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Due to the complex lateral structure of Distributed Feedback lasers (DFB) and Master Oscillator Power Amplifiers (MOPAs), one-dimensional methods like the classical Transfer Matrix Method (TMM) are not suitable for simulating the optical wave in these devices. Therefore, we applied Trigonometric Finite Wave Elements (TFWE) that generalize the TMM in two or three dimensions. By coupling the dynamic wave equation with simplified temperature and drift-diffusion models, we can simulate the dynamic behavior of DFB lasers and MOPAs. Furthermore, by Fourier transformation, we can calculate the modes of the laser cavity and the corresponding wavelengths. By this approach, the influence of injection current and temperature on the resulting modes and output power can be analyzed in detail.

We present a new method to simulate optical waves in large geometries. This method is based on newly developed finite elements, so-called trigonometric finite wave elements (TFWEs). They are constructed by linear elements as well as by trigonometric functions such that the one-dimensional Helmholtz equation is exactly solved under certain conditions. In comparison with the transfer matrix method, the TFWE method offers equally good results, but it can be extended to higher dimensions and applied to time-dynamic problems. The analysis of TFWEs shows that these elements approximate functions with certain oscillation properties more accurately than standard finite elements. Thus, a finite element discretization with TFWEs leads to a smaller system of equations which eases the solving process. Numerical results obtained by applying the TFWE method to the simulation of the optical wave in distributed feedback lasers are presented.

In this paper, we describe a new approach to combine the conjugate gradient method and the multigrid method. This approach simultaneously constructs conjugate new correction directions based on restricted gradients. The computational amount is O(N), where N is the number of unknowns. The algorithm is easy to implement. It only requires restriction and prolongation operators, matrix vector multiplications on several levels, and scalar products. Therefore, the algorithm can be applied to accelerate a multilevel algorithm with slow convergence. Numerical results for Poisson's equation with jumping coefficients and a Stokes type equation are presented.

Modern simulation of solid state lasers and amplifiers is a multi-physics problem. It requires the simulation of light with different techniques, as well as coupling of optical effects with other physical effects like deformation and stress inside a laser crystal. We present and overview simulation techniques which are necessary for an accurate modelling of solid state laser. These include ray tracing for modeling of pump light, Gauss mode analysis for stability calculations of a laser cavity, and vectorial beam propagation method for the amplifier simulation. It is also necessary to perform mechanical or rate equations simulations. Structural mechanics simulation is required for the calculation of thermal lens and thermally induced birefringence effects inside a laser crystal. Coupling Gauss mode analysis and rate equations leads to the dynamic mode analysis (DMA), which is used to calculate output power and beam quality of a laser. Furthermore, we present a mode amplification method, which allows us to simulate spectral narrowing in laser amplifiers and power and beam quality calculation. The above mentioned simulation techniques have been integrated into laser simulation software package ASLD. We have used highly efficient algorithms and modern software techniques, together with a user friendly GUI. This enables users to efficiently simulate complex resonator and amplifier designs and save their development time and costs. Furthermore, ASLD can be used for educational purpose at universities and research institutes.

We developed a complex physical model for simulating laser amplifiers to numerically analyze birefringence effects. This model includes pump configuration, thermal lensing effects, birefringence, and beam propagation in the laser amplifier. Temperature, deformation, and stress inside the laser crystal were calculated using a three-dimensional finite element analysis (FEA). The pump configuration is simulated using a three-dimensional ray tracing or an approximation based on super-Gaussian functions. Our simulations show the depolarization of a linearly polarized electromagnetic wave in a cylindrical laser crystal. These simulations were performed using a three-dimensional full vectorial beam propagation method (VBPM). Stress induced birefringence can be compensated well for moderate pumping powers. High power amplification requires sensitive alignment. Our simulation technique calculates the influence of the photo-elastic effect inside the laser crystal accurately. Detailed knowledge about beam waist and depolarization is needed to develop compensation techniques for high power output beams with low depolarization losses.

