Rigorous Coupled-wave Analysis Research Articles

Cascaded HfO2/SiO2 microstructure for symmetrical two-port beam dispersion

A new type of double-dielectric layer two-port beam splitter grating based on sandwich structure is proposed. This grating has the characteristic of zeroth order elimination. The structural parameters of the grating are optimized by the rigorous coupled-wave analysis (RCWA) and simulated annealing algorithm (SAA) to achieve the best performance of the grating. For both TE and TM polarizations, the diffraction efficiencies of ±1st orders can reach 49.34% and 49.15%, respectively. Meanwhile, the efficiency of the zeroth order is about only 0.5% for both polarizations. This novel microstructure has the significant characteristic of zeroth order elimination. Moreover, this grating has a wide incident bandwidth and excellent manufacturing tolerance. The simplified modal method (SMM) is also used to study the specific process of energy coupling in the grating.

Structural and optical properties of triple-layer for high-uniformity beam division

In this paper, a triple-layer grating beam splitter with three-port output is designed. Through the combination of rigorous coupled-wave analysis (RCWA) and simulated annealing algorithms (SAA), the calculation and optimization of each parameter of the grating is carried out to make the diffraction efficiency of the grating meet the conditions. At the incident wavelength of 800[Formula: see text]nm, the diffraction efficiencies of 0th order and ±1st order under TE polarization are 31.6% and 31.4%, respectively. The diffraction efficiencies of 0th order and ±1st order under TM polarization are 32.7% and 32.5%, respectively. It can be seen that not only the total diffraction efficiency under TE polarization and TM polarization exceeds 90%, but also the uniformity of diffraction efficiency at each order exceeds 99%. Finally, the influence of grating parameters and incident wave characteristics on diffraction efficiency is discussed.

Analysis and Prediction of Image Quality Degradation Caused by Diffraction of Infrared Optical System Turning Marks

This paper addresses the issue of reduced image quality due to annular turning marks formed by single-point diamond turning (SPDT) during the processing of metal-based mirrors and infrared lenses. An ideal single-point diamond turning marks diffraction action model to quantitatively analyze the impact of turning marks diffraction on imaging quality degradation is proposed. Based on this model, a fast estimation algorithm for the optical modulation transfer function of the system under turning marks diffraction (TMTF) is proposed. The results show that the TMTF algorithm achieves high computational accuracy, with a relative error of only 3% in diffraction efficiency, while being hundreds of times faster than rigorous coupled wave analysis (RCWA). This method is significant for reducing manufacturing costs and improving production efficiency, as it avoids the problem of being unable to compute large-size optical systems due to computational resource and time constraints.

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.

Conditions for Minimizing the Computational Complexity of the RCWA Calculation of the Diffraction Efficiency of Sawtooth Two-Layer Double-Relief Microstructures

In this study, novel recommendations are presented and substantiated for selecting the number of modes and optical thicknesses of flat lattice slabs that make up microreliefs, which minimize the computational complexity of the rigorous coupled-wave analysis calculation of the diffraction efficiency (DE) of a sawtooth two-layer two-relief microstructure, while maintaining the specified reliability of the calculation results. The computational complexity can be controlled by allowing one or another level of oscillation of the DE curves, depending on the angle of incidence of the radiation incident on the microstructure. In particular, the complexity of the thousands of DE calculations in the optimization process can be reduced by using the proposed methodology as well as increased computational complexity to verify the accuracy of the solution obtained as a result of the implemented optimization.

