The Single-Mode Homogeneously Broadened Laser I: Preliminaries

Abstract

We have now developed the bulk of the formalism we need and can turn our attention to rather more ambitious applications than the damped harmonic oscillator and the damped two-level atom. We restrict our attention in this book to the single-mode laser. In Volume 2 we consider the degenerate parametric oscillator and cavity QED. As can be judged from a quick look at Haken’s book on laser theory [7.1], the first of these examples can easily fill a book on its own. We will therefore have to be rather selective in what we cover in two chapters. Our main objective is to illustrate the things we have learned in a practical application: the derivation of a master equation and associated phase-space equation of motion, the reduction of the phase-space equation to a manageable form using van Kampen’s system size expansion, and the extraction of useful results from the resulting stochastic model. The topics that we address are covered in sections V and VI of Haken’s book. The treatment will be similar to the one found there; although, we do not follow Haken’s notation, and we will fill in the details in some of his calculations. The laser Fokker—Planck equation is derived using somewhat different methods by Louisell [7.2]. Laser theory can also be built around density matrix equations, following the approach of Scully and Lamb [7.3]. For a comparison with the phase-space method, the Scully-Lamb theory can be studied in the text by Sargent, Scully and Lamb [7.4].