Finite-difference Time-domain Solver Research Articles

Photonic-crystal-based hybrid wavelength-mode division multiplexer for SOI platforms

This paper presents a 12-channel hybrid wavelength-mode division multiplexer (WDM-MDM) based on 2D photonic crystals. The proposed device consists of microring resonators (MRRs) and asymmetric directional couplers (ADCs) to perform three-channel wavelength division multiplexing and four-channel mode division multiplexing operations, respectively. Each MRR can work bi-directionally, providing the same wavelength channels separately in two drop ports. The bus waveguides in the cascaded ADCs are optimized to convert the fundamental modes to the corresponding higher-order modes and are connected through taper regions for the smooth transition of modes. The designed device is simulated using the finite-difference time-domain solver, achieving a maximum channel spacing and insertion loss of 5.05 nm and 0.97 dB, respectively. The device size of the proposed WDM-MDM is 74.98µm×32.82µm. The fabrication tolerance study is performed for uniform over-etch and under-etch conditions. The temperature tolerance study on the resonant wavelength is performed, and the temperature coefficient shift of <0.0254nm/K is achieved. The proposed device can potentially increase the channel capacity for on-chip high-density optical interconnects.

Multifidelity adaptive sequential Monte Carlo for geophysical inversion

SUMMARY In the context of Bayesian inversion, we consider sequential Monte Carlo (SMC) methods that provide an approximation of the posterior probability density function and the evidence (marginal likelihood). These particle approaches build a sequence of importance sampling steps between gradually tempered distributions evolving from the prior to the posterior PDF. To automate the definition of the tempering schedule, adaptive SMC (ASMC) allows tuning the temperature increments on-the-go. One general challenge in Bayesian inversions is the computational burden associated with expensive, high-fidelity forward solvers. Lower-fidelity surrogate models are interesting in this context as they can emulate the response of expensive forward solvers at a fraction of their cost. We consider surrogate modelling within ASMC and introduce first an approach involving surrogate modelling only, in which either prior samples are used to train the surrogate, or the surrogate model is retrained by updating the training set during the inversion. In our implementation, we rely on polynomial chaos expansions for surrogate modelling, principal component analysis for model parametrization and a ground-penetrating radar cross-hole tomography problem with either an eikonal or finite-difference time-domain solver as high-fidelity solver. We find that the method based on retraining the surrogate during the inversion outperforms the results obtained when only considering prior samples. We then introduce a computationally more expensive multifidelity approach including a transition to the high-fidelity forward solver at the end of the surrogate-based ASMC run leading to even more accurate results. Both methods result in speed-ups that are larger than one order of magnitude compared to standard high-fidelity ASMC inversion.

High Field Confinement Enhancement in Silicon-based Photonic Crystal with Different Point Defects

Two-dimensional silicon-based photonic crystals as optical analogs to electronic semiconductors are presented in this paper, emphasizing the design and analysis of two-dimensional structures. Employing the Lumerical FDTD solver, we initially crafted defect-free photonic crystals within a hexagonal lattice of air holes on a silicon slab (6.57 μm along x, 6.57 μm along y, 0.75 μm along z). The lattice parameters (a = 0.365 μm, r = 0.1095 μm, with r = 0.3a) established a target resonant wavelength of 1.5 μm. Utilizing Finite Difference Time-Domain (FDTD), we evaluated electric field decay, resonant modes, and the Q factor. The defect-free structure exhibited a peak Q factor of 736.004 at a resonant wavelength of 1262.87 nm. Removal of a central hole enhanced the Q factor to 1286.96 at 1391.07 nm. Introducing various line defects, the structure with three holes removed from vertical positions emerged as the optimal candidate for silicon-based photonic crystal cavity resonators, displaying the highest Q factor near the target resonant wavelength. Additionally, the structure with seven holes removed showed stable linear decays at both resonant wavelengths, suggesting its potential as a cavity resonator design candidate.