Plus-shaped dielectric grating for seven-channel transmission

A new seven-channel transmission grating with plus-shaped array under normal incidence is proposed and discussed in this paper. Through the simulated annealing (SA) algorithm and rigorous coupled-wave analysis (RCWA), the novel microstructure can split the incident energy into 0-th/±1-st/±2-nd/±3-rd orders evenly. The influence of incident angle, period, incident wavelength, and other parameters on the diffraction efficiency are also analyzed in this paper. For transverse magnetic (TM) polarization, the range of period is 3062–3246 nm and the bandwidth of incident angle and wavelength is 1.96° and 32.3 nm, respectively. It can be concluded that the TM-polarized light of the designed grating has a good performance in incident bandwidth and fabrication tolerance. In addition, the efficiency of transverse electric (TE) polarization has the satisfactory uniformity of 2.40%. Therefore, the proposed grating has a certain significance for the research of multi-port beam splitter, especially for the seven-channel polarization-independent beam splitter.

A new scheme for seven-port division via reflective arrays on a connecting slab

A seven-port division is described via the connecting-slab-based reflective grating in this paper. The rigorous coupled wave analysis (RCWA) and simulated annealing algorithm (SAA) are chosen to analyze and optimize the performance of the grating. The total diffraction efficiency of TE and TM polarization is 96.75% and 95.53%, respectively. Besides, the target grating has good uniformity errors, which are reduced to 3.69% and 1.76% for TE and TM polarization, respectively. The modal method provides a physical explanation for the energy transformations within the target grating. Furthermore, the manufacturing tolerance is discussed for the seven-port division grating. Through analysis and discussion, various performances of the grating can be better demonstrated. Compared with most seven-port grating splitters reported previously, the grating in this paper achieves better diffraction efficiency uniformity and higher efficiency.

One-dimensional photonic crystal magnetic sensor design based on Bloch surface waves with high sensitivity and high figure of merit (FOM)

A novel Bloch surface wave (BSW)-based one-dimensional photonic crystal magnetic sensor is proposed. Grating is used to realize the coupling of electromagnetic waves and BSW, and magnetic fluid is placed at the bottom of the sensor as the sensing medium. The sensing characteristics of a one-dimensional photonic crystal magnetic sensor were analyzed using the rigorous coupled wave analysis (RCWA) method. Based on the azimuthal interrogation method, the effects of different pole angles, defect layers, and structural parameters on sensitivity and figure of merit (FOM) were investigated. According to the drift of the resonance peak, the azimuthal sensitivity S = 9 °/mT, and the maximum detection sensitivity S = 14 °/mT were obtained (converted to refractive index sensitivity S = 6536 °/RIU and maximum detection sensitivity S = 9333 °/RIU). Excitingly, we found that the introduction of a defective layer can significantly improve the FOM (1925 RIU-1 to 69,444 RIU-1). The results show that the designed magnetic sensor structure has high sensitivity and a high FOM, which is an order of magnitude higher than other magnetic sensors. This work provides a guideline for the future development of one-dimensional photonic crystals in the field of weak magnetic sensing.

Coupled-mode theory for resonant gratings with a varying period

We propose a coupled-mode theory for resonant diffraction gratings with a varying period. We consider diffractive structures, in which the reciprocal lattice vector, a quantity inversely proportional to the period, varies linearly in the direction of periodicity. It is shown that optical properties of such a structure essentially depend on the period change rate. On the basis of a comparison with the results of rigorous numerical simulations using the rigorous coupled-wave analysis, high accuracy of the proposed theoretical model is demonstrated. In particular, the developed coupled-mode theory describes the broadening of the resonant peak and the appearance of secondary maxima caused by a non-zero period change rate. The obtained results can be used for the development of linear variable filters based on resonant diffraction gratings with varying parameters.

Triple-channel reflective splitter in terahertz band by second-order Littrow illumination

In this paper, a triple-channel reflective beam splitter in terahertz band with connecting layer under second Bragg incidence is presented. A rigorous coupled-wave analysis is applied to optimize the profile of the grating at 2.52 THz. The optimal parameters of the grating are also verified by using the finite element method to ensure the accuracy of the data. The impact of the incident angle, incident wavelength, duty cycle, and period is analyzed in detail. For the optimized grating working in terahertz band, results for diffraction efficiencies approaching over 30% for transverse-electric polarization in three propagating orders and for transverse-magnetic polarization in the -1st order and -2nd order are derived. Obtaining stable and superior performances, the proposed three-port beam splitter working in the terahertz band is novel and could be an inspiration to design new gratings.

