Lin Werner Zschiedrich

• Zuse Institute Berlin

We present a framework for the efficient and accurate computation of resonance modes in photonic waveguides. The framework is based on AAA rational approximation with the application of special light sources. It allows one to calculate only relevant modes, such as the fundamental resonance modes localized in the central core of the waveguides. We d...

Luminescent coupling is a characteristic of multi-junction solar cells which has often been neglected in models of their performance. The effect describes the absorption of light emitted from a higher band gap semiconductor by a lower band gap semiconductor. In this way, light which might have been lost can be utilized for current generation. We pr...

A theoretical framework for the rational approximation of optical response functions in resonant photonic systems is introduced. The framework is based on the AAA algorithm and further allows to solve the underlying nonlinear eigenproblems and to efficiently model sensitivities. An adaptive sampling strategy exploits the predominance of resonances...

Plasmonic antennas with helical geometry can convert linearly polarized dipole radiation into purely circularly polarized far-fields, and vice versa. Besides large Purcell enhancements, they possess a wide tunability due to the geometry dependence of their resonant modes. Here, the coupling of a dipole emitter embedded in a thin film to plasmonic s...

Accurate measurements of micro- and nanoscale features in optical microscopy demand comprehensive modelling approaches. In this study, we introduce an enhanced evaluation method, utilizing rigorous simulations based on a finite element method algorithm within an advanced Bayesian optimization framework. We provide an in-depth explanation of the mea...

Exceptional points are spectral degeneracies of non-Hermitian systems where both eigenfrequencies and eigenmodes coalesce. The eigenfrequency sensitivities near an exceptional point are significantly enhanced, whereby they diverge directly at the exceptional point. Capturing this enhanced sensitivity is crucial for the investigation and optimizatio...

We present a fabrication uncertainty aware and robust design optimization approach that can be used to obtain robust design estimates for nonlinear, nonconvex, and expensive model functions. It is founded on Gaussian processes and a Monte Carlo sampling procedure, and assumes knowledge about the uncertainties associated with a manufacturing process...

Resonance expansions are an intuitive approach to capture the interaction of an optical resonator with light. Here, we present a quasinormal mode expansion approach for quadratic observables exploiting the rigorous Riesz projection method. We demonstrate the approach by a numerical implementation of a state-of-the-art quantum light source and empha...

Dimensional microscopy is an essential tool for non-destructive and fast inspection of manufacturing processes. Standard approaches process only the measured images. By modelling the imaged structure and solving an inverse problem, the uncertainty on dimensional estimates can be reduced by orders of magnitude. At the same time, the inverse problem...

Resonances are omnipresent in physics and essential for the description of wave phenomena. We present an approach for computing eigenfrequency sensitivities of resonances. The theory is based on Riesz projections and the approach can be applied to compute partial derivatives of the complex eigenfrequencies of any resonance problem. Here, the method...

We present an approach for computing eigenfrequency sensitivities of resonances. The theory is based on Riesz projections for Maxwell's equations. Its numerical realization essentially relies on direct differentiation of scattering problems. We use a numerical implementation to demonstrate the performance of the approach compared to differentiation...

Quasinormal mode (QNM) expansion is a popular tool to analyze light-matter interaction in nanoresonators. However, expanding far-field quantities such as the energy flux is an open problem because QNMs diverge with an increasing distance to the resonant systems. We introduce a theory to compute modal expansions of far-field quantities rigorously. T...

We analyse possibilities to quantitatively evaluate the surface second-order optical nonlinearity in noncentrosymmetric materials based on polarization-resolved analysis of far-field radiation patterns of second-harmonic generation. We analytically demonstrate that for plane-wave illumination the contribution to the second-harmonic signal from the...

The cover image presents the first stand‐alone telecom quantum light source launching single photons directly into a single‐mode optical fiber. It includes a semiconductor quantum dot (QD) which is excited by an integrated laser and cooled by compact Stirling cooler at 40 K. The advanced quantum device includes all filter elements to suppress inten...

We propose an algorithm for general nonlinear eigenvalue problems to compute physically relevant eigenvalues within a chosen contour. Eigenvalue information is explored by contour integration incorporating different weight functions. The gathered information is processed by solving a nonlinear system of equations of small dimension prioritizing eig...

A user‐friendly, fiber‐coupled, single‐photon source operating at telecom wavelengths is a key component of photonic quantum networks providing long‐haul, ultra‐secure data exchange. To take full advantage of quantum‐mechanical data protection and to maximize the transmission rate and distance, a true quantum source providing single photons on dema...

