Spatially nondegenerate four-wave mixing in a broad area semiconductor laser: Modeling

We present a numerical model of spatially nondegenerate four-wave mixing in a bulk broad area semiconductor laser with an external reflector and a spatial filter. The external reflector provides a feedback with an off-aixs direction of propagation. Such a configuration has experimentally been seen to improve the coherence of the output of a broad area laser. While the far-field of a broad area laser is often double-lobed. the reflector feeds only one of the lobes back into the cavity in the same angle as the emission angle. As our model assumes only four waves inside the cavity it consists of four coupled equations for the field components in the cavity and a rate equation is used to describe the carrier density of the semiconductor material. The interference pattern of the four field components inside the cavity induces a periodic spatial modulation of the carrier density and thus of the complex permittivity through spatial hole burning. Carrier diffusion will tend to wash out the nonlinearly induced grating. Hence carrier diffusion is included in the model. We discuss the configuration of the external reflector for optimum output.