Rigorous Coupled-wave Analysis Research Articles

Numerical Estimation of Bending in Holographic Volume Gratings by Means of RCWA and Deep Learning

In this paper, we introduce a novel approach to model bending phenomena on holographic volume gratings based on Rigorous Coupled Wave Analysis (RCWA), in which the bending as a phase in the dielectric permittivity expansion is introduced, and the Shooting Method (SM) is employed to solve the resulting system of equations. Further validation of our model is conducted by comparing its predictions to those obtained from reference Finite-Difference Time-Domain (FDTD) simulations and Coupled Wave Theory (CWT, referring to Kubota’s model that includes the bending phenomenon). Furthermore, we propose a methodology for estimating the bending from the diffraction efficiency curves in transmission volume gratings based on deep learning models, with a subsequent study of their accuracy and applicability.

Influencing factors of self-aligned imaging in near-field lithography for the Fabry–Perot cavity effect

In near-field lithography, the Fabry–Perot (F-P) cavity enhancement effect can significantly improve image quality and resolution. This paper considers changes in the refractive index and air distance in self-aligned imaging. Simulation results demonstrate that the Fabry–Perot resonator effect achieves effective self-alignment in 3D imaging. The proposed structure builds on traditional near-field imaging structures and F-P resonator research, suggesting a Cu/SiO2 structure as the front layer. Rigorous coupled wave analysis (RCWA), finite element method (FEM), and finite-difference time-domain (FDTD) methods were employed to verify the self-alignment effect on single gratings and rectangular hole arrays. The results indicate that the self-alignment lithography method based on the F-P effect not only enhances lithography contrast and normalized image log-slope (NILS) but also shows robust performance against variations in air distance and complex refractive index. Notably, for the rectangular aperture array structure, with changes in air distance and complex refractive index within a certain range, the NILS remains stable above 2.8, and the contrast stays near 0.70. These simulation results confirm that the F-P resonator-based scheme is viable for plasma imaging lithography with small critical dimensions.

On the suitability of rigorous coupled-wave analysis for fast optical force simulations

Abstract Optical force responses underpin nanophotonic actuator design, which requires a large number of force simulations to optimize structures. Commonly used computation methods, such as the finite-difference time-domain (FDTD) method, and finite element methods (FEM), are resource intensive and require large amounts of calculation time when multiple structures need to be
compared during optimization. This research demonstrates that performing optical force calculations on 2D-periodic structures using the rigorous coupled-wave analysis (RCWA) method is typically on the order of 10 times faster than other approaches and with sufficient accuracy to suit optical design purposes. Moreover, this speed increase is available on consumer grade laptops, avoiding the need for a high performance computing resource.

Manufacturing Anti-Reflective Subwavelength Structures on ZnS Using Femtosecond Laser Bessel Beam with Burst Mode

Increasing the transmittance of zinc sulfide (ZnS) infrared windows can effectively improve the imaging quality of infrared detection. In this study, an anti-reflective subwavelength structure (ASS) was manufactured on ZnS using a femtosecond burst Bessel laser with the goal of achieving high transmittance in the mid-infrared range. The period and depth parameters of the ASS were initially determined using the effective medium approximation (EMA) theory and subsequently optimized using the rigorous coupled-wave analysis (RCWA) method to eliminate surface Fresnel anti-reflections. The depth of the ASS increases with the number of bursts, while the structure profile transitions from Gaussian to conical. In addition, the ASS achieves 86% transmittance in the 7–10 µm range, and the average transmittance improves by 10% in the 5–12 µm range. Moreover, the wide-angle ASS with the hydrophobicity (contact angle 160°) is achieved on the ZnS window. Ultimately, the ASS on ZnS enhances the clarity of the infrared image.

Germanium metalens for longwave infrared applications

Metalenses represent a paradigm shift in optics, offering unprecedented control over light manipulation. This study focuses on the design optimization of a polarization-insensitive germanium (Ge) metalens operating in the longwave infrared (LWIR) regime. Employing rigorous coupled-wave analysis (RCWA) and finite-difference time-domain (FDTD) simulations, a metalens with 1mm focal length was designed using nanopillars with 3.5µm height and radius ranging from 0.55µm to 1.2µm. Then, the impact of lattice size and numerical aperture (NA) on lens performance was investigated. The results indicate that smaller lattices allow finer phase control and enhanced transmittance stability across the phase profile if significant coupling effects are not verified. As the NA increases, the focal spot size decreases, albeit with diminishing returns towards the diffraction limit. To the best of our knowledge, it is the first work that shows high focal efficiency (~80%) across multiple NA’s for a LWIR metalens with a diameter under 1100µm. The proposed metalens is compatible with complementary metal-oxide-semiconductor (CMOS) technology and supports low-cost manufacturing.

