Rigorous Coupled-wave Analysis Research Articles

Silver Nanoparticles’ Localized Surface Plasmon Resonances Emerged in Polymeric Environments: Theory and Experiment

Considering that the plasmonic properties of metallic nanoparticles (NPs) are strongly influenced by their dielectric environment, comprehension and manipulation of this interplay are crucial for the design and optimization of functional plasmonic systems. In this study, the plasmonic behavior of silver nanoparticles encapsulated in diverse copolymer dielectric environments was investigated, focusing on the analysis of the emerging localized surface plasmon resonances (LSPRs) through both experimental and theoretical approaches. Specifically, two series of nanostructured silver ultrathin films were deposited via magnetron sputtering on heated Corning Glass substrates at 330 °C and 420 °C, respectively, resulting in the formation of self-assembled NPs of various sizes and distributions. Subsequently, three different polymeric layers were spin-coated on top of the silver NPs. Optical and structural characterization were carried out by means of UV–Vis spectroscopy and atomic force microscopy, respectively. Rigorous Coupled Wave Analysis (RCWA) was employed to study the LSPRs theoretically. The polymeric environment consistently induced a red shift as well as various alterations in the LSPR amplitude, suggesting the potential tunability of the system.

Process and optical modeling of black silicon

Black silicon is relevant for the photovoltaic industry when searching for low-reflectance, low-defect front surface, which is the goal of this work. We have fabricated samples using reactive ion etching (RIE) plus chemical etching for the smoothing, characterized them, and built modeling tools capable of reproducing the resulting geometric features, based on the process parameters. Reflectance is simulated using a proprietary rigorous coupled wave analysis (RCWA)-based tool, and compared with the experimental results. A good matching was achieved using a simple unit cell, and a better agreement when using a 0.5 square microns sample. Finally, an optimum trade-off between low reflectance and low thickness has been achieved.

Augmented reality display with high eyebox uniformity over the full field of view based on a random mask grating

Ensuring uniform illuminance in waveguide-based augmented reality (AR) display devices is crucial for providing an immersive and comfortable visual experience. However, there is a lack of a straightforward and efficient design method available to achieve illuminance uniformity over the full field of view. To address this issue, we propose a novel design that utilizes random mask gratings (RMGs) as the folding grating and the out-coupling grating. Unlike traditional approaches that modify the grating structure, we control the diffraction efficiency distribution by adjusting the filling factor of the mask while keeping the grating structure unchanged in one RMG. The grating structures are designed and optimized based on rigorous coupled wave analysis and particle swarm optimization. The feasibility of our method is verified by the simulation results in Lighttools. In the FOV range of 20°×15°, the eyebox uniformities of all fields are greater than 0.78, which can provide a good visual experience for users.

End-to-end simulations of exoplanet detection with multiplexed volume Bragg gratings

Direct imaging of exoplanets greatly enhances our ability to spectroscopically detect molecules in their atmospheres, but requires both excellent angular and spectral resolution. A highly promising approach uses multiplexed transmission gratings to achieve compressed sensing, but the published theoretical calculations are not realistic enough to determine whether the approach is feasible. We aim to determine the performance of recovering exoplanet signals of an instrument with multiplexed volume Bragg gratings in a full, detailed numerical simulation, specifically examining any effects caused by multiplexing several gratings. Our end-to-end simulation includes realistic stellar and planetary spectra, a closed-loop adaptive optics simulation, and rigorous coupled wave analysis to model the multiplexed gratings. We chose 20 passbands around expected methane absorption features that were optically combined using 20 gratings. We find that exoplanet signals can be recovered down to contrasts of $10^ $, without the addition of a coronagraph. Multiplexing a larger number of gratings improves the deepest recovered contrast, if photon noise is the dominant noise source. When residuals from our simple post-processing approach are the largest noise source, a larger number of multiplexed gratings decreases the performance, due to the stacking of the PSFs at different wavelengths. This is an artifact of our data reduction approach. We conclude that multiplexed Bragg gratings are a viable method to look for exoplanets with a compressed sensing approach and additional gains may be made in post-processing.

