5.1 Introduction

In Chapter 3, we discussed the basic concepts involved in the polarization of light waves. In various applications of polarized light, one often needs to know how the polarization of the incident wave changes when it is passed through an optical component such as a polarizer or a birefringent medium. This can be described by three formalisms - namely, Jones calculus, Mueller calculus, and the Poincaré sphere. In this chapter, we will discuss the Jones calculus approach, which is simpler than the Mueller calculus. It represents a given SOP by only a two-component vector known as a Jones vector and uses simple 2 × 2 matrices to calculate the effect of a polarizer or a birefringent medium on a given SOP.

5.2 Jones Vectors

As discussed in Chapter 3, the electric field vector of an arbitrarily polarized light wave can be described in terms of two orthogonal and linearly polarized components as

(5.1)

According to the Jones vector representation, the preceding SOP is represented in terms of a 2 × 1 matrix (column vector) as follows:

(5.2)

Using the complex variable notations, the preceding can also be written as

(5.3)