Intelligent algorithm of extreme gradient boosting based perfectly matched monolayer and its efficient absorption on airborne transient electromagnetics problems

In addition to requiring the accuracy and computational efficiency for solving low-frequency subsurface sensing problem on the airborne transient electromagnetics (ATEMs), to the best of our knowledge, the complexity of subsurface sensing problems should also be considered in order to reduce more and more computational resources, particularly for a large-scale complicated multis-cale problem with a difference between background and targets. For simulating the open-domain, the finite-thickness perfectly matched layer is used to truncate the computational region, while the whole domain becomes larger so that the problem turns more complex. As a result, we propose a novel perfectly matched monolayer (PMM) model based on the extreme gradient boosting (XGB), which is selected and added to further improve the performance during the finite-difference time-domain (FDTD) simulation. The proposed XGB-based PMM model can achieve higher accuracy by using the ensemble learning method of feature attention, and has less memory and time consumption at the same time. Besides, this model has significant advantages in terms of model training stability and its lightweight due to the fact that it relies on the characteristics of traditional machine learning models. Finally, three-dimensional numerical simulations of ATEM problems are carried out to prove the validity and stability of the proposal. The proposed model can not only achieve advantages in numerical accuracy, efficiency and problem complexity, but also be integrated into the FDTD solver to deal with the low-frequency ATEM problems.

Differentiable-Decision-Tree-Based Neural Turing Machine Model Integrated Into FDTD for Implementing EM Problems

As known to all, problems consume more and more computational resources, for example, memory and time, with the gradual enhancements of both the size of the physical domain and complexity in numerical methods. Computational efficiencies have to be obviously influenced, especially for the finite-difference time-domain (FDTD) solver due to its inflexibility in discretization principle. To further overcome this problem, the neural turing machine (NTM) model, based on the differentiable decision tree (DDT), is chosen and incorporated to improve the efficiencies during the FDTD solver in our work. The DDT-based NTM model has the remarkable advantages of both trees and neural networks, which can better explain for the numerical data. Meanwhile, it has full differentiability through neural networks and can be trained by the powerful deep-learning processes. The proposed DDT-based NTM model could not only enhance both accuracy and efficiency but also successfully integrate into the FDTD solver to implement the microstrip transmission line.

Subwavelength grating-based silicon photonic TE mode division multiplexer for C + L band operation

This paper reports a subwavelength grating (SWG) based multiplexer (MUX) on a silicon photonics platform capable of multiplexing three transverse electric modes. The designed MUX is simulated using a commercial 3D finite-difference time-domain solver and shows broadband operation over the whole C and L optical telecom bands from 1530 nm to 1625 nm wavelength range. The effective indices of the Bloch modes in the SWG waveguides are extracted from the band structure plot. The designed MUX consists of two co-directional coupling regions for fundamental to higher-order mode coupling, with each coupling stage consisting of single-mode and multimode SWG waveguides. The transmission characteristics, viz. transmittance, insertion loss, and return loss, are presented and discussed. The coupling lengths without the tapering regions for TE0–TE1 and TE0–TE2 mode couplings are 14μm and 1.48μm, respectively. The transmittance is >78% with the highest insertion loss and return loss of 1.1 dB and –15 dB, respectively. At 1550 nm, the transmission is >88%, insertion loss is <0.6 dB, and return loss is <−15 dB. A uniform under-etch and over-etch of 5 nm are taken for the fabrication tolerance study, which shows a maximum variation of 0.58 dB for the insertion loss with return loss <−14.6 dB at 1550 nm. Over the whole simulated range, the insertion loss is <1.4 dB, and return loss is <−14.6 dB with ±10 nm change in device dimension. A temperature tolerance study with 50 °C and 100 °C rise in temperature has been done, and the device retains its broadband operation over the simulated range. The maximum increase in insertion loss is 0.1 dB for the TE0–TE2 coupling, while the overall return loss of the device decreases to <−20 dB for the TE0–TE1 coupling.

Two-fluid physical modeling of superconducting resonators in the ARTEMIS framework

In this work, we implement a new London equation module for superconductivity in the GPU-enabled ARTEMIS framework, and couple it to a finite-difference time-domain solver for Maxwell's equations. We apply this two-fluid approach to model a superconducting coplanar waveguide (CPW) resonator. We validate our implementation by verifying that the theoretical skin depth and reflection coefficients can be obtained for several superconductive materials, with different London penetration depths, over a range of frequencies. Our convergence studies show that the algorithm is second-order accurate in both space and time, except at superconducting interfaces where the approach is spatially first-order. In our CPW simulations, we leverage the GPU scalability of our code to compare the two-fluid model to more traditional approaches that approximate superconducting behavior and demonstrate that superconducting physics can show comparable performance to the assumption of quasi-infinite conductivity as measured by the Q-factor.

