Small-signal analysis of semiconductor-laser dynamics in complicated cavities

Abstract

Sometimes the rate equations are inadequate even for a small-signal (linearized) analysis of semiconductor laser dynamics. A vertical cavity surface emitting laser with a vertically integrated and slightly detuned resonant cavity is an example. Because of the wavelength sensitivity of the multilayer structure, changes in refractive index inside the resonant cavity lead to large changes in photon life-time, which in turn modulate the intensity of the laser output (Q-switching). However a structure that has such a strong wavelength sensitivity violates one of the assumptions of the rate equation model: that the optical spatial mode pattern is independent of modulation frequency and that its contribution can be reduced to a single valued parameter such as cavity Q (or equivalently, photon lifetime). In the above example, and for other lasers having significant optical wavelength selectivity, it is better to replace the photonic rate equations (those beginning with dS/dt =) by a more basic electromagnetic analysis. This is done by considering the modulated light to be a sum of optical sidebands, and performing a transfer matrix analysis on each sideband separately, thus accounting for the wavelength dependence (1). The transfer matrix approach is convenient for numerical calculations, and results for the above structure will be shown.