Expanding RCWA capabilities with advanced S-matrix algorithms
Abstract
Modal methods are particularly well suited to layered photonic structures because electromagnetic propagation within each layer is described analytically. Here, we introduce a simple reformulation of the scattering-matrix (S-matrix) approach in which the S-matrix is defined as an intrinsic property of an individual layer, independently of its neighboring interfaces. This separation between layer propagation and interface coupling preserves the numerical stability of the conventional S-matrix formalism while providing a more modular description of multilayer structures. It also enables direct computation of the scattering coefficients between external plane waves and Bloch modes, as well as between Bloch modes themselves, providing generalized Fresnel coefficients for periodic interfaces. In addition, the reformulation allows the optical response to be evaluated simultaneously for many layer thicknesses or incident wavevectors, with only a modest computational overhead compared with a single calculation. Implemented in the RETICOLO freeware, these capabilities provide a practical framework for modal analysis, parameter sweeps, and the design of layered photonic structures.
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BibTeX
@misc{lalanne2026expanding,
title = {{Expanding RCWA capabilities with advanced S-matrix algorithms}},
author = {Philippe Lalanne and Jean-Paul Hugonin},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10076},
eprint = {2609.10076},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10076},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Expanding RCWA capabilities with advanced S-matrix algorithms
AU - Philippe Lalanne
AU - Jean-Paul Hugonin
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.10076
UR - https://arxiv.org/abs/2609.10076
AB - Modal methods are particularly well suited to layered photonic structures because electromagnetic propagation within each layer is described analytically. Here, we introduce a simple reformulation of the scattering-matrix (S-matrix) approach in which the S-matrix is defined as an intrinsic property of an individual layer, independently of its neighboring interfaces. This separation between layer propagation and interface coupling preserves the numerical stability of the conventional S-matrix formalism while providing a more modular description of multilayer structures. It also enables direct computation of the scattering coefficients between external plane waves and Bloch modes, as well as between Bloch modes themselves, providing generalized Fresnel coefficients for periodic interfaces. In addition, the reformulation allows the optical response to be evaluated simultaneously for many layer thicknesses or incident wavevectors, with only a modest computational overhead compared with a single calculation. Implemented in the RETICOLO freeware, these capabilities provide a practical framework for modal analysis, parameter sweeps, and the design of layered photonic structures.
ER -