TABLE OF CONTENTS A commonly used starting point for modelling lasers is a small-signal analysis of the rate equations of the form discussed in Section 4.1 where perturbations from the steady state are considered [1 3]. These solutions are often explicitly analytic and/or they can be rapidly computed. Appendix 4 gives an outline of such an analysis including carrier transport [4], from contacts to the radiative recombination region, which is not included in this chapter. Small-signal methods help to elucidate the physics of modulation and noise [5 8], especially around steady-state values which can be computed more readily than large-signal dynamic states. For Fabry Perot lasers, coupling of electron equations and photon equations has been done in a variety of ways well reviewed by Buus [9] but the power of computers has moved far in the last decade. DFB lasers have more complex structures and have led to new methods specifically to aid in this understanding. Transfer-matrix techniques, mentioned in Chapter 5, are also known as transmission matrices [10, 11] and are used for the analysis and design of multisection and nonuniform lasers by tracking their performance around specific frequencies. However, random spontaneous inputs to a laser give randomly varying outputs which then need averaging. The power-matrix method [12] is a transfer-matrix method which was specially developed to compute the mean-square values of optical power even though the laser is excited by a stochastic 'spontaneous' input. As has already been seen from Chapter 5, transfer-matrix techniques operate well for 'single-mode' lasers...