Eigendecomposition-free inverse design of meta-optics devices

The inverse design of meta-optics has received much attention in recent years. In this paper, we propose a GPU-friendly inverse design framework based on improved eigendecomposition-free rigorous diffraction interface theory, which offers up to 16.2 × speedup over the traditional inverse design based on rigorous coupled-wave analysis. We further improve the framework’s flexibility by introducing a hybrid parameterization combining neural-implicit and traditional shape optimization. We demonstrate the effectiveness of our framework through intricate tasks, including the inverse design of reconfigurable free-form meta-atoms.

Angular uniformity improvement of diffractive waveguide display based on region geometry optimization.

Augmented reality (AR) near-eye displays have significantly progressed due to advances in nanostructure fabrication. However, for diffractive waveguide AR displays requiring exit pupil expansion, the angular uniformity of each exit pupil position still needs to improve. In this paper, an angular uniformity improvement method based on region geometry optimization is proposed. This optimization method essentially introduces the interaction number of the light with the grating as one of the variables to manipulate the energy distribution. This distribution is obtained by the rigorous coupled wave analysis (RCWA) method and ray tracing process and is further optimized by a multi-objective genetic algorithm. A model is built, and the feasibility of the proposed method is verified. The diffractive waveguide system has a 10m m×10m m exit pupil size at the eye relief of 25mm and a field of view (FOV) of 21∘×12∘. After the optimization, the overall optical efficiency of the central field and the angular uniformity at the center exit pupil position increased from 0.9% and 66% to 3.1% and 80%, respectively.

Near-unity nonreciprocal thermal radiation in biaxial van der Waals material-Weyl semimetal heterostructures

Polaritons in natural van der Waals (vdW) materials have drawn significant attention as the unique optical properties and have opened doors for various potential applications. α-phase molybdenum trioxide (α-MoO3) has been revealed as a semiconducting anisotropic vdW material that holds great promise for manipulating orthogonal in-plane phonon polariton (PhP) modes in infrared (IR). Here, we consider an attenuated total reflection (ATR) geometry consisting of an α-MoO3 layer and a Weyl semimetal (WSM) interlayer sitting on a silver (Ag) substrate. The incorperated coupling prism is selected as KRS5 (thallium bromide-iodide) that can provide a larger wavevector. The spectral responses of the proposal have been investigated using electromagnetic (EM) simulations that utilize the anisotropic rigorous coupled-wave analysis (aRCWA). Our results demonstrate that the α-MoO3 thin layer can boost the constrast between the emissivity and absorptivity in a broad range of wavelength as compared to an uncoated device. The nonreciprocity at resonance wavelength can reach near-unity for both transverse electric (TE) and transverse magnetic (TM) wave incidence. The proposed α-MoO3/WSM heterostructure suggests great potentials for thermal radiation management with different demands.

Polarization-independent two-dimensional dielectric grating for 3 × 3 beam splitter

Conventional multi-port beam splitters with spot arrays, while being key components in diversiform optical systems, show polarization sensitivity and insufficient uniformity. Here, we proposed a polarization-independent high-efficiency 3 × 3 beam splitter based on the two-dimensional(2D) cylindrical dielectric grating (CDG), which could redistribute the incident light into nine beams with equal power. The proposed grating consists of a double-layer dielectric cylinder on the substrate of fused silica. The parameters of grating structure and fabrication tolerance are calculated by using rigorous coupled wave analysis (RCWA) and simulated annealing algorithm. The numerical results show that nine diffraction orders ((0, 0), (±1, 0), (0, ±1), (±1, ±1)) have average diffraction efficiencies of 10.12 % with uniformity of 2.8 % and mean polarization-independent loss (PDL) of 0.076 dB for TE and TM polarization. This work can open a new and positive way for researching the 2D multi-spot beam splitter and has promising applications in the field of three-dimensional(3D) imaging and reconstruction, microscopy techniques, material processing, etc.

Regime Map of the Effective Medium Approximation Modelling of Micro-Rough Surfaces in Ellipsometry.

