Rigorous Coupled Wave Analysis Simulations Research Articles

Germanium metalens for longwave infrared applications

Metalenses represent a paradigm shift in optics, offering unprecedented control over light manipulation. This study focuses on the design optimization of a polarization-insensitive germanium (Ge) metalens operating in the longwave infrared (LWIR) regime. Employing rigorous coupled-wave analysis (RCWA) and finite-difference time-domain (FDTD) simulations, a metalens with 1mm focal length was designed using nanopillars with 3.5µm height and radius ranging from 0.55µm to 1.2µm. Then, the impact of lattice size and numerical aperture (NA) on lens performance was investigated. The results indicate that smaller lattices allow finer phase control and enhanced transmittance stability across the phase profile if significant coupling effects are not verified. As the NA increases, the focal spot size decreases, albeit with diminishing returns towards the diffraction limit. To the best of our knowledge, it is the first work that shows high focal efficiency (~80%) across multiple NA’s for a LWIR metalens with a diameter under 1100µm. The proposed metalens is compatible with complementary metal-oxide-semiconductor (CMOS) technology and supports low-cost manufacturing.

Legume: A free implementation of the guided-mode expansion method for photonic crystal slabs

We describe legume, a free electromagnetic solver that implements the guided-mode expansion method for patterned multilayer waveguides, or photonic crystal slabs. legume has a built-in tool for automatic differentiation, which makes it suitable for the inverse design of photonic crystal structures with desired physical properties. Compared to a previous version of the method (M. Minkov et al., 2020 [12]), here we introduce several new features of the code, we discuss additional technical aspects of the method and its numerical implementation. The novel features that are treated in this paper include: (i) the separation of modes according to their mirror symmetry with respect to a vertical symmetry plane of the photonic structure, (ii) the problem of polarization mixing in coupling to far-field radiation modes, and (iii) the description of active two-dimensional layers through a suitably formulated radiation-matter coupling Hamiltonian, allowing to describe the physics of both weakly and strongly coupled exciton-photon modes, the latter leading to photonic crystal polariton eigenmodes. Detailed and direct comparisons with rigorous coupled-wave analysis simulations are used to test the accuracy of the method and the numerical efficiency of the code. These newly added features of the legume code significantly increase the prospective applications of guided-mode expansion, making it a very practical and versatile tool enabling the design of advanced photonic structures and the description of radiation-matter interaction. Program summaryProgram Title:legumeCPC Library link to program files:https://doi.org/10.17632/kf3cwknx4d.1Developer's repository link:https://github.com/fancompute/legumeLicensing provisions: MITProgramming language: PythonNature of problem: Dispersion and radiative losses of photonic eigenmodes in patterned multilayer waveguides/photonic crystal slabs/periodic metasurfaces. Interaction of photonic modes with exciton resonances leading to exciton-polaritons. Inverse design by optimization of the parameters.Solution method: Finite-basis expansion using a basis of guided modes of an effective homogeneous waveguide, perturbation theory to describe coupling with far-field radiation. Quantum theory of excitons, photons and their interaction to describe the occurrence of exciton-polaritons. Automatic differentiation via Autograd to implement inverse design. In this upgraded version of the legume code we implement symmetrization with respect to a vertical mirror plane and light-matter interaction for exciton-polaritons. Inverse design has been described previously, here we focus on the new features and applications of the code.

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.

Multidimensional structural coloration from hierarchically designed plasmonic structures

We propose a photonic strategy for multidimensional structural coloration that responds to varying illumination conditions. Both theoretical and experimental results verified that the combination of a metal/dielectric/metal cavity with a one-dimensional (1D) metal grating can increase the degree of freedom of structural coloration. We fabricated Ag/MgF2/Ag cavities coupled to 1D Ag gratings (pitches of 400, 570, and 800 nm) and obtained their photonic band dispersions (i.e., angle-resolved reflectance spectra) to unravel their mode characteristics. The 1D Ag grating and Ag/MgF2/Ag cavity induced surface plasmon polariton (SPP) and Fabry–Perot cavity modes, respectively. Notably, only a cavity mode emerged in the s-polarization and gradually blueshifted with increasing angle, whereas in the p-polarization, both SPP and cavity modes appeared and shifted oppositely with changes in the angle, leading to intricate color patterns at different wavelengths, angles, and polarizations. To further understand the effect of each mode upon structural coloration, we obtained the distribution of electric field intensity using rigorous coupled-wave analysis simulation, which identified multiple photonic bands in the p-polarization as various SPP-mediated hybrid modes.

