Josep Martin-Regalado

Polarization properties of vertical-cavity surface-emitting lasers

Polarization-state selection, polarization-state dynamics, and polarization switching of a quantum-well vertical-cavity surface-emitting laser (VCSEL) for the lowest order transverse spatial mode of the laser is explored using a recently developed model that incorporates material birefringence, the saturable dispersion characteristic of semiconductor physics, and the sensitivity of the transitions in the material to the vector character of the electric field amplitude. Three features contribute to the observed linearly polarized states of emission: linear birefringence, linear gain or loss anisotropies, and an intermediate relaxation rate for imbalances in the populations of the magnetic sublevels. In the absence of either birefringence or saturable dispersion, the gain or loss anisotropies dictate stability for the linearly polarized mode with higher net gain; hence, switching is only possible if the relative strength of the net gain for the two modes is reversed. When birefringence and saturable dispersion are both present, there are possibilities of bistability, monostability, and dynamical instability, including switching by destabilization of the mode with the higher gain to loss ratio in favor of the weaker mode. We compare our analytical and numerical results with recent experimental results on bistability and switchings caused by changes in the injection current and changes in the intensity of an injected optical signal.

Mechanisms of polarization switching in single-transverse-mode vertical-cavity surface-emitting lasers: thermal shift and nonlinear semiconductor dynamics.

We analyze polarization switching in vertical-cavity surface-emitting lasers, taking into account a proper semiconductor frequency-dependent complex susceptibility and spin-flip processes. Thermal effects are included as a varying detuning, and gain differences arise from birefringence splitting. We find that, for large birefringence, gain differences between the two linearly polarized modes are preponderant, and switching occurs owing to thermal shift. For small birefringence polarization switching from the high- to the low-gain mode occurs owing to the combined effect of birefringence and semiconductor phase-amplitude-coupled dynamics for a finite value of the carrier spin-flip rate.

Polarization switching in quantum-well vertical-cavity surface-emitting lasers

Switching between linearly polarized states of slightly different optical frequencies with the same transversemode pattern is found, as the injection current is increased. Switchings found here for semiconductor rateequation models incorporating a vector electric field, birefringence, and the alpha factor are similar to previously reported experimental results.

Polarization and transverse-mode dynamics of gain-guided vertical-cavity surface-emitting lasers

Transverse-mode competition and polarization selection in gain-guided vertical-cavity surface-emitting lasers are studied by use of a transverse continuous model that incorporates basic physical mechanisms of polarization dynamics. Polarization stability and polarization switching within the fundamental Gaussian mode are described. The first-order transverse mode always starts lasing orthogonally polarized to the fundamental one. At larger currents polarization coexists with several active transverse modes. These results are shown to be sensitive to the carrier spin-flip relaxation rate.

Polarization and transverse-mode selection in quantum-well vertical-cavity surface-emitting lasers: index- and gain-guided devices

We study polarization switching and transverse-mode competition in vertical-cavity surface-emitting lasers (VCSELs) in the absence of temperature effects. We use a model that incorporates the vector nature of the laser field, saturable dispersion, different carrier populations associated with different magnetic sublevels of the conduction and heavy hole valence bands in quantum-well media, spin-flip relaxation processes and cavity birefringence and dichroism. We consider both index- and gain-guided VCSELs and we find that spin-flip dynamics and the linewidth enhancement factor are crucial for the selection of the polarization state corresponding to a given injection current. For index-guided VCSELs the effect of spatial hole burning on the polarization behaviour within the fundamental mode regime is discussed. For gain-guided VCSELs, transverse-mode and polarization selection are studied within a Maxwell - Bloch approximation which includes field diffraction and carrier diffusion. Polarization switching is found in the fundamental mode regime. The first-order transverse mode starts lasing orthogonally polarized to the fundamental mode. At larger currents polarization coexistence with several active transverse modes occurs.

