Search

High-power optical systems are used in a number of industrial applications. One difficulty in designing such systems is that the beam itself is a significant source of heat, which changes the optical properties of the system. To reduce this effect, we propose a new thermal lensing compensation technique based on a detailed analysis of the optical properties of the high-power optical system. To this end, we have developed a new ray tracing simulation technique that accurately models optical propagation through inhomogeneous, anisotropic, and deformed media. This model enables the performance of systems in physically realistic situations to be evaluated efficiently. Experimental comparisons were conducted to validate the simulation. We found excellent agreement between the simulation and the measured data. We have validated the simulation technique for a single lens setup and a complex optical scanner system.

Far field calculations of beams, such as laser beams, are often applied in optical engineering. Current beam propagation methods fail in certain range parameters due to high storage requirements of the algorithms. This paper presents a new beam propagation method for far field calculations of distorted Gaussian beams in a homogeneous medium including optical elements, such as lenses. The method works even in the case of a large distance from the observation plane to the beam waist and can be applied to larger divergence angles. This new simulation technique factors out the phase of the Gaussian TEM00 beam and solves the resulting partial differential equation by suitable finite difference or finite element discretization methods.

A framework for simulation and compensation of thermal lensing in general optical systems is presented. In high-power optical systems, the beam itself can serve as a non-neglectable heat source, altering the properties of the optical system. For estimating the influence on the optical system, a ray tracing algorithm is used and coupled with a finite element framework. Ray tracing is used to model the optical beam and evaluate the properties of the system. The finite element framework is used to solve the heat and the linear elasticity equation. From the solution of the heat equation, the inhomogeneous refractive index distribution is obtained. Refractive index gradients make it necessary to solve the ray equation iteratively on the finite element mesh. Additionally, the linear elasticity equation results in a displacement vector, which gives the deformation of the optical elements. To solve the ray equation and consider the surface deformation, efficient continuous data interpolation on the finite element mesh is crucial, as the interpolation is a limiting factor for the overall computational performance. This could be achieved by using direct interpolation on the finite element mesh, which reduces memory requirement while improving the interpolation accuracy. With the help of this simulation framework, optical setups which completely compensate for thermal lensing could be found. This could be achieved by a combination of optical materials with positive and negative temperature coefficients and suitable coating parameters, such that the overall thermal lens, resulting form deformation and temperature gradients, is completely compensated. This is a highly coupled problem, as the optical beam, the thermal gradients, and the material deformation affect each other. Hence an iterative simulation setup is necessary, which simulates the optical system until a stable state is found.

We present a numerical simulation technique for short laser pulse amplification in solid-state crystals. It takes into account the full spatial pumping profile by solving the 3-dimensional photon transport and allows to calculate pulse energy accurately.

We present a Ritz-Galerkin discretization on sparse grids using prewavelets, which allows us to solve elliptic differential equations with variable coefficients for dimensions d ≥ 2. The method applies multilinear finite elements. We introduce an efficient algorithm for matrix vector multiplication using a Ritz-Galerkin discretization and semi-orthogonality. This algorithm is based on standard 1-dimensional restrictions and prolongations, a simple prewavelet stencil, and the classical operator-dependent stencil for multilinear finite elements. Numerical simulation results are presented for a three-dimensional problem on a curvilinear bounded domain and for a six-dimensional problem with variable coefficients. Simulation results show a convergence of the discretization according to the approximation properties of the finite element space. The condition number of the stiffness matrix can be bounded below 10 using a standard diagonal preconditioner.

International audience; Discrete geometric method (DGM) is implemented for solving Maxwell's equations on plasmonic structures. Surface plasmons introduce non-derivable field components at the metallic/dielectric interface that can influence the accuracy of DGM. An analysis shows that the proper setting of material parameters at the interface can increase the accuracy of numerical solutions. Numerical examples with a structured mesh and an unstructured mesh provide further evidence for the fact that a proper interface treatment is important to obtain accurate results with relatively less degrees of freedom for the simulation of plasmonic effects with DGM. Coupling with its flexibility and explicit formulation, DGM can be used as an accurate and fast solver for problems involving complex plasmonic structures.

