Rigorous Coupled-wave Analysis Method Research Articles

Mitigating the Impact of Asymmetric Deformation on Advanced Metrology for Photolithography

Controlling overlay in lithography is crucial for improving the yield of integrated circuit manufacturing. The process disturbances can cause undesirable morphology changes of overlay targets (such as asymmetric grating), which can significantly impact the accuracy of overlay metrology. It is essential to decouple the overlay target asymmetry from the wafer deformation, ensuring that the overlay metrology is free from the influence of process-induced asymmetry (e.g., grating asymmetry and grating imbalance). Herein, we use an asymmetric grating as a model and show that using high-diffraction-order light can mitigate the impact of asymmetric grating through the rigorous coupled-wave analysis (RCWA) method. In addition, we demonstrate the diffraction efficiency as a function of the diffraction order, wavelength, and pitch, which has guiding significance for improving the measurement accuracy of diffraction-based overlay (DBO) metrology.

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.

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.

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.

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.

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.

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 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 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.

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.

Band Dynamics of Multimode Resonant Nanophotonic Lattices with Adjustable Liquid Interfaces.

Subwavelength resonant lattices offer a wide range of fascinating spectral phenomena under broadside illumination. The resonance mechanism relies on the generation of lateral Bloch modes that are phase matched to evanescent diffraction orders. The spectral properties and the total number of resonance states are governed by the structure of leaky modes and the mode count. This study investigates the effect of interface modifications on the band dynamics and bound-state transitions in guided-mode resonant lattices. We provide photonic lattices comprising rectangular Si3N4 rods with a liquid film with an adjustable boundary. The band structures and band flips are examined through numerical simulations using the rigorous coupled-wave analysis (RCWA) method and analyzing the zero-order spectral reflectance as a function of the incident angle. The band structures and band flips are examined through numerical simulations, and the influences of the refractive index and the thickness of the oil layer on the band dynamics are investigated. The results reveal distinct resonance linewidths corresponding to different refractive indices of the oil layer. Furthermore, the effect of the oil thickness on the band dynamics is explored, demonstrating precise control over the number of propagating modes within the lattice structure. Theoretical simulations and experimental results are presented for a subwavelength silicon-nitride lattice combined with a liquid film featuring an adjustable boundary. The presence of a relatively thick liquid waveguiding region enables the emergence of additional modes, including the first four transverse-electric (TE) leaky modes, which produce observable resonance signatures. Through experimental manipulation of the basic lattice's duty cycle, the four bands undergo quantifiable band transitions and closures. The experimental results obtained within the 1400-1600 nm spectral range exhibit reasonable agreement with the numerical analysis. These findings underscore the significant role played by the interface in shaping the band dynamics of the lattice structure, providing valuable insights into the design and optimization of photonic lattices with adjustable interfaces.

Strongly enhanced sensitivities of CMOS compatible plasmonic titanium nitride nanohole arrays for refractive index sensing under oblique incidence.

Titanium nitride (TiN) is a complementary metal-oxide-semiconductor (CMOS) compatible material with large potential for the fabrication of plasmonic structures suited for device integration. However, the comparatively large optical losses can be detrimental for application. This work reports a CMOS compatible TiN nanohole array (NHA) on top of a multilayer stack for potential use in integrated refractive index sensing with high sensitivities at wavelengths between 800 and 1500 nm. The stack, consisting of the TiN NHA on a silicon dioxide (SiO2) layer with Si as substrate (TiN NHA/SiO2/Si), is prepared using an industrial CMOS compatible process. The TiN NHA/SiO2/Si shows Fano resonances in reflectance spectra under oblique excitation, which are well reproduced by simulation using both finite difference time domain (FDTD) and rigorous coupled-wave analysis (RCWA) methods. The sensitivities derived from spectroscopic characterizations increase with the increasing incident angle and match well with the simulated sensitivities. Our systematic simulation-based investigation of the sensitivity of the TiN NHA/SiO2/Si stack under varied conditions reveals that very large sensitivities up to 2305 nm per refractive index unit (nm RIU-1) are predicted when the refractive index of superstrate is similar to that of the SiO2 layer. We analyze in detail how the interplay between plasmonic and photonic resonances such as surface plasmon polaritons (SPPs), localized surface plasmon resonances (LSPRs), Rayleigh Anomalies (RAs), and photonic microcavity modes (Fabry-Pérot resonances) contributes to this result. This work not only reveals the tunability of TiN nanostructures for plasmonic applications but also paves the way to explore efficient devices for sensing in broad conditions.

