-based wavelength calibration, we obtained over several hours repeated LFC exposures interleaved with exposures of the FP etalon. The two types of exposures allow us to measure the spectrograph drift in independent ways, once relative to the LFC and once relative to the FP. After data reduction as described above, all LFC lines in the spectra are fitted individually to determine their positions on the detector (Methods). For the FP exposures, the gradient method 72 is used to non-parametrically detect shifts of the spectra on the detector. As shown in Fig.  4 a, we obtain separate drift measurements from the third- and fourth-harmonic and, in addition, one drift value from the FP, where we only use the FP lines that overlap spectrally with the third-harmonic (the FP calibration does not cover the UV). All three measurements agree well (within the amplitude of their scatter) and detect a systematic spectrograph drift of ca. −2 m/s over 4 h. The agreement between the third-harmonic and the FP validates the LFC, and the agreement between the fourth-harmonic with the two other measurements extends the validation to the UV regime. The slightly higher noise in the LFC data, i.e., remaining differences between third- and fourth-harmonic and scatter around the global trend, compared to the FP drift measurement, can probably be attributed to a combination of effects, e.g., intrinsic systematics of the spectrograph like detector stitching issues 73 or charge transfer inefficiency (CTI) 74 combined with a change in the flux levels of the LFC lines. Moreover, the line spacing of our comb (18 GHz), which is limited by our specific technical components, is less than half the FSR of the FP calibrator (39 GHz). As a result, comb line fitting (Methods) is more challenging, and a slightly higher scatter can be expected, when compared to the FP-based calibration. Implementing a comb with larger spacing or higher resolution spectrographs can address this challenge. The fact that, nevertheless, the scatter in the FP and comb-based calibrations are comparable, indicates that the obtained precision is here limited by the spectrograph, not by the comb (indeed, the scatter is consistent with the design goals of the spectrograph 60 ).

a Spectrograph drift measurement based on the Fabry-Pérot (FP) etalon in the visible (VIS) wavelength and the laser frequency comb (LFC) in VIS and ultraviolet (UV) wavelength range. The FP calibration data has been restricted to its spectral overlap with the VIS LFC; Error bars indicate formal uncertainties based on propagation of photon- and read-out noise. b Absolute spectroscopy of thorium emission lines by the LFC-calibrated spectrograph. The deviation of the literature values from our LFC-calibrated measurement is shown as a function of wavelength and separately for A and B fiber. Error bars indicate formal fitting uncertainties based on a propagation of photon- and read-out noise; dashed lines indicate 16th, 50th, and 84th percentiles. Right panel: histogram of the deviations, separated for Fiber A and B. Mean and standard deviation are indicated.

To test the accuracy of our LFC-based calibration, we compare it to the established laboratory wavelengths of the ThAr hollow-cathode lamp. For this, two exposures, one containing the LFC and the other the ThAr spectrum, are obtained in quick succession, which ensures that no relevant spectrograph drift happens between the two exposures. In the extracted LFC spectrum, individual lines are fitted (see above and Methods) and, together with the knowledge about their true, intrinsic frequencies (Eq. ( 1 )), a purely LFC-based wavelength solution, i.e., a relation between CCD pixel position and wavelength, is derived for the spectral region covered by the comb. This LFC wavelength solution is then applied to the extracted ThAr spectrum and, after fitting of line centroids, LFC-calibrated wavelengths are assigned to the thorium lines. These are then compared to the laboratory wavelengths 75 and the deviations are shown in Fig.  4 b. The histogram of all deviations shows a global offset of  −9 to  −14 m/s with a standard deviation of  >20 m/s, which is consistent with zero offset, and also with an equivalent comparison performed with the highly accurate ESPRESSO spectrograph 69 . We note that the large uncertainty (the standard deviation in the histogram) is not limited by the comb calibrator but due to the low number of only  ~100 ThAr lines that are available for comparison. The scatter of individual line deviations (and the difference between Fibers A and B), which significantly exceeds the formal uncertainties, has also been observed for other spectrographs (e.g., ESPRESSO 69 ) and seems to be a common systematic, probably related to an imperfect determination of the instrumental line-spread function. We confirm that this scatter is identical when comparing thorium lines to LFC or ThAr/FP wavelength solutions 69 , 71 . Therefore, we conclude that the LFC wavelength calibration is accurate to the level testable with SOPHIE. Both measurements combined validate on the proof-of-concept level that the generated astrocomb can provide precise and absolute calibration even at UV wavelengths.

