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1D Grating RCWA

Rigorous Coupled Wave Analysis (Fourier modal method) for 1D binary gratings. Compute reflection R(λ) and transmission T(λ). Runs in-browser via Pyodide + inkstone.
First load downloads ~35 MB (Pyodide + numpy + scipy + inkstone) — cached after.

v0.1.0·Updated 2026-06-10
Model & Assumptions Experimental
Model
Rigorous Coupled Wave Analysis (Fourier modal method). Fields are expanded in plane-wave harmonics of the grating period; an eigenvalue problem is solved in each layer. Powered by inkstone via Pyodide.
Assumptions
1D periodicity, infinite lateral extent, plane-wave illumination, isotropic materials in each layer.
Validity
Exact in the limit of sufficient Fourier orders. Convergence should be checked by increasing the truncation order — especially for metallic gratings where convergence can be slow.
Limitations
1D gratings only (no 2D periodicity). Browser memory limits the practical number of Fourier orders. First load downloads ~35 MB (Pyodide + numpy + scipy + inkstone).
References
M. G. Moharam & T. K. Gaylord, J. Opt. Soc. Am. 71, 811 (1981); L. Li, J. Opt. Soc. Am. A 14, 2758 (1997).
Module

Parameters

Grating

Number of Fourier orders used in the RCWA expansion. Higher values improve convergence for sharp or high-contrast gratings, but make the calculation slower.

Materials ε = n²

Top + i
Ridge + i
Groove + i
Substrate + i

Incidence

Wavelength sweep

RCWA (Fourier modal method). Expands fields in plane-wave harmonics of the grating period and solves the eigenvalue problem in each layer. Diffraction orders couple through the Fourier decomposition of ε(x).

Reflection / Transmission spectrum Initializing…
Geometry and solver conventions 1D periodic, φ = 0
RCWA 1D grating geometry convention A 1D grating with x-period Lambda, invariant y direction, z layer stacking, top superstrate, finite patterned grating, substrate, incident wave vector, incidence angle theta, and TE/TM polarization definitions. Ridge Groove Superstrate / top semi-infinite input Patterned layer ridge + groove Substrate semi-infinite output Λ period along x ridge width thickness d kinc θ surface normal
  • x is periodic with period Λ; y is invariant along the ridge direction.
  • z follows the layer stack from top/superstrate to substrate.
  • The incident plane wave enters from the top region; θ is measured from the surface normal in the x-z plane.
  • s/TE means E along y; p/TM means E lies in the x-z incidence plane.