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Showing papers on "Semiconductor optical gain published in 2010"


Journal ArticleDOI
TL;DR: What is believed to be the first experimental observation of lasing from the direct gap transition of Ge-on-Si at room temperature using an edge-emitting waveguide device is reported.
Abstract: Monolithic lasers on Si are ideal for high-volume and large-scale electronic-photonic integration. Ge is an interesting candidate owing to its pseudodirect gap properties and compatibility with Si complementary metal oxide semiconductor technology. Recently we have demonstrated room-temperature photoluminescence, electroluminescence, and optical gain from the direct gap transition of band-engineered Ge-on-Si using tensile strain and n-type doping. Here we report what we believe to be the first experimental observation of lasing from the direct gap transition of Ge-on-Si at room temperature using an edge-emitting waveguide device. The emission exhibited a gain spectrum of 1590-1610 nm, line narrowing and polarization evolution from a mixed TE/TM to predominantly TE with increasing gain, and a clear threshold behavior.

902 citations


Journal ArticleDOI
TL;DR: In this paper, the authors theoretically study the dynamics and the mode-locking properties of semiconductor Fabry-Perot lasers with intracavity saturable absorber by using a travelling-wave model and a time-domain description of the optical response of the semiconductor materials.
Abstract: We theoretically study the dynamics and the mode-locking properties of semiconductor Fabry-Perot lasers with intracavity saturable absorber by using a travelling-wave model and a time-domain description of the optical response of the semiconductor materials. Our description enables us to incorporate important features as for instance the abrupt spectral variations of the absorption in the saturable absorber. We analyze the influence of several key parameters that affect the stability of the mode-locking regime and show that this modelling approach can be used, upon proper fitting of the material parameters, for optimization of the design of semiconductor mode-locked lasers.

82 citations


Journal ArticleDOI
TL;DR: In this article, the ultrafast gain recovery dynamics of a quantum dot optical amplifier is investigated on the basis of semiconductor Bloch equations including microscopically calculated carrier-carrier scattering rates between the two-dimensional carrier reservoir and the confined quantum dot ground and first excited state.
Abstract: In this work the ultrafast gain recovery dynamics of a quantum dot semiconductor optical amplifier is investigated on the basis of semiconductor Bloch equations including microscopically calculated carrier-carrier scattering rates between the two-dimensional carrier reservoir and the confined quantum dot ground and first excited state. By analyzing the different scattering contributions we show that the cascading process makes a major contribution to the ultrafast recovery dynamics.

68 citations


Journal ArticleDOI
TL;DR: It is demonstrated experimentally that localized emission states in coupled broad-area semiconductor lasers can carry a finite orbital angular momentum and possess the chirality of optical vortices together with the properties of localized structures in dissipative systems, namely, the coexistence with a low intensity homogeneous emission and the mutual independence.
Abstract: We demonstrate experimentally that localized emission states in coupled broad-area semiconductor lasers can carry a finite orbital angular momentum. The resulting structures therefore possess the chirality of optical vortices together with the properties of localized structures in dissipative systems, namely, the coexistence with a low intensity homogeneous emission and the mutual independence. These results open the way to the realization of arrays of optically addressable and bistable chiral laser pixels.

66 citations


Journal ArticleDOI
TL;DR: In this article, the spin modulation in semiconductor lasers can improve performance, as compared to the conventional (spin-unpolarized) counterparts, leading to an enhanced bandwidth and desirable switching properties.
Abstract: We provide an analytic study of the dynamics of semiconductor lasers with injection (pump) of spin-polarized electrons, previously considered in the steady-state regime. Using complementary approaches of quasi-static and small signal analyses, we elucidate how the spin modulation in semiconductor lasers can improve performance, as compared to the conventional (spin-unpolarized) counterparts. We reveal that the spin-polarized injection can lead to an enhanced bandwidth and desirable switching properties of spin-lasers.

51 citations


Journal ArticleDOI
TL;DR: Watt-level core pumping of the single-mode fiber Raman lasers with low-noise disk lasers together with semiconductor saturable absorber mirror mode locking represents a highly practical solution for short-pulse operation.
Abstract: A 1.6µm mode-locked Raman fiber laser pumped by a 1480nm semiconductor disk laser is demonstrated. Watt-level core pumping of the single-mode fiber Raman lasers with low-noise disk lasers together with semiconductor saturable absorber mirror mode locking represents a highly practical solution for short-pulse operation.

