TPDSci Scattering matrix problems

Consider Eq. 1 in Scattering matrix. Prove that for a unpolarized incident electromagnetic radiation (ER) beam and an arbitrary scattering matrix, M, we can write:

S_s1(ξ) = M₁₁(ξ) / ( r² k² ) S_i1 (1)

where S_s1 is an element [1] of the Stokes vector of the ER scattered at direction ξ, M₁₁ is an element [1, 1] of the scattering matrix, r is the distance from the particle at which the scattered light is measured, and k is the wavenumber of ER illuminating a particle, and S_i1 is the element [1] of the Stokes vector of the incident ER. [Hint topic]
Prove that an element M₁₂ of the scatttering matrix can be obtained from the following equation resulting from using the following combinations of an analyzer and a polarizer (HO and VO; see Scattering matrix measurement for the explanation of this notation) with an arrangement shown in Fig. 1 for a unpolarized [hint topic] incident electromagnetic radiation (ER) beam with unity irradiance and for an arbitrary scattering matrix, M:

M₁₂ = (S_s1^HO - S_s1^VO) / 2 (2)

where S_s1 is an element [1] of the Stokes vector of the scattered ER. Neglect a factor of 1 / ( r² k² ).

CITATION:
Jonasz M. 2006. Problems: Scattering matrix (www.tpdsci.com/Tpc/ScaMtx_P.php). In: Top. Part. Disp. Sci. (www.tpdsci.com).

HISTORY:
Published: 29-Sep-2006
Modified: 15-Oct-2006
Reviewed: PENDING

Topics in Particle and Dispersion Science