In Chapter 3, eigenvalue equations were derived by matching boundary conditions inside DFB laser cavities. From the eigenvalue problem, the lasing threshold characteristic of DFB lasers is determined. The single %/2-phase-shifted (PS) DFB laser is fabricated with a phase discontinuity of %/2 at or near the centre of the laser cavity. It is characterised by Bragg oscillation and a high gain margin value. On the other hand, the SLM deteriorates quickly when the optical power of the laser diode increases. This phenomenon, known as spatial hole burning, limits the maximum single-mode optical power and consequently the spectral linewidth | 4 Transfer Matrix Modelling in DFB Semiconductor Lasers INTRODUCTION In Chapter 3 eigenvalue equations were derived by matching boundary conditions inside DFB laser cavities. From the eigenvalue problem the lasing threshold characteristic of DFB lasers is determined. The single 2-phase-shifted PS DFB laser is fabricated with a phase discontinuity of 2 at or near the centre of the laser cavity. It is characterised by Bragg oscillation and a high gain margin value. On the other hand the SLM deteriorates quickly when the optical power of the laser diode increases. This phenomenon known as spatial hole burning limits the maximum single-mode optical power and consequently the spectral linewidth. Using a multiple-phase-shift MPS DFB laser structure the electric field distribution is flattened and hence the spatial hole burning is suppressed. In dealing with such a complicated DFB laser structure it is tedious to match all the boundary conditions. A more flexible method which is capable of handling different types of DFB laser structures is necessary. In section the transfer matrix method TMM 1-4 will be introduced and explored comprehensively. From the coupled wave equations it is found that the field propagation inside a corrugated waveguide . the DFB laser cavity can be represented by a transfer matrix. Provided that the electric fields at the input plane are known the matrix acts as a transfer function so that electric fields at the output plane can be determined. Similarly other structures like the active planar Fabry-Perot FP section the passive corrugated distributed Bragg reflector DBR section and the passive planar waveguide WG section can also be expressed using the idea of a transfer matrix. By joining these transfer matrices as a building block a general N-sectioned laser cavity model will be presented. Since the outputs from a transfer matrix automatically become the inputs of the following matrix all boundary conditions inside the composite cavity
