Traveling wave model of a multimode Fabry-Pérot laser in free running and external cavity configurations

We report the results of a numerical study of multimode behavior of a Fabry-Pérot laser. The model is based on traveling-wave equations for the slowly varying amplitudes of the counterpropagating waves in the cavity, coupled to equations for spatially dependent population inversion and polarization of a two-level active medium. Variations in the material variables on the scale of a wavelength are taken into account by means of an expansion in a Fourier series. Results are given for typical semiconductor laser parameters. Spatially distributed spontaneous emission noise and carrier diffusion are taken into account. The competing roles of Spatial Hole Burning (SHB), spontaneous emission noise, and carrier diffusion in determining multimode behavior are elucidated; with no carrier diffusion, spontaneous emission noise excites a large number of modes close to threshold, while SHB leads to a fixed number of significant lasing modes well above threshold. Carrier diffusion washes out the gratings in the material variables, and the resulting strengthening of the inter-mode coupling (cross-saturation) restores dominant single-mode emission well above threshold. We have also studied the effects of optical feedback and opportunities for mode selection with short external cavities; for an external cavity much shorter than the laser cavity length and a small field amplitude reflectivity coefficient, a single mode can be selected. For a large reflectivity coefficient, two groups of intracavity modes separated by the external cavity mode interspacing are selected. For an external cavity with a round trip time half that of the laser cavity, the laser can be forced with modest feedback to operate on two modes that are both quasiresonant with the external cavity. Mode selection is not found, even for weak feedback, when the external mode spacing is about 90% of the laser mode spacing.