Generalized Perturbation Theory for Weakly Deformed Microdisk Cavities
Abstract A perturbation treatment is derived for weakly deformed microdisk cavities in a more generalized scenario, where both resonant and non‐resonant surface scattering processes coexist. It is proved that the originally developed nondegenerate and degenerate perturbation theories are simplified...
| Main Authors: | , , , , , , |
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| Format: | Article |
| Language: | English |
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Wiley-VCH
2024-03-01
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| Series: | Advanced Physics Research |
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| Online Access: | https://doi.org/10.1002/apxr.202300105 |
| _version_ | 1797270001983422464 |
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| author | Xuenan Zhang Bin Liu Xue Zhou Xin Yan Fang Wang Zongfu Yu Tonglei Cheng |
| author_facet | Xuenan Zhang Bin Liu Xue Zhou Xin Yan Fang Wang Zongfu Yu Tonglei Cheng |
| author_sort | Xuenan Zhang |
| collection | DOAJ |
| description | Abstract A perturbation treatment is derived for weakly deformed microdisk cavities in a more generalized scenario, where both resonant and non‐resonant surface scattering processes coexist. It is proved that the originally developed nondegenerate and degenerate perturbation theories are simplified forms of the generalized theory in special cases. The validity of the perturbation theory is verified by the comparison with a full numerical method for two generic classes of deformed microdisk cavities: locally notched microdisks and smooth globally deformed microdisks. The simulation of these two classes of microdisk cavities using the perturbation theory unveils the distinct characteristics of optical modes from the ones predicted by the original nondegenerate and degenerate perturbation theories in the generalized scenario. Furthermore, a hybrid‐scattering‐based exceptional point is introduced for deformed microdisk cavities in the generalized scenario by using the perturbation theory. The exceptional point exhibits higher nonorthogonality over the originally proposed resonant‐scattering‐based exceptional point, as non‐resonant scattering processes provide an additional degree of freedom. Full numerical simulations demonstrate that the exceptional point is more robust against random surface roughness at cavity boundary than the resonant‐scattering‐based exceptional point. |
| first_indexed | 2024-04-25T01:57:20Z |
| format | Article |
| id | doaj.art-4eace64df6dc4e1cb3461af27f0546cc |
| institution | Directory Open Access Journal |
| issn | 2751-1200 |
| language | English |
| last_indexed | 2024-04-25T01:57:20Z |
| publishDate | 2024-03-01 |
| publisher | Wiley-VCH |
| record_format | Article |
| series | Advanced Physics Research |
| spelling | doaj.art-4eace64df6dc4e1cb3461af27f0546cc2024-03-07T15:43:42ZengWiley-VCHAdvanced Physics Research2751-12002024-03-0133n/an/a10.1002/apxr.202300105Generalized Perturbation Theory for Weakly Deformed Microdisk CavitiesXuenan Zhang0Bin Liu1Xue Zhou2Xin Yan3Fang Wang4Zongfu Yu5Tonglei Cheng6State Key Laboratory of Synthetical Automation for Process Industries College of Information Science and Engineering Northeastern University Shenyang 110819 ChinaState Key Laboratory of Synthetical Automation for Process Industries College of Information Science and Engineering Northeastern University Shenyang 110819 ChinaState Key Laboratory of Synthetical Automation for Process Industries College of Information Science and Engineering Northeastern University Shenyang 110819 ChinaState Key Laboratory of Synthetical Automation for Process Industries College of Information Science and Engineering Northeastern University Shenyang 110819 ChinaState Key Laboratory of Synthetical Automation for Process Industries College of Information Science and Engineering Northeastern University Shenyang 110819 ChinaDepartment of Electrical and Computer Engineering University of Wisconsin Madison Wisconsin 53706 USAState Key Laboratory of Synthetical Automation for Process Industries College of Information Science and Engineering Northeastern University Shenyang 110819 ChinaAbstract A perturbation treatment is derived for weakly deformed microdisk cavities in a more generalized scenario, where both resonant and non‐resonant surface scattering processes coexist. It is proved that the originally developed nondegenerate and degenerate perturbation theories are simplified forms of the generalized theory in special cases. The validity of the perturbation theory is verified by the comparison with a full numerical method for two generic classes of deformed microdisk cavities: locally notched microdisks and smooth globally deformed microdisks. The simulation of these two classes of microdisk cavities using the perturbation theory unveils the distinct characteristics of optical modes from the ones predicted by the original nondegenerate and degenerate perturbation theories in the generalized scenario. Furthermore, a hybrid‐scattering‐based exceptional point is introduced for deformed microdisk cavities in the generalized scenario by using the perturbation theory. The exceptional point exhibits higher nonorthogonality over the originally proposed resonant‐scattering‐based exceptional point, as non‐resonant scattering processes provide an additional degree of freedom. Full numerical simulations demonstrate that the exceptional point is more robust against random surface roughness at cavity boundary than the resonant‐scattering‐based exceptional point.https://doi.org/10.1002/apxr.202300105exceptional pointsmicrodisk cavitiesperturbation theorysurface scatteringwhispering‐gallery modes |
| spellingShingle | Xuenan Zhang Bin Liu Xue Zhou Xin Yan Fang Wang Zongfu Yu Tonglei Cheng Generalized Perturbation Theory for Weakly Deformed Microdisk Cavities Advanced Physics Research exceptional points microdisk cavities perturbation theory surface scattering whispering‐gallery modes |
| title | Generalized Perturbation Theory for Weakly Deformed Microdisk Cavities |
| title_full | Generalized Perturbation Theory for Weakly Deformed Microdisk Cavities |
| title_fullStr | Generalized Perturbation Theory for Weakly Deformed Microdisk Cavities |
| title_full_unstemmed | Generalized Perturbation Theory for Weakly Deformed Microdisk Cavities |
| title_short | Generalized Perturbation Theory for Weakly Deformed Microdisk Cavities |
| title_sort | generalized perturbation theory for weakly deformed microdisk cavities |
| topic | exceptional points microdisk cavities perturbation theory surface scattering whispering‐gallery modes |
| url | https://doi.org/10.1002/apxr.202300105 |
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