Thin film silicon solar cells are optimized in order to increase light absorption. Studying solar cells using experiments requires depositing different layers and building the thin film solar cell, which is usually time consuming and prone to error. Numerical simulation has shown promising results for the calculation of quantum efficiency of thin film solar cells with rough interfaces.

Polarization effects in laser crystals like Nd:YAG have a strong influence on output power and beam quality of laser resonators and laser amplifiers. Simulation techniques to analyze these effects are presented.

Birefringence influences the beam quality and output power of high power solid-state lasers. Inhomogeneous distribution of the thermal field inside the laser crystal rod leads to thermal strains and birefringence, due to the photoelastic effect. Analytical models have used the plane stress and plane strain assumption for an axial sym- metric pumped crystal. This leads in case of an [111]-cut to an axially symmetric birefringence pattern. However, numerical calculations of birefringence show a threefold symmetry pattern due to the anisotropic behavior of the photoelastic tensor. This disturbs the ideal use of a radial or azimuthal polarised beam. We analyzed a laser rod pumped at three sides with threefold symmetry, in order to reduce the effect of birefringence. Simulation results show birefringence is affected by rotation of the crystal around its [111]-axis. Smallest birefringence can be obtained by an optimal rotation with respect to the edges of the crystal. Therefore the output beam of this laser device is more suitable for generating radial or azimuthal polarisations.

Modern laser technology demands powerful numerical tools to predict the efficiency of laser configurations. Birefringence has a strong influence on the beam quality and output power of a laser amplifier. We developed a complex physical model for simulating laser amplifiers and analyzing the birefringence effects. This model includes pump configuration, thermal lensing effects, birefringence, and beam propagation in the laser amplifier. The pump configuration is simulated using a complete three-dimensional ray tracing or by an approximation based on super-Gaussian functions. For an accurate modeling of the thermal lensing effect, the deformation of the end faces and the polarization dependent index of refraction was taken into account. Temperature, deformation and stress inside the laser crystal were calculated by a three-dimensional finite element analysis (FEA). In particular, the refractive index was accurately calculated by considering its temperature dependency and the photo elastic effect. This refractive index was used in the simulation of laser beam propagation through an amplifier. These simulations were performed by a complete three-dimensional vectorial beam propagation method (VBPM). The advantage of VBPM is that it can be applied to a polarization dependent index of refraction. This is important when taking into account the birefringence obtained by the photo elastic effect inside the laser crystal. The beam propagation method is based on finite elements on block structured grids as well as a Crank-Nicolson approximation in the propagation direction (FE-BPM). Reflecting boundaries were eliminated by introducing a perfect matching layer (PML). Simulation results show that a complete three-dimensional simulation model was useful in analyzing and optimizing high power laser amplifiers. The value of our model lies in the fact that it can take into account the crystal cut direction. Based on this the birefringence for simulating the laser beam quality and output power can be calculated.

Thin film silicon solar cells are optimized to increase their efficiency. One technique to obtain higher efficiency is to increase path length of light using textured surfaces. The impact of these layers on efficiency is usually studied using experimental methods. This requires building of a solar cell and is time consuming and prone to error. Simulation is used to predict light scattering effects in large domains with textured layers. We studied these effects using a conformal finite integration technique (FIT) that efficiently simulates complex geometries with surface roughness. The simulated external quantum efficiency EQE for a solar cell with a μc-Si:H and aSi:H layers with surface roughness are presented.

Thermal lensing e ects and birefringence in laser crystals strongly in uence beam quality of high power solid state lasers. Particularly, the e ects of birefringence are important in laser ampli ers using Nd:YAG crystals. To study these e ects, a simulation tool was developed, which allows to calculate birefringence in laser crystals for di erent kind of crystal cuts and pumping con gurations. The photoelastic e ects were accurately calculated by FE method. Simulation results are presented for di erent crystals and pumping. We also show that birefringence is not radially symmetric for a 111-cut Nd:YAG crystal, even when the pumping con guration is radially symmetric.

