BALaser
A software tool for simulation of dynamics in Broad Area semiconductor Lasers
Content:
Introduction
High power high brightness edgeemitting broadarea (BA) semiconductor lasers and optical amplifiers are compact, efficient and reliable light sources playing a crucial role in different laser technologies, such as material processing, precision metrology, medical applications, nonlinear optics, sensor technology, etc.. BA lasers and amplifiers have a relatively simple geometry allowing an efficient energy pumping through a broad electric contact on the top of the device and can operate at high power (tens of Watts) regimes. However, BAS devices have one serious drawback: operated at high power, they suffer from a low beam quality due to simultaneous irregular contributions of different lateral and longitudinal optical modes. As a result, the emitted optical beam is irregular, has undesirable broad optical spectra, and large divergence. Thus, a quality improvement of the beam amplified in BAS amplifiers or generated by BAS lasers is a critical issue of the modern semiconductor laser technology.
Left: a schematic representation of a BA semiconductor laser. Right: typical simulated irregular spatialtemporal distribution of the optical field emission intensity in BA lasers.
BALaser is a software for simulation of the nonlinear dynamics in highpower edgeemitting (B)road(A)rea semiconductor (Laser)s. This software integrates numerically the 1 (time) + 2 (longitudinal and lateral) dimensional traveling wave model describing dynamics of broad area lasers, executes different data postprocessing routines, and visualises the obtained data. Data postprocessing and representation are done using MATLAB. For acceleration of the computations, the discretized PDEs are integrated numerically using multilevel parallel distributed computing with MPI.
Mathematical model and numerical algorithms
The dynamics of BAS devices can be described in different ways. The most comprehensive approach resolving the spatiotemporal evolution of full semiconductor equations selfconsistently coupled to the optical fields is given by 1 (time) + 3 (space) dimensional nonlinear PDEs. Since the height of the active zone where the optical beam is generated and amplified (y dimension) is considerably smaller than the longitudinal (z) and lateral (x) dimensions of a typical BAS device, a significant simplification can be achieved by averaging over the vertical direction and by describing certain effects phenomenologically. The resulting (2+1)dimensional dynamical traveling wave (TW) model can be resolved numerically orders of magnitudes faster allowing for parameter studies in an acceptable time.

1+2dimensional traveling wave model
The model is a degenerate system of second order PDEs for the slowly varying complex amplitudes of the counterpropagating optical fields, E(z,x,t)=(E^{+},E^{})^{T}, nonlinearly coupled to a rate equation for the real carrier density distribution N(z,x,t). It accounts for the diffraction of fields and diffusion of carriers in the lateral direction, whereas spatially nonhomogeneous device parameters capture the geometrical design of the device. The normalized TW model reads as
where μ is small and the complex matrix B models the carrier and frequency dependent semiconductor material gain, thermal and carrierinduced changes of the refractive index, as well as distributed coupling of counterpropagating fields. The boundary conditions for the optical fields at the longitudinal edges of the device account for reflections of the counterpropagating fields, injection of external optical beams or optical feedback from an external cavity. At the lateral boundaries of the computational domain, the optical fields and carriers usually are well damped. Here we assume either periodic boundary conditions [see WIAS Preprint 1806] or mixed Dirichlet (for the carrier densities) / approximate transparent (for the field functions) boundary conditions. This basic TW model can be extended for modeling of various relevant properties of BAS devices. It can also be reduced to lower dimensional systems, allowing a more detailed analysis, understanding and control of specific dynamical effects.

Parallel algorithm and its performance
For the precise dynamic simulations of long and broad devices and tuning/optimization of the model parameters require huge process time and memory resources. A proper resolution of rapidly oscillating fields in typical BAS devices in a sufficiently large optical frequency range requires a fine space (10^{6}10^{7} mesh points) and time (up to 10^{6} points for typical 5 ns transients) discretization. Dynamic simulations of such devices can easily take several days or even weeks on a single processor. Some speedup of computations is achieved by using problemdependent variable grid steps. However, for extended parameter studies with the simulation times up to 1000 ns parallel computers and parallel solvers have to be employed.
Speedup of computations in multiprocess simulations of three test problems defined on different spatial meshes N_{x}×N_{z}. Different bullets: tests with 1, 2, 4 or 8 processes on each node of parallel compute cluster.For the numerical integration of the TW model, we use either a splitstep fast Fourier transform based numerical method [WIAS Preprint 1806] or a full finite difference scheme. The method of domain decomposition is used to parallelize the sequential algorithm. Exemplary simulations of two test problems on the parallel cluster of computers show a good scaling of the algorithm [WIAS Preprint 1806]. For example, the simulations performed on 32 processors give a speedup factor of 25. That is, the simulations requiring two weeks of process time on a single processor computer can be efficiently performed over a single night. For a larger number of processes, the relative time needed for communications between them grows and implies a saturation of the speedup.