Sensing Mechanisms of Rough Plasmonic Surfaces for Protein Binding of Surface Plasmon Resonance Detection.

Surface plasmon resonance (SPR) has been utilized in various optical applications, including biosensors. The SPR-based sensor is a gold standard for protein kinetic measurement due to its ultrasensitivity on the plasmonic metal surface. However, a slight change in the surface morphology, such as roughness or pattern, can significantly impact its performance. This study proposes a theoretical framework to explain sensing mechanisms and quantify sensing performance parameters of angular surface plasmon resonance detection for binding kinetic sensing at different levels of surface roughness. The theoretical investigation utilized two models, a protein layer coating on a rough plasmonic surface with and without sidewall coatings. The two models enable us to separate and quantify the enhancement factors due to the localized surface plasmon polaritons at sharp edges of the rough surfaces and the increased surface area for protein binding due to roughness. The Gaussian random surface technique was employed to create rough metal surfaces. Reflectance spectra and quantitative performance parameters were simulated and quantified using rigorous coupled-wave analysis and Monte Carlo simulation. These parameters include sensitivity, plasmonic dip position, intensity contrast, full width at half maximum, plasmonic angle, and figure of merit. Roughness can significantly impact the intensity measurement of binding kinetics, positively or negatively, depending on the roughness levels. Due to the increased scattering loss, a tradeoff between sensitivity and increased roughness leads to a widened plasmonic reflectance dip. Some roughness profiles can give a negative and enhanced sensitivity without broadening the SPR spectra. We also discuss how the improved sensitivity of rough surfaces is predominantly due to the localized surface wave, not the increased density of the binding domain.

Sensitivity enhancement in OCD metrology by optimizing azimuth angle based on the RCWA simulation

Monitoring process using optical critical dimension (OCD) metrology has been performed with a pre-fixed and unoptimized azimuth angle for all modules. Azimuth angle has a great influence on the optical sensitivity and can be easily tuned by changing the wafer rotation. In this study, we suggest the optimal azimuth angle for both FinFET and MOSFET device based on the rigorous coupled wave analysis (RCWA). For FinFET device, the optical sensitivity at the optimal angle was improved around 30% for two modules compared to that of pre-fixed angle. For MBCFET, we demonstrated that the simulated sensitivity is consistent with experiment and confirmed 10% sensitivity enhancement at 25 degree in experiment.

Efficient Rigorous Coupled-Wave Analysis Simulation of Mueller Matrix Ellipsometry of Three-Dimensional Multilayer Nanostructures.

Mueller matrix ellipsometry (MME) is a powerful metrology tool for nanomanufacturing. The application of MME necessitates electromagnetic computations for inverse problems of metrology determination in both the conventional optimization process and the recent neutral network approach. In this study, we present an efficient, rigorous coupled-wave analysis (RCWA) simulation of multilayer nanostructures to quantify reflected waves, enabling the fast simulation of the corresponding Mueller matrix. Wave propagations in the component layers are characterized by local scattering matrices (s-matrices), which are efficiently computed and integrated into the global s-matrix of the structures to describe the optical responses. The performance of our work is demonstrated through three-dimensional (3D) multilayer nanohole structures in the practical case of industrial Muller matrix measurements of optical diffusers. Another case of plasmonic biosensing is also used to validate our work in simulating full optical responses. The results show significant numerical improvements for the examples, demonstrating the gain in using the RCWA method to address the metrological studies of multilayer nanodevices.

Al/Mo/SiC multilayer diffraction gratings with broadband efficiency in the extreme ultraviolet.