We present an algorithm for generating a surface approximation of microcrystalline silicon (μc-Si) layers after plasma enhanced chemical vapor deposition (PECVD) onto surface textured substrates, where data of the textured substrate surface are available as input. We utilize mathematical image processing tools and combine them with an ellipsoid generator approach. The presented algorithm has been tuned for use in thin-film silicon solar cell applications, where textured surfaces are used to improve light trapping. We demonstrate the feasibility of this method by means of optical simulations of generated surface textures, comparing them to simulations of measured atomic force microscopy (AFM) scan data of both Aluminum-doped zinc oxide (AZO, a transparent and conductive material) and μc-Si layers.

Depolarization effects in Nd:YAG amplifiers are accurately simulated by a vectorial beam propagation method. Simulations take into account birefringence, which was calculated by finite elements for different rotations and cuts of the crystal.

The implementation of numerical algorithms for solving partial differential equations costs a lot of time and the optimization of such codes is difficult. These problems can be reduced by expression templates for partial differential equations. Using this concept, one can implement numerical algorithms for PDE’s in a language which is close to the mathematical language. Expression templates give the compiler global informations on an expression such that the optimization of the code can be left to the compiler. Numerical results for the Stokes operator on general domains in 3D are presented.

A multilevel algorithm is presented that solves general second order elliptic partial differential equations on adaptive sparse grids. The multilevel algorithm consists of several V-cycles in \(x\)- and \(y\)-direction. A suitable discretization provide that the discrete equation system can be solved in an efficient way. Numerical experiments show a convergence rate of order \(O(1)\) for the multilevel algorithm.

The combination technique is an algorithm for the approximate solution of partial differential equations on sparse grids that has to be combined with a suitable standard discretization. The advantage of the combination technique compared to the standard discretization is that the same accuracy is achieved with many fewer grid points. In this paper, the combination technique is used with a bilinear finite element discretization. Depending on the smoothness of the solution and the coefficients, it is proved for general second-order elliptic differential equations on the unit square that the combined solution converges with order O(h) or O(h log h-1) in the energy norm and with order O(h2 log h-1) or O(h3/2) in the L2-norm, respectively. This holds even if the bilinear form corresponding to the elliptic equation is not symmetric positive definite. The proof does not use an asymptotic error expansion, but Sobolev space techniques.

In this paper we analyze the approximation of functions on partially ordered sequences of regular grids. We start with the formulation of minimal requirements for useful grid transfer operators. We introduce the notions of nested and of commutative transfer operators. We define mutual coherence for representations on grids that are not related by coarsening or refining. We show necessary and sufficient conditions for mutual coherence and we show how a hierarchical decomposition is generated by a set of commutative transfer operators. The usual piecewise constant and piecewise d-linear approximations are identified as special instances of tensor product type. In the second part of the paper we derive error estimates for approximation in these spaces, in different norms on general d-dimensional dyadic sequences of regular and sparse grids. Some of these results have been published before, e.g., in doctoral theses by Bungartz and Pflaum. Here, the results are presented in a unified framework and the proofs are much simplified. We pay special attention to a convenient notation.

The e ciency of thin lm solar cells can be improved by various known and extensively studied light trappingtechniques such as textured interfaces, nano-particles, and so on. But all these methods are not expected toimprove the e ciency of the solar cells with by same amount. In this paper, textured interfaces and nano-particlesare simulated and their respective e ect on the absorption of the active layer, aSi : H in this case, is observed.The nano-particles are silver nano-particles and for the interface simulations, di erent AFM scans are used.For the nano-particles simulations di erent position in the layer stack is simulated. To achieve this, Maxwell'sequations are solved with Finite Di erence Method(FDM) and Finite Integration Technique(FIT) and specialscheme that accounts for the negative permittivity of silver. To accurately simulate the silver nano-particlesthe simulation is done with a ne discretization and run on high performance machines with a highly paralleliterative scheme.Keywords: Thin lm solar cells, FDTD, nano particles, textured interfaces

