# Abnormal refraction of EM waves in periodic metamaterials

Wednesday, October 4, 2006 - 3:00pm - 3:50pm

EE/CS 3-180

Alexander Figotin (University of California)

Joint work with I Vitebskiy.

Wave propagation in spatially periodic media, such as photonic crystals,

can be qualitatively different

from any uniform substance. The differences are particularly pronounced

when the electromagnetic wavelength

is comparable to the minimal translation of the periodic structure. In

such a case, the periodic medium cannot

be assigned any meaningful refractive index. Still, such important

features as negative refraction and/or

opposite phase and group velocities for certain directions of light

propagation can be found in almost any

photonic crystal. The only reservation is that unlike hypothetical

uniform left-handed media, photonic crystals

are essentially anisotropic at frequency range of interest. Consider now

a plane wave incident on a semi-infinite photonic crystal. One can

assume, for instance, that in the case of positive refraction,

the normal components of the group and the phase velocities of the

transmitted Bloch wave have the same sign,

while in the case of negative refraction, those components have opposite

signs. What happens if the normal

component of the transmitted wave group velocity vanishes? Let us call

it a zero-refraction case.

At first sight, zero normal component of the transmitted wave group

velocity implies total reflection of the

incident wave. But we demonstrate that total reflection is not the only

possibility. Instead, the transmitted

wave can appear in the form of an abnormal grazing mode with huge

amplitude and nearly tangential group

velocity. This spectacular phenomenon is extremely sensitive to the

frequency and direction of propagation of

the incident plane wave. We also discuss some possible applications of

this effect.

REFERENCES:

- A. Figotin, and I. Vitebskiy. Phys. Rev. E68, 036609 (2003).

- J. Ballato, A. Ballato, A. Figotin, and I. Vitebskiy. Phys. Rev. E71,

(2005).

Wave propagation in spatially periodic media, such as photonic crystals,

can be qualitatively different

from any uniform substance. The differences are particularly pronounced

when the electromagnetic wavelength

is comparable to the minimal translation of the periodic structure. In

such a case, the periodic medium cannot

be assigned any meaningful refractive index. Still, such important

features as negative refraction and/or

opposite phase and group velocities for certain directions of light

propagation can be found in almost any

photonic crystal. The only reservation is that unlike hypothetical

uniform left-handed media, photonic crystals

are essentially anisotropic at frequency range of interest. Consider now

a plane wave incident on a semi-infinite photonic crystal. One can

assume, for instance, that in the case of positive refraction,

the normal components of the group and the phase velocities of the

transmitted Bloch wave have the same sign,

while in the case of negative refraction, those components have opposite

signs. What happens if the normal

component of the transmitted wave group velocity vanishes? Let us call

it a zero-refraction case.

At first sight, zero normal component of the transmitted wave group

velocity implies total reflection of the

incident wave. But we demonstrate that total reflection is not the only

possibility. Instead, the transmitted

wave can appear in the form of an abnormal grazing mode with huge

amplitude and nearly tangential group

velocity. This spectacular phenomenon is extremely sensitive to the

frequency and direction of propagation of

the incident plane wave. We also discuss some possible applications of

this effect.

REFERENCES:

- A. Figotin, and I. Vitebskiy. Phys. Rev. E68, 036609 (2003).

- J. Ballato, A. Ballato, A. Figotin, and I. Vitebskiy. Phys. Rev. E71,

(2005).

MSC Code:

74Jxx

Keywords: