Polarization-dependent gain saturations in quantum-well lasers

Theoretical analyses of polarization-dependent optical gain saturation are given for semiconductor quantum-well (QW) lasers to investigate the conditions of polarization switching and bistable operations. Nonlinear susceptibilities, which give saturation coefficients, are obtained in the perturbative analyses of density matrices, where the relevant electronic states in the QW are calculated by diagonalizing Luttinger´s Hamiltonian, thus including valence band mixing. The present formulation is applied to InGaAsP QW lasers with edge-emitting and vertical-cavity surface-emitting laser (VCSEL) structures, and the self- and cross-saturation coefficients with parallel and orthogonal optical polarizations are numerically calculated, which are compared with those of bulk lasers. For the edge-emitting case, the saturation coefficients are strongly dependent on the photon energies, and the bistable operation condition is not satisfied in the gain peak, different from a bulk laser which showed only a slight energy dependence. In a VCSEL, the saturation coefficients are also dependent on the photon energies but the bistable operation condition is always satisfied.