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View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Digital.CSIC Polarization and Transverse Mo de Selection in Quantum Well VerticalCavity SurfaceEmitting Lasers Index and Gainguided Devices J MartnRegalado S Balle and M San Miguel Instituto Mediterraneo de Estudios Avanzados IMEDEA CSICUIB and Departament de Fsica Universitat de les Il les Balears E Palma de Mal lorca Spain A Valle and L Pesquera Instituto de Fsica de Cantabria CSICUC Facultad de Ciencias E Santander Spain Abstract We study p olarization switching and transverse mo de comp etition in Vertical Cavity Surface Emitting Lasers in the absence of temp erature eects We use a mo del that incorp orates the vector nature of the laser eld saturable disp er sion dierent carrier p opulations asso ciated with dierent magnetic sublevels of the conduction and heavy hole valence bands in quantum well media spinip relaxation pro cesses and cavity birefringence and dichroism We consider b oth indexguided and gainguided VCSELs and we nd that spinip dynamics and linewidth enhancement factor are crucial for the selection of the p olarization state corresp onding to a given injection current For indexguided VCSELs the eect of spatial hole burning on the p olarization b ehavior within the fundamental mo de regime is discussed For gainguided VCSELs transverse mo de and p olarization selection is studied within a MaxwellBlo ch approximation which includes eld diraction and carrier diusion Polarization switching is found in the funda men tal mo de regime The rst order transverse mo de starts lasing orthogonally p olarized to the fundamental mo de At larger currents p olarization co existence with several active transverse mo des o ccurs I INTRODUCTION Vertical Cavity Surface Emitting Lasers VCSELs present sp ecial optical and electrical prop erties singlelongitudinal mo de emission lowthreshold current lowdivergence circular out put b eam simplicity for building D arrays etc which make these devices extremely attractive for several applications such as opticalb er and freespace communications optical information storage laser printers etc They also oer a numb er opp ortunities to study fundamental asp ects of semiconductor laser dynamics Among the latter the issue of laser p olarization state selection and the comp etition of p olarization state and transverse mo de prole are particularly interesting Polarization selection in conventional edgeemitting lasers is largely determined by the geometry of the laser but the cylindrical symmetry of the VCSEL gives in principle no preference for any p olarization direction in the plane of the wafer This makes very relevant the question of p olarization selection by the nonlinear gain dynamics Such a question was examined at large in the early days of laser physics where preference for linear or circular p olarization for several gas lasers was understo o d in terms of symmetries asso ciated with dierent lasing transitions Pattern formation in the transverse prole of a laser b eam has received considerable attention in the general framework of nonlinear dynamics VCSELs are interesting in this asp ect b ecause they easily have a rather large Fresnel numb er whichfavors the app earance of transverse struc tures Polarization control and transverse mo de control are two linked practical problems which call for a b etter fundamental understanding of the physical mechanisms of p olarization and transverse mo de selection Light emitted from VCSELs is typically linearly p olarized with the vector eld oriented along one of two orthogonal crystal axis which are p erp endicular to the emission direction The two linearly p olarized mo des have also slightly dierent emission frequencies GHz due to the birefringence of the crystal Even though several VCSELs display stable linear p olarization emission at any value of the applied current many of these devices show a p olarization instability a relative abrupt switch in the orientation of the optical eld known as Polarization Switching PS This o ccurs as the injection current is increased further ab ove threshold Emission in b oth linearly p olarized mo des with dierent emission frequencies as well as in b oth linearly p olarized mo des with the same emission frequency elliptically p olarized light have b een rep orted These p olarization phenomena o ccur close to threshold within the fundamental transverse mo de regime For higher injection currents they may be accompanied by changes in the emission prole due to the excitation of higher order transverse mo des The onset of the rst order transverse mo de o ccurs for an applied current which strongly dep ends on the dimensions of the strip e contact In addition it is commonly observed that the rst order transverse