Two software operation regimes
The software tool BALaser can be executed in two different regimes. In the first of these regimes, the transient simulations for the fixed set of parameters are performed, and the calculated spatial distributions of optical fields and carrier density at a fixed time instant, as well as the temporallateral distribution of the emitted fields or time trace of the total emitted field intensity. The postprocessing of the calculated data gives us also the radiofrequency spectra, the timeevolution of the far fields, the time averaged far and nearfields as well as full or laterally/angularly resolved optical spectra.In the second regime, we can stepwise tune one or two model parameters within some defined limits, perform intermediate simulations for fixed parameters, and automatically estimate and record some fundamental characteristics of these intermediate transients (e.g., mean emission power, full optical spectra, instantaneous nearfield). This regime is very useful when studying the impact of one or another parameter on the device performance. However, for the execution of this regime we need to perform up to 1 microsecond transient calculations that, even on parallel computers, can require up to a few weeks of computation time.
For example, both these modes of operation were used for investigation of bistability in the Master Oscillator Power Amplifier (MOPA) laser (see figure below).
Simulated transients towards two different attractors at the same operation conditions (demonstration of bistability) in MOPA laser (a), spatial distributions of forward (b), backward (c) field intensities and carrier density (d) at the stable steady state, and numerical parameter continuation diagram (e) for increasing and decreasing injected current.
Applications, examples, comparisons with experiments
The TW model and our numerical algorithms were successfully used for simulations and optimization of existing laser devices as well as for simulation of novel broadarea semiconductor laser layouts. Several examples of our simulations are presented below.

Dynamics of Master Oscillator Power Amplifier (MOPA) lasers
The narrow waveguide of the distributed feedback (DFB) Master Oscillator (MO) generates a stable stationary optical field determined by a single transversal mode, which later is amplified in the tapered poweramplifier (PA) part of the MOPA device. An ideal MOPA laser should be able to maintain a good quality of the emitted beam. The operation of realistic MOPA devices, however, is spoiled by the amplification of the spontaneous emission in the PA, by the small separation of the MO and PA electrical contacts, and by the residual field reflectivity at the PA facet of the device. This residual reflectivity and thermally induced changes of the refractive index imply experimentally observable unwanted switchings between operating states determined by adjacent longitudinal optical modes.
Left: schematic representation of Master Oscillator Power Amplifier laser. Middle and right: measured (FBH Berlin) and simulated optical spectra of DFB MOPA laser as functions of the increased PA (top row) and MO (lower row) injected current.

Suppression of mode jumps in MOPAs
We have done a set of simulations to inspect an impact of laser design parameters on the stability of the MOPA device. For example, in the theoretical paper [WIAS Preprint 1444] we have demonstrated that a proper choice of the field coupling parameter within the DFB MO part of the device makes it less sensitive to the optical feedback, leading to a stabilization of the laser emission (see the second and the fourth panels of the figure below).
Simulated optical spectra of DFB MOPA devices with different DFB field coupling coefficients κ as functions of increased injected current.

Stabilization of BAS lasers by a dual offaxis optical injection
In this example we demonstrate theoretically the stabilization of the emission of a BAS laser by a pair of coherent optical plane waves injected into the laser along opposite angles to the optical axis. We have performed a series of simulations for fixed frequency detuning ω and increased intensity of the optical injection.
(a): schematic representation of BA semiconductor laser with a dual optical injection. Optical spectra (b) and farfields (c), as well as maximal, minimal and mean emission power (d) for the increased injection power and fixed frequency detuning in this laser. (e): laser stabilization region in injection power / frequency detuning plane.
Essential characteristics (optical spectra, farfields, field intensities) of typical observed dynamical states for ω=0 and different injection intensities are shown in the figure above. Here, one can distinguish three qualitatively different regimes, separated by thin horizontal lines. Especially interesting is the middle regime, where a stationary state having a well pronounced central angular component (a stabilized mode of the laser) can be observed. The last panel of the the same figure, which shows a laser stabilization region in the injection power / frequency detuning plane, summarizes a series of simulations for different values of ω.More details on this topic can be found in WIAS Preprints 1703 and 1598.

