Bessel Functions and Analysis of Circular Waveguides
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914201466830848 |
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| author | Mora-Paz, Jaime Demkowicz, Leszek Taylor, Christina G. Grosek, Jacob Henneking, Stefan |
| author_facet | Mora-Paz, Jaime Demkowicz, Leszek Taylor, Christina G. Grosek, Jacob Henneking, Stefan |
| contents | The paper is devoted to the study of circularly coiled optical slab waveguides, which is also applicable to acoustical waveguides. We use a change of variables and the classical Frobenius method to compute Bessel functions of complex order and complex argument, and combine it with a perfectly matched layer technique to solve the relevant Bessel eigenvalue problem and deliver accurate loss factors for eigensolutions to the three-layer optical slab waveguide problem. The solutions provide a benchmark for verifying model implementations of this problem and allow for a numerical verification of the Glazman criterion that provides a foundation for the well-posedness and stability analysis of homogeneous circular waveguides with impedance boundary conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_04348 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bessel Functions and Analysis of Circular Waveguides Mora-Paz, Jaime Demkowicz, Leszek Taylor, Christina G. Grosek, Jacob Henneking, Stefan Computational Physics 34B30, 65L15, 78M99, 33C10 J.2 The paper is devoted to the study of circularly coiled optical slab waveguides, which is also applicable to acoustical waveguides. We use a change of variables and the classical Frobenius method to compute Bessel functions of complex order and complex argument, and combine it with a perfectly matched layer technique to solve the relevant Bessel eigenvalue problem and deliver accurate loss factors for eigensolutions to the three-layer optical slab waveguide problem. The solutions provide a benchmark for verifying model implementations of this problem and allow for a numerical verification of the Glazman criterion that provides a foundation for the well-posedness and stability analysis of homogeneous circular waveguides with impedance boundary conditions. |
| title | Bessel Functions and Analysis of Circular Waveguides |
| topic | Computational Physics 34B30, 65L15, 78M99, 33C10 J.2 |
| url | https://arxiv.org/abs/2512.04348 |