WOLFRAM|DEMONSTRATIONS PROJECT

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.