46 citations


Journal ArticleDOI
TL;DR: 6.6 W of output power at the fundamental wavelength of 1.3 µm represents the best achievement reported to date for this type of lasers.
Abstract: 3 W at genuine red wavelength of 650 nm has been achieved from a semiconductor disk laser by frequency doubling. An InP based active medium was fused with a GaAs/AlGaAs distributed Bragg reflector resulting in an integrated monolithic gain mirror. 6.6 W of output power at the fundamental wavelength of 1.3 µm represents the best achievement reported to date for this type of lasers.

44 citations


Journal ArticleDOI
TL;DR: In this paper, a mode-locked Raman fiber laser was demonstrated to achieve stable pedestal-free 1.97 ps pulses at 1.38 µm with passive mode-locking by nonlinear polarization evolution.
Abstract: A mode-locked Raman fiber laser pumped by 1.3 µm semiconductor disk laser is demonstrated. Direct Watt-level core-pumping of the single-mode fiber Raman lasers and amplifiers with low-noise disk lasers is demonstrated to represent a highly practical solution as compared with conventional scheme using pumping by Raman wavelength convertors. Raman laser employing passive mode-locking by nonlinear polarization evolution in normal dispersion regime produces stable pedestal-free 1.97 ps pulses at 1.38 µm. Using semiconductor disk lasers capable of producing high power with diffraction-limited beam allows Raman gain to be obtained at virtually any wavelength of interest owing to spectral versatility of semiconductor gain materials and wafer-fusing technology.

44 citations


Journal ArticleDOI
13 Jul 2010-Chaos
TL;DR: The practical use of optically injected edge-emitting and vertical cavity semiconductor lasers and laser amplifiers is illustrated with examples of applications including, among others, optical logic and chaotic communication.
Abstract: The nonlinear properties of semiconductor lasers and laser amplifiers when subject to optical injection are reviewed and new results are presented for multisection lasers, vertical cavity semiconductor optical amplifiers, and surface-emitting lasers. The main underlying material parameters are outlined and the key design approaches are discussed for both edge-emitting and vertical cavity devices. An overview of theoretical modeling approaches is discussed and a summary of key experimental results is presented. The practical use of optically injected edge-emitting and vertical cavity semiconductor lasers and laser amplifiers is illustrated with examples of applications including, among others, optical logic and chaotic communication.

42 citations


Journal ArticleDOI
TL;DR: Animations of compilations of the RF spectrum as a function of optical feedback level, injection current and modulation signal strength is demonstrated as a new tool to give insight into the dynamics.
Abstract: The nonlinear dynamics of two semiconductor laser systems: (i) with optical feedback, and (ii) with optical feedback and direct current modulation are evaluated from multi-GHz-bandwidth output power time-series. Animations of compilations of the RF spectrum (from the FFT of the time-series) as a function of optical feedback level, injection current and modulation signal strength is demonstrated as a new tool to give insight into the dynamics. The results are contrasted with prior art and new observations include fine structure in the RF spectrum at low levels of optical feedback and non-stationary switching between periodic and chaotic dynamics for some sets of laser system parameters. Correlation dimension analysis successfully identifies periodic dynamics but most of the dynamical states are too complex to be extracted using standard algorithms.

41 citations


Journal ArticleDOI
TL;DR: In this paper, the authors investigate the properties of a passively mode locked quantum dot semiconductor laser under the influence of cw optical injection and demonstrate that the waveform instability at high pumping for these devices can be overcome when one mode of the device is locked to the injected master laser and additionally show spectral narrowing and tunability.
Abstract: We investigate numerically and experimentally the properties of a passively mode locked quantum dot semiconductor laser under the influence of cw optical injection. We demonstrate that the waveform instability at high pumping for these devices can be overcome when one mode of the device is locked to the injected master laser and additionally show spectral narrowing and tunability. Experimental and numerical analyses demonstrate that the stable locking boundaries are similar to these obtained for optical injection in CW lasers. © 2010 American Institute of Physics.

