What is a zero refractive index material? | Hacker News Reader

What is a zero refractive index material?

skullsinthestars.com

224 points_Microft69 comments

For anyone who hasn't studied electrodynamics or advanced optics, Grant Sanderson (3Blue1Brown) recently made a detailed video explaining what the refractive index really means, probably the clearest reasonably accessible explanation of this topic anywhere to date:

https://www.youtube.com/watch?v=KTzGBJPuJwM

https://www.youtube.com/watch?v=Cz4Q4QOuoo8

The first video is really a tour de force. Too bad it saw such limited traction here: https://news.ycombinator.com/item?id=38482549

For those without a lot of patience, skip ahead to 6:45 or so (in the fist linked video) which is a really cool, "a-ha!" moment of why light "slows down" when it hits light. He also points out that he's really just animating feinman lectures, so giving credit where it's due. Gonna have to go dig out those books. Big thanks to jacobolus for linking these videos

To be clear there are numerous explanations for why light slows down in a medium and they are almost all incorrect in one way or another.

This video uses the explanation that light interacts with electrons in a medium which causes the electrons to produce an electromagnetic wave whose interference pattern changes the phase of the light wave, kicking it back.

The problem is that an interference pattern can never change the speed of a wave, it can change the phase of the wave and adjust it, but that won't explain how light passing through a medium takes longer to traverse that medium than light travelling in a vacuum.

I don't know of a visualization or explanation that captures why light slows down in a medium, and the video linked is still a good way to get a sense of what's happening, but it's worth knowing that there is still a great deal being left out of that explanation.

It is nevertheless better than explanations involving the absorption an reemission of photons or that light bounces around within the internal structure of a medium. Both of those explanations manage to explain how light takes longer to pass through a medium but fails to explain how light keeps a consistent direction as opposed to scattering randomly.

The explanation in the video manages to explain how light maintains a consistent direction but fails to explain how light will actually take longer to pass through a medium compared to a vacuum.

I thought that Grant's video did a great job of explaining it was all phase kicks, and how it all depended on resonant frequencies of the medium.

[Edit]In the second video above, he notes that phase kicks don't change the speed of the wave, even though the wavelengths can stretch out, it's still lower than the speed of light in vacuum.

Phase kicks don't change the speed of a wave. If you setup a similar experiment with sound or water where you constructed an interference pattern that kicked back the phase of the wave, the wave wouldn't slow down.

If you want an actual non-layman explanation for why light slows down ib a medium you need to express the light and medium interaction in terms of polaritons. Of course this is incredibly difficult to do so for even simple cases, so alas a whole suite of simplified explanations exist that seek to explain some aspect of the situation while failing to explain others.

https://en.m.wikipedia.org/wiki/Polariton

Could you elaborate please?

So, there no slowdown by phase shift at all? But.. are you sure, because it looks like the phase shift is the real effect and logically speaking result of the phase shift will be the effect that look like slowdown for outside observer.

Also, how can you simulate similar effect in water and sound if there no sound polarization?

The phase shift is dependent on both the resonance frequency of the medium and the incident light. In the case of X-rays, the refractive index can go below 1, resulting in total external reflection for a few tenths of a degree. Even in this case, the speed of the X-ray itself stays below that of C, even though the "wavelength" appears to be longer than in vacuum.

> logically speaking result of the phase shift will be the effect that look like slowdown for outside observer.

If there was a phase shift but no slowdown, wouldn't we expect individual photons to propagate through a 10km loop of fibre optic cable without any slowdown, which would be measurable?

You would certainly see an apparent slowdown due to phase shift if you consider a continuous wave that spans the entire medium, yes for sure and so this explanation and model does have merit, I don't want to dismiss it entirely.

But this model won't be useful for understanding pulses of light through a medium. For example if I emit a very short pulse of light through a medium and measure how long it takes the head of the pulse to traverse the medium, using this model won't work. A phase shift won't move the head of a pulse of light backwards, it will just adjust the amplitude of the head as it propagates through the medium.