A new ray tracing method for the propagation of electrical fields in inhomogeneous and weakly anisotropic media is presented. With this method, we can efficiently simulate the propagation of laser beams in solid-state laser amplifiers, which suffer from high thermal loads. As a result of this method, we can find optical compensation setups that significantly reduce the depolarization losses in high-power solid-state amplifiers. To the best of our knowledge, we theoretically demonstrate for the first time that [100]-cut YAG crystals reduce the depolarization by more than a magnitude in comparison to [111]-cut crystals while achieving an overall better beam quality at the same time.

A ray tracing model for thermal effects solid-state single-pass amplifiers is presented, which is able to simulate thermal lensing, depolarization and beam quality degradation. The ray tracing algorithm is based on alternatively evaluating the axial and radial gradient and thereby finding the trajectory in thermally influenced media. This enables to find the focal length distribution of the system. Additionally, to the position of the rays, its phase is also determined, which enables to reconstruct the wavefront of the beam after passing through the crystal. This wavefront is used for a Zernike polynomial analysis to determine spherical aberration, which is linked to the beam quality of the passing beam. Furthermode the total depolarization is obtained by finding the change of polarization for each ray separately. The simulation for thermal lensing is compared with a single-pass Nd:YVO4 system, the beam degradation is compared with a Nd:YVO4-MOAP system. Both show good agreement with the simulation data, as long as the gain of the system is homogeneous.

Optical simulations are a crucial part in designing and understanding new solar cell devices to help with the transition to more environmentally friendly energy generation. We present a multicore wavefront diamond blocking scheme with multi-dimensional cache block sharing for our hybrid-parallel (MPI+OpenMP) optical solar cell simulation code utilizing the Time Harmonic Inverse Iteration Method (THIIM) to discretize Maxwell’s equations. This approach allows to decouple the code from the main memory bandwidth bottleneck and achieves a single node speed-up of up to three compared to an optimal implementation with pure spatial blocking and a multi node speed-up of up to two even with large numbers of compute nodes.

This work demonstrates a new simulation technique, which combines the previously published Dynamic Mode Analysis with the coupling of arbitrary sets of rate equations. Those arbitrary sets include the representation of gain media, which state population is influenced by interionic mechanisms. Especially the state population of Er:YAG is strongly influenced by upconversion and cross relaxation, which impacts the population inversion and the generated heat load. Therefore, the simulation of a resonator based on 50%-doped Er:YAG is performed and compared to experimental results. The accuracy of the presented technique is pointed out by a fine agreement between simulation and experiment with respect to gained cw output power and slope efficiency. Moreover, a finite element analysis of the heat load and the 3-dimensional population inversion in the crystal is illustrated.

The numerical simulation of a regenerative amplifier based on codoped Tm,Ho:YAG is presented. Within this work, a maximum pulse energy of 3.1 mJ is observed for 0.9 kW CW end-pumping at 785 nm. The simulation results demonstrate that interionic mechanisms such as upconversion and energy transfer significantly influence the population of states and consequently, the amplification. In detail, the most dominant mechanisms are identified by introducing the rate term kxNiNm as a quantity to compare the strength of all occuring interionic mechanisms. It can then be shown that the energy transfer mechanism E6512 between Holmium and Thulium ions is the greatest source of population loss for the upper lasing state 5 I7 in Holmium. In summary, the presented model represents an efficient tool to characterize the influence of interionic mechanisms on the extractable energy in solid-state media under pulsed operation.