Al/Mo/SiC periodic and aperiodic multilayers were optimized and deposited on high groove density gratings to achieve broadband efficiency in the extreme ultraviolet (EUV). Grating efficiencies were measured by monochromatic synchrotron radiation under 5° and 45° incident angles in the wavelength ranges 17-25 nm and 22-31 nm, respectively. We study the influence of the number of deposited periods on the initial trapezoidal profile and the EUV diffraction efficiency. We propose models of periodic and aperiodic coatings based on a combination of characterizations and compare rigorous coupled-wave analysis (RCWA) simulations with experimental data. We demonstrate the possibility to select the optimal balance between peak efficiency and bandwidth by adjusting the number of periods in the case of periodic multilayer grating. We also report unprecedented broadband diffraction efficiency with an Al/Mo/SiC aperiodic multilayer grating.

Decorrelation of optical critical dimensions in mid-infrared ellipsometric spectroscopy of high aspect ratio etch profiles

Monitoring the high aspect ratio etch profiles in state-of-the-art three-dimensional NAND memory fabrication processes has pushed metrology technologies to new limits. Here, we discuss how a mid-infrared ellipsometric measurement can yield angstrom level discrimination in critical dimension changes of memory channel hole (CH) profiles across such a memory chip. Using finite-difference time-domain and rigorous coupled-wave analysis simulations, we demonstrate how dispersion mitigated mid-infrared beam penetration into these memory structures permits parameter decorrelation and the measurement of the full CH profile.

Rigorous coupled-wave analysis of a multi-layered plasmonic integrated refractive index sensor

We apply the rigorous coupled-wave analysis (RCWA) to the design of a multi-layer plasmonic refractive index sensor based on metallic nanohole arrays integrated with a Ge-on-Si photodetector. RCWA simulations benefit from modularity, frequency-domain computation, and a relatively simple computational setup. These features make the application of RCWA particularly interesting in the case of the simulation and optimization of multi-layered devices in conjunction with plasmonic nanostructures, where other methods can be computationally too expensive for multi-parameter optimization. Our application example serves as a demonstration that RCWA can be utilized as a low-cost, efficient method for device engineering.

Profilometry and stress analysis of suspended nanostructured thin films

The profile of suspended silicon nitride thin films patterned with one-dimensional subwavelength grating structures is investigated using atomic force microscopy. We first show that the results of the profilometry can be used as input to rigorous coupled wave analysis simulations to predict the transmission spectrum of the gratings under illumination by monochromatic light at normal incidence and compare the results of the simulations with experiments. Second, we observe sharp vertical deflections of the films at the boundaries of the patterned area due to local modifications of the tensile stress during the patterning process. These deflections are experimentally investigated for various grating structures and discussed on the basis of a simple analytical model and finite element method simulations.

Nano-grooves etching on top of GaN-LED for light extraction enhancement

Nano-grooves etched through top p-GaN layer were proposed to promote GaN-LED light extraction of small angles. The properties of grating with an optimized period of 500 nm were investigated theoretically and experimentally. The extraction efficiency increased by 50% in the ±10° incident angle range was verified by finite element modeling and rigorous coupled-wave analysis simulations, and sufficiently explained by transmission diffractive grating theory. The GaN-LED with a depth and period of 120 nm and 500 nm, respectively, etched inside a 20 µm diameter ring contact was fabricated and characterized by atomic force microscopy and electroluminescence testing, and the obtained results were in agreement with the design and simulations.

Optimized SrVOx/Ag/SrVOx Multilayers As High Transparency Electrodes for UV Optoelectronic Devices

