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# Can Light Travel Infinitely Fast?

Posted October 21, 2015 2:00 PM by Quasar

Researchers have created for the first time an on-chip metamaterial with a refractive index of zero, meaning that the phase of light traveling through the material can move infinitely fast. The research was conducted at Harvard's John A. Paulson School of Engineering and Applied Sciences, and is published in the journal Nature Photonics.

You might be wondering how exactly light can travel infinitely fast when according to special relativity, the speed of light (~300 million km/s) is a hard limit that no matter or information can surpass. The catch here is that the infinite speed refers to the phase velocity of light, or how fast the crests of the wavelength move. As Sommerfeld pointed out way back in 1907, "the signal velocity and the process of propagation have nothing to do with the phase velocity," so relativity and causality are preserved.

Upon entering a standard material, like the glass in a window, light's phase velocity slows down as its wavelength is compressed. Exiting the material, the phase velocity speeds up as its wavelength stretches back out. The index of refraction (n) is the ratio of maximum speed of light (c) and the phase velocity (v) of the light traveling through a material (n = c / v).

Interesting behavior is observed when the refractive index is zero. Light stops acting as a wave with crests and troughs moving through space. Instead, a constant phase is created where all crests or all troughs stretch out in wavelengths of infinite length, oscillating only as a variable of time and not space. This phase velocity of infinite speed does not, however, allow information or matter to exceed the speed of light; phase velocity is distinct from the velocity of a complete signal carrying data.

New zero-index metamaterial consisting of silicon pillar arrays embedded in a polymer matrix and clad in gold film. (Image: Peter Allen/Harvard SEAS)

Metamaterials with a refractive index of zero have been developed before, but this particular breakthrough is unique in the fact that it is on-chip and can interface with standard photonic components and chips. Traditionally, integrated photic components have had ineffective optical energy confinement. With this new metamaterial, high internal phase velocity allows lossless energy transmission, permitting the light to be manipulated without losing energy.

The material will allow researchers to investigate the physics of zero refractive index in integrated photonic circuits, with potential applications in quantum computing and quantum optics. Entanglement between even distant quantum bits could be improved as incoming light waves are effectively spread infinitely long. Furthermore, photons from a quantum emitter in a zero-index waveguide would always be in phase with each other, enabling interesting research avenues in quantum optics.

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#1

### Re: Can Light Travel Infinitely Fast?

10/21/2015 2:06 PM

Compared to walking it sure seems like it, but it's all relative.

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#2

### Re: Can Light Travel Infinitely Fast?

10/21/2015 2:12 PM

Define infinitely...

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#5

### Re: Can Light Travel Infinitely Fast?

10/21/2015 9:27 PM

It's like having a conversation with a 7 year old and a disagreeable wife at the same time.

You have to experience it first hand to be able to grasp the concept in order for it to have a definable meaning. Those who have been there just know. Those who have not can not relate.

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#6

### Re: Can Light Travel Infinitely Fast?

10/21/2015 10:48 PM

I believe that is one of the levels in Dante's inferno....determining which, would be a daunting task indeed...luckily you have an escape pod in your workshop....haha

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#9

### Re: Can Light Travel Infinitely Fast?

10/22/2015 8:41 AM

Does having four dogs (one of which is a cross between Rottie and Beagle that is undergoing growth spurt and teething at the same time, and is eating our furniture, literally) and a disagreeable wife count as also one of the levels of hell?

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#19

### Re: Can Light Travel Infinitely Fast?

10/22/2015 12:44 PM

No,, that's just part of being a redneck....

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#8

### Re: Can Light Travel Infinitely Fast?

10/22/2015 8:40 AM

Apparently, as the article stated, there is an infinite speed phase velocity ∞, in a medium with zero refractive index, n=c/v where v is the phase velocity. Note that in all media, the frequency stays the same, even in zero index media.

as n--> 0, v-->∞, f= constant, and λ-->∞

Interesting that emitted photons from such a medium would exhibit pure phase synchronization, since the wavelength is infinite.

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#24

### Re: Can Light Travel Infinitely Fast?

10/22/2015 7:05 PM

Interesting observation and comment. If the wavelength is infinite, wouldn't that be Direct Current?

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#25

### Re: Can Light Travel Infinitely Fast?

10/22/2015 7:10 PM

... or zero current? How do you do an RMS on an infinite wavelength?

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#3

### Re: Can Light Travel Infinitely Fast?

10/21/2015 4:57 PM

Note that is phase velocity they are talking about. A good example of phase velocity versus true velocity is ocean waves striking a shoreline almost but not directly head on, so that the wave hitting the shore moves much faster than the wave itself. A similar thing happens in waveguides that are close to the cutoff freqency of the microwaves.

