Rigorous Coupled-wave Analysis Research Articles

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.

Design of large-deflection-angle high-diffraction-efficiency high-dispersion hybrid gratings

Gratings are key components in many optical systems such as spectrometers. Improving their dispersion is very important for their applications, but improving the single-order diffraction efficiency of an ultrahigh dispersion grating is still very challenging. Here, we propose an analytical approach for the design of a new type of grating named hybrid grating, which consists of a subwavelength grating and a non-subwavelength grating. The proposed analytical approach is based on a physical model in which the non-subwavelength grating acts as an ultrathin reflection grating and the subwavelength grating acts as an antireflection coating. Using the rigorous coupled-wave analysis and the finite-difference time-domain method, we numerically demonstrate that multiple hybrid gratings designed at different wavelengths using the proposed analytical approach show a diffraction efficiency of greater than 95 % in the -1st diffraction order for TE-polarized light, an angular dispersion of greater than 0.8 mrad/nm and a deflection angle of greater than 80°. Furthermore, we numerically demonstrate that by using a combined approach to optimize the parameters of a hybrid grating, the diffraction efficiency in the -1st diffraction order for TE-polarized light can be increased to more than 97 % under the condition that the angular dispersion and the deflection angle of the hybrid grating remain unchanged. Our work provides an avenue for rapid design of gratings with high angular dispersion, large deflection angle and high diffraction efficiency.

Three-dimensional plasmonic lithography imaging modeling based on the RCWA algorithm for computational lithography.

This paper reminds the principle and characteristics of plasmonic lithography, and points out the importance of establishing a fast and high precision plasmonic lithography imaging model and developing computational lithography. According to the characteristics of plasmonic lithography, the rigorous coupled-wave analysis (RCWA) algorithm is a very suitable alternative algorithm. In this paper, a three-dimensional plasmonic lithography model based on RCWA algorithm is established for computational lithography requirements. This model improves the existing RCWA algorithm, that is, deduces the formula for calculating the light field inside the structure and proposes the integration, storage and invocation of the scattering matrix to improve the computation speed. Finally, the results are compared with commercial software for the two typical patterns. The results show that the two calculation results are very close, with the root mean square error (RMSE) less than 0.04 (V/m)2. In addition, the calculation speed can be increased by more than 2 times in the first calculation, and by about 8 times by integrating, storing and invoking the scattering matrix, which creates conditions for the development of plasmonic computational lithography.

Design of VO2-based spacecraft smart radiator with low solar absorptance

Thermochromic film with the ability to self-adaptively switch emittance is important for spacecraft missions experiencing rapidly increasing demand. Current research on thermochromic films primarily focuses on optimizing emittance tunability, while the solar absorptance of these films remains high, limiting their practical application in spacecraft thermal control. In this work, a VO2-based spacecraft smart radiator with low solar absorptance and high emittance tunability is proposed. The smart radiator is a multilayer structured film composed of a switchable resonator (i.e., a superposed Fabry-Perot cavity) and a solar reflector (i.e., a Distributed Bragg Reflector). The performance of the smart radiator is optimized by combining the Rigorous Coupled Wave Analysis method and Genetic Algorithm, achieving a normal solar absorptance of 0.121 and emittance tunability of 0.825. The solar absorptance and emittance tunability of the smart radiator remain excellent even at large incident angles. The underlying mechanisms involved in the smart radiator are attributed to the combination of superposed Fabry-Perot resonance and multiple solar reflectance. In addition, we provide a numerical example using a geosynchronous orbit satellite to demonstrate that the regulation range of the net heat dissipation flux density can increase from 146.5–463.9 W/m2 by using Optical Solar Reflector to 0–494.6 W/m2 when using the proposed smart radiator within the permissible temperature range (263.15–318.15 K) of spacecraft. This VO2-based spacecraft smart radiator with outstanding properties which outperform the existing thermochromic films reveals the promising potential of thermochromic films for spacecraft intelligent thermal control applications.

Conical diffractions of multilayered gratings modeled by Cartesian rigorous coupled-wave analysis.

Rigorous coupled-wave analysis (RCWA) has become one of the most efficient electromagnetic solvers to cope with the diffractions of large-scale periodic nanostructures. Conventional RCWAs focus on planar diffractions and their iterative stabilities. Conical diffractions, as more general incidence cases, are paid little attention in developing their universal and stable implementations for multilayered gratings. Here, we reformulate RCWA algorithms step by step for conical diffractions in a global Cartesian coordinate system. By applying some mathematics tricks, it is found that boundary conditions in conical diffractions can be reduced to the same forms as that of planar diffractions. Conventional stable algorithms including enhanced transmittance matrices and scattering matrices can be directly implemented to attain robust diffraction efficiencies as well as electromagnetic fields for multilayered gratings. An exemplary application in diffractive-waveguide-based augmented reality verified our algorithms.