Microresonator-based UV astrocombs

Finally, we explore photonic chip-integrated microresonators (microcombs 24 , 25 , 26 ) as the fundamental IR comb generator. While their current level of maturity is lower than that of EO comb generators or mode-locked lasers, microcombs can provide compact and energy efficient 76 high-repetition rate, low-noise femtosecond pulses 77 , and their potential for microresonator astrocombs has already been demonstrated in the IR spectral range 27 , 28 . Combined with highly-efficient frequency conversion in LiNbO 3 waveguides, potentially in a resonant configuration 78 , 79 , 80 , they could open new opportunities for space-based calibrators, where energy consumption, size, and robust integration are key. Such space-based systems could calibrate ground-based observatories through the atmosphere, or provide calibration to space-based observatories, which would entirely avoid limiting atmospheric effects, such as absorption or turbulence. Therefore, as a proof-of-concept, we replace the electro-optic comb generator with a silicon nitride microresonator 81 , 82 (Fig.  5 c, photo) operating at f rep  = 25 GHz (Methods). A portion of the generated comb spectrum is bandpass-filtered and pre-amplified in an erbium-doped fiber amplifier (Fig.  5 a). Figure  5 b shows the IR comb spectrum generated by the microresonator as well as the filtered and amplified spectrum. The remainder of the setup is the same as described before for the EO astrocomb (Fig.  3 a). While we do not stabilize the microcomb spectra, we observe broadband harmonics of distinct comb lines, similar to the EO comb configuration (Fig.  5 c), illustrating the potential of implementing all nonlinear optical components via highly-efficient photonic integrated circuits.

a Modified setup for microresonator-based ultraviolet (UV) astrocomb generation. b Microresonator comb output spectrum (gray); bandpass-filtered and pre-amplified microresonator-based comb spectrum. c Microresonator-based UV fourth-harmonic and visible (VIS) third-harmonic comb spectra, following the scheme in Fig.  3 . The photo shows the photonic chip with the microresonator (dashed-line box) and the inset shows a scanning electron microscope image of the Si 3 N 4 resonator waveguide.

Although lithium niobate is known to show photo-induced damage by visible and ultraviolet light, we did not observe any signs of degradation in our experiments and attribute this to the relatively low flux levels in these wavelength domains (The power in the harmonics and corresponding conversion efficiencies are presented in the  SI , Section  4 and Supplementary Fig.  7 ). In a dedicated experiment, described in Section  5 of the  SI and Supplementary Fig.  8 , we transmitted light of a 405 nm laser diode through the waveguide and did also not observe any degradation. Zirconium-doping of the lithium niobate can further increase the damage threshold for visible and ultraviolet light 83 .

In this work, we demonstrate astronomical spectrograph calibration in the UV wavelength range with a laser frequency comb. This demonstration is particularly relevant to the emerging field of optical precision cosmology with next-generation instruments and telescopes. Our astrocomb’s architecture is based on periodically poled lithium niobate nanophotonic waveguides tailored to provide efficient frequency conversion of a robust, alignment-free 18 GHz electro-optic frequency comb. Moreover, we show the compatibility of the approach with photonic chip-integrated microcombs, creating opportunities for future space-based systems. This nonlinear transfer of a microcomb to VIS and UV wavelengths also adds new operating domains to the repertoire of these sources. The approach demonstrated here can be utilized to extend calibration beyond established wavelength ranges towards shorter wavelengths. Future work may pursue wider harmonic spectra ( SI , Section  5 ), where however, consistency of the generated spectra via suitable control of the fundamental comb’s offset-frequency (as described above) and noise suppression as previously demonstrated for electro-optic combs 63 would need to be implemented. With improved coupling to the waveguide 47 , 84 this could enable gap-free VIS and UV operation based on robust telecommunication-wavelength IR lasers. Similar results may be possible also in other waveguide materials such as aluminum nitride (AlN), where broadband phase matching may be achieved through chirped geometries 85 . In addition to the development of the comb source itself, spectral flattening 86 will be needed to ensure optimal exposure of the CCD and to avoid systematic effects that can arise from strong modulation of the comb's spectral envelope. In sum, the demonstrated approach opens a viable route towards astronomical precision spectroscopy in the ultraviolet based on robust infrared lasers and may eventually contribute to major scientific discoveries in cosmology and astronomy.