Here is another example:

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#13

### Re: Can Light Travel Infinitely Fast?

10/22/2015 11:16 AM

Thanks! GA! It is extremely rare that a short example in words only, helps me more than an extensive set of graphics.

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#4

### Re: Can Light Travel Infinitely Fast?

10/21/2015 6:16 PM

It would be interesting to discover how a velocity in excess of the speed of light can be measured.

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#11

### Re: Can Light Travel Infinitely Fast?

10/22/2015 8:55 AM

That would have to be measured by the pucker factor of those riding the ride. Google "pucker factor" to learn more about this measurement. Warp 7 produces a pucker factor of 107, and as I was telling a co-worker yesterday as he was stating we need warp 7 in getting engineering controls installed in one of our plants, "We already warped the probe seven times, isn't that enough already?" In reference to over-heating a depth sensor type flow meter on some really steamy water flow.

One other way to measure faster than light travel: space curvature measurements? knowledge of space curvature in the "warping" craft and the time of "warpage" might allow a back of envelope calculation within a few light years, but it might not make the best speedometer, or odometer, so one will need a device to roll against the warpage of space, good luck coming up with that one.

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#15

### Re: Can Light Travel Infinitely Fast?

10/22/2015 11:35 AM

You would use two very accurate clocks that have been synchronized and then moved apart. Light speed is about 1 foot per nanosecond, so the measurement is easily within the capability of atomic clocks.

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#17

### Re: Can Light Travel Infinitely Fast?

10/22/2015 11:51 AM

You would use two very accurate clocks that have been synchronized and then moved apart. Light speed is about 1 foot per nanosecond, so the measurement is easily within the capability of atomic clocks.

The trick is knowing what you are measuring the same event at both ends. A blip moving at phase velocity appears to travel faster than the underlying signals. But in reality, you are not measuring the same event at both ends.

If an ocean wave hits the beach at an angle close to 90 degrees, the crest of the wave hitting the shore appears to travel much faster than the wave. But you are not seeing the same event, i.e., the same part of the wave hitting the shore. You are seeing a series of very similar events that appear as one.

http://physics.stackexchange.com/questions/6912/in-superluminal-phase-velocities-what-is-it-that-is-traveling-faster-than-light

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#7

### Re: Can Light Travel Infinitely Fast?

10/22/2015 6:40 AM

If I understand it aright, a refractive index of zero means that the angle of refraction will be zero whatever the angle of incidence. This impliess that after passing through this material a beam of light will be absolutely parallel, better even than a laser.

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#10

### Re: Can Light Travel Infinitely Fast?

10/22/2015 8:49 AM

Yes, I suppose so indeed, if the material were transparent to the light in question, but we are talking about silicon and gold as the materials here, so really is it transparent? Apparently, the device has a narrow acceptance angle to begin with.

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#12

### Re: Can Light Travel Infinitely Fast?

10/22/2015 10:41 AM

When light travels from a medium of higher refractive index to a lower one, it bends away from the direction normal to the surface, according to the Snell's law. (Reverse direction of arrow in diagram below.)

If the angle of incidence in the denser medium is great enough, the sine of the angle in the less dense medium will be greater than 1. In this case there is total internal reflection. (You might have noticed the mirror like appearance of the water surface in an aquarium when viewed from below.)

https://en.wikipedia.org/wiki/Total_internal_reflection

Light entering a medium of zero refractive index would always experience total reflection, no matter what the angle of incidence.

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#14

### Re: Can Light Travel Infinitely Fast?

10/22/2015 11:21 AM

Yes! GA

This is why I don't trust this article or at least the author's translation of a complex experiment. I'll reference instead the Hyper Physics page on Snell's law and the relationship between the index of refraction and the velocity of light in a media. (The Wikipedia page is very good but a little verbose for my point.) The article implies that if n=0 (index of refraction) then v=∞ (the velocity in the media). However, for n to actually equal zero then light in the faster media cannot enter at all the slower media for sinθ=0 happens when θ=90°. Light from the infinitely fast media cannot enter an ideal vacuum and light in the ideal vacuum cannot enter the infinitely fast media.

At best, this is a misunderstanding by the reporting author. Phase velocity instead of light velocity might be the difference.

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#16

### Re: Can Light Travel Infinitely Fast?

10/22/2015 11:36 AM

Another GA! Doesn't that mean that light can NOT enter a medium of zero index of refraction?