Quasinormal mode (QNM) expansion is a popular tool to analyze light-matter interaction in nanoresonators. However, expanding far-field quantities such as the energy flux is an open problem because QNMs diverge with an increasing distance to the resonant systems. We introduce a theory to compute modal expansions of far-field quantities rigorously. T...

Photonic quantum technologies are based on the exchange of information via single photons. The information is typically encoded in the polarization of the photons and security is ensured intrinsically via principles of quantum mechanics such as the no-cloning theorem. Thus, all optical quantum communication networks rely crucially on the availabili...

We discuss an approach for modal expansion of optical far-field quantities based on quasinormal modes (QNMs). The issue of the exponential divergence of QNMs is circumvented by contour integration of the far-field quantities involving resonance poles with negative and positive imaginary parts. A numerical realization of the approach is demonstrated...

Many nanophotonic devices rely on the excitation of photonic resonances to enhance light-matter interaction. The understanding of the resonances is therefore of a key importance to facilitate the design of such devices. These resonances may be analyzed by use of the quasi-normal mode (QNM) theory. Here, we illustrate how QNM analysis may help study...

A user-friendly fibre-coupled single-photon source operating at telecom wavelengths is a key component of photonic quantum networks providing long-haul ultra-secure data exchange. To take full advantage of quantum-mechanical data protection and to maximize the transmission rate and distance, a true quantum source providing single-photons on demand...

Plasmonic devices with feature sizes of a few nanometers exhibit effects which can be described by the nonlocal hydrodynamic Drude model. We demonstrate how to exploit contour integral methods for computing eigenfrequencies and resonant states of such systems. We propose an approach for deriving the modal expansion of relevant physical observables....

We present an effective method for direct fiber coupling of a quantum dot (QD) that is deterministically incorporated into a cylindrical mesa. For precise positioning of the fiber with respect to the QD-mesa, we use a scanning procedure relying on interference of light reflected back from the fiber end-face and the top surface of the mesa, applicab...

Plasmonic devices with feature sizes of few nanometers exhibit effects which can be described by the nonlocal hydrodynamic Drude model. We demonstrate how to exploit contour integral methods for computing eigenfrequencies and resonant states of such systems. We propose an approach for deriving the modal expansion of relevant physical observables. W...

Strong coupling of plasmonic excitations and dipolar emitters, such as organic molecules, have been studied extensively in the last years. The questions whether strong coupling can be achieved with a single molecule only and how this is unambiguously proven are still under debate. A critical issue of plasmonic in contrast to photonic systems is add...

Optical resonators are widely used in modern photonics. Their spectral response and temporal dynamics are fundamentally driven by their natural resonances, the so-called quasinormal modes (QNMs), with complex frequencies. For optical resonators made of dispersive materials, the QNM computation requires solving a nonlinear eigenvalue problem. This r...

Optical scatterometry is a method to measure the size and shape of periodic micro- or nanostructures on surfaces. For this purpose the geometry parameters of the structures are obtained by reproducing experimental measurement results through numerical simulations. We compare the performance of Bayesian optimization to different local minimization a...

Optical scatterometry is a method to measure the size and shape of periodic micro- or nanostructures on surfaces. For this purpose the geometry parameters of the structures are obtained by reproducing experimental measurement results through numerical simulations. We compare the performance of Bayesian optimization to different local minimization a...

We report on an auxiliary field approach for solving nonlinear eigenvalue problems occurring in nano-optical systems with material dispersion. The material dispersion can be described by a rational function for the frequency-dependent permittivity, e.g., by a Drude-Lorentz model or a rational function fit to measured material data. The approach is...

Decomposing the field scattered by an object into vector spherical wave functions (VSWF) is a useful tool when discussing its optical properties on more analytical grounds. Thus far, it was frequently required in the decomposition that the scattered field is available on a spherical surface enclosing the scatterer. This requirement is adapted to th...

We propose an algorithm for general nonlinear eigenvalue problems to compute eigenvalues within a chosen contour and to compute the corresponding eigenvectors. Eigenvalue information is explored by contour integration incorporating different weight functions. The gathered information is processed by solving a nonlinear system of equations of small...

Optical resonators are widely used in modern photonics. Their spectral response and temporal dynamics are fundamentally driven by their natural resonances, the so-called quasinormal modes (QNMs), with complex frequencies. For optical resonators made of dispersive materials, the QNM computation requires solving a nonlinear eigenvalue problem. This r...

We introduce a theory to analyze the behavior of light emitters in nanostructured environments rigorously. Based on spectral theory, the approach opens the possibility to quantify precisely how an emitter decays to resonant states of the structure and how it couples to a background, also in the presence of general dispersive media. Quantification o...