Massively parallel FDTD-FBMC simulations of nonlinear hole dynamics in silicon at cryogenic temperatures driven by intense EM THz pulses

THz spectroscopy with intense electromagnetic (EM) pulses offers unique avenues to study the charge carrier dynamics in semiconductors. Quantitative analysis of the experiment requires a detailed microscopic model that is based on the wave propagation within the sample and on the strongly nonparabolic dispersion relation of the valence bands. With a finite difference time domain (FDTD) solver for the EM wave in conjunction with a full band Monte Carlo (FBMC) model for the holes the generation of higher harmonics by the nonlinear hole response in the p-doped silicon sample can be simulated. Due to impurity freeze-out at the cryogenic temperature the hole density is low and the FDTD solver can be decoupled from the FBMC model by a perturbation approach. This enables the independent processing of a very large number of holes on a computer cluster with nearly 100% computational efficiency resulting in a very low level of stochastic noise, which is necessary to achieve a reasonable signal to noise ratio for the faint higher harmonics. The simulations show that at THz frequencies and cryogenic temperatures strong generation of higher harmonics is only possible, if the band structure is nonparabolic.

Plasmonic volcano-like fiber-optic probe for Raman enhancement.

Light-matter interaction is a fascinating topic extensively studied from classical theory, based on Maxwell's equations, to quantum optics. In this study, we introduce a novel, to the best of our knowledge, silver volcano-like fiber-optic probe (sensor 1) for surface-enhanced Raman scattering (SERS). We employ the emerging quasi-normal mode (QNM) method to rigorously calculate the Purcell factor for lossy open system responses, characterized by complex frequencies. This calculation quantifies the modification of the radiation rate from the excited state e to ground state g. Furthermore, we use and extend a quantum mechanical description of the Raman process, based on the Lindblad master equation, to calculate the SERS spectrum for the plasmonic structure. A common and well-established SERS probe, modified by a monolayer silver nanoparticle array, serves as a reference sensor (sensor 2) for quantitatively predicting the SERS performance of sensor 1 using quantum formalism. The predictions show excellent consistency with experimental results. In addition, we employ the FDTD (finite-difference time-domain) solver for a rough estimate of the all-fiber Raman response of both sensors, revealing a reasonable range of SERS performance differences compared to experimental results. This research suggests potential applications in real-time, remote detection of biological species and in vivo diagnostics. Simultaneously, the developed FDTD and quantum optics models pave the way for analyzing the response of emitters near arbitrarily shaped plasmonic structures.

Electromagnetic Modeling Using an FDTD-Equivalent Recurrent Convolution Neural Network: Accurate computing on a deep learning framework

In this study, a recurrent convolutional neural network (RCNN) is designed for full-wave electromagnetic (EM) modeling. This network is equivalent to the finite difference time domain (FDTD) method. The convolutional kernel can describe the finite difference operator, and the recurrent neural network (RNN) provides a framework for the time-marching scheme in FDTD. The network weights are derived from the FDTD formulation, and the training process is not needed. Therefore, this FDTD-RCNN can rigorously solve a given EM modeling problem as an FDTD solver does.

High density vertical optical interconnects for passive assembly.

The co-packaging of optics and electronics provides a potential path forward to achieving beyond 50 Tbps top of rack switch packages. In a co-packaged design, the scaling of bandwidth, cost, and energy is governed by the number of optical transceivers (TxRx) per package as opposed to transistor shrink. Due to the large footprint of optical components relative to their electronic counterparts, the vertical stacking of optical TxRx chips in a co-packaged optics design will become a necessity. As a result, development of efficient, dense, and wide alignment tolerance chip-to-chip optical couplers will be an enabling technology for continued TxRx scaling. In this paper, we propose a novel scheme to vertically couple into standard 220 nm silicon on insulator waveguides from 220 nm silicon nitride on glass waveguides using overlapping, inverse double tapers. Simulation results using Lumerical's 3D Finite Difference Time Domain solver are presented, demonstrating insertion losses below -0.13 dB for an inter-chip spacing of 1 µm; 1 dB vertical and lateral alignment tolerances of approximately 2.6 µm and ± 2.8 µm, respectively; a greater than 300 nm 1 dB bandwidth; and 1 dB twist and tilt tolerances of approximately ± 2.3 degrees and 0.4 degrees, respectively. These results demonstrate the potential of our coupler for use in co-packaged designs requiring high performance, high density, CMOS compatible out of plane optical connections.