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#18

### Re: Can Light Travel Infinitely Fast?

10/22/2015 12:31 PM

That would be my take on it. You should get total reflection at all angles.

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#20

### Re: Can Light Travel Infinitely Fast?

10/22/2015 1:36 PM

But if the light can never actually enter the medium of zero refractive index, then any discussion of phase velocity therein is meaningless.

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#21

### Re: Can Light Travel Infinitely Fast?

10/22/2015 1:59 PM

Yup!

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#22

### Re: Can Light Travel Infinitely Fast?

10/22/2015 2:08 PM

will light emitted within the medium ever be coupled out?

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#23

### Re: Can Light Travel Infinitely Fast?

10/22/2015 2:31 PM

Media with zero refractive index, nope.

Some might call this one of the foundations of the multiverse concept. Anything that actually travels faster than c (not a mathematical construct like phase velocity) cannot interact with things slower than the speed of light.

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#27

### Re: Can Light Travel Infinitely Fast?

10/23/2015 8:16 AM

Yes, but you must be clear if you meant c en vacuo, or c en medio.

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#26

### Re: Can Light Travel Infinitely Fast?

10/23/2015 4:37 AM

Sorry, I'm still lost on this. Quote from the abstract of the original paper "Light refracts perpendicular to the facets of a prism made of this metamaterial, directly demonstrating that the index of refraction is zero." To me that implies that light enters the material and is refracted perpendicularly therein.

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#29

### Re: Can Light Travel Infinitely Fast?

10/23/2015 9:41 AM

the facets are the flat parts of the prism, and if it refracts perpendicular to that, it is not in the prism, but traveling along the surface of the prism en vacuo, for example, which is the high index medium in this case.

I took it upon myself to set up a spreadsheet to calculate the "critical index of refraction to get 90 degrees refraction (total actual reflection along the boundary) using Snell's Law, and interestingly, there is no incidence where the index can be greater than unity for this to happen, regardless of angle of incidence. For indices greater than unity, the ray always enters the higher index medium, unless the angle is greater than the specular reflection angle?

How is this useful? Are they able to switch on/off this property on the chip? It would seem so, or there would be no real way to understand by probing it?

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#30

### Re: Can Light Travel Infinitely Fast?

10/23/2015 12:51 PM

I am not clear what question you are answering "NO" to. I did read the link, and it clearly states that light enters the material perpendicular to the facets.

I did calculations on a hypothetical medium where there is a vacuum above the medium, and the medium has whatever refractive index is required (by Snell's law) to produce a refraction angle of 90 degrees (surface propagation of the group).

in that calculation 0 radians is normal to the surface. π radians would be coming from the opposite surface (not sure how that works). π/2 radians would be incident parallel with the surface (not sure how that could refract into the material either).

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#31

### Re: Can Light Travel Infinitely Fast?

10/23/2015 1:35 PM

I was responding to "the facets are the flat parts of the prism, and if it refracts perpendicular to that, it is not in the prism, but traveling along the surface of the prism..."

Now, I can read this a couple of ways:

1. I assumed that "perpendicular to that" meant "perpendicular to the facet", or more accurately, "normal to the facet". This corresponds to Rixter's statement to the effect that light can only enter the material if it is [very nearly] normal to the surface. In this case it could be argued that it is not refraction at all, since no deviation of the ray occurs.

2. If "perpendicular to that" meant "perpendicular to the incoming ray", then the ray is bent 90°, and does not enter the metamaterial at all, but travels along the surface (as you indicate). This is counter-intuitive, but if true, it would not be the first time I found something counter-intuitive to be true. If it is indeed true, then in which of the infinite possible directions along that surface does it travel? ...or does a single incoming ray somehow get converted into a a full disk traveling in in all possible directions along that surface.

I strongly tend to accept the #1 interpretation.

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#28

### Re: Can Light Travel Infinitely Fast?

10/23/2015 9:05 AM

Actually, light can enter only if the angle of incidence (and its sine) is exactly zero, i.e., the beam is exactly perpendicular to the surface. I hope this clears it up.

http://spectrum.ieee.org/tech-talk/computing/hardware/zeroindex-metamaterials-open-new-possibilities-in-optical-chips

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#32

### Re: Can Light Travel Infinitely Fast?

10/23/2015 7:29 PM

Here is a picture that sort of shows what is happening. The light has to enter and leave the zero refractive index meta-material exactly perpendicular to the surface. The phase is frozen until it exits the other side.

http://www.nature.com/nphoton/journal/v9/n7/fig_tab/nphoton.2015.107_F2.html

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