Chirped grating for TE-five/TM-three reflective distribution feature

This research expounds on a novel reflective chirped grating, characterized by its differentiated functionality under various polarization modes. Under perpendicular incidence, this intricately grating produces a quintuple-channel diffraction output of the 0th, ±1st, and ±2nd orders in transverse electric (TE) polarization and a triple-channel diffraction output of the 0th and ±1st orders in transverse magnetic (TM) polarization. Both polarization modes exhibit excellent overall diffraction efficiency and uniformity. At an incident wavelength of 1550 nm, the diffraction efficiencies for the 0th, ±1st, and ±2nd orders under TE polarization are 20.16%, 19.27%, and 20.25%, respectively. Simultaneously, under TM polarization, the efficiencies for the 0th and ±1st orders are 31.79% and 31.57%, respectively. Grating parameters were meticulously derived using the finite element method (FEM) and subsequently corroborated through rigorous coupled-wave analysis (RCWA) to ensure superior grating accuracy. The study also exhaustively analyzes the manufacturing tolerances and robustness of the grating, affirming its practical applicability and effectiveness in practical applications. The dual-function grating splitter proposed in this paper enables the implementation of multiple functionalities within simple setups, suitable for applications requiring varied beam splitting. As photonic systems and fiber technology evolve, the potential applications of dual-function reflective splitters in these fields are increasingly highlighted.

Inverse design of metamaterial for dual-band infrared camouflage along with dual-band thermal management

The optical metamaterial for infrared camouflage with thermal management is an artificial structure available to not only evade the detection of various thermal imagers operating in distinct infrared wavebands but also ensure the thermal stability of the target. However, designing such an optical metamaterial is challenging due to the necessity to optimize numerous structural parameters simultaneously, especially metamaterials that are compatible with multiple functions. Herein, this paper proposes a novel inverse design method, combining African vultures optimization algorithm (AVOA) with rigorous coupled-wave analysis (RCWA), to design an optical metamaterial capable of achieving infrared camouflage and thermal management compatibly. The proposed metamaterial enables dual-band infrared camouflage for mid-wave infrared (MWIR, 3–5 μm) and long-wave infrared (LWIR, 8–14 μm), along with thermal management through dual-band non-atmospheric windows of 5–8 μm and 14–17 μm. Comparing to other intelligent optimization algorithms, the AVOA is exceptionally efficient, which only takes less time than others to get better results. This work not only provides theoretical guidance to design an optical metamaterial for infrared camouflage with thermal management, but also has the potential to solve the multi-objective optimization problems of multi-band or wide-band radiative modulation.

Plasmonic and photonic refractive index biosensor based on bound states in the continuum

In this paper, we propose a novel structure for biosensors based on a diffraction grating to diagnose four types of cancers cells. This biosensor is used to detect Hela, Jurkat, PC12, MDA-MB-231 and MCF-7 cancerous cells, based on their refractive indices. The present configuration consists of a glass layer covered by a gold layer, a grating coated by a silicon nitride layer separating the sensor from sensing medium. Bound states in the continuum (BIC) in a hybrid plasmonic-photonic structure can be achieved at Γ point and off-Γ. The symmetry-protected BIC is formed at the Γ-point of the periodic system due to the strong coupling between plasmonic or photonic modes. On the other hand, the Friedrich-Wintgen (FW) BICs can be readily achieved off-Γ due to the strong coupling between plasmonic and photonic modes. A comparative study is made on the basis of three BICs (plasmonic BIC, photonic BIC, and FW-BIC). Here, numerical analysis based on the Rigorous coupled-wave analysis method (RCWA) is performed to optimize the biosensor sensitivity, by also considering the full width at half maximum (FWHM), detection accuracy (DA), and figure of merit (FoM). The FW BIC-based biosensor for photonic mode exhibits the highest S of 1208nm/RIU, low FWHM of 0.5 nm, the maximum DA of 2 nm −1, and best FoM of 2416 RIU −1.

