Derivation and application of master equation methods for semiconductor lasers

Abstract

With the advent of the laser, an interest in the statistical properties of light was born. New theories, which required an understanding of how the lasing medium interacts quantum mechanically with incident light were developed to classify and quantify light. For many laser systems, gaining an understanding of the physical processes occurring in the medium, and translating these into a mathematical formalism has been achieved with relative speed and ease, and the resulting theories form part of the core of the field we know as quantum optics. In the case of semiconductor lasers however, progress has not been so swift, nor the description so complete. The many and complex processes occurring in a semiconductor laser are not well understood and this has led to many-body and solid-state phenomenological descriptions of the semiconductor laser rather than a quantum optical one. Although some attempts have been made at obtaining a fully quantum mechanical description, phenomenological descriptions have been resorted to to describe poorly understood or complex processes such as pumping and scattering. The work in this thesis was inspired by the lack of such a theory, and by the belief that it should be possible to give a description of the semiconductor laser in terms familiar to quantum opticians. With the continued and current interest in non-classical properties of light, such a theory could be very useful in predicting such properties of semiconductor lasers. Since semiconductor lasers have great potential for use in high speed electro-optic, or even optical communications, low-noise operation of these devices is a desired and indeed essential goal. Our first attempt at formulating such a theory was a simple single-mode description, using as a basis for comparison of results the more phenomenological work of Yamamoto and coworkers [Yamamoto 1986, Machida 1987, Yamamoto 1987]. Our work was based on a master equation description of the system however, and thus the methodology differed significantly from that of these authors.