40 research outputs found
treams -- A T-matrix scattering code for nanophotonic computations
We report the publication of treams, a new software for electromagnetic
scattering computations based on the T-matrix method. Besides conventional
T-matrix calculations for individual scatterers and finite clusters of
particles, a unique feature of the code is its full support for periodic
boundaries in one, two, and all three spatial dimensions. We use highly
efficient and quickly converging lattice summation techniques based on the
Ewald method to evaluate the arising lattice sums in these cases. In addition
to the common use of vector spherical waves as a basis set for the T-matrix,
vector cylindrical waves are also implemented. To describe stratified media,
vector plane waves are used with an S-matrix description of the electromagnetic
scattering. All basis sets and the associated methods can be used together with
chiral constitutive relations.
This contribution outlines the basic methods implemented and the program
structure. Two interfaces to the implemented functionality are available: a
flexible and fast low-level interface and a high-level interface for added
convenience and plausibility checks. We conclude with two examples: a
demonstration of the field calculation in various lattices and the explorations
of quasi-bound states in the continuum. The presented code was already used in
calculations for various physical systems: from the mode properties of
molecular arrays in cavities to analytical models for metasurfaces and from
moir\'{e} lattices to the homogenization of artificial photonic materials. With
the publication of treams and the associated documentation, we hope to empower
more scientists to make an efficient, fast, and precise exploration of
nanophotonic systems that can be described in the broader framework of
scattering theory. The full code is published at
https://github.com/tfp-photonics/treams with the documentation at
https://tfp-photonics.github.io/treams
Lattice Sums Accommodating Multiple Sublattices for Solutions of the Helmholtz Equation in Two and Three Dimensions
The evaluation of the interaction between objects arranged on a lattice
requires the computation of lattice sums. A scenario frequently encountered are
systems governed by the Helmholtz equation in the context of electromagnetic
scattering in an array of particles forming a metamaterial, a metasurface, or a
photonic crystal. While the convergence of direct lattice sums for such
translation coefficients is notoriously slow, the application of Ewald's method
converts the direct sums into exponentially convergent series. We present a
derivation of such series for the 2D and 3D solutions of the Helmholtz
equation, namely spherical and cylindrical solutions. When compared to prior
research, our novel expressions are especially aimed at computing the lattice
sums for several interacting sublattices in 1D lattices (chains), 2D lattices
(gratings), and 3D lattices. We verify our results by comparison with the
direct computation of the lattice sums
Simulation of light scattering in large, disordered nanostructures using a periodic T-matrix method
To model and design light propagation in disordered optical nanostructures and materials, any applicable simulation technique has to cope with enormous computational challenges in a bearable time frame. To circumvent these, the introduction of an artificial periodicity to the disordered particle structure allows to rely on computational techniques that exploit periodic boundary conditions. Choosing a rather large periodicity promises to preserve randomness in form of a close-range disorder but can introduce false interferences. So far, it remains open how the artificial periodicity has to be chosen to minimize its detrimental influence. Here, we combine the superposition T-matrix scheme with an Ewald sum formulation to account for light scattering in periodic particle arrangements that contain hundreds to thousands of individual scatterers per unit cell. Simulations reveal that the periodicityâs influence cannot be minimized by simply choosing one single period much longer than the excitation wavelength. The excitation of lattice induced resonances prevents so. However, choosing a periodicity that does not sustain such detrimental features allows for reliable predictions. With that, the presented approach is suitable to derive spectral information about wave-optical phenomena in large, random particle arrangements with a spatial extend beyond those accessible with other full-wave solvers
Self-Assembled Arrays of Gold Nanorod-Decorated Dielectric Microspheres with a Magnetic Dipole Response in the Visible Range for Perfect Lensing and Cloaking Applications
Photonic nanostructures made of a dielectric sphere covered with many metallic nanospheres fabricated by self-assembly constitute a basic building block for optical metamaterials with a magnetic response in the visible. However, they suffer from limited degrees of freedom to tune their response. Once the involved materials are chosen, the response is mostly determined. To overcome such a limitation, we design, fabricate, and characterize here a bottom-up metamaterial in which metallic nanorods are used instead of nanospheres. Nanorods offer the ability to tune the spectral position of the resonances by changing their aspect ratio. Building blocks consisting of dielectric spheres covered with metallic nanorods are fabricated and characterized. They are also deposited in densely packed arrays on a substrate using a blade coating deposition of the dielectric spheres first and a subsequent deposition of the metallic nanorods. Full-wave optical simulations support the spectroscopic characterization. These simulations also indicate a dominant magnetic dipolar response of the building blocks. These arranged coreâshell structures are promising materials for applications such as perfect lensing and cloaking
Computation of Electromagnetic Properties of Molecular Ensembles