GaN-based ultraviolet LEDs are important for their use in various applications such as space-to-space communications, curing, sterilization, etc. For these applications, the development of high-efficiency UV LEDs is needed. However, UV LEDs show relatively lower external quantum efficiencies than visible LEDs. To enhance the performance of UV optoelectronic devices by increasing light extraction, it is essential to develop p-type transparent conducting electrodes (TCEs) with high transparency in the UV region. Sn-doped indium oxide (ITO) is typical material for transparent conducting electrodes (TCEs) because of its low resistivity (< 10-4 Ω·cm) and high transmittance (> 85%) in the visible range. However, ITO has large light absorption below 400 nm wavelength and the poor electrical properties when it is thinner than 50 nm. Thus, there is a need for alternative TCEs that have high transmittance in the UV light region (200 – 400 nm). Extensive studies have been conducted to develop TCEs such as graphene, CNT, metal nanowire, and oxide/metal/oxide (OMO) multilayer. Among them, the OMO structure can be a good candidate for TCEs, because the mid-metal layer acts as a conduction path and the oxide layers can lead to zero reflection conditions.In this study, we used SrVOx (SVO) films to develop UV-transparent multilayer and investigated their structural, optical, and electrical properties as functions of SVO and Ag thickness by means of UV-VIS spectrometer, Hall-measurement, and transmission electron microscopy. Unlike ITO film, SVO film exhibited high transmittance (> 80%) up to 320 nm. It was shown that the SVO film showed larger optical bandgap (4.3 eV) than that of ITO (3.7 eV). For the OMO structures with Ag thickness of 15 nm, the sheet resistance was in the range 2.76 – 3.15 Ω/sq, depending on the SVO thickness. In particular, SVO (25 nm)/Ag (15 nm)/SVO (25 nm) sample exhibited the highest Haacke’s figure of merit (FOM) of 144.5 x 10-3 Ω-1 where the average transmittance of the OMO was 91.5% over the 360 – 400 nm wavelength. For the 25 nm-thick SVO-based OMO films, the transmittance and sheet resistance gradually decreased with increasing Ag thickness from 9 nm to 21 nm. For example, the sheet resistance of SVO/Ag/SVO samples was in the range 1.97 – 6.48 Ω/sq and the transmittance varied from 82.6 to 95.5%. Among these samples, SVO/Ag (15 nm)/SVO sample showed the highest FOM value. Rigorous coupled-wave analysis (RCWA) simulations were performed to understand the measured transmittance behavior and zero reflection condition in the SVO/Ag/SVO structure. These results imply that SVO-based OMO structure could be a potentially important TCEs for the fabrication of high-efficiency UV optoelectronic devices. Figure 1

Optimized SrVO3/Ag/SrVO3 Multilayers As High Transparency Electrodes for UV Optoelectronic Devices

GaN-based ultraviolet(UV) LEDs are important for their use in various applications such as space-to-space communications, curing, sterilization, etc. For these applications, the development of high-efficiency UV LEDs is needed. However, UV LEDs show relatively lower external quantum efficiencies than visible LEDs. To enhance the performance of UV optoelectronic devices by increasing light extraction, it is essential to develop p-type transparent conducting electrodes (TCEs) with high transparency in the UV region. Sn-doped indium oxide (ITO) is typical material for transparent conducting electrodes (TCEs) because of its low resistivity (< 10-4 Ω·cm) and high transmittance (> 85%) in the visible range. However, ITO has large light absorption below 400 nm wavelength and the poor electrical properties when it is thinner than 50 nm. Thus, there is a need for alternative TCEs that have high transmittance in the UV light region (200 – 400 nm). Extensive studies have been conducted to develop TCEs such as graphene, CNT, metal nanowire, and oxide/metal/oxide (OMO) multilayer. Among them, the OMO structure can be a good candidate for TCEs, because the mid-metal layer acts as a conduction path and the oxide layers can lead to zero reflection conditions.In this study, we used SrVO3 films to develop UV-transparent multilayer and investigated their structural, optical, and electrical properties as functions of SrVO3 and Ag thickness by means of UV-VIS spectrometer, Hall-measurement, and transmission electron microscopy. Unlike ITO film, SrVO3 films exhibited high transmittance (> 80%) up to 320 nm. It was shown that the SrVO3 film showed larger optical bandgap (4.3 eV) than that of ITO (3.7 eV). For the OMO structures with Ag thickness of 15 nm, the sheet resistance was in the range 2.76 – 3.15 Ω/sq, depending on the SrVO3 thickness. In particular, SrVO3 (25 nm)/Ag (15 nm)/SrVO3 (25 nm) sample exhibited the highest Haacke’s figure of merit (FOM) of 144.5 x 10-3 Ω-1 where the average transmittance of the OMO was 91.5% over the 360 – 400 nm wavelength. For the 25 nm-thick SrVO3-based OMO films, the transmittance and sheet resistance gradually decreased with increasing Ag thickness from 9 nm to 21 nm. For example, the sheet resistance of SrVO3/Ag/SrVO3 samples was in the range 1.97 – 6.48 Ω/sq and the transmittance varied from 82.6 to 95.5%. Among these samples, SrVO3/Ag (15 nm)/SVO sample showed the highest FOM value. Rigorous coupled-wave analysis (RCWA) simulations were performed to understand the measured transmittance behavior and zero reflection condition in the SrVO3/Ag/SrVO3 structure. These results imply that SrVO3-based OMO structure could be a potentially important TCEs for the fabrication of high-efficiency UV optoelectronic devices.