In this work, we discuss the precision of the effective medium approximation (EMA) model in the data analysis of spectroscopic ellipsometry (SE) for solid materials with micro-rough surfaces by drawing the regime map. The SE parameters ψ (amplitude ratio) and Δ (phase difference) of the EMA model were solved by rigorous coupled-wave analysis. The electromagnetic response of the actual surfaces with micro roughness was simulated by the finite-difference time-domain method, which was validated by the experimental results. The regime maps associated with the SE parameters and optical constants n (refractive index) and k (extinction coefficient) of the EMA model were drawn by a comparison of the actual values with the model values. We find that using EMA to model micro-rough surfaces with high absorption can result in a higher precision of the amplitude ratio and extinction coefficient. The precisions of ψ, Δ, n and k increase as the relative roughness σ/λ (σ: the root mean square roughness, λ: the incident wavelength) decreases. The precision of ψ has an influence on the precision of k and the precision of Δ affects the precision of n. Changing σ alone has little effect on the regime maps of the relative errors of SE parameters and optical constants. A superior advantage of drawing the regime map is that it enables the clear determination as to whether EMA is able to model the rough surfaces or not.

Compact pupil-expansion AR-HUD based on surface-relief grating.

Augmented reality head-up display (AR-HUD) using diffractive waveguide is a challenging research field. It can drastically reduce the system volume compared with AR-HUD based on freeform mirror. However, one of the remaining challenges that affects the performance of the diffractive waveguide is to expand the eye-box while maintaining the illuminance uniformity. In this paper, a one-dimensional pupil expansion diffractive optical waveguide system for AR-HUD is presented. The optimization of grating parameters is based on scalar diffraction theory and rigorous coupled wave analysis (RCWA). Then, the illuminance uniformity is optimized through non-sequential ray tracing. We simulate and construct a waveguide-based AR-HUD. The presented AR-HUD realized an exit pupil size of 80 mm × 15 mm and a field of view of 10° × 5° at the wavelength of 532 nm.

Enhancing surface sensing performance of cascaded high contrast gratings using bound states in the continuum.

We proposed the cascaded high contrast grating (CHCG) structure to enhance surface sensing capabilities through bound states in the continuum (BICs). Utilizing the finite element method (FEM) and rigorous coupled-wave analysis (RCWA), we studied the dispersion relations, far-field contribution CHCGs, and near-field distributions of BICs corresponding to resonance peaks at different wavelengths. Results demonstrate the ability to precisely control symmetry-protected BIC (SP-BIC) and Friedrich-Wintgen BIC (FW-BIC) resonance peaks by altering incident angles and structural parameters, enhancing structure robustness and tunability. Significantly, modes 1 and 2 have demonstrated substantial enhancement in surface refractive index sensing, achieving highest sensitivities at 51 nm/RIU and the figure of merit reaching 490.8 RIU-1, indicating notable advancement in detecting subtle surface changes. In contrast, mode 3 has shown robust performance in bulk refractive index sensing, achieving a sensitivity of 602 nm/RIU and a figure of merit of 5189.65 RIU-1. These findings underscore the significant potential of the structure as a high-performance integrated sensor, particularly for precise environmental and biological monitoring in surface refractive index sensing.

Optical diffraction properties of three superimposed self-organized nanostructures induced by a laser process.

Controlling the diffraction properties of materials over a large area holds great promise for a wide range of optical applications. Laser-based techniques have emerged as a viable solution to address this need. Here, we present the diffraction properties of laser-induced self-organized structures, which consist of three interlaced grating-like structures: self-organized nanoparticles, self-organized cracks, and laser marking lines. Under normal incidence external illumination, the sample exhibits an asymmetric diffraction pattern. However, when the incidence angle is tilted, circular diffraction patterns are observed in the plane perpendicular to both the sample and the incidence plane. These phenomena are attributed to the combination effect of the diffraction gratings. To elucidate the underlying physics of multiple diffraction, we use rigorous coupled-wave analysis (RCWA) and grating equations written in direction cosine space, extended to account for the presence of three superimposed gratings. Exploiting the laser-induced diffraction properties of these samples may have great potential for various industrial implementations, including security, display, and design.

