Dispersion Relations for Negative Index Materials and Slow Light

摘要

In this work we theoretically model continuous and pulse wave propagation using the underlying dispersion relations. We also derive the dispersion relations of the underlying wave equations based on the real and imaginary parts of the propagation constant which are related through Hilbert transformation to ensure causality. Also, in this paper we show that by using a model of photorefractive two wave coupling, we can derive the dispersion relation for pulsed propagation and coupling in a diffusion dominated photorefractive material. We note that the dispersion relation we have found in photorefractive material also obeys the Hilbert transform property. Finally, we show that the group velocity of light can be slowed down by means of phase coupling in the photorefractive two-wave mixing process.