Stimuli-Responsive Microarray Films for Real-Time Sensing of Surrounding Media, Temperature, and Solution Properties via Diffraction Patterns.

Stimuli-responsive polymers have attracted increasing attention over the years due to their ability to alter physiochemical properties upon external stimuli. However, many stimuli-responsive polymer-based sensors require specialized and expensive equipment, which limits their applications. Here an inexpensive and portable sensing platform of novel microarray films made of stimuli-responsive polymers is introduced for the real-time sensing of various environmental changes. When illuminated by laser light, microarray films generate diffraction patterns that can reflect and magnify variations of the periodical microstructure induced by surrounding invisible parameters in real time. Stimuli-responsive polyelectrolyte complexes are structured into micropillar arrays to monitor the pH variation and the presence of calcium ions based on reversible swelling/shrinking behaviors of the polymers. A pH hysteretic effect of the selected polyelectrolyte pair is determined and explained. Furthermore, polycaprolactone microchamber arrays are fabricated and display a thermal-driven structural change, which is exploited for photonic threshold temperature detection. Experimentally observed diffraction patterns are additionally compared with rigorous coupled-wave analysis simulations that prove that induced diffraction pattern alterations are solely caused by geometrical microstructure changes. Microarray-based diffraction patterns are a novel sensing platform with versatile sensing capabilities that will likely pave the way for the use of microarray structures as photonic sensors.

Phase Imbalance Optimization in Interference Linear Displacement Sensor with Surface Gratings.

In interferential linear displacement sensors, accurate information about the position of the reading head is calculated out of a pair of quadrature (sine and cosine) signals. In double grating interference schemes, diffraction gratings combine the function of beam splitters and phase retardation devices. Specifically, the reference diffraction grating is located in the reading head and regulates the phase shifts in diffraction orders. Measurement diffraction grating moves along with the object and provides correspondence to the displacement coordinate. To stabilize the phase imbalance in the output quadrature signals of the sensor, we propose to calculate and optimize the parameters of these gratings, based not only on the energetic analysis, but along with phase relationships in diffraction orders. The optimization method is based on rigorous coupled-wave analysis simulation of the phase shifts of light in diffraction orders in the optical system. The phase properties of the reference diffraction grating in the interferential sensor are studied. It is confirmed that the possibility of quadrature modulation depends on parameters of static reference scale. The implemented optimization criteria are formulated in accordance with the signal generation process in the optical branch. Phase imbalance and amplification coefficients are derived from Heydemann elliptic correction and expressed through the diffraction efficiencies and phase retardations of the reference scale. The phase imbalance of the obtained quadrature signals is estimated in ellipticity correction terms depending on the uncertainties of influencing parameters.

Palladium-coated narrow groove plasmonic nanogratings for highly sensitive hydrogen sensing.

