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The Fresnel Rhomb

The phenomenon of TIR was first used by Fresnel to create circularly polarized light from linearly polarized light. In order to use TIR, Fresnel constructed a glass rhomb.

Using input L+45P light, circularly polarized light can be obtained by creating a phase shift (δ) of 45° at the lower and upper surfaces of the glass rhomb, respectively. The Mueller matrix for two reflections is

where δ_U,L are the phase shifts at the upper and lower surfaces, respectively. For glass such as BK7 the refractive index is n = 1.5151 at 6328 Å (HeNe). From the equation for δ on the previous page the angle of incidence of I = 55°05' yields a phase shift of δ = 45.0°. Then δ_U + δ_L = 90°, so the Mueller matrix for the Fresnel rhomb is

For an input L+45P beam S_L+45P = {1, 0, 1, 0} and the Stokes vector of the output beam is then S_RCP = {1, 0, 0, 1}.