Fully integrated optical sensor system with intensity interrogation

Introduction: Today sensor systems based on integrated photonics devices are the most important branch of embedded information and control systems for various functions. The output characteristics of a sensor system are significantly determined by the efficiency of the interrogator. The intensity interrogator based on a microring resonator can provide a high scanning rate and sensitivity that meets the requirements of a wide range of applications. Purpose: To develop an effective sensor system composed of a refractometric sensor and an interrogator located on the same photonic integrated circuit for marker-free determination of the concentration of substances in liquids. Methods: We use the numerical simulation of electromagnetic field propagation in a waveguide system (integrated silicon waveguides on a silicon dioxide substrate) in the research. The simulation has been carried out using the Ansys Lumerical environment, the FDTD (Finite Difference Time Domain) solver. The parameters of the microring resonators were optimized to obtain the coupling coefficients between the waveguides, providing the operation in the critical coupling mode. Results: We propose the concept of a fully integrated photonic sensor system based on micro-ring add-drop resonators. A sensor based on microring resonators has been developed, which consists of two half-rings with a radius of 18 μm, connected by sections of straight waveguides 3 μm long. An interrogator represented by a microring resonator with a radius of 10 µm has been developed. According to simulation results with a broadband source, the achieved sensor sensitivity was 110 nm per refractive index change, or 1350 dB per refractive index change. We propose a technique for choosing the optimal characteristics of the sensor and interrogator targeted to improve the complete system efficiency. Practical relevance: Sensor systems based on photonic integrated circuits can meet the demand for devices characterized by low power consumption, small size, immunity to electromagnetic interference and low cost.

Genetic algorithms for the design of planar THz antenna

This paper proposes a genetic algorithm for the design of passive components operating at THz frequencies and its experimental validation using an exemplar patch antenna. The patch antenna is based on an SU8 substrate, with a binary array describing the placement of metal “bits” replacing the conventional patch. These “bits” are constrained at 25 × 25 μm2, ensuring ease of fabrication. Optimal configurations of this array are determined using a finite-difference time-domain solver coupled to the genetic algorithm, which simulates and optimizes for maximum power collection in the frequency range of 0.10–5.0 THz. The aim was to produce an evolved patch antenna design with double the power collection efficiency across the majority of the frequency range compared to a reference, plain patch antenna of the same size. This was successful with a 5.3 dB mean improvement in simulated power collection compared to a plain reference patch. A vector network analyzer in conjunction with 0.80–1.0 THz frequency extenders was used to validate the simulation results. The antennas were arranged in pairs with variable feed length to determine the feedline attenuation and validate the simulated antenna directionality.

Self-assembled monolayer silver nanoparticles: Fano resonance and SERS application

Plasmonic response of noble metal nanoparticle are of fundamental interest in nanophotonic applications, such as photocatalysis, information storage, sensing, optical switches, and nonlinear optics. We comprehensively investigate the Fano resonance and SERS (surface–enhanced Raman scattering) application of self–assembled monolayer silver nanoparticles using commercial FDTD (finite difference time domain) solver, cartesian multipole decompositions method, two coupled oscillators model and experiments. We found that the higher–energy antibonding mode is not only from the antibonding dipole–dipole mode (ADD), but also from the antibonding quadrupole–quadrupole mode (AQQ) and the hybridized magnetic mode when the particle size is relatively large in homodimer, as for the heterodimer, the case will change even more. The effects of dimer gap and size are discussed in details. A two coupled oscillators model is used to illustrate the mechanism of the Fano resonance, and the energy storage as a function of radiation loss and intrinsic loss in the plasmonic system is qualitatively evaluated, which is directly related to the near–field enhancement. Finally, SERS (surface–enhanced Raman scattering) experiments are carried out to meet the numerical results, and the SERS performance is also investigated and given.