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.

Modeling selective narrowband light absorption in coaxial InAs-GaAs0.1Sb0.9 nanowires with partial shell segment coverage

Vertical III-V nanowire (NW) arrays are promising candidates for infrared (IR) photodetection applications. Generally, NWs with large diameters are required for efficient absorption in the IR range. However, increasing the NW diameter results in a loss of spectral selectivity and an enhancement in the photodetector dark current. Here, we propose a nanophotonic engineering approach to achieving spectrally-selective light absorption while minimizing the volume of the absorbing medium. Based on simulations performed using rigorous coupled-wave analysis (RCWA) techniques, we demonstrate dramatic tunability of the short-wavelength infrared (SWIR) light absorption properties of InAs NWs with base segments embedded in a reflective backside Au layer and with partial GaAs0.1Sb0.9 shell segment coverage. Use of a backside reflector results in the generation of a delocalized evanescent field around the NW core segment that can be selectively captured by the partially encapsulating GaAs0.1Sb0.9 shell layer. By adjusting the core and shell dimensions, unity absorption can be selectively achieved in the 2 to 3 μm wavelength range. Due to the transparency of the GaAs0.1Sb0.9 shell segments, wavelength-selective absorption occurs only along the InAs core segments where they are partially encapsulated. The design presented in this work paves the path toward spectrally-selective and polarization-dependent NW array-based photodetectors, in which carrier collection efficiencies can be enhanced by positioning active junctions at the predefined locations of the partial shell segments.

Numerical study of feature-distribution effects foranti-reflection structured surfaces on binary gratings.

Suppressing Fresnel reflections from dielectric boundaries using periodic and random antireflection structured surfaces (ARSSs) has been vigorously studied as an alternative to thin film coatings for high-power laser applications. A starting point in the design of ARSS profiles is effective medium theory (EMT), approximating the ARSS layer with a thin film of a specific effective permittivity, which has features with subwavelength transverse-scale dimensions, independent of their relative mutual positions or distributions. Using rigorous coupled-wave analysis, we studied the effects of various pseudo-random deterministic transverse feature distributions of ARSS on diffractive surfaces, analyzing the combined performance of the quarter-wave height nanoscale features, superimposed on a binary 50% duty cycle grating. Various distribution designs were investigated at 633nm wavelength for TE and TM polarization states at normal incidence, comparable to EMT fill fractions for a fused silica substrate in air. The results show differences in performance between ARSS transverse feature distributions, exhibiting better overall performance for subwavelength and near-wavelength scaled unit cell periodicities with short auto-correlation lengths, in comparison to equivalent effective permittivity designs that have less complicated profiles. We conclude that structured layers of quarter-wavelength depth and specific feature distributions can outperform conventional periodic subwavelength gratings as antireflection treatments on diffractive optical components.

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.

Dual-band refractive index sensor with cascaded asymmetric resonant compound grating based on bound states in the continuum.

We propose a cascaded asymmetric resonant compound grating (ARCG) for high-performance dual-band refractive index sensing. The physical mechanism of the sensor is investigated using a combination of temporal coupled-mode theory (TCMT) and ARCG eigenfrequency information, which is verified by rigorous coupled-wave analysis (RCWA). The reflection spectra can be tailored by changing the key structural parameters. And by altering the grating strip spacing, a dual-band quasi-bound state in the continuum can be achieved. The simulation results show that the highest sensitivity of the dual-band sensor is 480.1 nm/RIU, and its figure of merit is 4.01 × 105. The proposed ARCG has potential application prospects for high-performance integrated sensors.

Optical imprinting subwavelength-period liquid crystal polarization gratings with dual-twist templates.

