Rigorous Coupled-wave Analysis Algorithm Research Articles

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.

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.

A self-aligned lithography method based on Fabry-Perot resonator effect

Fabry-Perot (F-P) resonator is widely applied in the field of optics such as micro-ring resonator and photonic crystal, but there are not yet relevant reports about optical imaging. We propose a self-aligned lithography method based on F-P resonator effect and realize self-aligned effect successfully by controlling film stack parameters. The self-aligned structure is composed of Ag/photoresist/Ag film stack and wafer layer which contains SiO2 layer and SiO2/Si gratings. A rapid simulation model based on Rigorous Coupled Wave Analysis algorithm is established to optimize the best parameters of the self-aligned structure. Then rigorous Finite Difference Time Domain model and Finite Element Method model are used to verify the self-aligned effect and the results show that such process has extremely large mask critical dimension (CD) and overlay variation. The mask CD could be tuned more than 50% of structure period while the wafer CD maintains in the range less than 10%, and the maximum mask overlay offset could be ± 25% of half pitch while the wafer pattern center maintains unchanged. All the results show that the proposed method has lots of process robustness and could increase the application area of imaging lithography technology.

Minimizing surface reflectance of crystalline silicon: A simulation based study

Silicon has been a popular choice for optoelectronic devices and solar cells since its discovery mainly due to its abundance in nature. However, methods to improve light trapping and hence increase the efficiency of these devices has always been a subject of great interest. The objective of this study has been to minimize the surface reflectance of thin film silicon through use of anti-reflection coating and surface patterning. In this study, the most effective anti-reflectance coating (ARC) is determined amongst three well known materials namely, Silicon Nitride(Si3N4), Titanium Dioxide(TiO2) and Magnesium Fluoride (MgF2) by simulation through S4 software by implementing Rigorous Coupled Wave Analysis Algorithm (RCWA). The best possible combination of the substrate and ARC is determined for a working wavelength range of 300 nm to 900 nm by varying the thickness of ARC. The best possible combination of substrate and ARC has been subjected to further investigation by imparting patterns and minimum average reflectance of 0.135986 was obtained experimentally.

Computation of intensity and polarization state of diffracted fields from reflective gratings in conical geometry.

Conical diffraction geometry has interesting properties for monochromatization of short pulse sources of extreme-UV or soft X-ray radiation, like high harmonic generation in gases. It enables high diffraction efficiency at the cost of a reduced angular dispersion. Computation of grating efficiency is complex when the incidence plane is not perpendicular to the grating lines because S and P polarizations are coupled. We have therefore developed a special code, named COROX, which implements a rigorous coupled-wave analysis algorithm. The code is able to compute the complex diffracted field from any incidence direction and polarization on any kind of grating (thick lamellar and blazed gratings with single or multilayer coating). COROX is developed with C++ and uses an eigen linear algebra library. This paper outlines the method of computation, and the results are given for a 150 l/mm blazed grating in a conical Littrow configuration.

Robust visibility of graphene monolayer on patterned plasmonic substrates

Single and few-layer graphene flakes, while visible on a dielectric surface with customized thickness, cannot be optically imaged when exfoliated directly on semiconductors or metal substrates with arbitrary thickness. In this paper, we show that such graphene flakes become visible through a conventional microscope on a substrate patterned with a submicron sized, hexagonally packed array of gold disks. The interaction of the metal pattern with the incident light generates surface plasmon polaritons (SPPs) and results in enhanced reflectivity for certain angles and wavelengths. In the areas where graphene flakes are present, the interaction of the SPP with incident radiation is altered and consequently decreases the reflectivity in this region and increases the contrast, which accounts for the visibility of the graphene flakes on such substrates. We validate the observed contrast in visibility utilizing an in-house developed modified form of rigorous coupled wave analysis algorithm to appropriately incorporate the optical properties of two-dimensional materials. We present a parametric study of the contrast of graphene flakes on the patterned substrate to demonstrate the robustness of the visibility.

Surface plasmon-enhanced optical absorption in monolayer MoS2 with one-dimensional Au grating

The optical absorption of a composite photonic structure, namely monolayer molybdenum disulfide (MoS2)-covered Au grating, is theoretically investigated using a rigorous coupled-wave analysis algorithm. The enhancement of localized electromagnetic field due to surface plasmon polaritons supported by Au grating can be utilized to enhance the absorption of MoS2. The remarkable enhancement of absorption due to exciton transition can also be realized. When the period of grating is 600 nm, the local absorption of the monolayer MoS2 on Au grating is nearly 7 times higher than the intrinsic absorption due to B exciton transition. A further study reveals that the absorption properties of Au grating can be tailored by altering number of MoS2 layers, changing to a MoS2 nanoribbon array, and inserting a hafnium dioxide (HfO2) spacer. This work will contribute to the design of MoS2-based optical and optoelectronic devices.

