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Stabilized scattering matrix formulation for 2D periodic multilayer dielectrics

Andersson, Michael LU and Sjöberg, Daniel LU orcid (2025) In Technical report
Abstract
This paper proposes an alternative semi-analytical Fourier modal method adapted for general periodic anisotropic gratings made of dielectrics with moderate to low index profiles corresponding to materials ranging from conventional dielectric 3D printing materials to ceramic materials. The proposed method is closely related to classical Rigorous Coupled-Wave Analysis built on scattering matrices, however a key difference is that the new scheme relies on the recently reported concept of stabilized wave propagation operators, leading to improved numerical stability and accuracy for a wider range of structures where e.g., evanescent waves are present. Multilayer structures can be handled in a stable manner using the dissipative property of the... (More)
This paper proposes an alternative semi-analytical Fourier modal method adapted for general periodic anisotropic gratings made of dielectrics with moderate to low index profiles corresponding to materials ranging from conventional dielectric 3D printing materials to ceramic materials. The proposed method is closely related to classical Rigorous Coupled-Wave Analysis built on scattering matrices, however a key difference is that the new scheme relies on the recently reported concept of stabilized wave propagation operators, leading to improved numerical stability and accuracy for a wider range of structures where e.g., evanescent waves are present. Multilayer structures can be handled in a stable manner using the dissipative property of the Redheffer star product for cascading scattering matrices from which the reflection and transmission of the whole structure is derived. Numerical examples of practical interest as well as importance for future development demonstrate the method’s accuracy, efficiency as well as stability through comparison with solutions obtained by finite elements as well as results published in the literature. (Less)
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type
Book/Report
publication status
published
subject
in
Technical report
pages
28 pages
report number
TEAT-2783
ISSN
1652-4462
language
English
LU publication?
yes
id
65d99548-43c9-4e2f-b783-b4a10643cc69
date added to LUP
2025-04-28 06:16:46
date last changed
2025-04-29 11:23:01
@techreport{65d99548-43c9-4e2f-b783-b4a10643cc69,
  abstract     = {{This paper proposes an alternative semi-analytical Fourier modal method adapted for general periodic anisotropic gratings made of dielectrics with moderate to low index profiles corresponding to materials ranging from conventional dielectric 3D printing materials to ceramic materials. The proposed method is closely related to classical Rigorous Coupled-Wave Analysis built on scattering matrices, however a key difference is that the new scheme relies on the recently reported concept of stabilized wave propagation operators, leading to improved numerical stability and accuracy for a wider range of structures where e.g., evanescent waves are present. Multilayer structures can be handled in a stable manner using the dissipative property of the Redheffer star product for cascading scattering matrices from which the reflection and transmission of the whole structure is derived. Numerical examples of practical interest as well as importance for future development demonstrate the method’s accuracy,  efficiency as well as stability through comparison with solutions obtained by finite elements as well as results published in the literature.}},
  author       = {{Andersson, Michael and Sjöberg, Daniel}},
  issn         = {{1652-4462}},
  language     = {{eng}},
  number       = {{TEAT-2783}},
  series       = {{Technical report}},
  title        = {{Stabilized scattering matrix formulation for 2D periodic multilayer dielectrics}},
  url          = {{https://lup.lub.lu.se/search/files/218089800/Andersson_-N_Sj_berg-D_TEAT-7283_2025.pdf}},
  year         = {{2025}},
}