Journal ArticleDOI
TL;DR: In this paper, the bifurcation scenario and the evolution of the counter-propagating modes in a semiconductor ring laser when their symmetry is broken are studied. And a two-dimensional asymptotic model for this asymmetric ring laser can be used to interpret and predict regions of multistability and excitability in the laser.
Abstract: We study the bifurcation scenario and the evolution of the counter-propagating modes in a semiconductor ring laser when their symmetry is broken. We show how a two-dimensional asymptotic model for this asymmetric ring laser can be used to interpret and predict regions of multistability and excitability in the laser. The theoretical predictions and insights in these different dynamical regimes of the asymmetric semiconductor ring laser are confirmed and further explored experimentally in a semiconductor ring laser set-up that allows to controllably break the Z2-symmetry of the laser.

Journal ArticleDOI
TL;DR: From the results, it can conclude that once the optical modes are phase locked, the optical linewidth associated to every individual longitudinal mode of the device under test does not have a significant impact on the mode-beating signal on neither the pulse width nor its respective timing jitter.
Abstract: Timing-jitter measurements in optically generated subpicosecond pulses by a quantum-dash passively mode-locked semiconductor laser as a function of the bias current are reported. All the measurements are retrieved from a second-harmonic-generation frequency-resolved optical gating system. A decreasing trend in the pulse width and the associated timing jitter is found with the bias current. Additionally, the optical and mode-beating linewidths are analyzed in terms of both the mode wavelength and the bias current. From our results, we can conclude that once the optical modes are phase locked, the optical linewidth associated to every individual longitudinal mode of the device under test does not have a significant impact on the mode-beating signal on neither the pulse width nor its respective timing jitter.

Journal ArticleDOI
TL;DR: Two-photon gain is directly observed and characterized in electrically pumped room-temperature semiconductor devices, in good agreement with theory, and is demonstrated experimentally in semiconductor structures.
Abstract: We demonstrate experimentally two-photon gain in semiconductor structures, shown previously only in dilute atomic systems. Two-photon gain is directly observed and characterized in electrically pumped room-temperature semiconductor devices, in good agreement with theory. The semiconductor structure was designed to enhance the two-photon interaction and reduce parasitic effects. The nonlinear two-photon amplification is studied directly by examining the current dependence of the optical intensity growth, and indirectly by monitoring the reduction in one-photon emission due to two-photon transitions above transparency.

Journal ArticleDOI
TL;DR: A rate equation model is developed to quantitatively describe mode interactions due to mutual gain depletion in dual wavelength mid-infrared quantum cascade lasers based on heterogeneous cascades.
Abstract: We investigated dual wavelength mid-infrared quantum cascade lasers based on heterogeneous cascades. We found that due to gain competition laser action tends to start in higher order lateral modes. The mid-infrared mode with the lower threshold current reduces population inversion for the second laser with the higher threshold current due to stimulated emission. We developed a rate equation model to quantitatively describe mode interactions due to mutual gain depletion.

