Page "Polarization (waves)" Paragraph 39

where J is an overall ( real ) gain / loss factor.

Here D is a traceless matrix such that αDe gives the derivative of e with respect to z.

If D is Hermitian the effect is dichroism, while a unitary matrix models birefringence.

The matrix D can be expressed as a linear combination of the Pauli matrices, where real coefficients give Hermitian matrices and imaginary coefficients give unitary matrices.

The Jones matrix in each case may therefore be written with the convenient construction