Quantum Optics for Engineers

16

Quantum Polarization

16.1  Introduction

In this chapter we examine the quantum aspects of polarization primarily via the Dirac notation (Dirac, 1978) and also using density matrices. The approach follows the style of Feynman (Feynman et al., 1965). Classical polarization is examined in Chapter 15.

16.2  Linear Polarization

Linear polarization in the x direction represented in the Jones calculus by (Jones, 1947)

$\left(\begin{array}{c}{E}_{0x}\\ E_{0y}\end{array}\right)=\left(\begin{array}{c}1\\ 0\end{array}\right)$

(16.1)

is expressed simply as |x〉 in the bra–ket representation. Linear polarization in the y direction described in the Jones calculus by

$\left(\begin{array}{c}{E}_{0x}\\ E_{0y}\end{array}\right)=\left(\begin{array}{c}0\\ 1\end{array}\right)$

(16.2)

is expressed simply as |y〉 in the bra–ket representation.

Rotation of axes, x → x′ and y → y′, as illustrated in Figure 16.1, leads directly to the ...