Pole-Expansion of the T-Matrix Based on a Matrix-Valued AAA-Algorithm
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arXiv
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| Auteurs principaux: | , , , , , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866910028225576960 |
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| author | Fischbach, Jan David Betz, Fridtjof Rebholz, Lukas Garg, Puneet Frizyuk, Kristina Binkowski, Felix Burger, Sven Hammerschmidt, Martin Rockstuhl, Carsten |
| author_facet | Fischbach, Jan David Betz, Fridtjof Rebholz, Lukas Garg, Puneet Frizyuk, Kristina Binkowski, Felix Burger, Sven Hammerschmidt, Martin Rockstuhl, Carsten |
| contents | The transition matrix (T-matrix) is a complete description of an object's linear scattering response. As such, it has found wide adoption for the theoretical and computational description of multiple-scattering phenomena. In its original form, the T-matrix describes the interaction of a scatterer with a monochromatic source. In practice, however, information about the T-matrix is usually needed in an extended spectral domain. To access the frequency-dispersion, one might naively sample T-matrices over a finely resolved set of discrete frequencies and store one T-matrix per frequency. This approach has multiple drawbacks: it is computationally expensive, requires excessive memory, and it disregards the physical origin of the spectral features, weakening physical interpretability. To overcome these major limitations, we leverage a pole-expansion technique to represent the T-matrix with arbitrary frequency resolution within a selected frequency domain via a set of resonant contributions. A matrix-valued variant of the recently established adaptive Antoulas-Anderson (AAA) algorithm for rational approximation enables us to compute the pole-expansion at minimal computational cost using only a small number of direct evaluations. We demonstrate the benefits of such a representation with examples ranging from semi-analytically accessible scatterers to quasi-dual bound states in the continuum. To allow the wider community to capitalize on these findings, we provide open-source tools to perform the presented pole-expansion of the T-matrix. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_18414 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Pole-Expansion of the T-Matrix Based on a Matrix-Valued AAA-Algorithm Fischbach, Jan David Betz, Fridtjof Rebholz, Lukas Garg, Puneet Frizyuk, Kristina Binkowski, Felix Burger, Sven Hammerschmidt, Martin Rockstuhl, Carsten Optics Computational Physics The transition matrix (T-matrix) is a complete description of an object's linear scattering response. As such, it has found wide adoption for the theoretical and computational description of multiple-scattering phenomena. In its original form, the T-matrix describes the interaction of a scatterer with a monochromatic source. In practice, however, information about the T-matrix is usually needed in an extended spectral domain. To access the frequency-dispersion, one might naively sample T-matrices over a finely resolved set of discrete frequencies and store one T-matrix per frequency. This approach has multiple drawbacks: it is computationally expensive, requires excessive memory, and it disregards the physical origin of the spectral features, weakening physical interpretability. To overcome these major limitations, we leverage a pole-expansion technique to represent the T-matrix with arbitrary frequency resolution within a selected frequency domain via a set of resonant contributions. A matrix-valued variant of the recently established adaptive Antoulas-Anderson (AAA) algorithm for rational approximation enables us to compute the pole-expansion at minimal computational cost using only a small number of direct evaluations. We demonstrate the benefits of such a representation with examples ranging from semi-analytically accessible scatterers to quasi-dual bound states in the continuum. To allow the wider community to capitalize on these findings, we provide open-source tools to perform the presented pole-expansion of the T-matrix. |
| title | Pole-Expansion of the T-Matrix Based on a Matrix-Valued AAA-Algorithm |
| topic | Optics Computational Physics |
| url | https://arxiv.org/abs/2602.18414 |