Waveguide and microresonator fabrication

Lithium niobate waveguides for UV comb generation are fabricated from an 800-nm-thick x-cut LiNbO 3 layer on 3 μm SiO 2 and bulk Si substrate (NANOLN). First, chromium (Cr) electrodes for periodic poling are fabricated using electron-beam lithography and lift-off. Ferroelectric domain inversion is performed by applying a high-voltage waveform across the electrodes, adapted from ref. 87 ( SI , Fig.  5 ). After poling, the electrodes are removed via chemical etching. Waveguides are patterned using electron-beam lithography on a Cr hard mask. Cr is etched using argon (Ar) ion-beam etching and subsequently, the lithium niobate layer is fully etched (no slab remaining) via reactive-ion etching with fluorine chemistry. The remaining Cr hard mask is later removed with chemical etching. Lastly, a 3-μm-thick SiO 2 cladding layer is deposited using chemical vapor deposition and waveguide facets are defined by deep etching to ensure low-loss coupling to the waveguides. More details regarding the fabrication of lithium niobate waveguides can be found in  SI , Section  2 .

The Si 3 N 4 microresonator is designed with a finger shape 82 and fabricated via the subtractive processing method as described in ref. 81 . The height and the width of the SiN waveguide are 740 nm and 1800 nm respectively, which result in a group velocity dispersion coefficient of β 2  = –73 ps 2 /km for the fundamental TE mode at the pump wavelength. The total linewidth of the critically coupled resonator is 25 MHz. Lensed fibers are used for coupling into and out of the bus waveguide. More details are provided in Section  2 of the  SI , including Supplementary Figs.  4, 5 .

CW laser frequency lock

A narrow-linewidth CW laser at telecommunication-wavelength 1556.2 nm (Redfern Integrated Optics, RIO Planex) is split and one part is used for EO comb generation. The other part is frequency-doubled and brought into resonance with the 5 S 1/2 ( F g  = 3) − 5 D 5/2 ( F e  = 5) two-photon transition in 85 Rb atoms in a microfabricated atomic vapor cell, similar to ref. 88 . A stable frequency lock of the CW laser to the two-photon transition is achieved by means of synchronous detection and by modulating the laser’s injection current. Using the same vapor cell and a laser with higher phase noise, we measured the fractional frequency instability of our system to an Allan deviation better than 2 × 10 −12 for averaging times from 1 to 10 4  s.

Miniature atomic frequency source

The 10 MHz sine wave output of a commercial miniature atomic frequency source is provided to the microwave synthesizer as a stable reference. The miniature atomic clock we use is based on a transition in the ground state of 85 Rb. Its relative frequency stability is specified by the manufacturer to be better than 1 × 10 −10 (1 × 10 −11 ) at 1 s (100 s) averaging time; daily drift  <1 × 10 −11 .

Mode-scrambler and calibration unit

The mode-scrambler suppresses detrimental laser speckles on the CCD (modal noise) that would result from the coherent LFC illumination after propagating through the multimode fiber train of the SOPHIE spectrograph. It consists of a rotating diffuser disc and has a throughput of  ca. 5% effectively washing out any laser speckle pattern. Averaged over one CCD exposure time, it populates all fiber modes and, therefore, ensures a speckle-free image of the spectrographs’s entrance aperture on the CCD. After the mode-scrambler, the light is guided by a multimode fiber to the calibration unit. The calibration unit selects one of the installed calibration light sources or, via a temporarily added additional input port, the light from the LFC. The selected light is then sent to the spectrograph’s front-end, mounted at the Cassegrain focus of the OHP 1.93 m telescope, where it is simultaneously injected into A and B fibers feeding the spectrograph 60 .

LFC line fitting and computation of drift

The LFC lines are fitted to find their exact center positions. Due to the limited resolution of the spectrograph, the comb lines are not fully separated but partially overlap, particularly in the UV domain. Therefore, always three LFC lines are fitted together, a central line of interest and two flanking ones to model the flux contributed by their wings. In addition, the diffuse background flux is locally modeled by a polynomial of first order. A detailed characterization of the SOPHIE instrumental line-spread function is not available. Therefore, we have to resort to model all lines with a simple Gaussian shape. In addition, due to the limited sampling (about 2.5 pixels per FWHM) on the detector, a simultaneous and unconstrained fit of all nine model parameters (positions and amplitudes of the three lines in question, one common linewidth, and amplitude and slope for the diffuse background) leads to degeneracies and unphysical fit results. The width of all LFC lines in the fit is, therefore, fixed to an FWHM of 2.47 pixels. This value was inferred from the thorium lines and, although not capturing the variation of the instrumental line-spread function along individual spectral orders or with wavelength in general, was found to better describe the line shapes than a width that is fixed in velocity units.

