Rigorous Coupled-wave Analysis Research Articles

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.

Directional spectral emissivity characterization and modeling of laser-patterned steel surfaces

We present preliminary results on the fabrication of patterned surfaces by Direct Laser Interference Patterning and the characterization and theoretical interpretation of their infrared emissivities. The upgraded experimental method is capable of studying the full directional emission of samples under a controlled atmosphere at high temperatures. The effects of surface patterning can be quantitatively studied and modeled using a numerical method based on rigorous coupled-wave analysis (RCWA), a technique usually employed for periodic surfaces. The results show that laser interference patterning is capable of modifying the infrared emission of metallic materials, and that these changes can be accurately measured and numerically reproduced.

Optical enhancement of perovskite solar cells by metallic nano-patterns

The integration of metallic nanoparticles (MNPs) with plasmonic effects is an alternate approach for managing photons and charge carriers, and is considered a promising method for advancing solar cell technologies. Plasmonic-enhanced solar energy harvesting involves three mechanisms: hot-electron injection, light trapping, and modulation of energy flow direction through dipole-dipole coupling. These phenomena have been observed to significantly enhance the performance of silicon, gallium arsenide, dye-sensitized, and organic solar cells. However, for emerging perovskite solar cells, the light trapping effect, specifically, the far-field scattering via MNPs, has been seldom reported. The anomalous phenomenon is primarily attributed to the size constraints imposed on MNPs by the thickness of the functional layers in cell devices. According to the theory of localized surface plasmon resonance (SPR), the characteristic size of the MNPs needs to be larger than 90 nm to achieve optimal photon scattering. Conversely, charge transport layers like NiO<sub>x</sub> and SnO<sub>2</sub> in perovskite solar cells are typically thin, ranging from a few to several tens of nanometers in thickness. Therefore, the community of perovskite solar cells still faces a great challenge in harvesting light through plasmonic scattering.<br>Compared to MNPs, the shape, size, periodicity, and other characteristic parameters of two-dimensional metal patterns within the horizontal plane are not limited by the thickness of the device's functional layer, thus enabling a more flexible regulation of the SPR response band, vibration intensity, and dissipation method of plasmonic energy. In this study, based on the finite-difference time-domain (FDTD) method and rigorous coupled-wave analysis (RCWA), we systematically investigated the SPR spectra of different metal patterns. The results demonstrate that by optimizing characteristic parameters such as pattern shape, thickness, and periodicity, a significant SPR phenomenon can be observed in the near-infrared region, with scattering dominating over extinction. For the optimal metal ring pattern, the SPR peak corresponds to a wavelength of 772 nm, with relative absorption, scattering, and extinction cross-sections of 0.54, 1.39, and 1.93, respectively. The weighted average absorption of the perovskite response layer in the range of 700-850 nm increased from 53.61% to 65.36%. Correspondingly, the photocurrent density of the device increased from 20.39 to 22.72 mA/cm<sup>2</sup>, and the photoelectric conversion efficiency was relatively improved by 11.45%. This research provides a novel path for light trapping design in perovskite solar cells in the near-infrared region, and serves as a "spectrum-based" reference for SPR regulation in other similar devices.

Polarization mixing, bound states in a continuum, and exciton-polaritons in photonic crystal slabs by a guided-mode expansion approach

Photonic crystal (PhC) slabs, or patterned multilayer waveguides, are known to support truly guided modes with no losses, as well as quasi-guided modes that lie in the continuum of far-field radiation. In this contribution, we present a guided-mode expansion approach – and the corresponding free software named legume – that allows calculating a number of features of PhC slabs: (a) symmetry properties and the issue of polarization mixing in coupling to far-field radiation; (b) the occurence of bound states in a continuum, which have infinite Q-factor and give rise to topological singularities of the far-field polarization; (c) the description of active two-dimensional layers through a suitably formulated light-matter coupling Hamiltonian, allowing to describe the regime of strong coupling leading to photonic crystal polaritons. Comparison with rigorous coupled-wave analysis, and the insurgence of non-hermitian features in the optical properties, are also addressed.

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.

A Design Strategy for Surface Nanostructures to Realize Sensitive Refractive-Index Optical Sensors.