Building integrated semitransparent thin-film solar cells is a strategy for future eco-friendly power generation. Organic photovoltaics in combination with dielectric mirrors (DMs) are a potential candidate as they promise high efficiencies in parallel to the possibility to adjust the color and thus the transparency of the whole device. A fully solution processed and printable DM with an easily adjustable reflection maximum is presented that can be facilely attached to solar cells. The DM is optimized via optical simulations to the particular needs of the device with regard to photocurrent enhancement. The excellent agreement between experimental and theoretical results confirms the high optical quality of the printed layers with respect to homogeneity and surface roughness. The used inks are organic–inorganic nanocomposites with a large refractive index contrast of ≈0.7. The short-circuit current is enhanced by up to ≈24% for a semitransparent polymer solar cell.

We present a simulation tool to model performance of a bulk solid state laser and propose several ways how this tool can be used to enhance educational experience of the student studying laser technology. In one of the possible approaches, the ASLD software can complement available educational laser kits to provide the students with more universal practical training. In the second approach, which is the primary focus of this contribution, the ASLD software can be used as a development tool that allows students to verify their understanding of the subject as well as to propose and verify their own design ideas. The software can be extremely helpful if an experimantal setup has to be built from already present optical components in order to reduce the cost of training or if specific design objectives have to be attained.

This paper demonstrates a one dimensional numerical model for single-pass solid state laser amplifiers. It is shown that after amplification the temporal shape of individual pulses within a pulse train can significantly vary, which results in an unstable interpulse spacing and a non reliable temporal pulse stability. Moreover possible adjustments of the pump pulse duration are pointed out in order to secure a stable temporal intensity output of the seed pulse train. In detail, the model is based on a non-linear time-dependent photon transport equations combined with a four level rate equations system and a pulsed end-pumping configuration.

Q-switching is considered as a favorable technology to generate short duration and high peak power pulses, which is widely used in industry. We derive a new model to simulate passively Q-switched solid state lasers in a three-dimensional (3D) space. In our model, several Gaussian modes are considered. Compared with single-mode models, 3D multimode models are much more capable of reflecting laser behaviors. In our modeling, the single-mode system is extended to a multimode system, which calculates photon numbers for different modes separately. In order to realize the numerical simulation of our multimode model, we apply a finite volume discretization respectively to the gain medium and saturable absorber, then the discretized multimode passively Q-switched laser system is obtained. The numerical results and applications of our model are shown at the end of the paper. The modeling and simulation of passively Q-switched solid state lasers can help to optimize laser designs.

Laser crystals like Nd:YAG are widely used in laser resonators. The stress-induced birefringence of such laser crystals has a strong influence on beam quality, power, and polarization of the output laser beam. Detailed simulations using 3-D finite-element analysis and a 2-D Jones matrix analysis were performed to analyze these effects. The finite-element analysis is used to calculate stress and birefringence depending on the cut direction of the crystal and its rotation. Eigenvalues and eigenvectors of the electromagnetic field inside the resonators are calculated by Jones matrix analysis. The analysis includes resonators with Brewster plates. Output power and beam quality are calculated by dynamic multimode analysis. Simulation results are presented for [100]-cut, [110]-cut, and [111]-cut Nd:YAG crystals.

Simulation and experimental improvement of a pulsed Cr,Tm,Ho:YAG (CTH:YAG) laser is presented. In order to simulate the CTH-Laser a generalized version of the Dynamic Mode Analysis (gDMA) is introduced, which includes an abstract formalism to describe arbitrary rate equations. This novel version of DMA enables the coupling between individual modes of the resonator and the complex excitation dynamics of the CTH state system. With the proposed method gDMA a full 3D simulation was conducted and the beam quality of the generated pulses could be calculated for various crystal diameters. Based upon the simulation results the crystal diameter was decreased in experiment. This reduction led to an improvement of M2 from 36 to 27, which is in good agreement with the experimental results. Additionally, the pulse energy depending on the pump power exhibits a close agreement with the experimental measurements. Moreover, the strength of each interionic mechanism in Cr,Tm,Ho:YAG is analyzed and the back transfer from Holmium to Thulium is identified to be the most dominant loss source for stimulated emission at 2090 nm. All in all, the presented extension of DMA represents an accurate and efficient method to simulate the amplification of higher order modes in gain media with strong interionic mechanisms.

