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Matrix Square Root Based Differentiable RCWA Implementation for High-Performance Parallel Computing.

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Title: Matrix Square Root Based Differentiable RCWA Implementation for High-Performance Parallel Computing.
Authors: Van der Ceelen, Frank1 F.vanderCeelen@tudelft.nl, Shao, Yifeng1, Coene, Wim1,2
Source: Progress in Electromagnetics Research C. 2026, Vol. 163, p60-72. 13p.
Subjects: High performance computing, Matrix functions, Wave analysis, Parallel programming, Eigenanalysis, Automatic differentiation, Nanostructures
Abstract: Rigorous Coupled-Wave Analysis (RCWA) is a semi-analytical method, used to determine the optical response of nanostructures, such as meta-materials. Recently, the ability to combine RCWA with automatic differentiation for optical response optimization has been demonstrated. We seek to build upon this use by attempting to address RCWA's poor performance on parallel computer architecture, stemming from the presence of an eigendecomposition. We do this by outlining an alteration of RCWA, which replaces the eigendecomposition with a matrix square root and matrix exponential evaluation. Furthermore, we demonstrate that these matrix functions can be evaluated using algorithms which are both differentiable and readily evaluated in parallel. Finally, we show that replacing the eigendecomposition with these matrix functions resolves the bottleneck and paves the way for higher-accuracy parameter retrieval using RCWA approaching real-time performance, without compromising stability. [ABSTRACT FROM AUTHOR]
Copyright of Progress in Electromagnetics Research C is the property of Electromagnetics Academy and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: <searchLink fieldCode="JN" term="%22Progress+in+Electromagnetics+Research+C%22">Progress in Electromagnetics Research C</searchLink>. 2026, Vol. 163, p60-72. 13p.
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  Data: Rigorous Coupled-Wave Analysis (RCWA) is a semi-analytical method, used to determine the optical response of nanostructures, such as meta-materials. Recently, the ability to combine RCWA with automatic differentiation for optical response optimization has been demonstrated. We seek to build upon this use by attempting to address RCWA's poor performance on parallel computer architecture, stemming from the presence of an eigendecomposition. We do this by outlining an alteration of RCWA, which replaces the eigendecomposition with a matrix square root and matrix exponential evaluation. Furthermore, we demonstrate that these matrix functions can be evaluated using algorithms which are both differentiable and readily evaluated in parallel. Finally, we show that replacing the eigendecomposition with these matrix functions resolves the bottleneck and paves the way for higher-accuracy parameter retrieval using RCWA approaching real-time performance, without compromising stability. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Progress in Electromagnetics Research C is the property of Electromagnetics Academy and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.2528/PIERC25091202
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      – Code: eng
        Text: English
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        PageCount: 13
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      – SubjectFull: High performance computing
        Type: general
      – SubjectFull: Matrix functions
        Type: general
      – SubjectFull: Wave analysis
        Type: general
      – SubjectFull: Parallel programming
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      – SubjectFull: Eigenanalysis
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      – SubjectFull: Automatic differentiation
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      – SubjectFull: Nanostructures
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      – TitleFull: Matrix Square Root Based Differentiable RCWA Implementation for High-Performance Parallel Computing.
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            – D: 01
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              Text: 2026
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