A quarter-wave stack alternates silicon nitride ( ) and silica ( ) layers

PHYSICS · Subjective · Fermi University Physics · Optics & Photonics · Wave propagation and light in media · Interference and diffraction

What an Instrument Can See, Ch Media that are designed: plasmons, metamaterials and photonic crystals

Problem

A quarter-wave stack alternates silicon nitride (

n_H=2.02

) and silica (

n_L=1.444

) layers, designed for a centre wavelength

\lambda_0=1064\,\mathrm{nm}

(the Nd:YAG laser line). Using the closed-form expression for the fractional bandwidth of a quarter-wave stack,

\frac{\Delta\omega}{\omega_0}=\frac{4}{\pi}\arcsin\!\left(\frac{n_H-n_L}{n_H+n_L}\right),

find the wavelengths marking the two edges of the photonic band gap.