Thermophotovoltaic emitter design with a hyper-heuristic custom optimizer enabled by deep learning surrogates

Micro/nanostructures hold promise for use as emitters to boost the efficiency of thermophotovoltaic (TPV) systems. For example, periodic gratings may alter the spectrum of irradiation on the photovoltaic cell to better match the spectral response of the cell. Photons with energies slightly higher than the bandgap of the semiconductor are the most desired as they generate electron-hole pairs with minimal thermalization losses. This prompts the use of gratings as selective emitters, and the choice of grating geometry has been an active research topic. Even for a one-dimensional (1D) grating, millions of possible geometries exist, and each grating requires computationally intensive full-wave simulation, e.g., the rigorous coupled-wave analysis (RCWA), to calculate the spectral, directional emissivity. Since optimization algorithm performance is problem-dependent, in this work, a hyper-heuristic search enabled by a fully connected neural network surrogate of the native RCWA is employed to select an algorithm for a specific grating design problem. A comparison with existing untuned algorithms for an ideal emitter problem demonstrates that the hyper-heuristically generated algorithm yields superior performance. This algorithm is then employed for the optimization of the emitter for a full TPV system comprising a heated 1D tungsten binary grating paired with a 300 K InGaSb cell. The system is optimized for maximum power or efficiency at 2000 K and 1500 K, respectively, and the grating properties for the optimized cases are analyzed.

Rigorous coupled-wave analysis of unilateral Smith-Purcell radiation from asymmetric resonators.

The Smith-Purcell radiation produced by electrons moving closely to a grating can be enhanced by resonances. Here, we show a method to manipulate the directionality of the resonance-enhanced radiation. Using the rigorous coupled-wave analysis method, we compare the radiation from symmetric and asymmetric gratings, showing that the enhanced Smith-Purcell radiation can become unilateral with a perturbation that breaks the structural symmetry. Our work provides an effective method for frequency-domain calculation of Smith-Purcell radiation and also an approach to realize more efficient use of the radiation.

Mask correction method for surface plasmon lithography.

Surface plasmon lithography (SPL) has emerged as an innovative approach to nano-fabrication, offering an alternative to traditional patterning methods. To enhance its pattern fidelity in manufacturing, it is essential to incorporate mask correction to reduce critical dimension (CD) errors between the intended target features and the photoresist image. Traditionally, the aerial image of SPL has been modeled and simulated using methods such as finite difference time domain (FDTD) or rigorous coupled wave analysis (RCWA). These models have allowed us to obtain aerial images of the mask patterns. However, relying solely on the aerial image proves insufficient for meeting the rigorous manufacturing standards for mask correction. In our research, we propose a comprehensive model that combines the optical model, employing the FDTD method, and the resist model, tailored to the specific surface plasmon lithography process. Test patterns were meticulously designed with a target CD of 130nm, and the model was applied to simulate these test patterns, producing the after-development image (ADI) under predefined process conditions. Following a thorough analysis and data processing of the test patterns and ADI data, we established rule tables for the correction of both 1D line patterns and line end patterns. The simulation results unequivocally demonstrate the improved CD error performance achieved by the post-corrected patterns.

ZnO Matrices as a Platform for Tunable Localized Surface Plasmon Resonances of Silver Nanoparticles

In this study, the localized surface plasmon resonances (LSPRs) of Ag nanoparticles (NPs) embedded in ZnO dielectric matrices were studied. Initially, continuous Ag thin films were deposited on Corning glass substrates via magnetron sputtering, followed by post annealing, resulting in the formation of self-assembled nanoparticles. In some cases, a heated substrate holder was employed to induce NP formation during the deposition. The morphology of nanoparticles was studied using atomic force microscopy (AFM). Ultraviolet–visible spectroscopy (UV-Vis) probed the LSPRs. Subsequently, a 70 nm thick ZnO layer was deposited on top of the Ag thin films. For the Ag films, LSPR characteristics were found to depend on the initial film thickness. The ZnO capping layer induced an intense red shift, suggesting its potential as a mechanism for tailoring LSPRs. Lastly, theoretical calculations with the rigorous coupled-wave analysis (RCWA) method were carried out for comparison with the experimental results.

Experimental study and modeling of extreme ultraviolet 4000 lines/mm diffraction gratings coated with periodic and aperiodic Al/Mo/SiC multilayers.