Rigorous Coupled Wave Analysis for Plasmonic Nanoparticles

Electromagnetic simulation packages for nanoparticles have become of interest for science and engineering community because of interesting properties of nanomaterials, such as, plasmonics and localized field enhancement. There are several approaches to calculate electromagnetic wave responses including time domain and frequency domain; each approach does have its own pros and cons. In this paper, we discuss basic principle of Rigorous coupled wave analysis (RCWA) and some key issues of 2D Rigorous Coupled Wave Analysis (RCWA) for nanoparticle simulation, such as, the computing demands (long computation time and memory consumption) and staircase approximation. We also suggest some feasible approaches to get around the issues and speed up the calculation, such as, employing Li Feng Li’s RCWA algorithm for circular and elliptical rods, making use of the symmetry of spherical shape particles to reduce redundancies in computation and building up an Eigenvector/Eigenvalue database of difference radii of disks, so that these disks can be stacked together to form various sizes of nanospheres.

New alignment mark designs in single patterning and self-aligned double patterning

In single patterning, the increase of odd order diffractive power and decrease of even order diffractive power may improve the wafer alignment performance. A Fourier model is given to quantitatively describe the diffractive optical power of grating structures. Four novel alignment mark structures with higher odd order wafer qualities (WQs) have been optimized based on the model. The accuracy of our model has been validated with almost the same results for different alignment marks using our model and rigorous coupled wave analysis (RCWA). Moreover, three dimensions (3D) of alignment mark should be optimized to get higher WQs for self-aligned double patterning (SADP). Our paper proposes a model to simplify the 3D RCWA algorithm where WQs of SADP grating structures could be split into two different one-direction grating structures. The advantage of the equation makes the evaluation of different grating period of SADP mark fast, accurate and simple. The models and structures of all the designed alignment marks will make it easier for engineers to choose the property alignment mark faced with single patterning or SADP process.

Development of an energy-saving glass using two-dimensional periodic nano-structures

A new type of energy-saving glass, Ag inlaid with SiO2 nano-structures (Inlay SiO2), is numerically developed here to offer modern buildings a passive but promising way of saving power under sunlight. The profile of glass is identified after optimizing optical responses using the genetic algorithm and a fitness function. Wavelength-selective reflectance (R) and transmittance (T) are demonstrated with validated programs based on the rigorous coupled-wave analysis algorithm. The high T and low R in the visible range not only saves energy for lighting but diminishes reflected and stray light. The low T and high R in the near-infrared reduce the cost for air-conditioning. Besides the cost can be further reduced, the superiority of this glass over current commercially available products includes the material commonness, light weight, and freedom from adhesion as well as oxidation. The fabrication tolerance of each dimension is further investigated to determine the key one. Other structure configurations are also approached to explore possibilities of alternates.

Localized input fields in rigorous coupled-wave analysis.

We introduce a new treatment for localized input fields in coupled-wave theory. It consists of a combination of angular spectrum decomposition and a cyclic formulation of rigorous coupled-wave analysis (RCWA), which does not require the computation of several standard RCWA calculations. The cyclic approach especially concerns the definition of the convolution matrix of the permittivity and enables the processing of multiple input plane waves in a single RCWA calculation. At the same time it ensures physically meaningful simulation results for finite truncation limits and thus inherently conserves energy. By adapting the three-dimensional (3D)-RCWA algorithm to efficiently simulate the effects of localized and arbitrarily polarized input fields to 3D volume gratings, various advanced diffraction problems such as fiber coupling, the influence of distorted plane waves, or the effects of focused beams on diffraction gratings can be investigated. Therefore, the impact of this work should concern many fields of application.

Optical absorption in InP/InGaAs/InP double-heterostructure nanopillar arrays for solar cells

The light trapping properties of InP/InGaAs/InP double-heterostructure nanopillar arrays (DH-NPAs) solar cells have been theoretically investigated. The influence of the geometric parameters on the optical absorption of DH-NPAs has been thoroughly analyzed by using rigorous coupled wave analysis algorithm and finite element method. The optical absorption enhancement of DH-NPAs as compared to InP/InGaAs/InP double-heterostructure nanowire arrays (DH-NWAs) in the whole wavelength regime has been demonstrated. The short-circuit current of DH-NPAs with the optimized design can achieve 61.3 mA/cm2, which is 15% higher than that of DH-NWAs with the same geometric configurations, and three times higher than that of thin-film layer with the same thickness. Meanwhile, the absorption profiles at different wavelength and angle-dependant optical properties of DH-NPAs are also evaluated.

