Theory of Cherenkov radiation in periodic dielectric media: Emission spectrum

Details Theory of Cherenkov radiation in periodic dielectric media: Emission spectrum Theory of Cherenkov radiation in periodic dielectric media: Emission spectrum

2008-08-26

arxiv.org/abs/0808.3519v3

Physics

Optics

to appear in Phys. Rev. A

Scientific paper

10.1103/PhysRevA.79.013829

The Cherenkov radiation is substantially modified in the presence of a medium with a nontrivial dispersion relation. We consider Cherenkov emission spectra of a point charge moving in general three- (3D) and two-dimensional (2D) photonic crystals. Exact analytical expressions for the spectral distribution of the radiated power are obtained in terms of the Bloch mode expansion. The resulting expression reduces to a simple contour integral (3D case) or a one-dimensional sum (2D case) over a small fraction of the reciprocal space, which is defined by the generalized Cherenkov condition. We apply our method to a specific case of an electron moving with different velocities in a 2D square-lattice photonic crystal. Our method demonstrates an excellent agreement with numerically rigorous finite-difference time-domain calculations while being less demanding on computational resources.

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