mo de starts lasing orthogonally p olarized to the fundamental mo de An explanation oered to p olarization state selection in VCSELs is based on the dierent rates of the thermal wavelength shift of the gain curve and the cavity resonances combined with the uncontrolled strain present in the growth pro cess whichmay cause VCSEL anisotropies birefringence and dichroism As a consequence of the birefringence of the crystal the two linearly p olarized states exp erience slightly dierent material gains in suchaway that the mo de with higher gain to loss ratio dominates at threshold When the injected current is increased ab ove the lasing threshold selfheating of the active region pro duces a faster red shift of the gain peak relative to the cavity resonances so that the gain dierence between the linearly p olarized mo des changes Within this framework i stable p olarization emission o ccurs when the gain dierence favors the same p olarization mo de at any currentvalue ii PS is exp ected when there is an exchange of the relative gain of the two mo des iii co existence of b oth linearly p olarized states occurs if the gain dierence is to o small Several p oints are worth noting in the ab ove explanation In the rst place since the fre quency splitting b etween orthogonal linearly p olarized states is often very small as compared to the width of the gain curve b elow or of the order of GHz as compared to nm or more y be minute so PS in the fundamental mo de should be resp ectively the gain dierences ma dicult to observe Second it do es not explain the preference for linearly p olarized emission in front of ie circularly p olarized light in VCSELs with very small anisotropies Finally it predicts stable p olarization emission if thermal eects are minimized on the device while PS is a well known phenomenon in gas lasers in which thermal eects are not imp ortant In fact recent exp eriments in gainguided VCSELs by indicate that PS is still observed when the active region temp erature is kept constant by using fast pulse low duty cycle op eration Such PS do es not t in the scheme just discussed but it is consistent with the mechanisms invoked for PS in the mo del intro duced in Ref SFM mo del The SFM mo del takes into account the vector nature of the laser eld saturable disp ersion asso ciated with the linewidth enhancement factor and the carrier dynamics asso ciated with the dierent magnetic sublevels of the conduction and heavy hole valence bands in a quantum well It predicts the preference of quantum well material for linearly p olarized emission due to the nite coupling via spinip relaxation pro cesses between the carrier p opulations involved in the two natural circularly p olarized emission channels For a p erfect isotropic cavity the linearly p olarized laser lightis randomly oriented in the plane of the active region while for an anisotropic cavity the cavity anisotropies x the direction of linearly p olarized emission A detailed study of the stability of the solutions of the SFM mo del incorp orating cavity anisotropies reveals that the p olarization state selection within the fundamental mo de regime in VCSELs is governed by the coupling b etween the two carrier p opulations in the presence of amplitudephase coupling linewidth enhancement factor As the injection current is scanned ab ove the lasing threshold stable p olarization emission p olarization switching p olarization co existence or elliptically p olarized emission can b e predicted dep ending on the VCSEL anisotropies The studies in were based on rateequations for the amplitudes of the two circularly p olarized mo des disregarding spatial eects However SpatialHoleBurning and carrier dif fusion may have an imp ortant role in the interplay between p olarization and transverse mo de selection Two dierent situations can b e distinguished according to the transverse structure of the VCSEL In indexguided devices the mo dal proles and frequencies are determined by the builtin refraction index distribution of the VCSEL thus allowing for a description in terms of mo dal amplitudes Instead for gainguided devices a mo dal description is not strictly valid b ecause the eld prole is fully determined by the carrier distribution which in turn is dynamically coupled to the eld through stimulated emission In this pap er we consider an extension of the SFM mo del to incorp orate spatial eects in both indexguided and gainguided VCSELs Concerning indexguided VCSELs p olarization prop erties have already b een analyzed in Ref by using a mo del that includes birefringence and spatial hole burning eects In this pap er we incorp orate saturable disp ersion and p olariza tion sensitive dynamics of the carriers in semiconductor quantum well media and

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