Optical Filter with Sinusoidally Varying Permittivity Using Mathieu's Equation

n

avg

n

ampl

0.25

Λ (nm)

140

cycles

9

graphical output

reflectance

transmittance

Mathieu characteristic exponent

This Demonstration shows the reflection and transmission of light propagating through a dielectric whose permittivity

ϵ(x)

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

λ

0

and the width of the peak

δλ/λ

are displayed within the graphic. Forbidden optical ranges occur in the imaginary part of the characteristic equation.