Spatio-temporal dynamics of gain-guided semiconductor laser arrays

A continuous model based on the coupled field-matter Maxwell-Bloch equations for a two-level homogeneously broadened single mode laser is developed. The model includes a Langevin formulation to model thermal and spontaneous emission noises and accounts for carrier diffusion, optical field diffraction and current spreading. Our model is flexible enough to simulate any gain-guided longitudinally uniform laser geometry and is applied to both a single-stripe and a four-stripe gain-guided semiconductor lasers where the influence of the injection current, the interstripe distance and carrier diffusion is discussed within the context of the laser dynamics. We show that an array operating with quasi-independent stripes may be achieved at low pumps and larger interstripe distances. However, as injection current is increased or the interstripe distance is decreased, the device passes through a variety of dynamical instabilities which can be analyzed in the context of lateral cavity modes. Moreover, we also show that the array dynamics is strongly influenced by carrier diffusion which may also lead to different thresholds for each element of the array.

Polarization dynamics of birefringent index-guided vertical-cavity surface-emitting lasers

We study the polarization behavior of birefringent multi- transverse mode index-guided Vertical-Cavity Surface- Emitting Lasers during CW and modulation operation. The model we use incorporates the (alpha) -factor, different carriers populations associated with different magnetic sublevels of the conduction and heavy hole valence bands in quantum well media, spin-flip relaxation processes and cavity anisotropies. The effect of carrier diffusion and spatial hole burning on the polarization behavior within the fundamental mode regime is also considered. We find that spin-flip dynamics and the (alpha) -factor are crucial for the selection of the polarization state corresponding to a given injection current. We also analyze the direct-current polarization modulation response for both the small and large signal modulation regimes. In both cases the current is modulated around the polarization switching (PS) current, but in the large signal modulation regime the current goes from below threshold to above the PS current. A frequency doubled polarized output is obtained under large signal modulation for modulation frequencies smaller than 10 MHz. At greater frequencies (around 100 MHz) transient mode polarization partition noise becomes important. At the greatest considered frequency (1 GHz) no PS is observed. Finally the effect of multiple transverse mode operation is addressed by considering the two lowest order modes: LP01 and LP11.

Polarization state selection and switching in VCSELs

We extend previous analyses of a recently developed model describing polarization switching in VCSELs. We report on elliptically polarized states and their stability, as well as on the effect of small amplitude anisotropies on polarization state selection caused by birefringence and saturable dispersion. We also study polarization switching by optical injection.

Polarization properties and transverse mode characteristics in quantum well vertical cavity surface-emitting lasers

Switching between linearly polarized states of slightly different optical frequencies is found in the fundamental transverse mode pattern is described as the injection current is increased. Polarization switchings obtained here as the injection current is increased in a semiconductor rate equation model incorporating a vector electric field, birefringence and the linewidth enhancement factor, are similar to previously reported experimental results for the fundamental mode. Polarization properties of higher order Gauss-Hermite modes are also analyzed.

Dynamics of Polarization States in a Vertical-Cavity Surface Emitting Semiconductor Laser with an Axial Magnetic Field.

Laser arrays are a method to produce intense coherent beams with low divergence in the far field. In the past years the research focussed on 1D arrays of semiconductor laws, because they can be easily realized with conventional edge emitting lasers. Recently, the advances in the technology of vertical cavity surface emitting laser, allowed for the fabrication of bi-dimensional arrays with an extremely large number of components. In this paper we generalize the coupled mode theory of [Z] to study the supermodes of a 2 0 array, i.e. the stationary solutions in which all lasers oscillate at the same frequency and the relative phases are h e d . We consider only coupling with the first and second neighbours. For each supermode the mode amplitude of every laser and the common frequency correspond respectively to the eigenvectors and the eigenvalues of a suitable tridiagonal matrix. The linear stability analysis performed in the particular case 2 x 2 shows that the only supermode which is stable for reasonable values of the parameters is the one where each laser is T out-of-phase with its first neighbours. The same result was obtained in the 1D case [3], but our analysis shows that in the 2D case the width of the stability domain is one half. Following [4] we have also considered the effects that arise when two orthogonal statu for light polarization are possible. When the array oscillates on one supermode, we have demonstrated that polarization switchings can occur, in which all lasers simultaneously switch from one polarization state to the orthogonal one.