RCWA4D: Electromagnetic solver for layered structures with incommensurate periodicities

We describe RCWA4D, an electromagnetic solver for layered structures with incommensurate periodicities. Our method is based on an extension of the rigorous coupled wave analysis. We illustrate our method on the example of twisted bilayer photonic crystal and show that various properties of such structures can be reliably simulated. The method can be generalized to multi-layer structures in general in which each layer is periodic or quasi-periodic.

Diffraction by gratings: from the C-method to the stochastic C-method

The Chandezon, or C-method, is an efficient and versatile numerical method for modeling diffraction problems involving smooth surface relief gratings. For some grating profiles, the C-method is limited when the height-to-period ratio exceeds a factor of three. This is due to the formation of ill-conditioned matrices for inversion. Here, the stochastic C-method (SCM) is introduced as a solution that leverages stochastic differential equations to overcome these numerical difficulties. The SCM is developed by altering the physical model of the grating profile function to include an additive Brownian noise component. The inclusion of noise dramatically expands the applicability of the C-method and enriches the physical model. Numerical experiments show that the SCM achieves a precision on the order of 10−5 for diffracted/transmitted amplitudes on sinusoidal profiles with height-to-period ratios as high as 72. These results are in agreement with those obtained using multi-precision and the rigorous coupled wave analysis (RCWA).

Localized Surface Plasmon Resonances of AgAl Alloy Nanoparticles Self-Organized by Annealing of Ag/Al Bilayer Films

Plasmonic applications have traditionally relied on noble metals such as gold (Au) and silver (Ag) for their excellent plasmonic performance in the visible and near-infrared spectrum. However, these metals are costly, scarce, and have limitations such as low stability (Ag) and interband transition losses, which restrict their spectral range. To address these issues, alternative plasmonic materials have been explored. One such material is aluminum (Al), which is inexpensive, abundant, and exhibits remarkable plasmonic properties in the UV region as well as wide tunability. Al is also compatible with complementary metal–oxide semiconductor (CMOS) fabrication processes and is very stable due to its ultrathin native oxide layer. Alloying different metals can combine their advantageous properties, resulting in enhanced tunable optical characteristics. This study investigates the LSPR properties of AgAl alloy nanoparticles grown after the annealing of precursor AgAl bilayer films. Interestingly, LSPRs were also observed in some cases for the as-deposited bilayers. The experimental results were complemented with simulations conducted via the rigorous coupled-wave analysis (RCWA) method. The investigated materials could be potentially useful for applications in energy harvesting or color printing.

High-efficiency three-port beam splitter under normal incidence

A fused-silica three-port grating under TE-polarized normal incidence is designed and manufactured with improved diffraction efficiency (DE) and bandwidth. A physical explanation of the grating diffraction is provided using the simplified mode method (SMM), and parameters of the grating structure were optimized using rigorous coupled-wave analysis (RCWA). For a given set of optimized parameters, a transmitted three-port grating with an area of 170mm×170mm was fabricated by scanning beam interference lithography (SBIL), and diffraction properties were investigated. The average DEs for the +1, 0, and 1 orders of the 25 sampling points are 29%, 30%, and 31% at a 632.8 nm incident wavelength. Additionally, the measured DEs of the +1, 0, and 1 orders all exceed 25% at the wavelength range from 613 to 653 nm.

A comparative simulation study of light–matter coupling in 1D photonic crystals with 2D perovskite active layer

Light–matter interaction operating in the strong coupling regime offers wide prospects of applications going from nano-photonics to quantum communications. The most practical implementations are to embed the active matter into Fabry–Perot microcavities or photonic crystals. In this work we focus on the strong coupling of two-dimensional (2D) perovskite in 1D grating waveguide. We use rigorous coupled wave analysis to simulate electromagnetic wave confinement in the 1D waveguide. Various sets of waveguide geometrical parameters are examined to achieve the strong coupling regime for three different configurations of the active layer in the waveguide. To extract quantitatively the relevant physical parameters, such as strength of light–matter interaction, we develop a Hamiltonian formalism to reproduce results obtained by simulation. It is shown that the strongest interaction is to have the active layer inserted in the main slab of the waveguide. It is, however, still weaker by about 20% as compared to the use of Fabry–Perot microcavities.

