  This paper describes a calculation of the spontaneous emission limited
linewidth of a semiconductor laser consisting of hybrid or heterogeneously
integrated, silicon and III-V intracavity components. Central to the approach
are a) description of the multi-element laser cavity in terms of composite
laser/free-space eigenmodes, b) use of multimode laser theory to treat mode
competition and multiwave mixing, and c) incorporation of quantum-optical
contributions to account for spontaneous emission effects. Application of the
model is illustrated for the case of linewidth narrowing in an InAs quantum-dot
laser coupled to a high-Q SiN cavity.