Multilayer coated diffraction gratings are crucial components for extreme ultraviolet (EUV) applications such as spectroscopy or spectro-imaging. However, for high groove density, the smoothening of the grating surface profile with multilayer deposition remains a limitation that requires further investigation. In this paper, we report on the design, characterization, and modeling of 4000 lines/mm diffraction gratings coated with periodic and aperiodic Al/Mo/SiC multilayers for EUV radiation. Two types of gratings with different groove depths are compared. Multilayer coatings were designed using a genetic algorithm to maximize the first-order diffraction efficiency in the 17-21 and 19-23nm wavelength ranges at normal incidence. Periodic and aperiodic multilayers with different numbers of layers were deposited by magnetron sputtering on the two types of fused silica gratings, and the grating groove profile evolution was measured by atomic force microscopy and cross-section transmission electron microscopy. The first-order diffraction efficiency was measured in the EUV at 5° incidence using monochromatic synchrotron radiation and modeled using the rigorous coupled-wave analysis method. The simulation models refined by using the Debye-Waller factor to account for the multilayer interfacial roughness show good agreement with experimental data. The results reported in this study will allow for designing efficient EUV multilayer gratings for high-resolution spectro-imaging instruments.

Trapezoidal dual-function splitter under second Bragg incidence

In this paper, a reflective trapezoidal dual-functional beam splitter grating is proposed, which performs two independent functions at 1550 nm. For TE polarization, the grating can achieve a uniform three-port output with efficiencies of 32.85%, 32.89%, and 32.75% for 0th, -1st, and -2nd orders respectively. For TM polarization, the grating can achieve a highly-efficient single-channel output of order -2nd with an efficiency of 93.27%. HfO2 is chosen as the material of grating ridge layer, the structural parameters of the grating are studied by using rigorous coupled-wave analysis (RCWA) and simulated annealing algorithm (SAA), and the results are verified by using finite element method (FEM). In addition, the influence of structure and incident error on grating efficiency was also analyzed, the results indicate that the grating has good incident bandwidth and manufacturing tolerance with excellent performance.

Optimization of the efficiency of a nanowire solar cell by nanowire tapering

Thermodynamics shows that the open-circuit voltage (Voc) of a solar cell is dependent on the external radiative efficiency at Voc. In planar solar cells with low photon recycling probability, this efficiency is limited to 2% due to total internal reflection of the emitted light, providing a penalty of 101 mV to the Voc. Tapered nanowire solar cells allow for an adiabatic expansion of the guided optical mode into air, allowing to reduce this loss. For this purpose, we first perform simulations of the photon escape probability in tapered nanowires with both finite difference time domain simulations as well as with rigorous coupled-wave analysis, showing photon escape probabilities up to 47.2% for normally tapered nanowires and up to 92% for inversely tapered nanowires. We subsequently show that by fine tuning the recipe for reactive ion etching of the tapered InP nanowires, we can decrease the nanowire tapering angle from 4.5° down to 1.8°, allowing to significantly increase the measured external radiative efficiency. We finally observe an open-circuit voltage of 0.746 V at a tapering angle of 2.46°.

Design of double-lattice GaN-PCSEL based on triangular and circular holes.

We have theoretically designed a double-lattice photonic crystal surface-emitting laser (PCSEL) based on triangular and circular holes. In the design, porous-GaN which has the properties of lower refractive index and high quality stress-free homo-epitaxy with GaN, was first proposed to be the cladding layer for GaN-PCSEL. The finite difference-time domain (FDTD), the plane wave expansion (PWE), and the rigorous coupled-wave analysis (RCWA) method were employed in the investigation. Our simulations achieved a radiation constant of up to 50 cm-1 and a slope efficiency of more than 1 W/A while maintaining a low threshold gain. We conducted a systematic study on the effects of the filling factor, etching depth, and holes shift, on the performance of the PCSEL. The findings indicate that increasing the filling factor improves the radiation constant and slope efficiency. Asymmetric hole patterns and varying etching depths have a similar effect. The introduction of asymmetric patterns and a double lattice in the photonic crystal breaks the symmetry of electric fields in the plane, while different etching depths of the two holes break the symmetry in the vertical direction. Additionally, altering the shift of the double lattice modifies the optical feedback in the resonators, resulting in variations of cavity loss and confinement factor.