arXiv subjects

Felix Binkowski

Publications and source records attributed to Felix Binkowski.

At least 19 recordsLinked to original sources

arXiv2026

AAA rational approximation for scatterometry of nanoscale gratings

We investigate the applicability of AAA rational approximation to scatterometry-related response functions of nanoscale gratings. A silicon line grating with material dispersion is considered. We compare the convergence of AAA rational approximation with that of cubic spline interpolation as the number of frequency samples is increased. The results demonstrate the potential of rational approximation, consistent with the pole structure of the considered response function arising from resonance effects of the grating.

physics.optics↗

arXiv2026

Design of monolithic microcavities for enhancing organic quantum emitters

Single organic molecules are a well-established platform for high-quality single-photon generation: they can emit lifetime-limited photons with high purity and indistinguishability. However, their emission is accompanied by a pronounced red-shifted phonon sideband and higher-order vibrational peaks, which reduce the fraction of photons emitted into the desired narrowband zero-phonon line. The standard approach to suppressing this unwanted emission is to integrate the emitter into a monolithic photonic nanostructure that provides Purcell enhancement. However, incorporating organic materials using clean-room techniques has proven challenging, and has in fact so far prevented their integration into monolithic microcavities altogether. As a result, efficient, narrowband organic single-photon sources for applications in quantum information processing have remained elusive despite their considerable promise. Here, we propose three monolithic microcavity designs tailored to provide sufficient Purcell enhancement for organic quantum emitters. The Purcell effect induced by these cavities preferentially enhances emission into the 0-0 zero-phonon line, increasing spectral purity, photon extraction, and shortening the excited-state lifetime, which in turn relaxes the requirements for generating indistinguishable photons. The cavities have been optimized using Bayesian optimization and the adaptive Antoulas-Anderson (AAA) algorithm for rational approximation, which offer global optimization and the efficient reconstruction of spectra from scattering simulations, respectively. These structures are compatible with both standard clean-room processing and single-molecule preparation techniques. Therefore, they offer a clear route to realize high-quality, practically monochromatic organic single-photon light sources.

quant-ph↗

arXiv2026

Pole-Expansion of the T-Matrix Based on a Matrix-Valued AAA-Algorithm

The transition matrix (T-matrix) is a complete description of an object's linear scattering response. As such, it has found wide adoption for the theoretical and computational description of multiple-scattering phenomena. In its original form, the T-matrix describes the interaction of a scatterer with a monochromatic source. In practice, however, information about the T-matrix is usually needed in an extended spectral domain. To access the frequency-dispersion, one might naively sample T-matrices over a finely resolved set of discrete frequencies and store one T-matrix per frequency. This approach has multiple drawbacks: it is computationally expensive, requires excessive memory, and it disregards the physical origin of the spectral features, weakening physical interpretability. To overcome these major limitations, we leverage a pole-expansion technique to represent the T-matrix with arbitrary frequency resolution within a selected frequency domain via a set of resonant contributions. A matrix-valued variant of the recently established adaptive Antoulas-Anderson (AAA) algorithm for rational approximation enables us to compute the pole-expansion at minimal computational cost using only a small number of direct evaluations. We demonstrate the benefits of such a representation with examples ranging from semi-analytically accessible scatterers to quasi-dual bound states in the continuum. To allow the wider community to capitalize on these findings, we provide open-source tools to perform the presented pole-expansion of the T-matrix.

physics.optics↗

arXiv2025

High Purcell enhancement in all-TMDC nanobeam resonator designs with active monolayers for nanolasers

We propose a nanobeam resonator incorporating an active monolayer, designed to achieve a high Purcell enhancement. The resonator is fully composed of transition-metal-dichalcogenide materials and intended to operate as a high-beta-factor nanolaser. A theoretical framework that models and optimizes the Purcell enhancement associated with the emission from atomically thin layers is developed. This framework is based on a resonance expansion, enabling spectral resolution of physical quantities governed by high-Q resonances. The numerical optimization of the resonator leads to the presence of a high-Q resonance supporting a strong electric field confinement in the monolayer to maximize the modal gain.

physics.optics↗

arXiv2025

Uncovering hidden resonances in non-Hermitian systems with scattering thresholds

The points where diffraction orders emerge or vanish in the propagating spectrum of periodic non-Hermitian systems are referred to as scattering thresholds. Close to these branch points, resonances from different Riemann sheets can tremendously impact the optical response. However, these resonances are so far elusive for two reasons. First, their contribution to the signal is partially obscured, and second, they are inaccessible for standard computational methods. Here, the interplay of scattering thresholds with resonances is explored and a multi-valued rational approximation is introduced to access the hidden resonances. The theoretical and numerical approach is used to analyze the resonances of a plasmonic line grating. This work elegantly explains the occurrence of pronounced spectral features at scattering thresholds applicable to many nanophotonic systems of contemporary and future interest.