Weakly guiding approximation of a three-dimensional waveguide model for extreme ultraviolet lithography simulation

A three-dimensional (3D) waveguide model is applied in extreme ultraviolet (EUV) lithography simulations. The 3D waveguide model is equivalent to rigorous coupled-wave analysis, but fewer field components are used to solve Maxwell’s equations. The 3D waveguide model uses two components of vector potential, A x and A y , corresponding to the two polarizations. The electric field of the A x polarization is approximately parallel to the x axis, and the electric field of the A y polarization is approximately parallel to the y axis. The 3D waveguide model solves a coupled vector wave equation for two polarizations. The refractive index of conventional EUV absorbers is close to that of vacuum. The weakly guiding approximation in optical fiber theory is applied to the 3D waveguide model. The coupled vector wave equations for the two polarizations are decoupled into two independent scalar wave equations. Maxwell’s equations are simplified to a set of scalar wave equations. The weakly guiding approximation reduces the computation time to solve the equations. The computation time required to solve the weakly guiding approximation is about 1/5 of the time to solve the original 3D waveguide model.

Ultrahigh reflectivity photonic crystal membranes with optimal geometry

Photonic crystal (PhC) structures with subwavelength periods are widely used for diffractive optics, including high reflectivity membranes with nanoscale thickness. Here, we report on a design procedure for 2D PhC silicon nitride membrane mirrors providing optimal crystal geometry using simulation results obtained with rigorous coupled-wave analysis. The Downhill Simplex algorithm, a robust numerical approach to finding local extrema of a function of multiple variables, is used to optimize the period and hole radius of PhCs with both hexagonal and square lattices, as the membrane thickness is varied. Following these design principles, nanofabricated PhC membranes made from silicon nitride have been used as input couplers for an optical cavity, resulting in a maximum cavity finesse of 33 000, corresponding to a reflectivity of 0.999 82. The role played by the spot size of the cavity mode on the PhC was investigated, demonstrating the existence of an optimal spot size that agrees well with predictions. We find that, compared to the square lattice, the hexagonal lattice exhibits a spectrally wider reflective range, less sensitivity to fabrication tolerances, and higher reflectivity for membranes thinner than 200 nm, which may be advantageous in cavity optomechanical experiments. Finally, we find that all of the cavities that we have constructed exhibit well-resolved polarization mode splitting, which we expect is due primarily to a small amount of anisotropic stress in the silicon nitride and PhC asymmetry arising during fabrication.

Temperature-Dependent Localized Surface Plasmon Resonances of Noble Nanoparticles Covered with Polymers

Self-assembled gold and silver nanoparticles were fabricated in medium vacuum conditions on Corning glass substrates by means of DC magnetron sputtering. The samples were deposited either at 420 °C or 440 °C, or they were initially deposited at room temperature followed by post annealing. Subsequently, they were covered with three different polymers, namely Polystyrene-block-polybutadiene-blockpolystyrene (PS-b-PBD-b-PS), Polystyrene-co-methyl methacrylate (PS-co-PMMA) and Polystyreneblock-polyisoprene-block-polystyrene (PS-b-PI-b-PS), using spin coating. Localized surface plasmon resonances were recorded in the temperature range of −25 °C–100 °C. We show that the resonance position changes systematically as a function of temperature. Theoretical calculations carried out via the Rigorous Coupled Wave Analysis support the experimental results. Based on these findings, the investigated materials demonstrate potential as components for the development of temperature sensors.

Legume: A free implementation of the guided-mode expansion method for photonic crystal slabs