Morphological Design of the Photonic Crystals Influence on Improving the Optoelectronic Properties of a-SiGe:H Thin Film Solar Cell

Abstract: With their nano-engineered feature, Photonic Crystals (PhCs) allow the best control of the propagation and absorption of light in an increased way. In our work, we applied the Rigorous Coupled Wave Analysis (RCWA) method to calculate the diffraction efficiency, field distribution, for a specific incidence angle and absorption energy in a periodic structures using unpatterned, 1DPhC, half circle and triangular grating structures with both a-Si:H, a-SiGe:H thin film semiconductor materials with different gratings of PhCs to improve optical absorption, taking into account the J-V solar cell characteristics. According to our simulation, the ideal result was in the case of triangular grating with a-SiGe:H semiconductor material so for the presence of Germanium, which enhances light absorption by reducing the band gap energy. The optical light absorption was more than 85.7% by increase the lattice parameter from 0.3µm to 0.5µm. Moreover, we found a solar cell efficiency enhancement of 16.6%, with a total improvement of 7.74%; as compared with unpatterned grating. Concerning the incidence angle effect, the better one is ranged between 50° and 70° with a peak absorption ratio of 99%. Keywords: Photonic crystals, RCWA, Incidence angle, Triangular grating, Solar cell.

Low Threshold Current and Polarization-Stabilized 795 nm Vertical-Cavity Surface-Emitting Lasers

Low threshold current and polarization-stabilized 795 nm vertical-cavity surface-emitting lasers (VCSELs) are fabricated by integrating a surface grating of high polarization selectivity and high reflectivity. The rigorous coupled-wave analysis method is used to design the surface grating. For the devices with a grating period of 500 nm, a grating depth of ~150 nm, and a diameter of the surface grating region of 5 μm, a threshold current of 0.4 mA and an orthogonal polarization suppression ratio (OPSR) of 19.56 dB are obtained. The emission wavelength of 795 nm of a single transverse mode VCSEL is achieved at a temperature of 85 °C under an injection current of 0.9 mA. In addition, experiments demonstrate that the threshold and output power also depended on the size of the grating region.

Analysis of optical propagation characteristics of the ultra-long period grating using RCWA.

There have been significant research and analyses on the diffraction efficiency and characteristics of spectral grating with a wavelength-scale period. However, thus far an analysis on a diffraction grating with an ultra-long pitch over several hundred times of the wavelength (>100µm) and a very deep groove over dozens of micrometers has not been performed. We analyzed the diffraction efficiency of these gratings by using the rigorous coupled-wave analysis (RCWA) method and confirmed that the RCWA analytic results correspond well to the actual experimental results on the wide-angle beam-spreading phenomenon. In addition, because a long-period grating with a deep groove results in a small diffraction angle with relatively uniform efficiency, it is possible to convert a point-like distribution to a linear distribution for a short working distance and a discrete distribution for a very long working distance. We believe that a wide-angle line laser with a long grating period can be used in various applications, such as level detectors, precision measurements, multi-point light detecting and ranging (LiDAR) light sources, and security systems.

Weyl semimetal mediated epsilon-near-zero hybrid polaritons and the induced nonreciprocal radiation.

Polaritonic excitation and management in ultra-thin polar crystals has recently received significant attention and holds new promise for epsilon-near-zero (ENZ) modes. However, manipulation of the ENZ mode via anisotropic magneto-optic (MO) material remains elusive. Herein, we provide an effective strategy for constructing an ENZ polar thin film with dependence on Weyl semimetals (WSM). The thermal radiation of the proposed device is explored with electromagnetic (EM) simulations that utilize the anisotropic rigorous coupled-wave analysis (aRCWA) method. Strong coupling of the ENZ mode to WSM polaritons has been demonstrated, and the structural parameters hold tolerance on the order of hundreds of nanometers, which is highly favorable for low-cost fabrication and high-performance application. By changing both the azimuthal angle (ϕ) and angle of incidence (θ), the nonreciprocity (η) can be effectively influenced. The distribution of η is symmetrical with ϕ = 180°, η = 0 when ϕ = 90° and ϕ = 270°. The mechanism of this proposal is owing to the hybrid polaritons supported by the polar thin film and nonreciprocal radiation of WSM, which is validated by examining the amplitude distribution of the magnetic field. The nonreciprocal emitter described herein allows simultaneous control of spectral distribution and polarization of radiation, which will facilitate the active design and application of mid-infrared (MIR) thermal emitters.

Polarization-driven thermal emission regulator based on self-aligned GST nanocolumns

The increasing advances in thermal radiation regulators have attracted growing interest, particularly in infrared sources, thermal management, and camouflage. Despite many advances in dynamic thermal emitters with great controllability, sustained external energy is required to maintain the desired emission. In this study, we present a polarization-driven thermal emission regulator based on a two-way control: i) phase change and ii) polarization tuning. Based on a conventional, non-volatile phase change material, i.e., Ge2Sb2Te5 (GST), we newly introduce an anisotropic medium for facile emissivity regulation without heat energy consumption. A rigorous coupled-wave analysis method provides design guidelines for finding optimal structural parameters. We utilized a simple glancing angle deposition process which induces tilted self-aligned nanocolumns with anisotropic properties. The fabricated sample shows polarization-sensitive thermal regulation through thermal imaging spectroscopic measurement. Additionally, we manufactured a multispectral visibly/thermally camouflaged patch that identifies encrypted information at a specific polarization state for a proof-of-concept demonstration.