You still need a way to explain how it is that the head of the pulse actually takes longer to travel through the medium and that's not something a phase shift can explain.

The understanding of a refractive index only cares about 'phase speed' in steady state. At least, that is what the video claims to be about. For that case, phase kicks are a sufficient explanation no?

I can imagine things get really weird with pulses, but that's out of scope for the video.

> Phase kicks don't change the speed of a wave.

"Phase kicks" explain the phase velocity. The speed of a wave is the group velocity. Phase velocity is omega(k)/k, group velocity is omega'(k). So if "phase kicks" explain phase velocity sufficiently so it's valid for a range of frequencies, then it also explains group velocity by taking the derivative of the dispersion relation.

That's true for a steady-state wave, and hence this model is accurate for a steady-state light wave. But if you were to consider short pulses of light then there is no longer a relationship between the group velocity and phase velocity.

The group velocity of these pulses through a medium will still be lower than the speed of light in a vacuum and phase kicks won't influence the group velocity.

Explaining how the group velocity of light can be slower in a medium than in a vacuum requires analyzing the coupling of photons with electrons to form polariton quasiparticles. You can then calculate the mass of these polaritons which in turn gives you the speed and get the full picture. Doing this, however, is incredibly complex and so it's much easier to consider simplified scenarios like either the steady-state case where you can simply reason about the scenario in terms of interference patterns between the light wave and the electromagnetic waves produced by oscillating electrons, or you can consider some non-steady state scenarios involving photons themselves being absorbed and reemitted by electrons but neither of these explanations fully capture the phenomenon.

A pulse of wave is a superposition of steady-state waves. Group velocity, phase velocity and dispersion relation have one-to-one correspondence.

I agree that the phase-kick classical model is a very simplified material model, which probably breaks down in certain ways. But it does yield a dispersion relation, therefore both phase and group velocities.

I'm not sure if this will be satisfying because it is a mathematical explanation rather than an intuitive one. If you combine two of maxwell's equations, you get a wave equation for electric/magnetic fields. However, there is an extra term in there, which is the effect of a time changing current on the magnetic field. In a material, the time changing electric field induces such a current, which in turn has the mathematical effect of reducing the coupling between the electric and magnetic field, creating the equation for a wave that is slower.

Something that might be comforting about light going slower than the speed of light is that the speed of light is not a special property of light, but it is a property of space time. It just so happens that light is the only way we have experience on this magic speed. Light isn't physically bound to go "the speed of light".

The actual answer is the assumptions which define a self-propagating wave do not apply once the wave leaves a vacuum. When it becomes incident onto some medium, due to the coupling of electrons within the medium to the electromagnetic field, the pure electromagnetic wave gets transformed into a phonon, which is a combination of electromagnetic and mechanical oscillation within the medium (and therefore has speed <c, depending on the particular properties of the medium). When the phonon subsequently leaves the system, those traveling oscillations induce a new self-propagating wave on the other side, sending the light on its way as usual.

What does it mean for something to oscillate electromagnetically and mechanically simultaneously?

Doesn't mechanical oscillation already occupy all three spatial dimensions plus a time dimension?

The phonon oscillates both the electrons and the EM field.

A photon is EM only.

So you’re correct that it occupies all four dimensions, but we’re discussing an excitation in one field (photon) changing to an oscillation in multiple (phonon) and then back to only one field (photon).

Can you explain this in a step by step manner?

I really can't quite grasp how the photon/phonon switches back and forth like this.

1. The photon moves through free space, where only the EM field is disturbed.

2. The photon enters a material, where the disturbance in the EM field couples to the electron waves — creating a phonon.

3. The phonon travels through the material, as an oscillation in both electrons and EM.

4. The phonon reaches the edge of the material, where there are no more electrons and reverts to a wave of just EM — a photon.

5. The photon continues in free space.

The reason this happens is the photon changes the electron behavior, which in turn changes the photon behavior. This is because EM interacts with charged particles like electrons.

