Chapter 5 - Operators in paraxial quantum optics

Abstract

The concept of modes as monochromatic solutions of Maxwell's equations has a central position in optics. Conserved physical quantities as energy, momentum and angular momentum are often expressed in terms of linear operators acting on modes. Beams of light as used in experiments in optical communication often use beams of laser light, traveling through optical elements. The light propagating from one element to the next one can be described as a segment of a paraxial mode. As is well known from basic quantum mechanics, quantum systems of any kind are described in terms of linear algebra, where the states are elements of a Hilbert space, and observable quantities take the form of linear operators acting on this state space. Therefore in quantum optics linear operators acting on state space arise next to operators acting on modes. Finally we introduce operators acting on paraxial modes that define basis sets of paraxial Gaussian modes. In this chapter we analyze the analogies and differences of the various operators that appear in paraxial quantum optics.