Beam shaping in BAS amplifiers with periodically modulated electrical contacts
In this theoretical example we demonstrate the improvement of the lateral beam profile in BA semiconductor amplifiers with periodic modulation of the gain and refractive index in both longitudinal and lateral directions. Such a modulation can be effectively realized by periodic structuring of the electrical contact.
Left: schematic representation of BA semiconductor amplifier with periodically modulated electrical contact. Right: beam power distribution (top) and central part of the corresponding farfield, with half maxima indicated by yellow lines (bottom) in conventional and periodically modulated amplifiers.We show, that an appropriate modulation leads to a significant compression of the farfields, which is strongly desirable in the real world applications. This field compression is clearly seen in the right lower panel of the figure above (compare it to left lower panel of the same figure, showing farfields of the conventional, nonmodulated BAS amplifier).
More details can be found in WIAS Preprints 1946, 1790, 2088.
Related publications
All publications listed below are discussing different structures of BA lasers lasers and were supported by simulations of BALaser.
Numerical algorithms and model analysis
 M. Radziunas, ''Modeling and simulations of edgeemitting broadarea semiconductor lasers and amplifiers'', In R. Wyrzykowski et al.(Eds.), PPAM 2015, Part II, LNCS 9574, pp. 269276, Springer, 2016. ISBN: 9783319321516.
 M. Radziunas, R. Čiegis, ''Effective Numerical Algorithm for Simulations of Beam Stabilization in Broad Area Semiconductor Lasers and Amplifiers'', Math. Model. Anal. 19(5), pp. 627646, 2014.
 M. Radziunas, R. Čiegis, ''Modeling and simulations of beam stabilization in edgeemitting broad area semiconductor devices'', In R.~Wyrzykowski et~al.(Eds.), PPAM 2013, Part II, LNCS 8385, pp. 332342, Springer, 2014. ISBN: 9783642551949 (Print) 9783642551956 (Online). WIASPreprint, (1806).
 R. Čiegis, M. Radziunas, ''Effective Numerical Integration of Traveling Wave Model for EdgeEmitting BroadArea Semiconductor Lasers and Amplifiers'', Math. Model. Anal. 15(4), pp. 409430, 2010.
 R. Čiegis, I. Laukaitytė, M. Radziunas, ''Numerical algorithms for Schrödinger equation with artificial boundary conditions'', Num. Funct. Anal. and Optimization 30(910), pp. 903923, 2009. WIASPreprint, (1446).
 I. Laukaityte, R. Ciegis, M. Lichtner, M. Radziunas, ''Parallel numerical algorithm for the traveling wave model'', in Parallel Scientific Computing and Optimization. Springer Optimization and Its Applications, eds. R. Ciegis, D. Henty, B. Kagstrom and J. Zilinskas, Vol. 27, Springer, pp. 237251, 2009. ISBN 9780387097060.
 R. Ciegis, M. Radziunas, M. Lichtner, ''Numerical algorithms for simulation of multisection lasers by using traveling wave model'', Math. Model. Anal. 13(3), pp. 327348, 2008. pdf file.
 M. Lichtner, M. Radziunas, L. Recke, ''Well posedness, smooth dependence and center manifold reduction for a semilinear hyperbolic system from laser dynamics'', Mathematical Methods in Applied Sciences 30(8), pp. 931960, 2007.