Strong coupling of plasmonic excitations and dipolar emitters, such as organic molecules, have been studied extensively in the last years. The questions whether strong coupling can be achieved with a single molecule only and how this is unambiguously proven are still under debate. A critical issue of plasmonic in contrast to photonic systems is add...

Decomposing the field scattered by an object into vector spherical harmonics (VSH) is the prime task when discussing its optical properties on more analytical grounds. Thus far, it was frequently required in the decomposition that the scattered field is available on a spherical surface enclosing the scatterer; being with that adapted to the spatial...

The spontaneous emission rate of fluorescencent species in general is affected by its environment. Geometrical structure and material composition of the environment can yield strongly increased rates. This effect is known as Purcell effect, and the magnitude of enhancement of the emission rate in a cavity is known as Purcell factor. The Purcell fac...

We present a numerical method for the accurate and efficient simulation of strongly localized light sources, such as quantum dots, embedded in dielectric micro-optical structures. We apply the method in order to optimize the photon extraction efficiency of a single-photon emitter consisting of a quantum dot embedded into a multi-layer stack with fu...

We present a numerical method for the accurate and efficient simulation of strongly localized light sources, such as quantum dots, embedded in dielectric micro-optical structures. We apply the method in order to optimize the photon extraction efficiency of a single-photon emitter consisting of a quantum dot embedded into a multi-layer stack with fu...

We introduce a theory to analyze the behavior of light emitters in nanostructured environments rigorously. Based on spectral theory, the approach opens the possibility to quantify precisely how an emitter decays to resonant states of the structure and how it couples to a background, also in the presence of general dispersive media. Quantification o...

We present a Newton-like method to solve inverse problems and to quantify parameter uncertainties. We apply the method to parameter reconstruction in optical scatterometry, where we take into account a priori information and measurement uncertainties using a Bayesian approach. Further, we discuss the influence of numerical accuracy on the reconstru...

An efficient numerical method for computing angle-resolved light scattering off periodic arrays is presented. The method combines finite-element discretization with a Schur complement solver. A significant speed-up of the computations in comparison to standard finite-element method computations is observed.

An efficient numerical method for computing angle-resolved light scattering off periodic arrays is presented. The method combines finite-element discretization with a Schur complement solver. A significant speed-up of the computations in comparison to standard finite-element method computations is observed.

The finite-element method is a preferred numerical method when electromagnetic fields at high accuracy are to be computed in nano-optics design. Here, we demonstrate a finite-element method using hp-adaptivity on tetrahedral meshes for computation of electromagnetic fields in a device with rough textures. The method allows for efficient computation...

The finite-element method is a preferred numerical method when electromagnetic fields at high accuracy are to be computed in nano-optics design. Here, we demonstrate a finite-element method using hp-adaptivity on tetrahedral meshes for computation of electromagnetic fields in a device with rough textures. The method allows for efficient computation...

Rigorous optical simulations of 3-dimensional nano-photonic structures are an important tool in the analysis and optimization of scattering properties of nano-photonic devices or parameter reconstruction. To construct geometrically accurate models of complex structured nano-photonic devices the finite element method (FEM) is ideally suited due to i...

Methods for solving Maxwell's equations are integral part of optical metrology and computational lithography setups. Applications require accurate geometrical resolution, high numerical accuracy and/or low computation times. We present a finite-element based electromagnetic field solver relying on unstructured 3D meshes and adaptive hp-refinement....

Nonlocal hydrodynamic Drude model overcomes the limitations of the conventional Drude model in describing light-matter interactions in nanoplasmonic structures. Here we present a weak formulation based rigorous numerical method for it, which avoids spurious resonances as in the case of the curl-free approximation setting. The simulated results agre...

In many experimentally realized applications, e.g. photonic crystals, solar cells and light-emitting diodes, nanophotonic systems are coupled to a thick substrate layer, which in certain cases has to be included as a part of the optical system. The finite element method (FEM) yields rigorous, high accuracy solutions of full 3D vectorial Maxwell's e...

We use a finite-element method to obtain highly converged results for a nano-optical light scattering setup with a non-periodic geometry.

An overview on recent applications of the finite-element method Maxwell-solver JCMsuite to simulation tasks in nanooptics is given. Numerical achievements in the fields of optical metamaterials, plasmonics, photonic crystal fibers, light emitting devices, solar cells, optical lithography, optical metrology, integrated optics, and photonic crystals...