physics.optics↗

arXiv2024

Resonance modes in microstructured photonic waveguides: Efficient and accurate computation based on AAA rational approximation

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 demonstrate the framework using an example from the literature, a hollow-core photonic crystal fiber. This waveguide supports many other modes, such as cladding modes and higher-order modes. These nonrelevant modes are not calculated, so that challenging post-processing with mode filtering is not required.

physics.comp-ph↗

arXiv2024

A framework to compute resonances arising from multiple scattering

Numerous natural and technological phenomena are governed by resonances. In nanophotonics, resonances often result from the interaction of several optical elements. Controlling these resonances is an excellent opportunity to provide light with properties on demand for applications ranging from sensing to quantum technologies. The inverse design of large, distributed resonators, however, is typically challenged by high computational costs when discretizing the entire system in space. Here, this limitation is overcome by harnessing prior knowledge about the individual scatterers that form the resonator and their interaction. In particular, a transition matrix multi-scattering framework is coupled with the state-of-the-art adaptive Antoulas-Anderson (AAA) algorithm to identify complex poles of the optical response function. A sample refinement strategy suitable for accurately locating a large number of poles is introduced. We tie the AAA algorithm into an automatic differentiation framework to efficiently differentiate multi-scattering resonance calculations. The resulting resonance solver allows for efficient gradient-based optimization, demonstrated here by the inverse design of an integrated exciton-polariton cavity. This contribution serves as an important step towards efficient resonance calculations in a variety of multi-scattering scenarios, such as inclusions in stratified media, periodic lattices, and scatterers with arbitrary shapes.

physics.comp-ph↗

arXiv2024

Efficient rational approximation of optical response functions with the AAA algorithm

We introduce a theoretical framework for the rational approximation of optical response functions in resonant photonic systems. 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 in the physical response. We investigate a chiral metasurface and show that the chiroptical response on parameter variations can be accurately modeled in the vicinity of the relevant resonance frequencies.

physics.optics↗

arXiv2024

Computing eigenfrequency sensitivities near exceptional points

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 optimization of exceptional-point-based applications, such as optical sensors. We present a numerical framework, based on contour integration and algorithmic differentiation, to accurately and efficiently compute eigenfrequency sensitivities near exceptional points. We demonstrate the framework to an optical microdisk cavity and derive a semi-analytical solution to validate the numerical results. The computed eigenfrequency sensitivities are used to track the exceptional point along an exceptional surface in the parameter space. The presented framework can be applied to any kind of resonance problem, e.g., with arbitrary geometry or with exceptional points of arbitrary order.

physics.comp-ph↗

arXiv2024

Fabrication uncertainty guided design optimization of a photonic crystal cavity by using Gaussian processes

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. The approach itself is iterative. First, a large parameter domain is sampled in a coarse fashion. This coarse sampling is used primarily to determine smaller candidate regions to investigate in a second, more refined sampling pass. This finer step is used to obtain an estimate of the expected performance of the found design parameter under the assumed manufacturing uncertainties. We apply the presented approach to the robust optimization of the Purcell enhancement of a photonic crystal nanobeam cavity. We obtain a predicted robust Purcell enhancement of $\overline{F}_{\mathrm{P}} \approx 3.3$. For comparison we also perform an optimization without robustness. We find that an unrobust optimum of $F_{\mathrm{P}} \approx 256.5$ dwindles to only $\overline{F}_{\mathrm{P}} \approx 0.7$ when fabrication uncertainties are taken into account. We thus demonstrate that the presented approach is able to find designs of significantly higher performance than those obtained with conventional optimization.

eess.SP↗

arXiv2023

Poles and zeros in non-Hermitian systems: Application to photonics

Resonances are essential for understanding the interactions between light and matter in photonic systems. The real frequency response of the non-Hermitian systems depends on the complex-valued resonance frequencies, which are the poles of electromagnetic response functions. The zeros of the response functions are often used for designing devices, since the zeros can be located close to the real axis, where they have significant impact on scattering properties. While methods are available to determine the locations of the poles, there is a lack of appropriate approaches to find the zeros in photonic systems. We present an approach to compute poles and zeros based on contour integration of electromagnetic quantities. This also allows to extract sensitivities with respect to geometrical or other parameters enabling efficient device design. The approach is applied to a topical example in nanophotonics, an illuminated metasurface, where the emergence of reflection zeros due to the underlying resonance poles is explored using residue-based modal expansions. The generality and simplicity of the theory allows straightforward transfer to other areas of physics. We expect that easy access to zeros will enable new computer-aided design methods in photonics and other fields.

