Cherenkov Emission Generated by a Modulated Source in 2D Dispersive Photonic Crystal Slabs

This work presents a systematic numerical study of Cherenkov optical radiation generated by a modulated source that moves with uniform velocity on a two-dimensional (2D) photonic crystal (PCr) slab surface. We apply the FDTD technique with emphasis on the dispersion properties of the periodic medium to perform our numerical analysis. The field oscillations generated at the passage of a modulated source in the PCr produce a series of spectral resonances corresponding to the eigenmodes in the spatial frequency domain for the photonic slab. The amplitudes of the field oscillations have maximal values in the group cone closely to the path of the moving charge.

The Korteweg–de Vries, Burgers and Whitham limits for a spatially periodic Boussinesq model

We are interested in the Korteweg–de Vries (KdV), Burgers and Whitham limits for a spatially periodic Boussinesq model with non-small contrast. We prove estimates of the relations between the KdV, Burgers and Whitham approximations and the true solutions of the original system that guarantee these amplitude equations make correct predictions about the dynamics of the spatially periodic Boussinesq model over their natural timescales. The proof is based on Bloch wave analysis and energy estimates and is the first justification result of the KdV, Burgers and Whitham approximations for a dispersive partial differential equation posed in a spatially periodic medium of non-small contrast.

Dispersion relations and wave propagation in photonic hypercrystals

A photonic hypercrystal is a subwavelength periodic structure consisting of alternate layers of hyperbolic metamaterial and dielectric material. The structure can be treated as an effective medium as well as a periodic medium. Since two length scales are involved, the better treatment is to treat the hyperbolic metamaterial as an effective medium and the overall structure as a periodic medium. The dispersion relations are derived and plotted to show the appearance of propagating bands and gaps in the frequency and wave vector domains. Then using the transfer matrix approach, the transmissivity versus the frequency plot for propagating waves and grayscale plot of the transmission coefficient in the frequency versus wave vector plane for the evanescent waves are plotted and analyzed.