Robert A. Indik

Effective Bloch equations for semiconductor lasers and amplifiers

A set of effective Bloch equations is established for semiconductor bulk or quantum-well media. The model includes the nonlinear carrier-density dependence of the gain and refractive index and their respective dispersions (frequency dependences). A comparative study is performed between the full microscopic semiconductor Bloch equations and this effective model for pulse propagation to show the range of validity of the present model. The results show that this model agrees well with the microscopic model provided carrier depletion is the dominant saturation mechanism relative to the plasma heating. The effective Bloch equations provide an accurate and practical model for modeling amplifiers with pulses of duration greater than a few picoseconds. By capturing the large bandwidth and the carrier density dependence of the gain, it also provides a reliable model for studying the complex spatiotemporal multilongitudinal and transverse mode dynamics of a variety of wide-aperture high-power semiconductor lasers. The model goes beyond the traditional rate equations and is computationally much more efficient to simulate than the full model.

Semiconductor laser array dynamics: numerical simulations on multistripe index-guided lasers

The space–time dynamical behavior of multistripe index-guided semiconductor laser arrays is studied by using an extension of the usual phenomenological laser model to include transverse diffraction of the counterpropagating optical fields and transverse diffusion of the excited carriers. Our results confirm that evanescently coupled multistripe lasers are a fascinating manifestation of spatiotemporal complexity in spatially extended nonlinear systems. Stabilization of the laser output can be achieved by injection locking the array with a weak external injected signal, and we show that the stability of the externally driven array depends on the transverse profile of the injected signal. A numerical algorithm is presented that takes advantage of high-performance parallel computing architectures to solve the coupled partial differential equations describing the light–matter interaction in the laser structure. Both the model and the numerical algorithm are sufficiently flexible and modular to support arbitrary laser geometries and to allow for inclusion of important many-body semiconductor effects in future studies.

Dynamic instabilities in master oscillator power amplifier semiconductor lasers

We investigate theoretically the master oscillator power amplifier using a semiconductor laser model that is fully time and space (laterally and longitudinally) resolved. We numerically examine the stability of the device and identify the nature of the different instabilities. These can arise from undamped relaxation oscillations, beating between the longitudinal modes of any of the cavities that comprise the device, or lateral filamentation.

Local adaptive Galerkin bases for large-dimensional dynamical systems

The authors suggest and develop a method for following the dynamics of systems whose long-time behaviour is confined to an attractor or invariant manifold A of potentially large dimension. The idea is to embed A in a set of local coverings. The dynamics of the phase point P on A in each local ball is then approximated by the dynamics of its projections into the local tangent space. Optimal coordinates in each local patch are chosen by a local version of a singular value decomposition (SVD) analysis which picks out the principal axes of inertia of a data set. Because the basis is continually updated, it is natural to call the procedure an adaptive basis method. The advantages of the method are the following. (i) The choice of the local coordinate system in the local tangent space of A is dictated by the dynamics of the system being investigated and can therefore reflect the importance of natural nonlinear structures which occur locally but which could not be used as part of a global basis. (ii) The number of important or active local degrees of freedom is clearly defined by the algorithm and will usually be much lower than the number of coordinates in the local embedding space and certainly considerably fewer than the number which would be required to provide a global embedding of A. (iii) While the local coordinates indicate which nonlinear structures are important there, the transition matrices which glue the coordinate patches together carry information about the global geometry of A. (iv). The method also suggests a useful algorithm for the numerical integration of complicated spatially extended equation systems, by first using crude integration schemes to generate data from which optimal local and sometimes global Galerkin bases are chosen.

Three-dimensional simulations of degenerate counterpropagating beam instabilities in a nonlinear medium

Abstract We report our findings from a detailed series of three-dimensional simulations of degenerate counterpropagating beam instabilities in a nonlinear Kerr medium. These simulations show the formation of far field intensity patterns with both radial and hexagonal symmetries in agreement with recent experiments. Moreover, we suggest that the ring patterns which are characteristic of degenerate conical emission are transient phenomena which are always replaced by hexagons for long enough times, at least close to the plane-wave threshold. For misaligned input beams we observe the formation of a stabel point defect, a penta-hepta pair, in the hexagonal pattern.

Full space-time simulation for high-brightness semiconductor lasers

A semiconductor laser model is presented, which resolves the full time, longitudinal and lateral space dependences. The model is applied to an investigation of the dynamical stability of an integrated master-oscillator power-amplifier (MOPA) device. The model captures the full gain and refractive index bandwidth as a function of total carrier density. Our simulation confirms, for the first time, some recent experimental observations of high frequency whole beam oscillations and experimental reports that complex transverse filamentation occurs at high power amplifier currents.

Defects are weak and self-dual solutions of the Cross-Newell phase diffusion equation for natural patterns

Abstract We show that defects are weak solutions of the phase diffusion equation for the macroscopic order parameter for natural patterns. Further, by exploring a new class of nontrivial solutions for which the graph of the phase function has vanishing Gaussian curvature (in 3D, all sectional curvatures) excetp at points, we are able to derive explicit expressions which capture the anatomies of point and line (and surface) defects in two and three dimensional patterns, together with their topological characters and energetic constraints.

Enhanced stability of MFA-MOPA semiconductor lasers using a nonlinear, trumpet-shaped flare

Monolithically integrated flared amplifier master oscillator power amplifier (MFA-MOPA) lasers are studied using a high-resolution computational model that resolves time as well as longitudinal and transverse space dependences and includes Lorentzian gain and dispersion dynamics. By altering the linear flare of the power amplifier into a nonlinear, trumpet-shaped flare to overlap the gain region to the expanding field, the instability threshold of the MOPA is increased by /spl sim/2 for single-longitudinal, single-transverse mode operation and /spl sim/3 for single-transverse mode operation. This enables the MOPA to maintain a stable, near-diffraction limited output beam for higher currents before the onset of transverse instabilities. Thus the trumpet-flared MOPA emits an output beam of significantly higher power and brightness. This increased stability is due to a large reduction in feedback from the output facet of the trumpet shaped MFA-MOPA.

The influence of electron-hole-scattering on the gain spectra of highly excited semiconductors

A microscopic treatment of the influence of electron-hole-scattering on the optical dephasing and the lineshape in semiconductor gain media is presented. The calculations incorporate non-diagonal- and diagonal-scattering contributions to the optical polarisation. The strong compensation between both contributions leads to gain spectra, which are significantly modified in comparison to those obtained using a pure dephasing approximation.

Modulational-induced optical pattern formation in a passive optical-feedback system

Two-dimensional metastable patterns can appear randomly across a broad laser beam profile in a passive optical ring cavity. The instability responsible for pattern formation is primarily modulational in nature, leading to a competitive interaction between strongly saturated solitary-wave ringlike and filamentary spatial structures. The complexity of pattern formation depends sensitively on saturated filament density, which can be conveniently controlled in an optical-feedback arrangement. Our preliminary computational results suggest that the instability domain can be partitioned into two general categories: (1) rapid modulational growth to a single stationary filament or a long-lived metastable pattern involving five filaments growing directly from a shelflike ridge about the central filament or (2) a significantly slower formation of localized filaments forming primarily from a slow modulational growth on fully developed saturated solitary-wave rings. One-dimensional computations with a retarded material response indicate that the general trend of unstable formation should be relatively insensitive to finite retardation effects.