A plane Fabry-Perot etalon has an air spacer ( ) of thickness between two identical…

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

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

Problem

A plane Fabry-Perot etalon has an air spacer (

n=1

) of thickness

d = 150\,\text{mm}

between two identical mirrors of power reflectance

R = 0.98

. Treat the etalon as a linear shift-invariant filter acting on time. ((a)) Write the impulse response

h(t)

as a train of delta functions spaced by the round-trip time

T

, each weighted by the appropriate power of

R

, and state

T

and the free spectral range

\mathrm{FSR}

that follow. ((b)) Give the finesse

\mathcal F

and the linewidth (FWHM)

\Delta\nu

of the transfer function that is the Fourier transform of

h(t)

. ((c)) Give the photon lifetime

\tau_p

and the quality factor

Q

\lambda_0 = 500\,\text{nm}

. Take

c = 3.00\times10^8\,\text{m s}^{-1}