Composite, core-doped, and ceramic crystals are used to reduce the thermal lensing effect in laser crystals. An accurate simulation of laser resonators is needed to nd optimal doping structures for a required laser. Also simulation helps apply these crystals efficiently. In this work, results of simulations performed on resonators containing core-doped Nd:YAG ceramic crystals with radial dependent doping concentration, and composite crystals with different layers of doping concentration are presented. The absorbed pump light in crystals is simulated using the ray tracing algorithm. The thermal lensing effect has been computed by the nite element analysis of the temperature and deformation. The dynamic mode analysis (DMA) was used to compute the laser beam quality and output power. The DMA solves rate equations separately for each Gauss mode. It also calculates population inversion by solving rate equations on nite volume grids. This approach yields a few thousands of rate equations for population inversion on the nite volume grid. The advantage of this method for both mentioned crystals is that different decay rates can be associated to regions with different doping concentration. Simulation results have shown that sophisticated laser crystals are able to reduce thermal lensing effect and increase beam quality.

Semiconductor saturable absorber mirrors (SESAMs) are used to produce passively Q-switched ultrashort pulsed lasers. Numerical modeling of physical effects of SESAM is required to effectively design this type of lasers. For this purpose, simulations are performed to study the dynamic behavior of Gauss modes, gain of modes and saturation of the saturable absorber mirror. The laser beam quality has to be good enough in order to avoid chaotic laser behavior. We extended our dynamic mode analysis (DMA) algorithm to calculate laser beam quality. This simulation technique is based on rate equations for a set of Gauss modes and population inversions. Gain of each mode can be calculated separately by solving the corresponding set of rate equations. We have assumed that the reflectivity of the mirror is spatially invariant in the SESAMs model. An additional rate equation is required to include the saturation of SESAM. This equation considers parameters such as modulation depth, saturation fluence and relaxation time. Simulation results show that our model can predict pulse energy and non-chaotic behavior of the laser.

The results of Monte-Carlo-Random ray tracing and Finite Element Analysis are used either for a model of pump light propagation through the edged-pumped thin-disk or delivers realistic results for computing the output power of disk.

Using finite element analysis (FEA), we present a detailed analysis of birefringence in particular for [111]-cut Nd:YAG crystals. Accurate simulations show a non-radially symmetric behaviour.

Elliptic differential equations can be discretized with bilinear finite elements. Using sparse grids instead of full grids, the dimension of the finite element space for the 2D problem reduces from O(N 2 ) to O (N log N) while the approximation properties are nearly the same for smooth functions. A method is presented which discretizes elliptic differential equations on curvilinear bounded domains with adaptive sparse grids. The grid is generated by a transformation of the domain. This method has the same behaviour of convergence like the sparse grid discretization on the unit square.

We are studying the influence of spherical silver nanoparticles (AgNP) in absorbing media by numerically solving the Maxwell's equations. Our simulations show that the near-field absorption enhancement introduced by a single AgNP in the surrounding medium is increasing with the growing particle diameter. However, we observe that the relative absorption per particle volume is on a similar level for different particle sizes; hence, different numbers of particles with the same total volume yield the same near-field absorption enhancement. We also investigate the effect of non-absorbing shells around the AgNP with the conclusion that even very thin shells suppress the beneficial effects of the particles noticeably. Additionally, we include AgNP in an organic solar cell at different vertical positions with different particle spacings and observe the beneficial effects for small AgNP and the scattering dependent performance for larger particles.

Analysis of randomly textured interface in solar cells is an ambitious effort considering the numerous structures and variation in the texture. We use the Fourier transform based method, which takes randomly textured interface as initial input and manipulates its frequency spectrum to synthesize interface texture with the desired texture behavior. Afterward, the synthesized interfaces are applied to simulate flexible thin-film silicon tandem (aSi/μcSi) solar cells. Using the simulation, we have shown how interface between the back and front areas of the solar cell evolves, and the effect of the back contact; the front area roughness is analyzed and interference fringes observed on experiments are discussed. For the simulations, a finite integration technique with time-harmonic inverse iterative method is used. All simulations are performed on high-performance computers, which allows simulation of a big simulation domain (>5 μm×5 μm) with fine mesh size (

Here, we present a description of an inexpensive ultrafast self-starting passively mode-locked laser oscillator that can be constructed using widely available off-the-shelf optical components. Such a laser system can be used to teach students the principles of solid state laser engineering, demonstrate a number of nonlinear optical phenomena, and perform qualitative and quantitative comparisons between numerical laser modeling and experimental results.