Absorption enhancement using nanoneedle array for solar cell

A theoretical analysis of light trapping properties of Gallium arsenide (GaAs) nanoneedle arrays (NNAs) solar cells is presented. The effect of geometric parameters on the optical absorption of NNAs has been analyzed by using rigorous coupled wave analysis algorithm and finite element method. Compared with nanowire arrays and thin-film layer counterpart, higher light absorption efficiency can be achieved in GaAs NNAs, due to the graded refractive index of NNAs that incident light can be coupled into the NNAs efficiently. The absorption profiles at different wavelength and angle-dependant optical properties of NNAs are also evaluated. Meanwhile, the short-circuit current of GaAs NNAs for various lengths at fixed filling factor is obtained.

Evaluation of lithographic performance of extreme ultra violet mask using coherent scattering microscope

The authors report the application of a coherent scattering microscope (CSM) equipped with a femtosecond laser based extreme ultra violet (EUV) source to analyze aerial images for an EUV lithography mask. The CSM employs an EUV beam with a 13.5 nm wavelength and an incident angle of 6° for the wafer scanner emulation. The CSM consists of a condenser optics that delivers the EUV beam to the mask and detector that measures the field spectrum diffracted by the mask pattern. Using a pair of spherical and plane EUV mirrors, coherent EUV light is relayed to the mask and the light diffracted by the mask pattern is measured by a 1 in. size charge-coupled device detector. The integration time of the EUV beam in the detector is controlled by a high speed shutter. This device experimentally records the coherent diffraction pattern from the EUV mask and reconstructs its aerial image using a phase retrieval algorithm. These features made it possible to investigate the projected image properties, such as depth-of-focus, exposure latitude, mask error enhancement factor, horizontal–vertical critical dimension (H–V CD) bias, normalized image log slope (NILS), and so on. The device also provides a mask CD from a rigorous coupled-wave analysis algorithm modeling based on the Maxwell equation through measured diffraction patterns. NILS according to half-pitch design node was measured by CSM and simulated using a Solid-EUV simulator. Illumination conditions of NA and sigma (σ) values are 0.25 and 0.8, respectively, which are the same as those of the EUV exposure tool. The NILS measured by CSM and that simulated using the Solid-EUV have good consistency.

Polarized GaN-based light-emitting diode with an embedded metallic/dielectric subwavelength grating

Highly polarized light from an InGaN/GaN light emitting diode is proposed using an embedded multi-layer metallic/dielectric sub-wavelength grating and a dielectric transition layer. Transmission of transverse magnetic mode ( TTM), reflection of transverse electric mode, and polarization extinction ratio ( ER) were calculated using commercial “GSOLVER” software, based on a full vector implementation of Rigorous Coupled-Wave Analysis algorithm. TTM and ER were found to be largely enhanced by the presence of the transition layer, made of MgF 2 or SiO 2, placed between GaN and the grating section. TTM > 95% and ER > 34 dB for closely optimized Al/MgF 2 gratings were predicted. These values are significantly higher than those obtained by single-layer metallic gratings.

Development of mid-infrared surface plasmon resonance-based sensors with highly-doped silicon for biomedical and chemical applications

Biomedical and chemical sensors utilizing surface plasmon resonance (SPR) in the mid-infrared range were developed with the aid of highly doped silicon owing to its tailored optical constants. SPR may be excited by light incident on a periodic doping profile embedded in an intrinsic silicon film without constraints on the flow of chemical solutions or activities of biomedical samples. General guidance for tuning SPR wavelengths based on dispersion curves to catch different target materials in free space or water was also provided. The feasibility of sensors was demonstrated with a sharp spectral-directional reflectance dip, which shifted with optical constants variation. The effects of doping concentration, doping profile, and angle of incidence on sensor performance were numerically studied with a rigorous coupled-wave analysis algorithm. Developed sensors could work well for a real target and show superiority in sensitivity over existing sensors.

