A scalar product for the radiation of resonant modes
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866916881162567680 |
|---|---|
| author | Paszkiewicz-Idzik, Maria Rebholz, Lukas Rockstuhl, Carsten Fernandez-Corbaton, Ivan |
| author_facet | Paszkiewicz-Idzik, Maria Rebholz, Lukas Rockstuhl, Carsten Fernandez-Corbaton, Ivan |
| contents | We introduce the conformally-invariant scalar product, originally devised for radiation fields, to the study of the modes of optical resonators. This scalar product allows one to normalize and compare resonant modes using their corresponding radiation fields. Such fields are polychromatic fields free of divergences, which are determined from the complex frequencies and the modal fields on the surface of the resonator. The scalar product is expressed as surface integrals involving the modal fields, multiplied by closed-form factors incorporating the complex frequencies. In a practical application, we study the modes of disk-shaped whispering gallery resonators, and show that the proposed scalar product accurately predicts the geometry-dependent crossings and anti-crossings between modes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_02892 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A scalar product for the radiation of resonant modes Paszkiewicz-Idzik, Maria Rebholz, Lukas Rockstuhl, Carsten Fernandez-Corbaton, Ivan Optics We introduce the conformally-invariant scalar product, originally devised for radiation fields, to the study of the modes of optical resonators. This scalar product allows one to normalize and compare resonant modes using their corresponding radiation fields. Such fields are polychromatic fields free of divergences, which are determined from the complex frequencies and the modal fields on the surface of the resonator. The scalar product is expressed as surface integrals involving the modal fields, multiplied by closed-form factors incorporating the complex frequencies. In a practical application, we study the modes of disk-shaped whispering gallery resonators, and show that the proposed scalar product accurately predicts the geometry-dependent crossings and anti-crossings between modes. |
| title | A scalar product for the radiation of resonant modes |
| topic | Optics |
| url | https://arxiv.org/abs/2411.02892 |