Question

Please express the following states of polarization: horizontal, vertical, diagonal, antidiagonal using the Jones vector in the circular polarization basis.

Answer 1

Polarization of an EM wave can be expressed in a circular basis using Jones vectors. Horizontal, vertical, diagonal, and antidiagonal polarizations are represented as complex combinations of left-hand circular and right-hand circular polarized light with specific phase factors.

Step-by-step explanation:

In the context of electromagnetic (EM) waves, polarization refers to the orientation of the electric field. Polarization can be described using various basis systems, and the Jones vector formalism is a common representation in the linear polarization basis. In the circular polarization basis, we express different states of polarization as complex combinations of left-hand circular (LHC) and right-hand circular (RHC) polarized light.

The Jones vectors in the circular polarization basis for horizontal, vertical, diagonal, and antidiagonal polarization are:

Horizontal: (1/√2)(LHC + RHC)

Diagonal: (1/√2)(LHC + iRHC)

Antidiagonal: (1/√2)(LHC - iRHC)

To convert these states to the circular polarization basis, one would use a unitary transformation that includes phase factors corresponding to the circular components of the polarization.