In this paper, we propose novel plasmonic hydrogen sensors based on palladium coated narrow-groove plasmonic nanogratings for sensing of hydrogen gas at visible and near-infrared wavelengths. These narrow-groove plasmonic nanogratings allow the incident light to be coupled directly into plasmonic waveguide modes thereby alleviating the need for bulky coupling methods to be employed. We carried out numerical simulations of the palladium coated narrow-groove plasmonic nanogratings using rigorous coupled wave analysis (RCWA). When palladium is exposed to varying concentrations of hydrogen gas, palladium undergoes phase transition to palladium hydride (PdHx), such that there are different atomic ratios ‘x’ (H/Pd) of hydrogen present in the palladium hydride (PdHx) depending on the concentration of the hydrogen gas. RCWA simulations were performed to obtain the reflectance spectral response of the Pd coated nanogratings in both the absence and presence of hydrogen, for various atomic ratios ‘x’ (x ∼ 0.125 to 0.65) in palladium hydride (PdHx). The results of the RCWA simulations showed that as the dielectric permittivity of the palladium (Pd) thin film layers in between the adjacent walls of the plasmonic nanogratings changes upon exposure to hydrogen, significant shifts in the plasmon resonance wavelength (maximum Δλ being ∼80 nm for an increase in the value of the atomic ratio ‘x’ from 0 to 0.65) as well as changes in the differential reflection spectra are observed. The structural parameters of these Pd coated narrow groove nanogratings—such as the nanograting height, gap between the nanograting walls, thickness of the palladium layer, periodicity of the nanogratings—were varied to maximize the shift in the plasmon resonance wavelength as well as the differential reflectance when these nanostructures are exposed to different concentrations of hydrogen (i.e. for different atomic ratios ‘x’ in PdHx).

Reflective metamaterial polarizer enabled by solid-immersion Lloyd's mirror interference lithography

Metamaterials with induced form birefringence arising from orderly arrangements of subwavelength structures can realize effective refractive indices that do not exist in nature. Using lithographically-defined thin film or multilayered metasurfaces, such form birefringence can be used for polarization and phase control in thin-film elements. In this work, the authors experimentally demonstrate a highly birefringent omnidirectional broadband reflective metamaterial polarizer (RMP), fabricated using a solid-immersion Lloyd's mirror interference lithography (SILMIL) technique. This technique can create 55 nm half-pitch gratings, up to 200 nm tall, using single 405 nm exposures. Angle-resolved reflection spectra of SILMIL-fabricated subwavelength dual-silver grating RMPs exhibit excellent omnidirectionality over a broad spectral bandwidth in the optical range. The behavior and mechanism of the double-layer RMP has been analyzed with finite-difference time domain and rigorous coupled wave analysis simulations, showing coupling between excited surface plasmon polaritons and multiple Fabry–Perot resonances. Furthermore, the authors propose via simulation that by switching from a dielectric resonator to a metallic resonator, the SILMIL technique can be used to fabricate dual-layer thin-film metamaterials that have the capability of phase retardation control, providing a new scheme for reflective thin-film waveplates.

Suspended silicon nitride thin films with enhanced and electrically tunable reflectivity

We report on the realization of silicon nitride membranes with enhanced and electrically tunable reflectivity. A subwavelength one-dimensional grating is directly patterned on a suspended 200 nm thick, high stress commercial film using electron beam lithography. A Fano resonance is observed in the transmission spectrum of TM polarized light impinging on the membrane at normal incidence, leading to an increase in its reflectivity from 10% to 78% at 937 nm. The observed spectrum is compared to the results of rigorous coupled wave analysis simulations based on measurements of the grating transverse profile through localized cuts of the suspended film with a Focused Ion Beam. By mounting the membrane chip on a ring piezoelectric transducer and applying a compressive force to the substrate we subsequently observe a shift of the transmission spectrum by 0.23 nm.

Femtosecond laser fabrication of volume-phase gratings in CdSxSe1-x-doped borosilicate glass at a low repetition rate.

Volume-phase gratings (VPGs) were fabricated in CdSxSe1-x quantum-dot-doped borosilicate glass at a low repetition rate (800nm, 140fs, 1kHz). The VPGs were designed based on rigorous coupled wave analysis simulations. Results indicate that the inscribed thickness (L) is the key parameter to maximize the diffraction efficiency at order 1. Microscope images of the cross sections and diffraction efficiency measurements were taken in order to characterize the modification of the material at different laser-inscription parameters. A maximum VPG diffraction efficiency of 67% (at order 1) was achieved. Also, a refractive index change of Δn=2.25·10-3 is estimated from these VPG diffraction efficiency measurements. The measurements regarding polarization-insensitive diffraction efficiency showed that the birefringence produced in the substrate is negligible.