For the time it is in a material, a EM wave can’t be separated from the behavior of the electrons present: both and their mutual interaction are required to explain what happens.

That disturbance of both is “coupled” — and called a phonon.

Is this more than a change of terminology? Is it wrong to say that the electromagnetic oscillation is still there in the medium but coupled to a mechanical oscillation, and the coupled system is called a phonon? (I mean there's still an electromagnetic field in the material, it still gets excited, it's not replaced with a new field that fuses the EM and matter fields). Then the question is by which process exactly is the electromagnetic oscillation slowed down, and is the answer much different from the explanations above? I.e. the moving charges due to the mechanical oscillation add perturbations to the EM field such that the net effect is a slower propagating wave.

visualized well in “Picture Book of Quantum Mechanics” ch 1 (a fairly hardcore physics text that does indeed have many diagrams)

No need to dig out the books, they're available online, well formatted and a pleasure to read:

https://www.feynmanlectures.caltech.edu/

https://www.feynmanlectures.caltech.edu/II_32.html

Grant has singlehandedly taught me more than all of my elite education combined. Man is an absolute treasure

One remaining question I had after watching Grant's video was that, although the collective behavior of a bunch of light waves made sense via interference, how would a single photon's direction would change upon entering the medium?

The best answer I could find on physics stack exchange was that the single photon's wavefunction is delocalized, so that the photon's wavefunction, in fact, interacts with the entire medium, instead of at a single point.

Is this the correct way to state this phenomenon or is there a better understanding of how the light emitted from a single photon interacting with a medium would bend?

Huygens Optics (pretty much the only dedicated optics channel on Youtube) also recently made a video on this subject[1].He made some diffractive lenses via photolithography, and shows how the interference caused by variably spaced diffraction patterns causes refraction.

[1] https://youtu.be/SS2AbZVdk2A?si=5KTvkX-KVnxRUN7G

AhnLab Safe Transaction's anti-phishing protection erroneously blocks this domain. The log says:

    Date: <redacted>
    Security Threat: Phishing site
    Target: skullinthestars.com/
    Status: Block
    Scan Method: Anti-Phishing

Sigh. I wonder how much worse can these South Korean "security applications" get. For instance, AhnLab's website¹ doesn't even list Ahnlab Safe Transaction in their products.

For the curious ones, a related thread: "South Korea’s online security dead end" https://news.ycombinator.com/item?id=34231364

¹ https://www.ahnlab.com/

> We and our 772 advertising partners store and/or access information on your device [...]

> 772

Seriously...

A lot sites are like that (most big ones), that's the whole reason they started GDPR. All you have to do is add a few widgets/plugin/third party ads/traffic monitors/tracking and their dependencies and you'll get hundreds of "partners"

arstechnica, cnet, &c. all have 200+ "partners"

And unfortunately they've all settled on the apparently untested, "legitimate interest" loophole where these hundreds of partners have a "legitimate interest" in serving you personalised adverts.

thanks for the heads up. i wasn't that interested in this topic anyway.

There is an old science fiction concept of 'slow glass', where light travels very very slowly, with 1/2 day glass used for windows that allow light to dally for 1/2 day before it exits - also good for street lights. Extending it to week/glass, year glass and so on, with the glass becoming a defacto streaming video display to watch burglars/traffic etc. Interesting concept, smashing a pane of year glass - would it release all that energy as an e=mc2 blast?? https://sf-encyclopedia.com/entry/slow_glass

You can model refraction using waves in a water-tank; the waves slow down in shallow water, and speed up in deeper water. You can do things like make lenses.

So I suppose a near-zero refractive index would be modeled by a region of "infinite depth". Is there a relationship between wavelength and depth, such that for a given wavelength, there is some finite depth that behaves for practical purposes as if it were infinite?

I have no physics education beyond high school, but I briefly became obsessed with the idea of efficient collimation of light. I eventually concluded that it must be impossible, because it would imply a global decrease in entropy, much like Maxwell's demon.