Polarization states and far-field optical properties in dielectric photonic crystal slabs.

We study the role of topological singularities like Bound States in a Continuum (BICs) or Circularly Polarized States (CPSs) in determining ellipticity of the far-field polarization in dielectric metasurfaces. Using finite-difference time-domain as well as rigorous coupled-wave analysis simulations, we determine the behavior of the Stokes parameter S3 in the whole k space above the light cone, with special regard to the region close to the singularities. Moreover, we clarify the relation between the topological singularities and the circular dichroism in reflectivity.

From design to realization of high diffraction efficiency Littrow configuration diffraction gratings based on multilayer dielectric mirrors patterned with electron beam lithography

Diffraction efficiency (DE) and laser-induced damage threshold of Chirped pulse amplification (CPA) system diffraction gratings (DGs) are one of the main limiting factors for the anticipated progress of high peak power lasers. Optimization of a high reflectivity dielectric multilayer ZrO2/SiO2 stack mirror with a DG etched in the top SiO2 layer was carried out employing the Rigorous coupled wave analysis method. Two families of solutions possessing DE > 0.99 over the bandwidth of the 1030 nm wavelength ultrashort laser and withstanding different fabrication margins were identified for the Littrow configuration. DGs were produced and verified experimentally. Structures permitting variation in both the depth of the DG and filling factor without loss in DE were obtained for the 690 nm thick SiO2 layer. While the 770 nm thick layer permitted separation of the two parameters requiring either rigorous control of the DG depth or filling factor. DG realization technology was proposed employing electron beam lithography and inductively coupled plasma reactive ion etching. Measurements of the fabricated structures demonstrated 0.91 DE for the first diffraction order over the 60 nm bandwidth and under a 6° mounting error from the Littrow configuration. Spectral angular reflectance DE simulations and respective measurements indicated quantitative agreement. The work provides an integrated overview of high DE periodic structure numerical optimization and manufacturing roadmap which could be applied for the high-peak-power laser CPA system development.

Dual-polarization strong nonreciprocal thermal radiation under near-normal incidence

Performance of irreversible radiation is limited by the single polarization and large incident angles. Given potential applications of nonreciprocal thermal radiation, the implementation of irreversible radiation for both TE and TM polarizations at small angles is highly demanded. A solution that combines periodic silicon-based nanopore arrays with magneto-optical material (InAs) is proposed in this work. The results show that the absorptivity and emissivity of two polarizations are close to 98% with an incident angle of 1.5° and a high Q factor over 1680. By adjusting the applied magnetic field, the emissivity and transverse magneto-optical Kerr effect can be dynamically tuned. The validity of the calculation results is verified by the rigorous coupled-wave analysis and finite element method. Impedance matching theory and coupled mode theory are adopted to further analyze the physical origin. The proposed scheme and thermal radiator that allow nonreciprocal thermal radiation for both TE and TM polarizations at an extremely small incident angle offer valuable guidance to the development of dual-polarization nonreciprocal radiation devices.

Multi-band infrared camouflage compatible with radiative cooling and visible colors via a simple multilayer film structure

Conventional infrared camouflage materials are typically confined to special spectral ranges. To address challenges posed by the combination of both active and passive detection operating in different bands, a multi-band compatible camouflage material is highly required. Combining rigorous coupled-wave analysis and genetic algorithm, a 9-layer film structure composed of 3 thermally stable materials (SiO2, Ge and TiO2) on a quartz substrate is designed, which achieves multi-band infrared camouflage compatible with radiative cooling and visible colors. Specifically, the structure exhibits low average emissivity of 0.12 and 0.21 in the two atmospheric window bands of 3∼5 µm and 8∼14 µm, while it shows spectral emissivity favorable of radiative cooling (an average of 0.67) in the non-atmospheric window band of 5∼8 µm. The structure also achieves high absorptivity at two widely applied laser wavelengths of 1.06 µm (Nd:YAG lidar) and 10.6 µm (CO2 lidar). In addition, by manipulating the thickness of the top layer, the structure exhibits tunable visible colors covering green, blue and yellow, et al., without much influence on the above selective absorption and emission in the infrared bands. The multi-band selective absorption/emission characteristic is also applicable to large incident/emission angles. The underlying physics are analyzed in detail. The selective emission in the mid-infrared band is mainly caused by the forbidden bands formed by the multilayer film, while the high absorption at both laser wavelengths is attributed to the Fabry-Perot resonance supported in the structure and the intrinsic absorption of the materials. Finally, the overall camouflage performance of the structure is evaluated to make the results more intuitive. The significance of this work lies in the balance between the multi-band compatibility and structural simplicity of camouflage materials.