# Optical Filter with Sinusoidally Varying Permittivity Using Mathieu's Equation

Optical Filter with Sinusoidally Varying Permittivity Using Mathieu's Equation

This Demonstration shows the reflection and transmission of light propagating through a dielectric whose permittivity varies sinusoidally in the direction of propagation. Reflectance and transmittance can be displayed as a function of the number of periods of the truncated permittivity sinusoid. The effect of the sinusoid amplitude is displayed along with reflectance/transmittance. The reflectance, the wavelength at maximum reflectance and the width of the peak are displayed within the graphic. Forbidden optical ranges occur in the imaginary part of the characteristic equation.

ϵ(x)

λ

0

δλ/λ