Journal ArticleDOI
TL;DR: In this article, it was shown that both localized and extended modes in a random laser can provide a coherent random laser mechanism, depending on the material studied and the feedback provided by the surface plasmons.
Abstract: The field of extreme miniature sources of stimulated emission represented by random lasers and nanolasers has gone through an enormous development in recent years. Random lasers are disordered optical structures in which light waves are both multiply scattered and amplified. Multiple scattering is a process that we all know very well from daily experience. Many familiar materials are actually disordered dielectrics and owe their optical appearance to multiple light scattering. Examples are white marble, white painted walls, paper, white flowers, etc. Light waves inside such materials perform random walks, that is they are scattered several times in random directions before they leave the material, and this gives it an opaque white appearance. This multiple scattering process does not destroy the coherence of the light. It just creates a very complex interference pattern (also known as speckle). Random lasers can be made of basically any disordered dielectric material by adding an optical gain mechanism to the structure. In practice this can be achieved with, for instance, laser dye that is dissolved in the material and optically excited by a pump laser. Alternative routes to incorporate gain are achieved using rare-earth or transition metal doped solid-state laser materials or direct band gap semiconductors. The latter can potentially be pumped electrically. After excitation, the material is capable of scattering light and amplifying it, and these two ingredients form the basis for a random laser. Random laser emission can be highly coherent, even in the absence of an optical cavity. The reason is that random structures can sustain optical modes that are spectrally narrow. This provides a spectral selection mechanism that, together with gain saturation, leads to coherent emission. A random laser can have a large number of (randomly distributed) modes that are usually strongly coupled. This means that many modes compete for the gain that is available in a random laser, which leads to interesting physical phenomena like chaotic behavior. The precise nature of the modes in a random laser is the subject of a debate in the field that has lasted for several years and that now seems to have come to a conclusion. On one hand, researchers believed that it was essential to have localized modes that formed (random) 'ring cavities' in order to obtain random lasing, while others maintained the hypothesis that the modes of a random laser are spatially extended. The most likely answer is that both are right, meaning that both localized and extended modes can provide a coherent random laser mechanism, depending on the material studied. Stimulated emission in random lasers is enabled by a collective behavior of huge ensembles of microscopic or nanoscopic particles providing feedback and often gain. Of special interest for fundamental science and applications is the class of even more extreme lasers, in which both gain and feedback are provided by single nanoparticles. The challenge originates from the fact that the minimal size of the cavity supporting the photonic standing wave cannot be smaller than half the wavelength in the medium. Correspondingly, for visible light, the cavity size cannot be smaller than approximately 150 nm. Significantly smaller laser sizes (down to a few nanometers) can be achieved if the feedback is provided not by conventional photonic modes but rather by localized surface plasmons—oscillations of free electrons in a metallic particle, whose resonance frequency is the plasma frequency adjusted by the shape and size of the particle. The concept of such a device, called SPASER (an analog of laser, where 'sp' stands for surface plasmon) was theoretically proposed in 2003 and experimentally demonstrated in 2009. A SPASER generates stimulated surface plasmons. Out-coupling of surface plasmon oscillations to photonic modes constitutes a nanolaser. In this issue, the reader has the chance to see a collection of recent contributions to the two most fascinating areas of laser research—the emergent field of SPASERs and nanolasers and the more mature, though still highly intriguing, field of random lasers.

Journal ArticleDOI
TL;DR: The gain filter is experimentally determine, with an equivalent parabolic gain bandwidth of up to 51 nm, for broad-band InGaAs/GaAs quantum well gain surface-emitting semiconductor laser structures capable of producing pulses down to 60 fs width when mode-locked with an optical Stark saturable absorber mirror.
Abstract: We present a method to experimentally characterize the gain filter and calculate a corresponding parabolic gain bandwidth of lasers that are described by “class A” dynamics by solving the master equation of spectral condensation for Gaussian spectra. We experimentally determine the gain filter, with an equivalent parabolic gain bandwidth of up to 51 nm, for broad-band InGaAs/GaAs quantum well gain surface-emitting semiconductor laser structures capable of producing pulses down to 60 fs width when mode-locked with an optical Stark saturable absorber mirror.

Journal ArticleDOI
TL;DR: In this article, the authors derived a closed-form expression for the modulation bandwidth of a semiconductor quantum dot (QD) laser, which is inversely proportional to the inhomogeneous line broadening caused by the QD-size dispersion.
Abstract: We derive a closed-form expression for the upper limit for the modulation bandwidth of a semiconductor quantum dot (QD) laser. The highest possible bandwidth increases directly with overlap integral of the electron and hole wave functions in a QD, number of QD-layers, and surface density of QDs in a layer, and is inversely proportional to the inhomogeneous line broadening caused by the QD-size dispersion. At 10% QD-size fluctuations and 100% overlap, the upper limit for the modulation bandwidth in a single QD-layer laser can be as high as 60 GHz.

Journal ArticleDOI
TL;DR: In this paper, a 1 GHz hybrid mode-locked monolithic semiconductor laser fabricated on indium phosphide was demonstrated and its operating regimes were explored and optical pulses as short as 36 ps were measured.
Abstract: This letter demonstrates a 1-GHz hybrid mode-locked monolithic semiconductor laser fabricated on indium phosphide. Its operating regimes are explored and optical pulses as short as 36 ps were measured. The linear cavity is 41 mm long with integrated active quantum well and passive waveguide structures. To our knowledge, this is the lowest reported repetition rate for a monolithically integrated mode-locked semiconductor laser. We further describe optimization steps of the saturable absorber reverse bias, driving RF frequency, and the semiconductor optical amplifier gain current for minimal output pulsewidth.