Optical properties of iodine-based electrolyte used in bifacial dye-sensitized solar cells

As third-generation solar cells, dye-sensitized solar cells (DSSCs) can show bifacial harvesting capabilities by utilizing transparent conducting oxides as a counter electrode. Herein, the electrolyte is considered a critical layer from the optical perspective. In this paper, an attempt to estimate the optical properties of Iodine-based electrolytes, typically used in dye-sensitized solar cells, is demonstrated. The refractive index for electrolyte as an effective medium is calculated to be 1.4535 ± 0.005 for an effective thin film of 33.4 ± 0.5 μm thickness, using the near-infrared Fabry–Perot resonances. The extinction (absorption and scattering) and dispersion spectra for the prepared electrolyte were fitted using Lorentz–Dude (LD) model. Finally, the utility of the extracted optical parameters was examined through a finite difference time domain solver, Massachusetts Institute for Technology Electromagnetic Equation Propagation. The simulated optical transmission spectrum perfectly agreed with the measured spectrum with less than 0.1% root–mean–square error. The demonstrated attempt to accurately estimate the refractive index of electrolyte used in DSSCs fabrication may impacted theoreticians who are interested with the optoelectronic modelling of such electrochemical cells, as well as those dealing with optoelectronic devices informatics.

Gaussian dispersion analysis in the time domain: Efficient conversion with Padé approximants

We present an approach for adapting the Gaussian dispersion analysis (GDA) of optical materials to time-domain simulations. Within a GDA model, the imaginary part of a measured dielectric function is presented as a sum of Gaussian absorption terms. Such a simple model is valid for materials where inhomogeneous broadening is substantially larger than the homogeneous linewidth. The GDA model is the essential broadband approximation for the dielectric function of many glasses, polymers, and other natural and artificial materials with disorder. However, efficient implementation of this model in time-domain full-wave electromagnetic solvers has never been fully achieved. We start with a causal form of an isolated oscillator with Gaussian-type absorption — Causal Dawson-Gauss oscillator. Then, we derive explicit analytical formulas to implement the Gaussian oscillator in a finite-difference time-domain (FDTD) solver with minimal use of memory and floating point operations. The derivation and FDTD implementation employ our generalized dispersive material (GDM) model — a universal, modular approach to describing optical dispersion with Padé approximants. We share the FDTD prototype codes that include automated generation of the approximants and a universal FDTD dispersion implementation that employs various second-order accurate numerical schemes. The codes can be used with non-commercial solvers and commercial software for time-domain simulations of light propagation in dispersive media, which are experimentally characterized with GDA models. Program summaryProgram Title:MADISCPC Library link to program files:https://doi.org/10.17632/x69b4krsy8.1Licensing provisions: GPLv3Programming language: MATLABNature of problem: The problem of efficient time-domain simulation of the Gaussian absorption is essential for wideband modeling of the optical response from materials with inhomogeneous spectral broadening, such as glasses, polymers, and other natural and artificial composite materials with structural or phase disorder.Solution method: A Coupled Oscillator (CO) approximation to the Gaussian absorption in both the frequency and time domains is derived to solve this problem. The time-domain CO approximation is coupled to the finite-difference time-domain (FDTD) solver for the Maxwell equations in the MADIS (MAterial DIspersion Simulator) package. Verification of the Maxwell solvers' accuracy and stability is performed with the FDTD solver coupled to a compact universal implementation of the CO model, employing second-order schemes (either ADE or RC). Code prototypes of these efficient CO schemes can be ported to other methods and platforms for implementing the Gaussian absorption in open-source codes or commercial software.Additional comments including restrictions and unusual features: Patent pending. Restrict any commercial use, including for profit reproduction.