Refractive-index optical sensors have been extensively studied. Originally, they were surface plasmon resonance sensors using only a flat gold film. Currently, to develop practically useful label-free optical sensors, numerous proposals for refractive index sensors have been made using various nanostructures composed of metals and dielectrics. In this study, we explored a rational design strategy for sensors using surface nanostructures comprising metals or dielectrics. Optical responses, such as reflection and transmission, and resonant electromagnetic fields were computed using a numerical method of rigorous coupled-wave analysis combined with a scattering-matrix algorithm. As a result, good performance that almost reached the physical limit was achieved using a plasmonic surface lattice structure. Furthermore, to precisely trace the refractive-index change, a scheme using two physical quantities, resonant wavelength and reflection amplitude, was found to be valid for a 2D silicon metasurface.

Inverse design of a light nanorouter for a spatially multiplexed optical filter.

It is attractive to use an optical nanorouter by artificial nanostructures to substitute the traditional Bayer filter for an image array sensor, which, however, poses great challenges in balancing the design strategy and the ease of fabrication. Here, we implement and compare two inverse design schemes for rapid optimization of RGGB Bayer-type optical nanorouter. One is based on the multiple Mie scattering theory and the adjoint gradient that is applicable to arrays of nanospheres with varying sizes, and the other is based on the rigorous coupled wave analysis and the genetic algorithm. In both cases, we study layered nanostructures that can be efficiently modeled respectively which greatly accelerates the inverse design. It is shown that the color-dependent peak collection efficiencies of nanorouters designed in the two methods for red, green, and blue wavelengths reach 37%, 44%, and 45% and 52%, 50%, and 66%, respectively. We further demonstrate color nanorouters that provide light focusing to four quadrants working in both the visible and infrared bands, which promises multispectral imaging applications.

Terahercų emisijos spektroskopija pavidalų panašumui tirti: Ukrainos ir Lietuvos simbolių nagrinėjimas

In this paper, the thermal emission from the n-GaAs/GaAs structure equipped with the Ti/Au metasurface is being investigated in the terahertz region. The metacell shape was chosen to be of heraldic origin, that is either the Ukrainian Trident or the Lithuanian Columns of Gediminids. The experiments were performed using far-infrared Fourier spectroscopy, where the heated sample served as the source of THz radiation. The optical properties of such structures were simulated using the rigorous coupled wave analysis method in order to explain the origin of experimentally observed spectral features. The deconstruction of the simulated spectra was also performed by simulating the properties of simplified metacells which constitute the metacells of the heraldic symbols investigated here. The spectral analysis suggests the similarity between the investigated symbols, which is also reviewed from the historical point of view.

Efficient infrared nine-channel reflective polarization-dependent splitter

In order to meet the requirements of a multi-beam splitter in optical communication systems, an efficient infrared nine-channel reflective polarization-dependent beam splitter based on an addition-shaped ridge structure is proposed. All structural parameters of this polarization-dependent beam splitter are derived from the rigorous coupled-wave analysis. Upon the vertical entry of a plane wave with a wavelength of 800 nm into the grating, for transverse magnetic polarization, the diffraction efficiencies are 10.66%, 10.69%, 10.69%, 10.65%, and 10.67% at 0th, ±1st, ±2nd, ±3rd and ±4th orders, respectively. For transverse electric polarization, the diffraction efficiencies of the 0th, ±1st, ±2nd, ±3rd and ±4th orders are 10.79%, 10.86%, 10.88%, 10.84%, and 10.86%, respectively. In addition, the tolerance analysis in this paper reveals the practicality and efficiency of this beam splitter. Therefore, the addition-shaped ridge structure has a good performance of uniformity and broad application prospects in nine-channel reflective applications.

Wideband multimode smart modulator based on phase change materials

Optical components with switchable optical properties have garnered significant attention due to their wide range of potential applications in the fields of optical detection, radiative cooling, and energy conservation, etc. Most modulators focus on modulating a single parameter within a narrow spectral range, which often falls short of meeting the increasing demands of advanced photonic systems. In this study, we introduce a smart modulator capable of wideband modulation across three modes: transmission, absorption, and reflection. This modulation is triggered by the temperature-dependent phase transition of Vanadium dioxide (VO2) and In3SbTe2 (IST). We optimized the optical properties of the smart modulator using a combination of the Rigorous Coupled Wave Analysis method and Genetic Algorithm. As a result, we achieved average transmissivity, absorptivity, and reflectivity values of 0.785, 0.812, and 0.798, respectively, across the spectral range of 2.5 to 15 µm for each corresponding mode. Importantly, the multimode modulation performance remains excellent even at large incident angles. Furthermore, we demonstrate the exceptional performance of the smart modulator in practical applications, taking thermal fuses as an example. This showcases its effectiveness in thermal protection and modulation. The development of such wideband multimode smart modulators holds the potential to expedite the creation of compact, efficient, and multifunctional optical systems.

