Christoph Pflaum

• Friedrich-Alexander-University Erlangen-Nürnberg

Elliptic partial differential equations with variable coefficients can be discretized on sparse grids. With prewavelets being L ² ‐orthogonal, one can apply the Ritz‐Galerkin discretization to obtain a linear equation system with unknowns. However, for several applications like partial differential equations with corner singularities or the high‐di...

Based on commercial passenger-carrying airships like LZ129 or R100, a hypothetical electric rigid framed airship including a solar cell covered surface and a lithium-ion battery is designed. The size of the battery and the coverage with solar cells are selected such that long-haul flights are possible. To simulate flight times, weather data from 20...

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 p...

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 includi...

High-power laser beams are usually imaged with the help of suitable optics. The propagation of such beams, through optical systems, often result in a focus shift. This is mainly due to the deposited power in the beam acting as a heat source in the optical elements. Finally, the resulting change in temperature leads to both, a deformation of the len...

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 sig...

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.

Distorted Gaussian beams arise in several applications in optics. One of them is a laser amplifier. In a laser amplifier a Gaussian beam is distorted by thermal lensing effects, polarization effects and gain guiding. This leads to a decrease of the beam quality at the output of a laser amplifier. An important question is how to calculate this decre...

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...

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...

Solid‐state lasers are widely used for different industrial applications ranging from material processing to medical applications. For designing and optimization of a solid‐state laser an accurate simulation tool is need. Such a simulation tool has to be able to simulate different kind of physical effects like thermal effects, depolarization caused...

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-orth...

Sparse grids can be used to discretize elliptic differential equations of second order on a d-dimensional cube. Using the Ritz-Galerkin discretization, one obtains a linear equation system with (N (log N)d−1) unknowns. The corresponding discretization error is (N⁻¹ (log N)d−1) in the H¹-norm. A major difficulty in using this sparse grid discretizat...

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 absorp...

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 p...

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....

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 ult...

We present a Ritz-Galerkin discretization on sparse grids using pre-wavelets, which allows to solve elliptic differential equations with variable coefficients for dimension $d=2,3$ and higher dimensions $d>3$. The method applies multilinear finite elements. We introduce an efficient algorithm for matrix vector multiplication using a Ritz-Galerkin d...

We present a Ritz-Galerkin discretization on sparse grids using pre-wavelets, which allows to solve elliptic differential equations with variable coefficients for dimension $d=2,3$ and higher dimensions $d>3$. The method applies multilinear finite elements. We introduce an efficient algorithm for matrix vector multiplication using a Ritz-Galerkin d...

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+Op...

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...

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 mod...

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 sol...

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 finit...

The beam quality and output power of high power solid-state lasers is influenced by birefringence. Inhomogeneous distribution of the thermal field inside the laser crystal rod occurs due to non-uniform absorption of the pump light inside the crystal and a heat sink only at boundaries. Due to the photoelastic effect, this distribution leads to inhom...

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-e...

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.

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.

The joint project “Silicon-based thin-film solar cells on flexible metal substrates” (abbreviation: “SiSoFlex”) is funded as part of the Photovoltaics Innovation Alliance by the German Federal Ministry of Education and Research. The intended technical objectives of the project can be subdivided into various feasibility studies and into tests of new...

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 f...

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...

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...

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 configurat...

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. Simu...

We present an edge-pumped Yb:YAG /YAG trapezoid-shape thin disk laser with slanted faces of 30 degree. The crystal consist of a 0.2-mm-thick Yb:YAG crystal as a gain medium and a 1.3-mm-thick un-doped YAG crystal bonded on the gain medium . The crystal is pumped from four sides in such a way that pump light trapped inside the crystal after total re...

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 k...

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 gen...

The efficiency of thin film solar cells can be improved by various known and extensively studied light trapping techniques such as textured interfaces, nano-particles, and so on. But all these methods are not expected to improve the efficiency of the solar cells with by same amount. In this paper, textured interfaces and nano-particles are simulate...

The interaction between light and silver nanowires (Ag NWs) in a thin film is simulated by solving Maxwell's equations numerically. Time-harmonic inverse iterative method is implemented to overcome the problem of negative permittivity of silver, which makes the classical finite-difference time-domain iteration unstable. The method is validated by s...

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-d...

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 satu...

In this work, we present a novel edge-pumped Yb:YAG /YAG thin disk laser using a crystal with slanted faces which is pumped by four non-symmetric hollow ducts in order to obtain uniformity and homogeneity of the pump light distribution inside the crystal. Using the method of Reciprocity we determined an optimal Yb+3-concentration in order to improv...

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.

The difficulties of solving initial-value solid-state laser problems numerically arise from both stiffness of the problems and near-to-zero nonnegative exact solutions. Stability and non-negativity must be maintained simultaneously in the numerical solutions. Backward differentiation formulas (BDFs) is capable of dealing with stiff problems ,but is...

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 (...

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 freq...

The stability of solid-state lasers is influenced by the thermal lensing effect in the crystal. This effect is based on the deformation of the end faces of the crystal and the temperature dependence of the refraction index. It also depends on the photoelastic effect produced by thermal induced stress in the crystal. The analysis of the photoelastic...

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 ta...

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 o...

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 pro...

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 t...

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 t...

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 M...

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 i...

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 mo...

Trigonometric Finite Wave Elements (TFWE) are finite elements for solving problems in computational optics. The solution of those problems consist of highly oscillatory waves. TFWE are designed for obtaining optimal approximation properties for such kinds of waves with a changing wave number k. In this article, we study the convergence properties o...

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.

This paper will provide an insight into the design and software engineering aspects of a simulation software for time-harmonic electro-magnetic waves with application to the simulation of optical waves in lithography and thin-film solar cells. This design is oriented towards applicability to large systems, as it is driven by the computationally cha...

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 c...

A sophisticated light-management is indispensable for silicon thin-film silicon solar cells based on amorphous (a-Si:H) and microcrystalline ($mu$c-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 absorp...

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 al...

Expression Templates (ET) are a powerful tool for development of user-friendly numerical libraries. By this concept and by operator overloading in C++, numerical algorithms can be implemented in a mathematical notation without decreasing the performance in comparison to optimized C or FORTRAN codes. In this paper, we present new Expression Template...

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....

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 techni...

Dynamic Multimode Analysis investigates mode competition including thermal, spatial, and dynamic effects. However, the computational effort increases dramatically for super-gaussian beams in high-power lasers. We explain how this can be solved by precombining Gaussian modes.

To optimize the optical efficiency of silicon thin-film solar cells, the absorption and reflection of sunlight in these solar cells has to be simulated. Since the thickness of the layers of thin-film solar cells is of the size of the wavelength, a rigorous simulation by solving Maxwell’s equations is important. However, large geometries of the cell...

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.

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 Fi...

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 indivi...

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 solvin...

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...

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 3-D finite element analysis of the electric field without mode decomposition.

The conversion efficiency of thin-film silicon solar cells is significant affected by their nanostructure. The established methods to simulate thin-film solar cells are usually for perpendicular incident waves, only. However, real outdoor conditions often lead to oblique incident sunlight. Hence, the structure of the solar cell must be optimized, t...

The finite difference discretisation on staggered grids is a common technique to discretise Maxwell's equations and Stokes equations. The implementation of this discretisation on staggered grids is simplified and optimised by a new expression template concept. The MPI parallelisation is hidden in an underlying expression template library. The effic...

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...

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 t...