physics.optics↗

arXiv2023

Applying a Riesz-projection-based contour integral eigenvalue solver to compute resonance modes of a VCSEL

We investigate the calculation of resonance modes of a VCSEL with a Riesz projection eigenvalue solver. The eigenvalue solver is based on the principle of contour integration where for the solution of scattering problems physical right sides are used. Here, it is investigated how numerical parameters impact the performance of the method, where we focus on the computation of the fundamental VCSEL mode.

physics.comp-ph↗

arXiv2022

Resonance expansion of quadratic quantities with regularized quasinormal modes

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 emphasize the ability of the approach to provide modal expansions outside the underlying nanophotonic resonator.

physics.optics↗

arXiv2022

Computation of eigenfrequency sensitivities using Riesz projections for efficient optimization of nanophotonic resonators

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 is derived 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 using finite differences. The method is applied for the efficient optimization of the quality factor of a nanophotonic resonator.

physics.comp-ph↗

arXiv2022

Enhanced Purcell factor for nanoantennas supporting interfering resonances

We study the effect of coupled resonances and quasi-bound states in the continuum (quasi-BICs) on the Purcell factor in dielectric resonant nanoantennas. We analyze numerically interfering resonances in a nanodisk with and without a substrate when the modes are coupled to an emitter localized inside the nanodisk, and we quantify the modal contributions to the Purcell factor also reconstructing the radiation patterns of the resonant system. It is revealed that the Purcell effect can be boosted substantially for a strong coupling of resonances in the quasi-BIC regime.

physics.optics↗

arXiv2021

Hot electron generation through near-field excitation of plasmonic nanoresonators

We theoretically study hot electron generation through the emission of a dipole source coupled to a nanoresonator on a metal surface. In our hybrid approach, we solve the time-harmonic Maxwell's equations numerically and apply a quantum model to predict the efficiency of hot electron generation. Strongly confined electromagnetic fields and the strong enhancement of hot electron generation at the metal surface are predicted and are further interpreted with the theory of quasinormal modes. In the investigated nanoresonator setup, both the emitting source and the acceptor resonator are localized in the same volume, and this configuration looks promising to achieve high efficiencies of hot electron generation. By comparing with the efficiency calculated in the absence of the plasmonic nanoresonator, that is, the dipole source is located near a flat, unstructured metal surface, we show that the effective excitation of the modes of the nanoresonator boosts the generation efficiency of energetic charge carriers. The proposed scheme can be used in tip-based spectroscopies and other optoelectronic applications.

physics.optics↗

arXiv2020

A Riesz-projection-based method for nonlinear eigenvalue problems

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 eigenvalues with high physical impact. No auxiliary functions have to be introduced since linearization is not used. The numerical implementation is straightforward as the evaluation of the integrand can be regarded as a blackbox. We apply the method to a quantum mechanical problem and to two nanophotonic systems.

physics.comp-ph↗

arXiv2020

Long- and Short-Ranged Chiral Interactions in DNA Assembled Plasmonic Chains

Molecular chirality plays a crucial role in innumerable biological processes. The chirality of a molecule can typically be identified by its characteristic optical response, the circular dichroism (CD). CD signals have thus long been used to identify the state of molecules or to follow dynamic protein configurations. In recent years, the focus has moved towards plasmonic nanostructures, as they show potential for applications ranging from pathogen sensing to novel optical materials. The plasmonic coupling of the individual elements of such chiral metallic structures is a crucial prerequisite to obtain sizeable CD signals. We here identified and implemented various coupling entities - chiral and achiral - to obtain chiral transfer over distances close to 100 nm. The coupling is realized by an achiral nanosphere situated between a pair of gold nanorods that are arranged far apart but in a chiral fashion. We synthesized these structures with nanometer precision using DNA origami and obtained sample homogeneity that allowed us to directly demonstrate efficient chiral energy transfer between the distant nanorods. The transmitter particle causes a strong enhancement in amplitude of the CD response, the emergence of an additional chiral feature at the resonance frequency of the nanosphere, and a redshift of the longitudinal plasmonic resonance frequency of the nanorods. Numerical simulations closely match our experimental observations and give insights in the intricate behavior of chiral optical fields and the transfer of plasmons in complex architectures.

physics.optics↗