Silver nanowire films are a newly introduced choice for transparent electrodes in thin film solar cells. Simulation is an adequate and economic method to analyse and predict the optical properties of these films. We simulate the optical behavior of such films by solving Maxwell equations. The simulation technique is a finite integration technique (FIT) combined with a time harmonic inverse iteration method (THIIM) to handle the negative permittivity of silver. Parallel computation on high performance computers(HPC) is used to meet the large computational requirement of the problem. In agreement to preliminary experimental results, the simulation results show that transmission of light is larger than expected by a simple ray-tracing model.

A sophisticated light management is important to construct thin film solar cells with optimal efficiency. This is based on suitable nanostructures of different layers and materials with optimized optical properties. To design thin film solar cells with high efficiency, simulation of light-trapping is a very helpful tool. Such a simulation has to take into account the underlying physical properties like plasmonic effects of silver or interferences. To this end, it is important to solve Maxwell's equations on a discretization grid. To obtain an accurate simulation, the roughness of the top transparent conductive oxide (TCO) layer is described by AFM-scan data. To meet the high computational amount in solving Maxwells equations on a finite difference discretization grid, high performance computers (HPC) are used.

We derive a new model to simulate passively Q-switched intracavity frequency-doubling solid-state laser. By introducing a nonlinear loss term caused by frequency-doubling crystal into the rate equations ,we can express the effect of second-harmonic generation (SHG). We apply a finite volume discretization on gain medium, saturable absorber and frequency-doubling crystal. "Dynamic Multimode Analysis (DMA)" and several Gaussian modes are utilized. At the end, numerical results of passively Q-switched intracavity frequency-doubling solid-state laser are presented. In the case of large pump radius,chaoic phenomenon can be observed numerically. In order to realize the 3D simulation, we mainly use two technics: One is that common rate equations are extended to a set of 3D multimode rate equations, which calculate photon number for different modes separately. The other is to take into account a finite volume discretization.

Passive Q-switched lasers are constructed using saturable absorbers (SA). One characteristic of these lasers is that they are built with small dimensions. There are difficulties in designing lasers with a given pulse repetition rate or pulse energy using saturable absorbers. Numerical simulation of Q-switches facilitates the design and production of such lasers and helps to reduce development time and cost. This paper presents a new simulation method which calculates beam quality, maximal output power, pulse-width and pulse energy.

To optimize the quantum efficiency (QE) and short-circuit current density (JSC) of silicon thin-film solar cells, one has to study the behavior of sunlight in these solar cells. Simulations are an adequate and economic method to analyze the optical properties of light caused by absorption and reflection. To this end a simulation tool is developed to take several demands into account. These include the analysis of perpendicular and oblique incident waves under E-, H- and circularly polarized light. Furthermore, the topology of the nanotextured interfaces influences the efficiency and therefore also the short-circuit current density. It is well known that a rough transparent conductive oxide (TCO) layer increases the efficiency of solar cells. Therefore, it is indispensable that various roughness profiles at the interfaces of the solar cell layers can be modeled in such a way that atomic force microscope (AFM) scan data can be integrated. Numerical calculations of Maxwell's equations based on the finite integration technique (FIT) and Finite Difference Time Domain (FDTD) method are necessary to incorporate all these requirements. The simulations are performed in parallel on high performance computers (HPC) to meet the large computational requirements.

Simulations have to accurately model thermal lensing in order to help improving resonator design of diode pumped solid state lasers. To this end, a precise description of the pump light absorption is an important prerequisite. In this paper, we discuss the frequency dependency of the pump light absorption in the laser crystal and its influence on the simulated laser performance. The results show that the pump light absorption has to include the spectral overlap of the emitting pump source and the absorbing laser material. This information can either be used for a fully frequency dependent absorption model or, at least in the shown examples, to compute an effective value for an exponential Beer-Lambert law of absorption. This is particularly significant at pump wavelengths coinciding with a peak of absorption. Consequences for laser stability and performance are analyzed for different pump wavelengths in a Nd:YAG laser.

