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Name: Abhinav
Status: student
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Question:
What is the ultimate speed ( the upper limit of speed) in a medium with refractive index 1 and what is same for negative refractive index? I am asking about the speed of light in a medium in other than air/vacuum is not c - vacuum. In the medium, it is less than c - vacuum. Let the speed in a particular medium be 0.5c - vacuum. Then what is the maximum speed attainable in that medium? Can an object travel with 1.1c speed in that medium? What happens if it does? In metamaterials with negative refractive index what will be the maximum attainable speed of any particle?



Replies:
Abhinav,

First, consider what it means for light to travel slower in a medium. The AVERAGE speed of light is slower in the medium. Light is considered to be individual particles of energy called photons. When merged together in a stream, they behave like a wave of electric and magnetic energy, a beam of light. When passing through a vacuum, the photons just continue. When passing through a medium, a photon is often absorbed by an atom. If the right color, the right energy for the atom, it is completely absorbed, helping to make the material warmer. If that color is wrong for the atom, it is almost immediately ejected. These quick delays make the light take more time to pass through the material.

Consider walking. If you walk at three meters per second along an empty road, you travel six kilometers in two thousand seconds. If you stop occasionally on your trip to look at things or greet friends, you might only travel five thousand meters. You were walking at three meters per second, but someone timing the journey would say you traveled at 2.5 meters per second.

This is how a piece of glass can produce a rainbow. Different energy photons (i.e. different colors) are held for different times. Different colors have different indices of refraction. In reality, the speed of light is not reduced.

Dr. Ken Mellendorf
Physics Instructor
Illinois Central College


A quick answer, Abhinav:

You have to distinguish between "phase velocity" and "group velocity".

Refractive index predicts, strictly speaking, only the phase velocity of a continuous single-frequency wave. (wavelength crest-to-crest) divided by (time-repetition frequency) of a wave that always existed and always will, with exactly the same amplitude. You can't transmit information with an idealized continuos wave, you'd only communicate one digital bit in the life of the universe, or some such.

A group of waves contains a spread of frequencies and makes an identifiable modulation signal, such as an amplitude envelope. A burst or "bump" of waves, if you like. The wave-group is what carries information, such as a digital bit, and is analogous to a particle such as a photon. The group velocity is the speed of this burst-of-waves.

In a simple frequency-independent medium such as vacuum, groups travel exactly as fast as the wave-crests. But in resonant media, the bump-like shape can propagate slowly even as the waves it has made of, breeze through it faster. In effect it is a packet of oscillation standing in one place, that drifts slowly in some direction. If you look at most meta-materials, you can understand them as resonators distributed spatially throughout the medium. adding to the very normal frequency-independent reactance of the vacuum. Remember resonators have a decay-rate which is longer than the time-period of one wave. It takes a little longer to pump up their amplitude than it takes to just toss a wave through empty space.

Anyway, the velocity of a wave-group generally goes down below c as the medium is loaded with resonant reactance to drive the phase-velocity up above c and make the refractive index less than 1.0. I admit I do not know what media, if any, would have a negative refractive index (less than 0.0).

So I do not think any meta-materials will make any particle or communication or object travel faster than c.

Good luck reconciling this visceral point of view with your wave-velocity math. In any case I respect the effort.

Jim Swenson



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