Polarization and Transverse Mode Behaviour of VCSELs under Optical Injection

Abstract

A theoretical analysis of the polarization and transverse modes of Vertical-cavity Surface-emitting lasers with external optical injection is performed. We show that, for single-mode operation, weak injection of linearly polarized light can lead to stable output power in the injected polarization. We also show that, for multitransverse mode operation, weak injection of linearly-polarized light can lead to stable emission of the fundamental transverse mode in the injected polarization over wide current ranges. The previous selection can occur when the transverse modes have parallel or orthogonal polarizations.

Transverse Mode Switching and Locking in Vertical-Cavity Surface-Emitting Lasers Subject to Orthogonal Optical Injection

“…In this work, we consider a model [34], [35] that takes into account two of the mechanisms that can define the polarization of a VCSEL. The first one is associated with the combined effect of the VCSEL anisotropies, the linewidth enhancement factor and the spin-flip relaxation processes within a framework known as the SFM model [16].…”

“…Subscripts 0,1 will be used to denote the and modes, respectively. In the basis of the linearly polarized modes and considering radial symmetry of the cavity the optical field can be written as [34], [35] (1) where and are the modal profiles of the and modes, respectively, obtained by solving the Helmholtz equation [34]; and are the modal amplitudes of these modes; the subindex stands for the linear polarization state of the given mode; is the electric field decay rate that includes the internal and facet losses [2]; and is the alpha factor or linewidth enhacement factor that describes phase-amplitude coupling mechanisms in semiconductor lasers [2]. The equations describing the polarization and transverse mode behavior of the VCSEL with an injected optical field, written appropriately in the cylindrical basis, read [35] (2) is the total carrier number and is the difference in the carrier numbers of the two magnetic sublevels.…”

Transverse Mode Selection in Vertical-Cavity Surface-Emitting Lasers With Optical Injected Signal

“…In the first one, the "orthogonal optical injection" configuration, linearly polarized light is injected with a polarization that is orthogonal to the linear polarization of the free-running VCSEL [16]- [18], [29]- [30]. In the second one, the "parallel optical injection", both the VCSEL and the injected light polarizations are parallel [7]- [8], [11], [14]- [15], [20], [31]- [33]. Experimental results using parallel injection in a single-transverse mode VCSEL show that injection locking show a dependence on the injected power and frequency detuning that is similar to the one found in edge-emitting devices [31].…”

Experimental Study of Transverse Mode Selection in VCSELs Induced by Parallel Polarized Optical Injection

“…Modal selection in multitransverse mode VCSELs has been obtained when using orthogonal [27] and parallel optical injection [25][26]. Theoretical analyses of that problem have also been performed for the cases of orthogonal [27] and parallel optical injection [37][38][39][40].…”

“…The selection process under parallel optical injection depends on the polarization of the transverse modes of the solitary VCSEL. Selection of the fundamental transverse mode has been reported when both modes are orthogonally polarized [25][26], [37][38][39][40]. However different experimental results have been obtained when the free-running VCSEL has two parallelpolarized modes.…”