In this Letter, we report a dual-twist template imprinting method to fabricate subwavelength-period liquid crystal polarization gratings (LCPGs). In other words, the period of the template must be reduced to 800 nm-2 µm, or even smaller. To overcome the inherent problem that the diffraction efficiency shrinks as the period decreases, the dual-twist templates were optimized by rigorous coupled-wave analysis (RCWA). With the help of the rotating Jones matrix to measure the twist angle and thickness of the LC film, the optimized templates were fabricated eventually, and the diffraction efficiencies were up to 95%. Therefore, subwavelength-period LCPGs with a period of 400-800 nm were imprinted experimentally. Our proposed dual-twist template provides the possibility for fast, low-cost, and mass fabrication of large-angle deflectors and diffractive optical waveguides for near-eye displays.

Sc2O3 on sapphire all-crystalline grating–waveguide resonant reflectors

This paper reports the fabrication and first demonstration of all-dielectric crystalline grating–waveguide reflectors comprising a Sc2O3 waveguide grown on a sub-wavelength-patterned sapphire substrate. Rigorous coupled-wave analysis is employed to simulate the operation of the structure, suggesting a 100% resonance reflectivity in theory. Structuring of the sapphire substrate is achieved using inductively coupled plasma etching, whilst pulsed laser deposition is used for epitaxial growth of the Sc2O3 crystalline waveguide. Devices with distinct TE- and TM-polarisation resonances around 1030-nm for an angle of incidence near 10° are demonstrated, with reflectance approaching 90%. The discrepancy in reflectivity is attributed to the waveguide thickness variation and surface roughness. Refinement of the fabrication processes and tolerances should lead to improvement in the surface quality of the crystalline grating–waveguide structure and operation closer to the ideal resonance reflectivity.

P‐2.6: A method for accurately measuring the refractive index modulation of volume holographic grating

In this paper, we propose a method to accurately measure the refractive index modulation of VHG. By adjusting the position of the photon detector in real time, we can accurately measure the variation of the diffracted light intensity with the angle of the incident light, and combining the Rigorous Coupled Wave Analysis (RCWA) fitting, the refractive index modulation of the grating can be measured.

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.

Dual plasmonic modes in the visible light region in rectangular wave-shaped surface relief plasmonic gratings

Rectangular wave-shaped surface-relief plasmonic gratings (RSR-PGs) have been fabricated from a hybrid polymer by employing a simple nanoimprint photocuring lithography technique using a silicon template, followed by gold nanolayer metallization on top of the formed replica structure. By forming a one-dimensional (1D) plasmonic grating with a periodicity of approximately 700 nm, a reflectance spectral dip was experimentally observed in the visible light region, from 600 to 700 nm, with increasing incident angle from 45° to 60°. This dip can be associated with surface plasmon resonance (SPR) wave excitation, which is coupled with the diffraction order m = − 2. The calculations of reflectance spectra simulation using the rigorous coupled wave analysis (RCWA) method have also been carried out, resulting in the appearance of an SPR dip in the range of 600–700 nm, for incident angles in the range of 45°–65°, which agrees with the experimental results. Interestingly, these RSR-PGs show richer plasmon characteristics than the sine-wave-shaped plasmonic gratings. The experimental and spectral simulation results revealed two different plasmonic excitation modes: long-range SPR and quasi-localized SPR (LSPR). While the long-range SPR was formed above the ridge sections along the grating structure surface, the quasi-localized SPR was locally formed inside the groove. In addition, for RSR-PGs with a narrow groove section, the long-range SPR seems to be coupled with the periodic structure of the grating, resulting in the appearance of plasmonic lattice surface resonance (LSR) that is indicated by a narrower plasmon resonance dip. These characteristics are quite different from those found in the sine wave-shaped plasmonic gratings. The present results may thus provide better insights for understanding the plasmon excitations in this type of rectangular plasmonic grating and might be useful for designing their structure for certain practical applications.