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Diffractive Optical Elements
Published in Russell A. Chipman, Wai-Sze Tiffany Lam, Garam Young, Polarized Light and Optical Systems, 2018
Russell A. Chipman, Wai-Sze Tiffany Lam, Garam Young
The RCWA algorithm is widely used for analyzing periodic diffractive structures, such as diffraction gratings, wire grid polarizers, holograms, and all the examples presented in this chapter. RCWA calculates exact solutions for the reflection from and transmission through periodic structures. It is a relatively straightforward, non-iterative, and deterministic technique that calculates the amplitude coefficients for each diffraction order. The accuracy depends solely on the number of Fourier terms retained in the Floquet–Fourier expansions of the grating structure. The algorithm was initially developed for modeling volume holographic gratings and then extended to surface-relief and multilevel grating structures. RCWA has been successfully applied to transmission and reflection planar dielectric and/or absorption holographic gratings, arbitrarily profiled dielectric and/or metallic surface-relief gratings, multiplexed holographic gratings, two-dimensional surface-relief gratings, and anisotropic gratings, for both planar and conical diffraction.5,6,22–24 This section will provide a summary of the RCWA algorithm.
Silicon nanowire and nanohole arrays
Published in Klaus D. Sattler, Silicon Nanomaterials Sourcebook, 2017
RCWA is an efficient and accurate numerical tool especially suitable for solving the electromagnetic field in periodic nanostructures (Moharam et al. 1995a, 1995b; Lalanne 1997). With better algorithms using the correct Li’s factorization (Li 1996), the convergence of RCWA has been further accelerated and the memory requirement is significantly reduced. It is a semi-analytical method where the wave equation is solved analytically in the longitudinal direction. To implement the method, structures are divided into layers that are uniform in the longitudinal direction. The transverse problem is solved in reciprocal space by expressing the field as a sum of spatial harmonics. Thus, the wave equation transforms into a set of ordinary differential equations known as coupled-wave equations. The coupled-wave equation in the ith layer is expressed as
Hologram Diffraction Efficiency
Published in Raymond K. Kostuk, Holography, 2019
RCWA is based on a complete electromagnetic model of the diffraction process from a grating. Unlike the approximate methods, no assumptions about the number of diffraction orders or the thickness of the grating are made and both transmission and reflection orders are allowed at the same time. In this section, the main features of RCWA are described to illustrate the approach and to compare the predicted diffraction efficiency characteristics to those based on approximate coupled wave models. An extensive discussion of RCWA is provided in the review paper by Gaylord and Moharam [3] as well as in references [8] and [9].
Tuneable optical diffractive structures from liquid crystalline materials incorporated into periodic polymeric scaffolds
Published in Liquid Crystals, 2023
D. Bošnjaković, X. Zhang, I. Drevenšek-Olenik
The gratings modelled in this work, with D ~ 10 μm and Λ = 5 μm, according to the Gaylord and Moharam classification [47], belong to an intermediate diffraction regime, which is the regime between the thin (Raman-Nath) and thick (Bragg) gratings. Consequently, analytical results are very difficult to be obtained. Also, the scalar diffraction theory is not accurate enough. Therefore, to describe diffraction properties of such gratings it is necessary to use numerical methods. One such method, which is used to describe the propagation of light within periodically modulated optical medium, is the RCWA based on the coupled-wave theory (CWT) [48]. The RCWA is focused on solving Maxwell’s equations that describe the behaviour of the electromagnetic field in three regions: the incident/reflection region, the grating region and the transmission region (see Figure 1(b)). The frequency domain form of the Maxwell’s equations for the configuration as shown in Figure 1 (in the absence of free charges and free currents) is given by [49]
Bio-Inspired Stretchable Selective Emitters Based on Corrugated Nickel for Personal Thermal Management
Published in Nanoscale and Microscale Thermophysical Engineering, 2019
Martí Sala-Casanovas, Anirudh Krishna, Ziqi Yu, Jaeho Lee
This work computes the spectral optical properties of corrugated nickel, including reflectivity, transmissivity, and consequently emissivity, using the rigorous couple wave analysis (RCWA) [50,51] and finite-difference time-domain (FDTD) [52] methods (Figure 2). The RCWA method considers topographical variations and handles rigorous solutions of Maxwell’s equations [23,53]. Direct results from RCWA yield scattering matrices in the forward and reverse directions, from which reflectivity (ρ) and transmissivity (τ) are computed. The emissivity is assumed identical to the absorptivity by Kirchhoff’s law [54] and is computed from the reflectivity and transmissivity (α = 1-ρ-τ) [54]. The FDTD method discretizes the samples and solves for space- and time-variant Maxwell’s equation for each unit cell. RCWA is semi-analytical and treats the waves and fields as sets of gratings, hence making it very effective for corrugated structures. On the other hand, FDTD is superior in modeling curved surfaces and spherical shapes in full three-dimension. While FDTD is time-consuming, RCWA is more efficient towards optimizing the designs by variation of geometrical parameters.