A high reflector for a Nd:YAG laser cavity is to be built as the quarter-wave stack

PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Interference and diffraction · Interference and diffraction

What an Instrument Can See, Ch Multiple beams: the stack as a matrix and the etalon as a filter

Problem

(\mathrm{HL})^N\mathrm{H}

, using niobium pentoxide (

n_H=2.30

) and silica (

n_L=1.46

) layers on a sapphire substrate (

n_s=1.76

), lit from air (

n_0=1

) at

\lambda=1064

nm. The specification calls for a power reflectance

\mathcal R\ge0.9995

. ((a)) Using the closed-form admittance

Y=\dfrac{n_H^2}{n_0n_s}\left(\dfrac{n_H}{n_L}\right)^{2N}

recovered from the characteristic-matrix product, find the smallest integer

N

that meets the specification. ((b)) State the reflectance this minimum stack actually delivers, and confirm that one fewer pair falls short.