But this article seems to suggest that it might still be possible. Have I misread it? Or maybe misinterpreted — e.g. maybe "efficient" would cover a system that does require energy input, and just doesn't require discarding a lot of the input light?

Can anyone with more of a clue comment on this?

I find the idea exciting because I can imagine endless practical uses for an efficient collimator.

It'd be balanced by the difficulty in getting the light into the material in the first place. You're right, you can't change the laws of physics. Light will only enter an object with lower refractive index if its angle of incidence is close enough to straight on that the beam coming through into the material has somewhere to go that satisfies Snell's law. When the object's refractive index is near zero, the object will only accept incoming light across an extremely narrow angle. This solves your concerns about having a global decrease in entropy.

You can fudge this by making the incoming surface of the object match the shape of the incoming waves. Then all the light will be allowed in. However, that surface will only match the shape of the incoming waves for light originating from a tiny point in space. If your light source is larger than a tiny point in space, then the light coming from the larger area will bounce off the material and not enter it. In effect, the magic material will magically collimate a light source, but only if the light source is already fairly magic, and in that case a simple lens would suffice.

Thanks for the explanation.

It makes me a little sad, but maybe it's for the best; efficient collimation of light would offer enormous destructive potential for $cheap, and that's not something the world needs any more of.

it sounds like etendue

The first application that comes to mind for me, and of course I am not a quantum physicist so its entirely possible that my conceptions here are misguided, would be with creating even more perfectly coherent beams of laser light for use in the high precision environments of quantum laser experiments.

Possibly either at more affordable rates or to allow for an extremely temporally coherent wavefront in other shapes besides just the beam that is most commonly used? I could easily believe that there are potential experiments that are just waiting for the right technology to be viable.

This is cool. This is the sort of stuff I like to see on the internet.

I'm on my phone, and the privacy banner takes so much space I just see the title, a divider, and then the banner. I started reading the banner thinking it was the article...

For anyone who's interested, Fermilab has done several videos on this topic as well that I found highly informative:

https://www.youtube.com/watch?v=CUjt36SD3h8

https://www.youtube.com/watch?v=NLmpNM0sgYk

I don't understand why this does not imply the possibility of faster than light communication. If you had a long tube with a zero refractive index, couldn't you type Morse code into one end, by simply turning the signal on and off, and have the receiver receive the message immediately?

3blue1brown's video covers this. The effect of "changing speed" is a change to the light's wavelength, not the speed of an impulse through the material--imagine taking a standing wave and pushing the peaks and valleys up and down so the wavelength looks really long. And since the frequency is unchanged, there's your appearance of high speed. This happens because the material changes the phase of the wave continuously.

If you want to play around with different refraction values and see what happens I made a MetaPost script for that once: http://www.hugoblog.onrender.com/post/prism/

I'm getting an SSL error when trying to load that URL

https://hugoblog.onrender.com/post/prism/

Note that the sun produces collimated rays too. And the stars even moreso.

Which is to say, the rays are always parallel if the source is far enough away. Which feels like a good metaphor for something.

This kind of thing is super important for fiber optics.

This is a great article. Very interesting. Thanks for posting!

I recently developed a new interest in optics and it’s cool to see this posted on HN.

of possible interest: Discussions on Refraction of Light

https://archive.org/details/TarasovTarasovaDiscussionsOnRefr...

I would love to have a mug that is nearly invisible (when clean) until you pour beer into it.

Fascinating. Thank you for putting it together.

> "Privacy & Cookies: We and our 772 advertising partners store and/or access information on your device and also process personal data, like unique identifiers, browsing activity, and other standard information sent by your device including your IP address..."

There is no opt-out, which violates GDPR. If my data was collected on landing, I would like my data removed, please.

Have you contacted the owners of the website to get your data removed?

And give them more personal information?

I assumed OP was the website owner. But while my request is serious and legally binding, it was somewhat rhetorical as I do not expect the owners of a site with such a data policy would really be conscientious about contacting me to sort out which data is mine and removing it.