In order to increase the efficiency of thin-film solar cells, the nanostructure of these cells has to be optimized. To this end, simulations of the optical wave in thin-film solar cells are required. The frequency dependence of the refraction index of materials, like amorphous silicon (a-Si:H), cannot be described by dispersive models like Drude model. Therefore, single frequency simulations for the whole solar spectrum have to be performed. To discretize materials with negative permittivity efficiently, we developed a new finite-difference-frequency-domain method to avoid computationally intensive simulations. To demonstrate the efficiency of our method, we present 3-dimensional simulations for a tandem solar cell including interfaces described by AFM-scans. Plasmonic effects at the silver back-contact show the efficiency of our discretization in case of materials with negative permittivity.

We present a finite integration technique (FIT) simulator for modelling light diffraction from lithographic masks with complex shapes. This method has high flexibility in geometrical modelling and treating curved boundaries. The inherent feature of FIT allows more accurate electromagnetic field simulation in complex structures. This technique is also suited for fast EMF simulations and large 3D problems because of its parallelisation potential. We applied this method to investigate the effect of complex mask shapes on the printed image. We demonstrate results for a phase-shift mask (PSM) with footing extensions and surface roughness.

A sophisticated light-management is indispensable for silicon thin-film silicon solar cells based on amorphous (a-Si:H) and microcrystalline (μc-Si:H) silicon. The optical properties of thin-film solar cells have a significant influence on the conversion efficiency. The topology of the nano-textured interfaces affects the optical path and absorption. A rough transparent conductive oxide (TCO) film leads to a high quantum efficiency and shortcircuit current density. Simulations of various geometries indicate the optimal texture. Therefore, we simulate 3-dimensional tandem thin-film solar cells with different interfaces. The roughness can be identified by atomic force microscope (AFM) scans. In order to accurately analyze all aspects of the light propagation in solar cells, numerical simulations of Maxwell's equations are needed. By standard simulation programs for solving Maxwell's equations, it is difficult to simulate realistic textures of the solar cell layers. Therefore, a simulation tool based on the finite difference time domain (FDTD) method and the finite integration technique (FIT) is developed, which is able to integrate AFM scan data. To incorporate the nanostructure of a relevant section in the AFM scans, high computational domains are needed. This leads to a large number of grid points in the resulting discretization. Parallel computations on high performance computers are needed to meet the large computational requirements. The simulations show that the light propagation in the investigated thin-film device is a complex phenomenon depending on the wavelength and phase of the incident light.

The complex behavior of the optical wave in laser resonators requires a comprehensive model of thermal lensing and the dynamic, 3-dimensional behavior of the laser beam. To this end, we perform a combined finite element analysis (FEA) of the optical wave and of thermal lensing. Here, the simulation of the optical wave is the most challenging task. Therefore, we also discuss another method, Dynamic Multimode Analysis, which is suitable for a wide range of lasers. Finally, we present a complex heat model in order to analyze the interaction of heat generation, thermal lensing, laser dynamics, and the beam profile.

We present a finite integration technique (FIT) simulator for modelling light diffraction from lithographic masks with complex shapes. This method has high flexibility in geometrical modelling and treating curved boundaries. The inherent feature of FIT allows more accurate rigorous electromagnetic field simulation in complex structures. This technique is also suited for fast EMF simulations and large 3D problems because of its parallelisation potential. We applied this method to investigate the effect of various mask shapes on lithographically printed images. The imaging results were obtained using Dr.LiTHO's imaging simulator. We demonstrate results for attenuated phase-shift mask (PSM) with different absorber deviations from ideal shapes such as footing and oblique sidewalls.

Short-circuit current density and the quantum efficiency of thin-film solar cells are calculated by simulating Maxwell’s equations to improve light-management in these solar cells. Complete solar cell structures, based on AFM-scans, are simulated with high performance computing.