Within this work, the numerical solution of the photon transport equation for pulse amplification is presented. Several discretization schemes are introduced that enable the calculation of the coupling between the transport equation and population inversion. It is demonstrated that the presented discretization schemes are convergent with respect to the analytic Frantz–Nodvik solution. Specifically, the application of a prediction-correction approach based on Heun’s method leads to an improvement in accuracy compared to the pure explicit approach. Finally, novel discretization schemes are applied to simulate different regenerative amplifiers based on Ti:Sapphire and Ho:YAG. Moreover, bifurcation of the Ho:YAG system is analyzed, which results in the determination of stable operating regimes for pulsed amplification.

Understanding and optimizing the properties of solar cells is becoming a key issue in the search for alternatives to nuclear and fossil energy sources. A theoretical analysis via numerical simulations involves solving Maxwell's Equations in discretized form and typically requires substantial computing effort. We start from a hybrid-parallel (MPI+OpenMP) production code that implements the Time Harmonic Inverse Iteration Method (THIIM) with Finite-Difference Frequency Domain (FDFD) discretization. Although this algorithm has the characteristics of a strongly bandwidth-bound stencil update scheme, it is significantly different from the popular stencil types that have been exhaustively studied in the high performance computing literature to date. We apply a recently developed stencil optimization technique, multicore wavefront diamond tiling with multi-dimensional cache block sharing, and describe in detail the peculiarities that need to be considered due to the special stencil structure. Concurrency in updating the components of the electric and magnetic fields provides an additional level of parallelism. The dependence of the cache size requirement of the optimized code on the blocking parameters is modeled accurately, and an auto-tuner searches for optimal configurations in the remaining parameter space. We were able to completely decouple the execution from the memory bandwidth bottleneck, accelerating the implementation by a factor of three to four compared to an optimal implementation with pure spatial blocking on an 18-core Intel Haswell CPU.

Ultra-short pulses with high average power are required for a variety of technical and medical applications. Single, multi-pass, and regenerative amplifiers are used, in order to increase the power of ultra-short lasers. Typical laser crystals for such amplifiers include Ti:Sapphire or Yb:YAG laser crystals. Difficulties in the amplification of ultra-short pulses include gain narrowing effects and dispersion effects in the laser crystal. In particular, these complications arise, when a pulse stretcher is needed before amplification of the laser beam. We present a technique to model and simulate the amplification of ultra-short pulses. This technique allows to model both gain narrowing effects and decrease of beam quality caused by amplification of the laser beam. This requires a detailed 3-dimensional simulation of population inversion. Gain narrowing effects are taken into account by analyzing the gain of the spectrum of the laser beam. It is important to distinguish amplifiers with one or only two passes and a regenerative amplifier. These two different kind of amplifiers are modeled by different approaches. A regenerative amplifier is modeled by a set of time dependent rate equations. However, a single pass amplifier is modeled by a set of spatial dependent rate equations. In both cases, a system of rate equations arises from spectral discretization of the laser beam. Detailed simulation results are presented.

A stable iterative solver for the simulation of optical waves in metals using finite difference frequency domain (FDFD) method is presented. The corresponding discretization of Maxwell's equations enables simulating electromagnetic waves in structures when materials with negative permittivity are involved. Convergence of the iterative solver is proved for positive and negative permittivities. Numerical results are presented for a thin-film silicon solar cell structure containing silver back contact.

In this work we describe the design of our simulation tool for solid state lasers. The software is based on modules to simplify several complex processes. Primarily, the adaptation of laser physics (e.g. thermal lensing, optical wave) with the appropriate simulation technique. Another aspect is to provide the possibility of exchanging the applied calculation methods or even to change the representation of the computational domain on demand.

We present a comprehensive simulation model for high-power 3-level lasers based on a “Dynamic Multimode Analysis” (DMA) [1]. DMA has proven to be a powerful tool to analyze mode competition depending on thermal, spatial, and dynamic effects in the laser resonator and to predict power output, beam quality, and pulse profile for 4-level lasers with M2