> But while my request is serious and legally binding, [...]

Posting a comment on HN is somehow legally binding for a third party website whose operator likely never even heard of HN? Or what are you trying to say?

As I understand it, the request to have data removed is what's legally binding, not the format in which the user makes the request. If the site owners see it or otherwise become aware of it, they are obligated to remove my data even though it was a post on HN. Whether all of that actually happens is a different story. They could probably claim truthfully they don't know which data is mine. If I were determined, I'd contact them directly.

Don't be absurd. I'm a big proponent of GDPR but you seem to be under the impression that it's a magic spell. You seriously believe that, legally, if you post a comment on HN, you're putting an obligation on someone? I have a piece of the moon to sell you, then!

That is a misapprehension of what I wrote.

Also, I threw that in there because, if the site operators were to see "I don't expect them to actually remove my data", I do not want them to interpret that as releasing them from the obligation. It does not. It's just my prediction of how things will go.

Yes, there is an opt out, see the fourth sentence: * Otherwise, you can get more information, customize your consent preferences, or decline consent by selecting "Learn More".*

It's a dark pattern to only call it "Learn More", but I wouldn't bet it's a GDPR violation.

Thanks for the tip.

The opt out is supposed to be as easy as the opt in, so I'd bet it crosses the line.

Edit: furthermore, even after opting out, you nevertheless "agree" that (that is to say, you cannot opt out of):

  Certain information (like an IP address or device capabilities) is used to ensure the technical compatibility of the content or advertising, and to facilitate the transmission of the content or ad to your device.

  Match and combine data from other data sources

  Link different devices

  Identify devices based on information transmitted automatically

The first of those is surely a valid technical requirement, right? (I'm not a GDPR expert, by any means.)

In order to send you bits via IP, the server needs your IP address. In order to know the type of bits to send, it needs to understand the content-type, encoding, etc that your device supports.

From what I understand, GDPR applies only to retention of data, and not such technical requirements. It does not require operators to inform users unless the server will be retaining the IP address.

In any distributed system, what "retention" means is unclear* and, in the face of that lack of clarity, a company deciding to play it safe and require consent for things that GDPR says needs consent seems reasonable.

* If I put your content-type and IP address onto a queue for processing by another system, that's arguably retaining the data, even if that length of retention is typically measured in seconds. Given that, the safest thing for me to do is to require your consent for the retention of IP address and related data.

I suppose? The GDPR is very clear: if you serve European residents, you cannot collect their identifiable data without their informed consent, nor can you make consent the price of viewing your content. If you are found to do so, you are liable to huge fines.

The language of the law itself is not very far from that clarity. Check it out for yourself: https://commission.europa.eu/law/law-topic/data-protection/d...

I find it not credible that a company would read that second part, think "My goodness that sounds awful! Out of an abundance of caution, we better include language around arcane technical edge cases!" but then go on to violate the very, very clearly stated core intent of the law regarding consent and actual data retention and brokering.

So... it is confusing. Probably intentionally so. Perhaps their legal strategy would be to somehow conflate these edge cases? Try to baffle judges?

> The EDPB adopted Guidelines on dark patterns in social media platform interfaces[2]. The guidelines offer practical recommendations to designers and users of social media platforms on how to assess and avoid so-called “dark patterns” in social media interfaces that infringe on GDPR requirements.[1]

There calling it "deceptive design patterns". In short, tricking people is not consent.

[1] - https://edpb.europa.eu/news/news/2022/edpb-adopts-guidelines...

[2] - https://edpb.europa.eu/system/files/2023-02/edpb_03-2022_gui...

Just click on "disagree to all", no ?

At the time i wrote that, I did not understand that was behind the "learn more" button. However, if their data retention policy is accurate, even clicking "disagree to all" means they will retain data that individually identifies their users and they exchange this data with other brokers. This is strictly against the letter and spirit of the GDPR, opening them up to the possibility of massive fines.

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