Quad-channel waveguide-based near-eye display for metaverse

We present a quad-channel waveguide-based near-eye display as an ultra-wide-angle architecture for the metaverse. The core concept is to divide one field of view into four by placing the couplers within the regions, where only the subsets of field of view are located. Compared to its counterparts, including the single-, double- and triple- channels, our quad-channel waveguide can push the envelope of field of view further. With the aid of k-space diagram, the upper limit of field of view is illustrated and deduced. The design rules of the waveguide, sawtooth grating as the in-coupler, and slanted grating as the out-coupler are expounded. Through the rigorous coupled-wave analysis, the diffraction efficiencies of gratings can be calculated and optimized. As an overall evaluation, its key performance indicators are summarized as follows. Field of view is 100° (diagonal), eye relief is 10 mm, exit pupil is 11.5 × 11.5 mm2, average transmittance is 2.56 %, and average uniformity is 75 %.

Global rigorous coupled wave analysis for design of multilayer metasurface absorbers.

In this work, a novel Global NV-ETM RCWA method is proposed to accelerate the optimization of the periodic stepped radar absorbing structure. This method is based on the rigorous coupled-wave analysis (RCWA) utilizing the normal vector field (NV) and enhanced transmittance matrix (ETM) approach. The NV field dramatically improves the convergence rate for both dielectric and magnetic metasurfaces. The Global NV-ETM RCWA algorithm is developed to further accelerate the complete search calculations. Using the proposed method, the periodic stepped radar absorbing structures are efficiently optimized to realize the entire band absorption in 2-18 GHz. The optimization results demonstrate the Global NV-ETM RCWA method significantly increase the computational efficiency, with a 38-fold improvement over direct NV-ETM RCWA calculations when the truncation order N=3. This method provides a powerful tool for designing metasurface absorbers with various desired functionalities.

Significant Enhancement of Near-Field Radiative Heat Transfer by Misaligned Bilayer Heterostructure of Graphene-Covered Gratings

Abstract The near-field radiative heat transfer of heterostructure consisting of SiC gratings and graphene is investigated in this work. The rigorous coupled-wave analysis is employed to calculate the spectral heat flux. Nevertheless, monolayer heterostructure and nonmisaligned bilayer heterostructure consistently suffer from a lack of spectral heat flux. In this work, we investigate the prominent effect of misaligned bilayer heterostructure in enhancing near-field radiative heat transfer by plotting energy transmission coefficients and electromagnetic fields. The results show that when the misalignment reaches half a period, the bilayer heterostructure exhibits optimal performance with a total heat flux of 3.5 × 104 W/m2. Besides the well-known coupled surface phonon polaritons supported by SiC gratings, the surface plasmon polaritons supported by graphene dominate the enhancement of heat flux from 0.01 × 1014 rad/s to 1.5 × 1014 rad/s. Due to the spatial misalignment of the upper and lower gratings, the lower layer graphene surface plasmon polaritons are intensified, compensating for the lack of spectral heat flux. Meanwhile, the graphene surface plasmon polaritons and SiC surface phonon polaritons can be hybridized to form surface plasmon-phonon polaritons. In addition, the dynamic modulation of near-field radiative heat transfer in the misalignment state is achieved by manipulating the Fermi level of graphene. We finally show that the superiority of misaligned heterostructure is robust with respect to the frequency shift in the phonon band, providing an effective way to improve the near-field radiative heat transfer in different configuration.

Three-dimensional angular deviation and diffraction efficiency of a grating in Littrow-configuration ECDL

We consider in this paper the angular deviation and diffraction efficiency of the reflection gratings in Littrow-configuration for applications of external cavity diode laser using the rigorous coupled-wave analysis method. We consider the three-dimensional diffraction case in general, where the incidence plane is un-parallel with the grating vector, i.e. conical diffraction. The angular tolerance of arbitrary gratings under plane and conical diffraction are thus derived and presented. A typical blazed grating is chosen as an example to calculate its diffraction efficiency using the rigorous coupled-wave analysis method. Furthermore, we point out that the angular tolerance and reflection efficiency can be improved if the appropriate parameter settings are selected for Littrow-configuration devices, including incidence angle, diffraction order, grating period and blazed angle. Otherwise, a tiny slanting angle of the grating vector deviated from the incidence plane will deviate the feedback light away from entering the laser-diode-chip and halt laser oscillation in the external cavity. Finally, a general rule for the parameter settings in Littrow-configuration is provided as a benchmark.