This chapter discusses the spontaneous emission and optical gain in semiconductor lasers. Spontaneous emission which initiates lasing, optical gain which is essential to achieve lasing, and other processes involved in lasing all use quantum processes at the level of single atoms and electrons within the lasing material. Without simplifications, the physics and mathematics necessary to describe such atomic systems fully is too complicated, certainly for the level of this book. The simplification and approximations must, however, be done in a way which is adapted to the requirements of semiconductor lasers, and the limitations must be understood. The results and implications of quantum physics are discussed here but there are only illustrative outlines of any derivations.

This chapter presents two basic classical methods of modelling mathematically the operation of semiconductor lasers and shows that they are, indeed, just different aspects of the same physics of energy conservation and are wholly compatible with one another. The first method applies the concepts of photon/electron particle exchange where one discusses the rate of absorption and emission of photons along with the rate of recombination of holes and electrons, ensuring at each stage that there is a detailed balance between photon generation and electron/hole recombination leading to particle conservation and energy conservation. This is the standard rate equation approach which is robust and well researched but can be difficult to apply when there are strong nonuniformities, and even more difficult when the phase of the electromagnetic field is important. For distributed-feedback lasers, both the phase of the field and nonuniformities are important and so one has to abandon the photon-rate equation in favour of an approach based on interactions between electromagnetic fields and the electric dipoles in an active optical medium. The electromagnetic field analysis is essential when the refractive index/permittivity changes periodically inside the laser. The chapter then concludes with an analysis of the coupled-mode equations which determine how a fraction of the forward-travelling field is coupled into the reverse-travelling field with a medium which has a periodic permittivity, i.e. the waveguide contains a Bragg grating.

These more advanced problems of the static design of lasers are outlined here and the chapter ends with a discussion on some results of modelling the dynamic performance of DFB lasers, considering problems associated with carrier transport into quantum wells. The dynamic performance of DFB lasers highlights yet further the problems that have already been met with a uniform grating in a uniform DFB laser.

This chapter discusses mathematical modeling as a key component in the design of devices and systems in optoelectronics projects. One thrust of the book has been to lay out the physical and mathematical modelling techniques for the electromagnetic and electronic interactions within distributed feedback lasers to give better explanations and to facilitate new designs. Optical systems where arrays of devices may be interconnected are one such important area and are discussed. Novel concepts such as that of the push-pull laser, tunable lasers with Bragg gratings, and surface-emitting lasers are all candidate areas for applications of the modelling principles given in this text. The future for mathematical modelling, coupled with a sound physical under standing, is bright, extensive and assured.

This appendix gives a systematic approach to providing a program for solving propagation, confinement factor and far-field emission when electromagnetic waves are guided by slab waveguides. Almost arbitrary numbers of layers can be computed with complex refractive indices. Here, by examining a five-layer system, the way forward to a semi-automated method for an arbitrary number of layers with complex refractive indices is demon strated. Multilayer guides are particularly relevant in discussing DFB lasers where the longitudinally periodic profile of the permittivity has lateral variations across the waveguide which can be taken into account by having a series of layers with different patterns of permittivity, giving an average permittivity and an average periodic component which can be calculated using the programs.

This appendix provides a more detailed account of the classic rate equation analyses of appropriately uniform lasers and shows the first-order effects of carrier transport into the active quantum-well region, and the effects of spontaneous emission and gain saturation on damping of the photon-electron resonance. The appendix ends with large-signal rate equations showing the influence of four key parame ters which shape the main features of the large-signal response.

This appendix gives the detailed calculations for finding the steady state fields in a uniform DFB laser with uniform gain, and thereby finding the threshold conditions. The results are essential if one wishes to make comparisons with the numerical algorithms to estimate the accuracy of these algorithms. The appendix also provides a tutorial on the use of Pauli matrices for coupled differential equations.

The relative-intensity noise (RIN) is an important quantity in determining whether lasers are acceptable for use in optical-commu nication systems. Its analytic study can require extensive algebra, but in this appendix the emphasis is on the physical significance of RIN and simulations using time-domain modelling to estimate its value for DFB lasers.

Laser optoelectronic packaging of DFB-laser chips is reported. Thermal properties, laser monitoring by photodiode, package-related backreflection and fiber coupling is presented.

Programs written in MATLAB 4 that has been designed. Before obtaining the programs from the World Wide Web, users are recommended to create, within their main MATLAB directory, a subdirectory (or folder), say laser, with further sub-directories dfb, diff, fabpero, fftexamp, filter, grating, slab, spontan. Within MATLAB, the effective initiation file is the M-file called matlabrc.m and this should be backed up for future reference into a second file, say matlabrb.m.