Journal ArticleDOI
TL;DR: In this article, an experimental study of the gain recovery of an InAs-InGaAsP-InP columnar-quantum-dot semiconductor optical amplifier around 1550 nm is presented.
Abstract: We report an experimental study of the gain recovery of an InAs-InGaAsP-InP columnar-quantum-dot semiconductor optical amplifier around 1550 nm. We find a three-step recovery process that gives around 85% gain recovery in only 10 ps and 100% in around 30 ps in case of a quite complete gain saturation. We also give a possible physical explanation for the peculiar gain dynamics.

Journal ArticleDOI
TL;DR: The experiment proves that the spectrum characteristics of the UWB pulses satisfy Federal Communications Commission regulations, and the experimental results are consistent with the simulated results based on the laser's rate equations.
Abstract: We propose and demonstrate an approach to the generation of an ultrawideband (UWB) pulse utilizing the nonlinear dynamics of a semiconductor laser (SL). The output UWB chaotic optical pulses generated by the SL with optical feedback can be controlled when the feedback strength and driving current of the SL are tuned. Our experiment proves that the spectrum characteristics of the UWB pulses satisfy Federal Communications Commission regulations, and the experimental results are consistent with the simulated results based on the laser’s rate equations.

Book
01 Jan 2010
TL;DR: In this paper, the authors describe a few specific CW laser systems, including optical cavity as a frequency discriminator, and frequency and amplitude modulation in a semiconductor diode laser system.
Abstract: 1. Gaussian beams 2. Optical resonators 3. Energy relations in optical cavities 4. Optical cavity as frequency discriminator 5. Laser gain and some of its consequences 6. Laser oscillation and pumping mechanisms 7. Descriptions of a few specific CW laser systems 8. Laser gain in a semiconductor 9. Semiconductor diode lasers 10. Mode locked lasers and requency metrology 11. Laser frequency stabilization 12. Atomic and molecular discriminants 13. Frequency and amplitude modulation 14. Nonlinear optics

Journal ArticleDOI
TL;DR: This work investigated the amplification of wave propagating in a plasmonic metal-semiconductor-metal (MSM) waveguide filled with semiconductor gain medium and obtained the conditions required to achieve net optical gain.
Abstract: Interactions between a semiconducting gain medium and confined plasmon-polaritons are studied using a multilevel multi-thermal-electron finite-difference time-domain (MLMTE-FDTD) simulator We investigated the amplification of wave propagating in a plasmonic metal-semiconductor-metal (MSM) waveguide filled with semiconductor gain medium and obtained the conditions required to achieve net optical gain The MSM gain waveguide is used to form a plasmonic semiconductor nano-ring laser(PSNRL) with an effective mode volume of 00071μm3, which is about an order of magnitude smaller than the smallest demonstrated integrated photonic crystal based laser cavities The simulation shows a lasing threshold current density of 1kA/cm2 for a 300nm outer diameter ring cavity with 80nm-wide ring This current density can be realistically achieved in typical III-V semiconductor, which shows the experimental feasibility of the proposed PSNRL structure

Patent
05 Jul 2010
TL;DR: In this paper, an integrated semiconductor laser element includes: semiconductor lasers that oscillate at different oscillation wavelengths from one another, each laser oscillating in a single mode; an optical coupler; and a semiconductor optical amplifier.
Abstract: An integrated semiconductor laser element includes: semiconductor lasers that oscillate at different oscillation wavelengths from one another, each laser oscillating in a single mode; an optical coupler; and a semiconductor optical amplifier. At least one of active layers of the semiconductor lasers and an active layer of the semiconductor optical amplifier have a same thickness and a same composition that is set to have a gain peak wavelength near a center of a wavelength band formed by the oscillation wavelengths. The semiconductor optical amplifier includes: an equal width portion formed on a side of the optical coupler to guide light in a single mode; and an expanded width portion formed on a light output side. The width of the expanded width portion is set according to a total thickness of well layers of the active layer of the semiconductor optical amplifier.