We derive a new model and simulation technique called "Dynamic Multimode Analysis (DMA)" to simulate the 3-dimensional dynamic behavior of a laser. A Gaussian mode analysis is used to obtain resonator eigenmodes taking into account thermal aberrations. These modes are coupled by a set of rate equations to describe the dynamic behavior of the individual modes for cw and Q-switched lasers. Our approach analyzes mode competition and provides a detailed description of the laser beam in terms of output power, beam quality factor M(2), and pulse shape. Comparison of experimental data with our simulation results provides new insight into the effect of mode competition and the operation of Q-switched lasers.

Due to the lateral structure of Distributed Feedback lasers (DFB) and Master Oscillator Power Amplifiers (MOPAs), the one-dimensional classical Transfer Matrix Method (TMM) as well as similar one-dimensional methods do not lead to satisfactory simulation results. Therefore, we present a two-dimensional simulation technique based on Trigonometric Finite Wave Elements (TFWE) — a generalization of the TMM in two or three dimensions — that solves the time-dependent wave equation. By coupling the wave equation with a temperature and a drift-diffusion model, we can simulate the time-dynamic behavior of DFB lasers and MOPAs. Furthermore, by Fourier transformation, we can investigate which modes and which frequencies appear. In this way, the influence of the injected current and of the stripe width on the resulting modes and on the output power can be analyzed in detail.

The standard finite-difference time-domain equations can model propagation of wave in dispersive media. However in case of plasmas and metals, the negative values of permittivity makes the standard time iteration scheme unstable. We describe a numerical technique to solve Maxwell's equations in frequency domain in this case.

Light diffraction from lithography masks depends on the geometrical shape of the mask pattern which is created by an etch process. The analysis of relevant effects requires the application of an accurate electromagnetic field solver. In this paper, we present an appropriate simulation method based on the Finite Integration (FI) technique for solving Maxwell's equations.

The complex physical optics behavior in modern solid state lasers can only approximately be described using common simulation techniques, such as a Gaussian mode analysis or beam propagation methods. For this reason we present a new 3-dimensional, time-dependent method to model the laser beam in a resonator in a more comprehensive way. We transform the wave equation by a special ansatz and solve the resulting equation, which is similar to a Schroedinger equation, by a finite element analysis. In this paper we explain our new approach and present first numerical results for a simple laser cavity. The results are compared with those of a dynamic multimode analysis using Gaussian eigenmodes.

We present a new simulation technique for Distributed Feedback lasers in 2D. The method is based on recently developed Trigonometric Finite Wave Elements (TFWEs) that approximate oscillating and internally reflected optical waves. Since our method is derived from the Transfer Matrix Method (TMM), the TFWE method provides exactly the same results as the TMM for 1D problems but it can be extended to higher dimensions and to time-dynamic simulations. Therefore, large laser structures and the influence of the injected current can be simulated time-dynamically. Furthermore, the wavelengths of the competing modes can be detected using the Fast Fourier Transformation.

New simulation methods for solid-state lasers are presented: We describe a dynamic multimode analysis to model mode competition and Q-switching. Furthermore, we propose a 3D finite element analysis of the electric field without mode decomposition.

We present a new technique for the time-dynamic simulation of semiconductor lasers. The method is based on appropriate finite elements - so called Trigonometric Finite Wave Elements (TFWEs) - and a suitable model for the time-dynamic behavior of the semiconductor laser device. Due to their construction, TFWEs can be treated as a generalization of the Transfer Matrix Method (TMM) in two or three dimensions. Applying the TFWEs to the time-dynamic model, one can examine the behavior of the laser device in space and time even for large laser resonators occurring in Distributed Feedback lasers (DFB), disc lasers, and three-section lasers. In this paper, we present numerical results for a fully two-dimensional simulation of the DFB laser action.

The Transfer Matrix Method (TMM) is the standard method for simulating resonators with internal reflections occurring in Distributed Feedback (DFB) lasers and other laser types. A restriction of this method is that it cannot be applied to two dimensions or to time-dynamic simulations. We present a new Finite Element approach which can be treated as a generalization of the TMM in two or three dimensions. Furthermore, it can be used for time-dynamic problems as well as for large, tapered structures. We apply it to the time-dynamic simulation of the optical wave in DFB lasers and show numerical results.