Frobenius–Perron eigenstates in deformed microdisk cavities: non-Hermitian physics and asymmetric backscattering in ray dynamics
In optical microdisk cavities with boundary deformations the backscattering between clockwise and counter-clockwise propagating waves is in general asymmetric. The striking consequence of this asymmetry is that these apparently weakly open systems show pronounced non-Hermitian phenomena. The optical...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2016-01-01
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| Series: | New Journal of Physics |
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| Online Access: | https://doi.org/10.1088/1367-2630/18/1/015005 |
| _version_ | 1797750736334880768 |
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| author | Julius Kullig Jan Wiersig |
| author_facet | Julius Kullig Jan Wiersig |
| author_sort | Julius Kullig |
| collection | DOAJ |
| description | In optical microdisk cavities with boundary deformations the backscattering between clockwise and counter-clockwise propagating waves is in general asymmetric. The striking consequence of this asymmetry is that these apparently weakly open systems show pronounced non-Hermitian phenomena. The optical modes appear in non-orthogonal pairs, where both modes copropagate in a preferred sense of rotation, i.e. the modes exhibit a finite chirality. Full asymmetry in the backscattering results in a non-Hermitian degeneracy (exceptional point) where the deviation from closed system evolution is strongest. We study the effects of asymmetric backscattering in ray dynamics. For this purpose, we construct a finite approximation of the Frobenius–Perron operator for deformed microdisk cavities, which describes the dynamics of intensities in phase space. Eigenstates of the Frobenius–Perron operator show nice analogies to optical modes: they come in non-orthogonal copropagating pairs and have a finite chirality. We introduce a new cavity system with a smooth asymmetric boundary deformation where we demonstrate our results and we illustrate the main aspects with the help of a simple analytically solvable 1D model. |
| first_indexed | 2024-03-12T16:38:13Z |
| format | Article |
| id | doaj.art-226802b7e8134ee8bc93eea8fa24d8e4 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:38:13Z |
| publishDate | 2016-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-226802b7e8134ee8bc93eea8fa24d8e42023-08-08T14:38:34ZengIOP PublishingNew Journal of Physics1367-26302016-01-0118101500510.1088/1367-2630/18/1/015005Frobenius–Perron eigenstates in deformed microdisk cavities: non-Hermitian physics and asymmetric backscattering in ray dynamicsJulius Kullig0Jan Wiersig1Institut für Theoretische Physik , Otto-von-Guericke-Universität Magdeburg, Postfach 4120, D-39106 Magdeburg, GermanyInstitut für Theoretische Physik , Otto-von-Guericke-Universität Magdeburg, Postfach 4120, D-39106 Magdeburg, GermanyIn optical microdisk cavities with boundary deformations the backscattering between clockwise and counter-clockwise propagating waves is in general asymmetric. The striking consequence of this asymmetry is that these apparently weakly open systems show pronounced non-Hermitian phenomena. The optical modes appear in non-orthogonal pairs, where both modes copropagate in a preferred sense of rotation, i.e. the modes exhibit a finite chirality. Full asymmetry in the backscattering results in a non-Hermitian degeneracy (exceptional point) where the deviation from closed system evolution is strongest. We study the effects of asymmetric backscattering in ray dynamics. For this purpose, we construct a finite approximation of the Frobenius–Perron operator for deformed microdisk cavities, which describes the dynamics of intensities in phase space. Eigenstates of the Frobenius–Perron operator show nice analogies to optical modes: they come in non-orthogonal copropagating pairs and have a finite chirality. We introduce a new cavity system with a smooth asymmetric boundary deformation where we demonstrate our results and we illustrate the main aspects with the help of a simple analytically solvable 1D model.https://doi.org/10.1088/1367-2630/18/1/015005Frobenius–Perron operatorasymmetric backscatteringoptical cavitiesnon-Hermitian physicsopen systemsnonlinear dynamics |
| spellingShingle | Julius Kullig Jan Wiersig Frobenius–Perron eigenstates in deformed microdisk cavities: non-Hermitian physics and asymmetric backscattering in ray dynamics New Journal of Physics Frobenius–Perron operator asymmetric backscattering optical cavities non-Hermitian physics open systems nonlinear dynamics |
| title | Frobenius–Perron eigenstates in deformed microdisk cavities: non-Hermitian physics and asymmetric backscattering in ray dynamics |
| title_full | Frobenius–Perron eigenstates in deformed microdisk cavities: non-Hermitian physics and asymmetric backscattering in ray dynamics |
| title_fullStr | Frobenius–Perron eigenstates in deformed microdisk cavities: non-Hermitian physics and asymmetric backscattering in ray dynamics |
| title_full_unstemmed | Frobenius–Perron eigenstates in deformed microdisk cavities: non-Hermitian physics and asymmetric backscattering in ray dynamics |
| title_short | Frobenius–Perron eigenstates in deformed microdisk cavities: non-Hermitian physics and asymmetric backscattering in ray dynamics |
| title_sort | frobenius perron eigenstates in deformed microdisk cavities non hermitian physics and asymmetric backscattering in ray dynamics |
| topic | Frobenius–Perron operator asymmetric backscattering optical cavities non-Hermitian physics open systems nonlinear dynamics |
| url | https://doi.org/10.1088/1367-2630/18/1/015005 |
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