Semiconductor Thin Films Combined With Metallic Grating for Selective Improvement of Thermal Radiative Absorption/Emission

We propose in this work a structure of semiconductor thin films combined with a one-dimensional metallic grating, which allows for selective improvement of thermal radiative absorptivity (also emissivity) of the structure. Both shallow and deep gratings are considered in this work. Our numerical results obtained with a 2D rigorous coupled-wave analysis algorithm demonstrate that the proposed structure exhibits enhanced spectral absorptivity for photon energy slightly above the gap energy of the semiconductor (silicon in this work). Furthermore, the selectively improved absorptivity can be obtained in a wide range of incidence angles. As such, much smaller thickness of the semiconductor layer is required to absorb the same amount of high energy photons than in a conventional Si-based photovoltaic device. In addition, absorptivity for low energy photons in the new structure is lower due to the smaller semiconductor layer thickness. Therefore, the new structure may have potential applications in energy conversion devices.

Extraordinary Transmission through Metallic Grating withSubwavelength Slits for S-Polarization Illumination

Based on the rigorous coupled-waveanalysis algorithm, we have systematically analysed the effect ofthe geometrical parameters of a dielectric film coated metallicgrating with subwavelength slits on extraordinary opticaltransmission for s-polarization illumination. Results show thatthe dielectric film which sustains a waveguide electromagneticmode on the top of the metallic lamellar grating can stronglyenhance the transmittance, the positions of the transmission peaksare mainly determined by the period of the metallic grating, thethickness and refractive index of the dielectric film. Thisstructure shows potential applications in excellent polarizers orpolarization-isotropic devices at infrared spectral range byappropriately choosing the geometrical parameters.

Rigorous Coupled Wave Analysis of Bipolar Cylindrical Systems: Scattering from Inhomogeneous Dielectric Material, Eccentric, Composite Circular Cylinders

Rigorous Coupled Wave Analysis (RCWA) in bipolar coordinates for the first time is used to study electromagnetic (EM) scattering from eccentric, circular, multi-cylinder systems for which spatially, non uniform material (dielectric permittivity) occupies the regions between the interfaces of the cylinders. The bipolar RCWA algorithm presented herein consists of three basic steps which are; (1) solving Maxwell's equations in bipolar coordinates using a state variable (SV) formulation; (2) solving Maxwell's equations in the spatially uniform regions exterior to the inhomogeneous scattering object in terms of circular, cylindrical Bessel-Hankel functions; and (3) enforcement of EM boundary matching equations which leads to a final matrix equation solution of the system. In the paper extensive use of the residue theorem of complex variable theory was made in order to find fast and exact evaluations of the EM boundary interaction integrals that arose between the bipolar, SV solutions and the Hankel- Bessel solutions. In this paper very extensive reliance on the work of A. A. Kishk, R. P. Parrikar and A. Z. Elsherbeni (22) who studied EM scattering from uniform material multi-eccentric circular cylinders (called herein the KPE algorithm) was made in order to validate the numerical results of the bipolar RCWA algorithm. In this paper, two important system transfer matrices, called the Bessel transfer matrix (based on the KPE algorithm) and called the bipolar SV transfer matrix, were developed in order to validate the numerical accuracy of the RCWA algorithm. The Bessel and SV transfer matrices were very useful for validation purposes because, from the way they were both formulated, they could be meaningfully compared to one another, matrix element to matrix element.

Validation and Numerical Convergence of the Hankel-Bessel and Mathieu Rigorous Coupled Wave Analysis Algorithms for Radially and Azimuthally- Inhomogeneous, Elliptical, Cylindrical Systems - Abstract

A Rigorous Coupled Wave Analysis (RCWA) algorithm for electromagnetic (EM) scattering from radially and azimuthally inhomogeneous material elliptical systems based on State Variable (SV) techniques and based on circular-cylindrical Hankel-Bessel expansion modes is developed for the first time. The algorithm in conjunction with the elliptical system RCWA algorithm [1], which was based on SV techniques and Mathieu expansion modes, is used to validate and study numerical convergence of both elliptical RCWA algorithms. The formulation of the SV, Hankel-Bessel elliptical algorithm is presented. Two numerical elliptical examples are studied in detail by both algorithms, a homogeneous one which consists of three different uniform materials located in three elliptical regions and an inhomogeneous one which consists of an azimuthal, dielectric, step profile which is located between two uniform material elliptical regions. In this paper EM field scattering from a step profile which possessed a much larger dielectric step profile difference than was studied in [1] is presented. Validation and numerical convergence data of the Hankel-Bessel and the Mathieu [1] RCWA algorithm is presented for the first time, both in plot figures and in tables, when different numbers of expansion modes were used, when different number of layers were used, and when different numbers of SV harmonics were used. Validation of the RCWA algorithms was further carried out for the homogeneous case, by using Mathieu expansion modes in all regions and was carried out by using Hankel-Bessel expansion modes