Optical properties of lithium titanate as a potential layer in light harvesters

Various solar cell architectures and materials are currently studied, seeking enhanced photon management mechanisms. Herein, we provide an attempt to prepare, characterize, model, and simulate a novel semiconductor, Lithium Titanate, which has a band gap of 3.55 eV. The semiconductor was prepared from H2TiO3 and LiCO3 by calcination at 500 °C for 5 h after grinding with deionized water. XRD, SEM, EDX, and AFM carried out a complete morphological characterization on powder and thin-film levels. Additionally, experimentally validated atomistic DFT modeling was performed where the density of states and the imaginary part of the permittivity were extracted. Finally, the optical transmission spectrum was simulated for a 4.28 μm thickness film, with the aid of a finite-difference time-domain solver, against an experimentally measured spectrum, showing a root-mean-square mismatching error of 3.78%.

Nonlinear broadband time-domain admittance boundary condition for duct acoustics. Application to perforated plate liners

The behavior of perforated plates at high excitation level is generally modeled by a surface impedance that depends on the rms velocity in the perforations. A time-domain admittance boundary condition (TDABC) is developed to account for this variation using a multipole model. Two formulations are considered, based on the interpolation either of the admittance or of the multipole coefficients from a data set of reference values. These TDABC are implemented in a finite-difference time-domain solver of the linearized Euler equations and are validated by comparison with experimental results on an impedance tube. Application to a two-dimensional lined duct corresponding to the reference geometry of the NASA Grazing Incidence Tube is then performed. The spatial variation of the perforated plate liner impedance is highlighted and it is shown that assuming a uniform impedance can lead to an unacceptable prediction of the liner attenuation. These results are confirmed both for a harmonic or broadband excitation.

Compact Gas Sensor Using Silicon-on-Insulator Loop-Terminated Mach–Zehnder Interferometer

In this paper, we propose a compact optical gas sensor based on the widespread silicon-on-insulator (SOI) technology, operating in the near-infrared (NIR) region around the 1.55 µm wavelength. The sensor employs a loop-terminated Mach–Zehnder interferometer (LT-MZI) with a slot waveguide and a strip waveguide for the sensing arm and the reference arm, respectively. For the same arm length, the LT-MZI can achieve a detection limit two times lower than that of the conventional MZI. Different sensor components were designed, and the optimum dimensions were obtained using finite-difference eigenmode (FDE) and finite-difference time-domain (FDTD) solvers. With a sensing arm length of only 150 μm, our sensor achieves a device sensitivity of 1070 nm/RIU and a figure-of-merit (FOM) as high as 280.8 RIU−1 at the 1.55 μm wavelength. Higher values of FOM can be attained by employing a longer sensing arm. The whole sensor is subjected to air cladding; thus, there is no need for oxide deposition and a further lithography step for sensing-area patterning. The sensor is well suited for low-cost fabrication and large-scale production. Finally, the same LT-MZI device with strip and slot arms but with oxide cladding was fabricated and characterized. The measurements were in good agreement with the electromagnetic (EM) simulation results, ensuring the reliability of our proposed design.

A perspective on the pathway toward full wave simulation of large area metalenses

Metalenses for optical beam manipulation have a significant impact in many exciting applications due their compact, planar geometry and ease of fabrication. However, the enormous physical size of metalenses relative to the optical wavelength provides a barrier to performing accurate simulations in a reasonable time frame. In principle, full-wave simulation techniques, such as the finite-difference time-domain (FDTD) method, are ideal for metalens modeling as they give an accurate picture of the device performance. However, when applied using traditional computing platforms, this approach is infeasible for large-diameter metalenses and requires hours and days to simulate even devices of modest size. To alleviate these issues, the standard approach has been to apply approximations, which typically employ simplified models of the metalens unit cells or ignore coupling between cells, leading to inaccurate predictions. In this Perspective, first, we summarize the current state of the art approaches in simulating large scale, three-dimensional metalenses. Then, we highlight that advances in computing hardware have now created a scenario where the full-wave simulation of large area metalenses is feasible within a reasonable time frame, providing significant opportunities to the field. As a demonstration, we show that a hardware-accelerated FDTD solver is capable of simulating a fully 3D, large area metalens of size 100λ × 100λ, including the focal length, in under 5 min. The application of hardware-accelerated, full-wave simulation tools to metalens simulation should have a significant impact in the metalens field and the greater photonics community.