Mathematical analysis of whispering gallery modes in graded index optical micro-disk resonators
We study from a theoretical point of view whispering gallery modes (WGM) in graded index micro-disk resonators where the refractive optical index varies with the radial position. Using a quantum mechanical analogy, we highlight three different behaviors for the WGM depending on the sign of a key par...
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| Veröffentlicht in: | The European physical journal. D, Atomic, molecular, and optical physics Atomic, molecular, and optical physics, 2020-11, Vol.74 (11), Article 221 |
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| container_title | The European physical journal. D, Atomic, molecular, and optical physics |
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| creator | Balac, Stéphane Dauge, Monique Dumeige, Yannick Féron, Patrice Moitier, Zoïs |
| description | We study from a theoretical point of view whispering gallery modes (WGM) in graded index micro-disk resonators where the refractive optical index varies with the radial position. Using a quantum mechanical analogy, we highlight three different behaviors for the WGM depending on the sign of a key parameter expressed as the ratio of the refractive index value to its derivative at the cavity boundary. This results in three asymptotic expansions of the resonances for large polar mode index providing first-approximations of WGM in a simple and quick way. Besides, these expansions yield a theoretical fundation to considerations of V.S. Ilchenko, A.A. Savchenkov, A.B. Matsko, L. Maleki, J. Opt. Soc. Am. A
20
, 157 (2003), about three sorts of effective potentials for TE modes in a dielectric sphere.
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| doi_str_mv | 10.1140/epjd/e2020-10303-5 |
| format | Article |
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20
, 157 (2003), about three sorts of effective potentials for TE modes in a dielectric sphere.
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20
, 157 (2003), about three sorts of effective potentials for TE modes in a dielectric sphere.
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D, Atomic, molecular, and optical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Balac, Stéphane</au><au>Dauge, Monique</au><au>Dumeige, Yannick</au><au>Féron, Patrice</au><au>Moitier, Zoïs</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Mathematical analysis of whispering gallery modes in graded index optical micro-disk resonators</atitle><jtitle>The European physical journal. D, Atomic, molecular, and optical physics</jtitle><stitle>Eur. Phys. J. D</stitle><date>2020-11-01</date><risdate>2020</risdate><volume>74</volume><issue>11</issue><artnum>221</artnum><issn>1434-6060</issn><eissn>1434-6079</eissn><abstract>We study from a theoretical point of view whispering gallery modes (WGM) in graded index micro-disk resonators where the refractive optical index varies with the radial position. Using a quantum mechanical analogy, we highlight three different behaviors for the WGM depending on the sign of a key parameter expressed as the ratio of the refractive index value to its derivative at the cavity boundary. This results in three asymptotic expansions of the resonances for large polar mode index providing first-approximations of WGM in a simple and quick way. Besides, these expansions yield a theoretical fundation to considerations of V.S. Ilchenko, A.A. Savchenkov, A.B. Matsko, L. Maleki, J. Opt. Soc. Am. A
20
, 157 (2003), about three sorts of effective potentials for TE modes in a dielectric sphere.
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| subjects | Applications of Nonlinear Dynamics and Chaos Theory Asymptotic series Atomic Mathematical analysis Mathematical Physics Mathematics Molecular Numerical Analysis Optical and Plasma Physics Optics Physical Chemistry Physics Physics and Astronomy Quantum Information Technology Quantum mechanics Quantum Physics Refractivity Regular Article Resonators Spectroscopy/Spectrometry Spintronics Whispering gallery modes |
| title | Mathematical analysis of whispering gallery modes in graded index optical micro-disk resonators |
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