Question

What are Jones matrices and how to derive them?

Answer 1

I'm coding a software for an optics lab I'm working in and I need to know how to derive expressions for Jones matrices for various polarizes.

What does a Jones matrix represent and how would you derive them for say a linear polarizer with transmission axis oriented at an angle of 6060deg with the vertical?

Or even the simpler case of a half-wave plate with fast axis horizontal

Answer 2

$<b><i>In optics, polarized light can be described using the Jones calculus, discovered by R. C. Jones in 1941. Polarized light is represented by a Jones vector, and linear optical elements are represented by Jones matrices. When light crosses an optical element the resulting polarization of the emerging light is found by taking the product of the Jones matrix of the optical element and the Jones vector of the incident light. Note that Jones calculus is only applicable to light that is already fully polarized. Light which is randomly polarized, partially polarized, or incoherent must be treated using Mueller calculus.$