Modeling and simulations of multisection lasers
 M. Radziunas, R. Herrero, M. Botey, and K. Staliunas, ''Far field narrowing in spatially modulated broad area edgeemitting semiconductor amplifiers'', J. Opt. Soc. Am. B, 32(5), pp. 9931000, 2015. WIASPreprint, (2088).
 M. Radziunas, "Simulations and analysis of beam shaping in spatially modulated broad area edgeemitting devices", Proc. of the 24th IEEE International Semiconductor Laser Conference (ISLC 2014) , Palma de Mallorca, Spain, September 710, pp. 19  20, 2014. DOI: 10.1109/ISLC.2014.142 pdf file.
 M. Radziunas, R. Herrero, M. Botey, K. Staliunas, ''Simulations and analysis of beam quality improvement in spatially modulated broad area edgeemitting devices'', in SPIE Proceedings Series, (9134), art. no. 91340Q, 2014. WIASPreprint, (1946).
 M. Murad, M. Sorel, J.H. Marsh, A.C. Coleman, T. Ackemann, G.L. Oppo, M. Strain, M. Radziunas, M. Botey, R. Herrero, K. Staliunas, ''Control and enhancement of beam quality of broadarea semiconductor devices and arrays by multimode interference couplers and twodimensional gain modulation'', High Power Diode Lasers and Systems Conference (HPD), Coventry, UK, October 1617, pp. 89, 2013. DOI: 10.1109/HPD.2013.6706592
 M. Radziunas, M. Botey, R. Herrero, K. Staliunas, ''Intrinsic beam shaping mechanism in spatially modulated broad area semiconductor amplifiers'', Appl. Phys. Lett. 103(13), 132101, 2013. WIASPreprint (1790).
 M. Radziunas, K. Staliunas, ''Spatial"rocking" for improving the spatial quality of the beam of broad area semiconductor lasers'', in SPIE Proceedings Series, (8432), art. no. 84320Q, 2012. WIASPreprint, (1703).
 M. Radziunas, K. Staliunas, ''Spatial rocking in broad area semiconductor lasers'', Europhysics Letters 95, 14002 (6pp), 2011. WIASPreprint, (1598).
 V.Z. Tronciu, M. Lichtner, M. Radziunas, U. Bandelow, H. Wenzel, ''Improving the stability of distributedfeedback tapered masteroscillator poweramplifiers'', Optical and Quantum Electronics 41(7), pp. 531537, 2009. WIASPreprint, (1444).
 V.Z. Tronciu, M. Lichtner, M. Radziunas, U. Bandelow, H. Wenzel, "Improving the stability of distributedfeedback tapered masteroscillator poweramplifiers", Proc. of the 9th Int. Conf. on Numerical Simulation of Optoelectronic Devices NUSOD 09 , J. Piprek, YongTak Lee, eds., pp. 5556, 2009. pdf file.

Theory versus experiments
 V. Tronciu, S. Schwertfeger, M. Radziunas, A. Klehr, U. Bandelow, H. Wenzel, ''Amplifications of picosecond laser pulses in tapered semiconductor amplifiers: Numerical simulations versus experiments'', Opt. Communications 285, pp. 28972904, 2012. WIASPreprint (1657), 2011.
 A. Jechow, D. Skoczowsky, M. Lichtner, M. Radziunas, R. Menzel, "Highbrightness emission from stripearray broad area diode lasers operated in offaxis external cavities", in SPIE Proceedings Series, (7583), art. no. 758312, 2010.
 A. Jechow, M. Lichtner, R. Menzel, M. Radziunas, D. Skoczowsky, A. Vladimirov, ''Stripearray diodelaser in an offaxis external cavity: Theory and experiment'', Optics Express 17(22), pp. 1959919604, 2009. WIASPreprint, (1442).
 M. Spreemann, M. Lichtner, M. Radziunas, U. Bandelow, H. Wenzel, ''Measurement and Simulation of DistributedFeedback Tapered MasterOscillators PowerAmplifiers'', IEEE J. of Quantum Electronics 45(6), pp. 609616, 2009.
 M. Radziunas, V.Z. Tronciu, U. Bandelow, M. Lichtner, M. Spreemann, H. Wenzel, ''Mode transitions in distributedfeedback tapered masteroscillator poweramplifier'', Optical and Quantum Electronics 40(1415), pp. 11031109, 2008. WIASPreprint, (1366).
 M. Lichtner, M. Radziunas, U. Bandelow, M. Spreemann, H. Wenzel, ''Dynamic simulation of high brightness semiconductor lasers'', 8th Int. Conf. on Numerical Simulation of Optoelectronic Devices NUSOD 08 , J. Piprek, E. Larkins, eds., Nottingham, UK, September 15, 2008. pdf file.
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Dr. Mindaugas Radziunas,
WeierstrassInstitute for Applied
Analysis and Stochastics
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Tel.: (030) 20372441
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