We describe legume, a free electromagnetic solver that implements the guided-mode expansion method for patterned multilayer waveguides, or photonic crystal slabs. legume has a built-in tool for automatic differentiation, which makes it suitable for the inverse design of photonic crystal structures with desired physical properties. Compared to a previous version of the method (M. Minkov et al., 2020 [12]), here we introduce several new features of the code, we discuss additional technical aspects of the method and its numerical implementation. The novel features that are treated in this paper include: (i) the separation of modes according to their mirror symmetry with respect to a vertical symmetry plane of the photonic structure, (ii) the problem of polarization mixing in coupling to far-field radiation modes, and (iii) the description of active two-dimensional layers through a suitably formulated radiation-matter coupling Hamiltonian, allowing to describe the physics of both weakly and strongly coupled exciton-photon modes, the latter leading to photonic crystal polariton eigenmodes. Detailed and direct comparisons with rigorous coupled-wave analysis simulations are used to test the accuracy of the method and the numerical efficiency of the code. These newly added features of the legume code significantly increase the prospective applications of guided-mode expansion, making it a very practical and versatile tool enabling the design of advanced photonic structures and the description of radiation-matter interaction. Program summaryProgram Title:legumeCPC Library link to program files:https://doi.org/10.17632/kf3cwknx4d.1Developer's repository link:https://github.com/fancompute/legumeLicensing provisions: MITProgramming language: PythonNature of problem: Dispersion and radiative losses of photonic eigenmodes in patterned multilayer waveguides/photonic crystal slabs/periodic metasurfaces. Interaction of photonic modes with exciton resonances leading to exciton-polaritons. Inverse design by optimization of the parameters.Solution method: Finite-basis expansion using a basis of guided modes of an effective homogeneous waveguide, perturbation theory to describe coupling with far-field radiation. Quantum theory of excitons, photons and their interaction to describe the occurrence of exciton-polaritons. Automatic differentiation via Autograd to implement inverse design. In this upgraded version of the legume code we implement symmetrization with respect to a vertical mirror plane and light-matter interaction for exciton-polaritons. Inverse design has been described previously, here we focus on the new features and applications of the code.

Incoherent phenomena in anisotropic periodic structures: from modeling to experimental demonstration.

The periodic structures are widely studied in numerous optical applications and there is a number of good tools for numerical modeling of such a structures (for example rigorous coupled-wave analysis, finite-difference time-domain, finite element method etc.). However, when it comes to the modeling of incoherent effects in many cases of practical interest, the current methods are not rigorous enough or depend on computationally demanding averaging of coherent response. In this paper, we present a novel approach to modeling of incoherent effects in structures with lateral periodicity based on scattering matrix formalism, as a way to describe optical response of a structure, and on application of incoherent wave summation in the form of infinite geometric series and generalized Mueller matrix calculus. This method can be combined with any of the existing coherent methods of modeling periodic structures and it offers significantly faster computational performance than partially coherent/incoherent methods based on averaging. It is compared with other methods for modeling of incoherent effects and also with experimental spectroscopic data. This method is then used to explain phenomena emerging from the complex interaction between diffraction grating and thick substrate.

Polarization-independent nonreciprocal thermal radiation by cylindrical grating structure

Due to the significant application value of nonreciprocal thermal radiation in energy collection and conversion, it has always been an active research topic. The current research on polarization-independent nonreciprocal thermal radiation is characterized by low efficiency and a notable disparity in nonreciprocal efficiency between transverse electric (TE) and transverse magnetic (TM) polarizations. To address this issue, a polarization-independent nonreciprocal thermal radiation based on the two-dimensional grating structure is proposed, which is composed of silicon cylindrical grating ridges, magneto-optical materials InAs, and metal Ag. By the rigorous coupled-wave analysis (RCWA), the nonreciprocal efficiency exceeds 90 % at a wavelength of 11.763 μm under both TE and TM polarizations. Meanwhile, the difference in nonreciprocal efficiency between the two polarizations is less than 1 %. Through an examination of the magnetic field and electromagnetic distribution at resonance peaks that are polarization-independent, as well as an analysis of coupling mode theory, we have uncovered the underlying physical mechanisms responsible for this phenomenon. The device is capable of sustaining optimal performance across a wide range of structural parameters, offering a significant role for manufacturing applications. The research proposed in this article provides a novel approach for designing efficient polarization-independent nonreciprocal thermal radiation.

Grating design methodology for laser cooling

We present a design strategy for grating magneto-optical traps (GMOTs). It takes the three most relevant optical properties for laser cooling (radiation pressure balance, specular reflection cancellation, and diffracted polarization) to build a scalar figure of merit. We use a rigorous coupled wave analysis (RCWA) simulation to find a geometry that maximizes this figure of merit. We also introduce a criterion that takes into account the robustness of the manufacturing processes to select a geometry that is reliable to manufacture. Finally, we demonstrate that the fabricated grating exhibits the expected optical properties and achieves typical GMOT performance.