An optical element has a real

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Optics & Photonics · Polarisation and anisotropic media

What an Instrument Can See, Ch Polarisation as a statistical object: coherency and Mueller matrices

Problem

An optical element has a real, diagonal Jones matrix

\mathbf{J}=\operatorname{diag}(t_1,t_2)

on its own eigenaxes

x

and

y

, with

t_1

and

t_2

real amplitude coefficients (as for the boundary Jones matrix

\operatorname{diag}(r_s,r_p)

of this chapter). ((a)) Write the incident coherency matrix on the Pauli basis, apply

\mathbf{J}_{\mathrm{coh}}\to\mathbf{J}\mathbf{J}_{\mathrm{coh}}\mathbf{J}^\dagger

, and read off the output Stokes parameters

S_0',S_1',S_2',S_3'

in terms of

t_1

t_2

and the input Stokes parameters. ((b)) Check that your result reduces to the polariser result quoted in the text,

S_{\mathrm{out}}=\big(\tfrac12(S_0+S_1),\,\tfrac12(S_0+S_1),\,0,\,0\big)

, when

t_1=1

t_2=0

. ((c)) A diattenuating element has

t_1=0.90

and

t_2=0.30

. An input beam has

(S_0,S_1,S_2,S_3)=(2.0,\,1.0,\,1.0,\,0)\ \mathrm{mW\,mm^{-2}}

. Find the transmitted Stokes vector.