# Optical waveguide that can displace a 4D light field

Has anyone invented an optical waveguide that can "pipe" a scene from one place to another unaltered? More precisely, I want to displace (and/or rotate) a 4D light field.

An optical waveguide is an EM waveguide engineered to operate at visible wavelengths.

A light field is a computer graphics concept that represents the RGB intensities and directions of photons in a given linear span of a 3D room.

All the light in a room can be described as a 5D light field: the RGB value at each sample along 5 dimensions:

1. theta (compass bearing)
2. phi (inclination)
3. x (+x = right)
4. y (+y = down)
5. z (+z = into scene)

A 5D light field sampled along a 3D linear span comes out as still a 5D light field. But a 5D light field sampled along a 2D linear span (such as the aperture of a camera, eye, or display) comes out as a 4D light field.

Thus, this hypothetical "light field waveguide" could also be summarized as "the perfect periscope" or "fiber optics for images". You would be able to use one of these to, e.g. create a window between any two rooms, even if they are miles apart.

Any ideas on how to make one of these? Don't say light-field-camera -> video-streaming -> light-field-display, because I'm already working on that. ;)

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## 1 Answer

There is some work, pioneered by Nader Engheta and Mario Silveirinha. The basic idea is to make a waveguide out of a medium whose permeability $\varepsilon$ is close to zero, which basically allows a sort of "classical tunneling", since the phase velocity in the medium is very large. Say, transporting a light field unchanged from one end of the waveguide to the other.

It's been experimentally demonstrated for microwaves, but I doubt that it will be possible with visible wavelengths in the immediate future.

Here are some papers that you could read:

• Silveirinha & Engheta (2006). Tunneling of electromagnetic energy through subwavelength channels and bends using ε-near-zero materials. Phys. Rev. Lett. 97, 157403. http://prl.aps.org/abstract/PRL/v97/i15/e157403 (The original paper.)
• Liu, Cheng, Hand, Mock, Cui, Cummer, Smith (2008). Experimental demonstration of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequencies. Phys. Rev. Lett. 100, 023903. http://prl.aps.org/abstract/PRL/v100/i2/e023903 (Experimental demonstration for microwaves, using metamaterials, i.e. materials with repeated structures that are smaller than the wavelength.)
• Edwards, Alu, Young, Silveirinha, Engheta (2008). Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide. Phys. Rev. Lett. 100, 033903. http://prl.aps.org/abstract/PRL/v100/i3/e033903 (Published only a week after the above paper, this is another experimental demonstration for microwaves taking a different approach. Instead of using metamaterials, they operate the waveguide at its cutoff point. This makes the effect strictly monochromatic, I think, but the waveguide is much simpler and cheaper to make.)
• Silveirinha & Engheta (2009). Transporting an image through a subwavelength hole. Phys. Rev. Lett. 102, 103902. http://prl.aps.org/abstract/PRL/v102/i10/e103902 (Theoretical paper that describes transporting what you call a light field.)
• Silveirinha & Engheta (2012). Sampling and squeezing electromagnetic waves through subwavelength ultranarrow regions or openings. Phys. Rev. B 85, 085116. http://prb.aps.org/abstract/PRB/v85/i8/e085116 (Latest updates - I haven't kept abreast of any developments after 2009 so I'm not quite sure what's new here.)
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