A dichroic mirror is built from alternating quarter-wave layers of magnesium fluoride…

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 dichroic mirror is built from alternating quarter-wave layers of magnesium fluoride (

n_L = 1.38

) and zinc sulfide (

n_H = 2.35

), designed for a centre wavelength of

500\text{ nm}

. Using the closed-form result for the gap 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 short-wavelength and long-wavelength edges of the photonic band gap.