Analytical stability boundaries of an injected two-polarization semiconductor laser

Abstract

The classical problem of a semiconductor laser subject to polarized injection is revisited. From the laser rate equations for the transverse electric (TE) and transverse magnetic (TM) modes, we first determine the steady states. We then investigate their linear stability properties and derive analytical expressions for the steady, saddle-node, and Hopf bifurcation points. We highlight conditions for bistability between pure- and mixed-mode steady states for the laser subject to either TE or TM injection. To our knowledge, the first case has not been documented yet. An important parameter is the ratio of the polarization gain coefficients and we explore its effect on the stability and bifurcation diagrams.

Analysis of the polarization of single-mode vertical-cavity surface-emitting lasers subject to parallel optical injection

“…This is an unusual situation because optical injection in the polarization with smaller optical losses causes emission in the polarization with larger losses [19]. Very recently a linear stability analysis of the mixed-mode steady states of an optically injected twopolarization modes edge-emitting semiconductor laser has been performed [20]. Dynamical evolution of mixed-mode steady states and IL+PS states is similar for VCSELs for which the spin dynamics can be adiabatically eliminated [19], and so the linear stability analysis of [20] was successfully extended to the VCSEL case [19].…”

Theoretical and experimental study of polarization switching in long-wavelength VCSELs subject to parallel optical injection

“…We will term this situation as IL+PS. This corresponds to the experimental observation in VCSELs of the mixed-mode steady states predicted in [27]. We obtain analytical expressions for the power of both linear polarizations in the IL+PS state.…”

“…Studies of PS in VCSELs subject to parallel optical injection, in which the directions of the linearly polarized light from the master laser and the slave VCSEL are parallel, are scarce: just a couple of experimental works have reported PS in VCSELs under these circumstances [21][22]. An analytical study of an optically injected twopolarization modes semiconductor laser has recently shown that pure and mixed-mode steady states can coexist [27]. Linear stability techniques have been used to analyze bistability between pure-and mixed-mode steady states [27].…”

“…An analytical study of an optically injected twopolarization modes semiconductor laser has recently shown that pure and mixed-mode steady states can coexist [27]. Linear stability techniques have been used to analyze bistability between pure-and mixed-mode steady states [27].…”

Effects of quantum noise on the nonlinear dynamics of a semiconductor laser subject to two spectrally filtered, time-delayed optical feedbacks

“…Other feedback scenarios have included polarization rotated feedback where the polarization of the feedback light is rotated relative to the dominant polarization mode of the laser light [7,8,9]. Recently, the effects of injection on the stability properties 20 from two polarization modes has been studied [10].…”