Journal ArticleDOI
TL;DR: In this article, the material gain of equal width InGaAsP/InGaAsp multi-quantum well active layers is calculated solving the Luttinger-Kohn Hamiltonian, including tetragonal strain and confinement effects.
Abstract: The material gain of equal width InGaAsP/InGaAsP multi–quantum well active layers is calculated solving the Luttinger–Kohn Hamiltonian, including tetragonal strain and confinement effects. The calculated optical bandwidth reaches 150 nm with a maximum polarization sensitivity of 1 dB between transverse electric (TE) and transverse magnetic (TM) emission over the −3 dB optical bandwidth. The corresponding device characterized by amplified spontaneous emission measurements shows an optical bandwidth with constant TE/TM ratio of almost 100 nm which can be improved up to 113 nm by increasing the barrier material band gap energy. Further enlargement of the optical bandwidth is expected by reducing the quantum well width.

Journal ArticleDOI
TL;DR: In this paper, a two-electrode quantum-dot semiconductor optical amplifier (QD-SOA) is proposed to enhance gain recovery rate and cross-gain modulation (XGM) bandwidth.
Abstract: A two-electrode quantum-dot semiconductor optical amplifier (QD-SOA) is proposed to enhance gain recovery rate and cross-gain modulation (XGM) bandwidth. In the theoretical model, electron and hole dynamics as well as the carrier diffusion are accounted for in the quantum-dot rate equations, which are solved with forward and backward propagation equations of signal and amplified spontaneous emission. The simulation results show that two-electrode QD-SOA can distribute injection current density nonuniformly to maintain carriers in carrier reservoirs of quantum dot sufficient along the entire cavity length of the semiconductor optical amplifier, thus making gain saturation dynamics dominated by spectral hole burning at lower bias current than common QD-SOA. Besides, distributing more current density in the second section of the two-electrode QD-SOA at higher bias can greatly accelerate gain recovery as well as expand the XGM bandwidth.

Proceedings ArticleDOI
22 Nov 2010
TL;DR: The incorporation of Bismuth in III-V alloys, such as GaAsBi/GaAs provides a preferential semiconductor band structure to suppress non-radiative recombination and optical losses, improving the efficiency and temperature stability of infrared semiconductor lasers as mentioned in this paper.
Abstract: The incorporation of Bismuth in III–V alloys, such as GaAsBi/GaAs provides a preferential semiconductor band structure to suppress non-radiative recombination and optical losses, improving the efficiency and temperature stability of infrared semiconductor lasers.

Journal ArticleDOI
TL;DR: In this paper, the authors investigated the tolerance to external optical feedback of p-type doped InAs/InP quantum-dash-based distributed feedback (DFB) lasers for different values of the Bragg-grating coupling coefficient.
Abstract: The tolerance to external optical feedback of p-type doped InAs/InP quantum-dash-based distributed feedback (DFB) lasers is investigated for different values of the Bragg-grating coupling coefficient. We show that p-doping of the active layer not only enhances the differential gain but also results in small values of the linewidth enhancement factor, both parameters contributing to an increased tolerance to external optical feedback. A −18 dB onset of coherence collapse is reported for antireflection-coated devices, demonstrating the compatibility of quantum-dash-based DFB lasers with isolator-free operation.

Journal ArticleDOI
TL;DR: An improved model is developed in order to predict the RF behavior and the slow light properties of the SOA valid for any experimental conditions and validated by showing a good agreement with experiments for small and large modulation indices.
Abstract: We developed an improved model in order to predict the RF behavior and the slow light properties of the SOA valid for any experimental conditions. It takes into account the dynamic saturation of the SOA, which can be fully characterized by a simple measurement, and only relies on material fitting parameters, independent of the optical intensity and the injected current. The present model is validated by showing a good agreement with experiments for small and large modulation indices.

Journal ArticleDOI
TL;DR: In this article, the authors investigate optical near fields in semiconductor lasers and perform finite element simulations for two different laser types, namely a super large optical waveguide (SLOW) laser, which is an edge emitter, and a vertical cavity surface emitting laser (VCSEL).
Abstract: In the present paper we investigate optical near fields in semiconductor lasers. We perform finite element simulations for two different laser types, namely a super large optical waveguide (SLOW) laser, which is an edge emitter, and a vertical cavity surface emitting laser (VCSEL). We give the mathematical formulation of the different eigenvalue problems that arise for our examples and explain their numerical solution with the finite element method (FEM). Thereby, we also comment on the usage of transparent boundary conditions, which have to be applied to respect the exterior environment, e.g., the very large substrate and surrounding air. For the SLOW laser we compare the computed near fields to experimental data for different design parameters of the device. For the VCSEL example a comparison to simplified 1D mode calculations is carried out.