A method for automatic computation of parameter derivatives of numerically computed light scattering signals is demonstrated. The finite-element based method is validated in a numerical convergence study, and it is applied to investigate the sensitivity of a scatterometric setup with respect to geometrical parameters of the scattering target. The m...

Nanostructures, like periodic arrays of scatters or low-index gratings, are used to improve the light outcoupling from organic light-emitting diodes (OLED). In order to optimize geometrical and material properties of such structures, simulations of the outcoupling process are very helpful. The finite element method is best suited for an accurate di...

Of keen interest to the IC industry are advanced computational lithography applications such as Optical Proximity Correction, OPC, Optical Proximity Effect matching, OPEM, and Source-Mask Optimization, SMO. Lithographic mask models used by these simulators and their interactions with scanner illuminator models are key drivers impacting the accuracy...

We present simulation results on light extraction from nanostructured light-emitting devices and demonstrate convergence of the methods to high levels of numerical accuracy.

Photolithography simulations are widely used to predict, to analyze and to design imaging processes in scanners used for IC manufacture. The success of these efforts is strongly dependent on their ability to accurately capture the key drivers responsible for the image formation. Much effort has been devoted to understanding the impacts of illuminat...

Numerical simulations are an important tool for the design of opto-electronical components and devices. In order to obtain realistic results, a multitude of physical effects and theories have to be included, e.g., Maxwell's equations for lasing mode computations, heat transfer in active devices, and electronic transport. In our contribution we perf...

Nonlocal material response distinctively changes the optical properties of nano-plasmonic scatterers and waveguides. It is described by the nonlocal hydrodynamic Drude model, which -- in frequency domain -- is given by a coupled system of equations for the electric field and an additional polarization current of the electron gas modeled analogous t...

An important ingredient of VCSEL device simulation is the solution of the optical model. Challenges are the multiscale structure of realistic devices with thin layers in the Bragg mirror and active zone on the one hand and large total resonator volumes on the other hand. In order to compute the resonating modes and frequencies, Maxwell eigenvalue p...

EUV scatterometry is performed on 3D patterns on EUV lithography masks. Numerical simulations of the experimental setup are performed using a rigorous Maxwell solver. Mask geometry is determined by minimizing the difference between experimental results and numerical results for varied geometrical input parameters for the simulations.

For maximum fiber-coupled power, broad-area (BA) diode lasers must operate with small lateral far field angles. However, these structures are laterally multi-moded, with low beam quality and wide emission angles. We use a combination of device simulation and diagnostic measurements to determine the physical factors limiting the lateral far field an...

Simulations of light scattering off an extreme ultraviolet lithography mask with a 2D-periodic absorber pattern are presented. In a detailed convergence study it is shown that accurate results can be attained for relatively large 3D computational domains and in the presence of sidewall-angles and corner-roundings.

Optical metrology by scatterometry usually bases on the comparison of experimental and modeled light field data. When solving inverse scatterometric problems, often not only a single simulation has to be carried out, but multiple electromagnetic field solutions have to be computed for varying material and geometrical parameters of the system under...

Finite element methods (FEM) for the rigorous electromagnetic solution of Maxwell's equations are known to be very accurate. They possess a high convergence rate for the determination of near field and far field quantities of scattering and diffraction processes of light with structures having feature sizes in the range of the light wavelength. We...

High-Q optical resonances in photonic microcavities are investigated numerically using a time-harmonic finite-element method.

We apply a hybrid finite element / transfer matrix solver to calculate generation rate spectra of thin film silicon solar cells with textured interfaces. Our focus lies on interfaces with statistical rough textures. Due to limited computational domain size the treatment of such textures requires a Monte Carlo sampling of texture representations to...

We present algorithmic details and applications of the reduced basis method as efficient Maxwell solver to nanophotonic applications including examples from mask optimization in photolithography and parameter retrieval in inverse problems, e.g., in optical metrology. The reduced basis method is a currently studied approach to the multiple solution...

A continuously twisted PCF can be viewed as a one-dimensional metamaterial in which both ϵ and μ tensors develop off-diagonal elements. Finite-element calculations confirm the appearance of unique loss peaks in the experimental transmission spectrum.

Image modeling and simulation are critical to extending the limits of leading edge lithography technologies used for IC making. Simultaneous source mask optimization (SMO) has become an important objective in the field of computational lithography. SMO is considered essential to extending immersion lithography beyond the 45nm node. However, SMO is...

A bottleneck for computational lithography and optical metrology are long computational times for near field simulations. For design, optimization, and inverse scatterometry usually the same basic layout has to be simulated multiple times for different values of geometrical parameters. The reduced basis method allows to split up the solution proces...