For each exposure, the fitted line centroids are compared to the corresponding positions in the first exposure of the sequence, the differences converted to radial velocity shifts following the Doppler formula, and then combined to provide one average drift measurement per exposure.

Data availability

The data shown in the plots have been deposited in the Zenodo database https://zenodo.org/records/12607045 ; https://doi.org/10.5281/zenodo.12607045 .

Code availability

The numeric simulations in the current study used an open-source code available at https://github.com/pychi-code/pychi .

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Acknowledgements

This project has received funding from the Swiss National Science Foundation (Sinergia BLUVES CRSII5_193689 (F.B., D.G., and T.H.)), the European Research Council (ERC) under the EU’s Horizon 2020 research and innovation program (ERC StG 853564 (T.H.) and ERC CoG 771410 (V.T.-C.)), and through the Helmholtz Young Investigators Group VH-NG-1404 (T.H.); the work was supported through the Maxwell computational resources operated at DESY. The lithium niobate waveguides were fabricated in the EPFL Center of MicroNanoTechnology (CMi).

Open Access funding enabled and organized by Projekt DEAL.

Author information

These authors contributed equally: Markus Ludwig, Furkan Ayhan, Tobias M. Schmidt.

Authors and Affiliations

Deutsches Elektronen-Synchrotron DESY, Notkestr. 85, 22607, Hamburg, Germany

Markus Ludwig, Thibault Wildi, Thibault Voumard, Mahmoud A. Gaafar & Tobias Herr

École Polytechnique Fédérale de Lausanne (EPFL), 1015, Lausanne, Switzerland

Furkan Ayhan & Luis G. Villanueva

Observatoire de Genève, Département d’Astronomie, Université de Genève, Chemin Pegasi 51b, 1290, Versoix, Switzerland

Tobias M. Schmidt, François Wildi, Francesco Pepe, Bruno Chazelas & François Bouchy

Swiss Center for Electronics and Microtechnology (CSEM), 2000, Neuchâtel, Switzerland

Roman Blum, Ewelina Obrzud, Davide Grassani, Olivia Hefti, Sylvain Karlen & Steve Lecomte

Department of Microtechnology and Nanoscience, Chalmers University of Technology, 41296, Gothenburg, Sweden

Zhichao Ye, Fuchuan Lei & Victor Torres-Company

Observatoire de Haute-Provence, CNRS, Université d’Aix-Marseille, 04870, Saint-Michel-l’Observatoire, France

François Moreau & Rico Sottile

Q.ANT GmbH, Handwerkstraße 29, 70565, Stuttgart, Germany

Victor Brasch

Physics Department, Universität Hamburg UHH, Luruper Chaussee 149, 22607, Hamburg, Germany

Tobias Herr

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Contributions

M.L. built the setup for ultrahigh repetition rate pulse amplification and compression, designed, and tested the waveguides, F.A. developed the waveguide fabrication and poling process and fabricated the waveguides, T.S. developed analysis software and analyzed the calibration data, T.W. operated the microresonator comb and built the EOM setup, T.V. supported laser stabilization, R.B. designed, built, and operated the stabilized CW laser, Z.Y., F.L., and V.T.-C. designed and fabricated the microresonator, M.L., F.A., T.S., T.W., T.V., R.B., V.B., F.B., and T.H. performed the calibration experiments, F.W., F.P., M.A.G., E.O., D.G., S.K., S.L., F.M., B.C., and R.S. supported the experiments, O.H. performed the UV damage study, V.B., L.G.V., F.B., and T.H. conceived and supervised the project. M.L., F.A., T.M.S., and T.H. wrote the manuscript with input from all authors.

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Correspondence to Tobias Herr .

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Ludwig, M., Ayhan, F., Schmidt, T.M. et al. Ultraviolet astronomical spectrograph calibration with laser frequency combs from nanophotonic lithium niobate waveguides. Nat Commun 15 , 7614 (2024). https://doi.org/10.1038/s41467-024-51560-x

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Received : 28 August 2023

Accepted : 12 August 2024

Published : 02 September 2024

DOI : https://doi.org/10.1038/s41467-024-51560-x

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