Abstract

We present an exact treatment of electromagnetic wave propagation in a crystal medium with varying dielectric constant via quantum mechanical approach. Quantum mechanical equation involving dielectric constant was defined for incoming linearly polarized monochromatic electromagnetic wave derived from a re-normalized relativistic Langrangian equation, . Considering that the spatial waveform of the field inside the field medium is not sinusoidal, we applied the Fourier transform to obtain the dispersion relation and as such, the group velocity v_g of the waveform using the mean energy flux and energy density. The frequency of the forward propagating field and the reflected field that depicts the interaction of the field with the crystal, which on other hand explains the frequency range at which the crystal exhibit anti-reflection behavior, was also determined.

Key words: Dielectric constant, quantum mechanical approach, inhomogeneous crystal, group velocity, Langrangian equation, Fourier transforms.