Optical properties of cavities for plasmon lasers are investigated numerically. We use a time-harmonic finite-element package including a propagation-mode solver, a resonance-mode solver and a scattering solver for studying resonance wavelength and quality factor and for a transmission analysis.

Within this paper, we consider scattering problems with periodic exterior domains, modeled by the Helmholtz equation. Most current works on this subject make specific assumptions on the geometry of the periodic cell, e.g., special symmetries or shapes, and cannot be generalized to higher space dimensions in an easy way. In contrast our goal is the...

Optical properties of hybrid plasmonic waveguides and of low-Q cavities, formed by waveguides of finite length are investigated numerically. These structures are of interest as building-blocks of plasmon lasers. We use a time-harmonic finite-element package including a propagation-mode solver, a resonance-mode solver and a scattering solver for stu...

Optical resonances in 1D photonic crystal microcavities are investigated numerically using finite-element light scattering and eigenmode solvers. The results are validated by comparison to experimental and theoretical findings from the literature. The influence of nanometer-scale geometry variations on the resonator performance is studied. Limiting...

Optical properties of circular grating resonators in a silicon-on-insulator system are investigated numerically. These structures are of interest as building-blocks of integrated photonic devices. We use a time-harmonic 3D finite-element solver for studying transmission of waveguide modes through the system. We compare numerical results to experime...

We present an adaptive, error controlled reduced basis method for solving parameterized optical scattering problems. We present a 3-D optimization application from optical proximity correction (OPC) with extremely short online computation times.

Optical resonances in 1-D photonic crystal microcavities are investigated numerically using 3-D finite-element solvers. The results are compared to experimental results from the literature and validated by comparison to theoretical findings from the literature.

Optical resonances in microcavities are investigated numerically. A time-harmonic finite-element solver is used for simulating the effect of small geometry variations like sidewall-angles and feature placement on a nanometer scale.

Light transmission through a 2D-periodic array of small rectangular apertures in a film of highly conductive material is simulated using a finite-element method. It is demonstrated that well converged results are obtained using higher-order finite-elements. The influence of the array periodicity and of corner roundings on transmission properties is...

We have developed an interface which allows to perform rigorous electromagnetic field (EMF) simulations with the simulator JCMsuite and subsequent aerial imaging and resist simulations with the simulator Dr.LiTHO. With the combined tools we investigate the convergence of near-field and far-field results for different DUV masks. We also benchmark re...

Light transmission through circular subwavelength apertures in metallic films with surrounding nanostructures is investigated numerically. Numerical results are obtained with a frequency-domain finite-element method. Convergence of the obtained observables to very low levels of numerical error is demonstrated. Very good agreement to experimental re...

We use the finite-element method for simulating light transmission through a 2D-periodic array of rectangular apertures in a film of highly conductive material. We report results with a relative error of the transmissivity lower than 0.01%. This is an improvement of about one order of magnitude compared to previously reported results. Further, the...

This paper presents a new numerical method for the solution of exterior Helmholtz scattering problems, which is applicable to inhomogeneous exterior domains and a wide class of geometries. The algorithm is based on the pole condition, which is a general radiation condition and allows a treatment of exterior Helmholtz problems without an explicit kn...

A new approach to derive transparent boundary conditions (TBCs) for dispersive wave, Schrödinger, heat, and drift-diffusion equations is presented. It relies on the pole condition and distinguishes between physically reasonable and unreasonable solutions by the location of the singularities of the Laplace transform of the exterior solution. Here th...

Rigorous electromagnetic field simulations are an essential part for scatterometry and mask pattern design. Today mainly periodic structures are considered in simulations. Non-periodic structures are typically modeled by large, artificially periodified computational domains. For systems with a large radius of influence this leads to very large comp...

Rigorous computer simulations of propagating electromagnetic fields have become an important tool for optical metrology and design of nanostructured optical components. A vectorial finite element method (FEM) is a good choice for an accurate modeling of complicated geometrical features. However, from a numerical point of view solving the arising sy...

IntroductionFormulation of Propagation Mode ProblemDiscretization of Maxwell's Equations with the Finite Element Method Computation of Leaky Modes in Hollow Core Photonic Crystal FibersGoal Oriented Error EstimatorConvergence of Eigenvalues Using Different Error EstimatorsOptimization of HCPCF DesignKagome-Structured FibersConclusion References

We discuss realization, properties and performance of the adaptive finite element approach to the design of optical waveguides. Central issues like the construction of higher-order vectorial finite elements, local error estimation, automatic and adaptive grid refinement, transparent boundary conditions and fast linear system solution by domain deco...