We outline a methodology for efficiently computing the electromagnetic response of molecular ensembles. The methodology is based on the link that we establish between quantumâchemical simulations and the transfer matrix (Tâmatrix) approach, a common tool in physics and engineering. We exemplify and analyze the accuracy of the methodology by using the timeâdependent HartreeâFock theory simulation data of a single chiral molecule to compute the Tâmatrix of a crossâlike arrangement of four copies of the molecule, and then computing the circular dichroism of the cross. The results are in very good agreement with full quantumâmechanical calculations on the cross. Importantly, the choice of computing circular dichroism is arbitrary: Any kind of electromagnetic response of an object can be computed from its Tâmatrix. We also show, by means of another example, how the methodology can be used to predict experimental measurements on a molecular material of macroscopic dimensions. This is possible because, once the Tâmatrices of the individual components of an ensemble are known, the electromagnetic response of the ensemble can be efficiently computed. This holds for arbitrary arrangements of a large number of molecules, as well as for periodic or aperiodic molecular arrays. We identify areas of research for further improving the accuracy of the method, as well as new fundamental and technological research avenues based on the use of the Tâmatrices of molecules and molecular ensembles for quantifying their degrees of symmetry breaking. We provide Tâmatrixâbased formulas for computing traditional chiroâoptical properties like (oriented) circular dichroism, and also for quantifying electromagnetic duality and electromagnetic chirality. The formulas are valid for lightâmatter interactions of arbitrarilyâhigh multipolar orders
Modeling four-dimensional metamaterials: A T-matrix approach to describe time-varying metasurfaces
Exploring the interaction of light with materials periodically structured in space and time is intellectually rewarding and, simultaneously, a computational challenge. Appropriate computational tools are urgently needed to explore how such upcoming photonic materials can control light on demand. Here, we introduce a semi-analytical approach based on the transition matrix (also known as T-matrix) to analyze the optical response of a spatiotemporal metasurface. The metasurface consists of a periodic arrangement of time-varying scattering particles. In our approach, we depart from an individual scattererâs T-matrix to construct the effective T-matrix of the metasurface. From that effective T-matrix, all observable properties can reliably be predicted. We verify our semi-analytical approach with full-wave numerical simulations. We demonstrate a speed-up with our approach by a factor of more than 500 compared to a finite-element simulation. Finally, we exemplify our approach by studying the effect of time modulation on a Huygensâ metasurface and discuss some emerging observable features
A Multi-Scale Approach to Simulate the Nonlinear Optical Response of Molecular Nanomaterials
Nonlinear optics is essential for many recent photonic technologies. Here, we
introduce a novel multi-scale approach to simulate the nonlinear optical
response of molecular nanomaterials combining ab initio quantum-chemical and
classical Maxwell-scattering computations. In this approach, the first
hyperpolarizability tensor is computed with time-dependent density-functional
theory and translated into a multi-scattering formalism that considers the
optical interaction between neighboring molecules. A novel object is introduce
to perform this transition from quantum-chemistry to classical scattering
theory: the Hyper-Transition(T)-matrix. With this object at hand, the nonlinear
optical response from single molecules and also from entire photonic devices
can be computed, incorporating the full tensorial and dispersive nature of the
optical response of the molecules. To demonstrate the applicability of our
novel approach, the generation of a second-harmonic signal from a thin film of
a Urea molecular crystal is computed and compared to more traditional
simulations. Furthermore, an optical cavity is designed, which enhances the
second-harmonic response of the molecular film by more than two orders of
magnitude. Our approach is highly versatile and accurate and can be the working
horse for the future exploration of nonlinear photonic molecular materials in
structured photonic environments
On enhanced sensing of chiral molecules in optical cavities
The differential response of chiral molecules to incident left- and right-handed circularly polarized light is used for sensing the handedness of molecules. Currently, significant effort is directed toward enhancing weak differential signals from the molecules, with the goal of extending the capabilities of chiral spectrometers to lower molecular concentrations or small analyte volumes. Previously, optical cavities for enhancing vibrational circular dichroism have been introduced. Their enhancements are mediated by helicity-preserving cavity modes which maintain the handedness of light due to their degenerate TE and TM components. In this article, we simplify the design of the cavity and numerically compare it with the previous one using an improved model for the response of chiral molecules. We use parameters of molecular resonances to show that the cavities are capable of bringing the vibrational circular dichroism signal over the detection threshold of typical spectrometers for concentrations that are one to three orders of magnitude smaller than those needed without the cavities, for a fixed analyte volume. Frequency resolutions of current spectrometers result in enhancements of more than one order (two orders) of magnitude for the new (previous) design. With improved frequency resolution, the new design achieves enhancements of three orders of magnitude. We show that the TE/TM degeneracy in perfectly helicity-preserving modes is lifted by factors that are inherent to the cavities. More surprisingly, this degeneracy is also lifted by the molecules themselves due to their lack of electromagnetic duality symmetry, that is, due to the partial change of helicity during the light-molecule interactions