Balanced Gain-and-Loss Optical Waveguides: Exact Solutions for Guided Modes in Susy-QM
The construction of exactly solvable refractive indices allowing guided TE modes in optical waveguides is investigated within the formalism of Darboux–Crum transformations. We apply the finite-difference algorithm for higher-order supersymmetric quantum mechanics to obtain complex-valued refractive...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-08-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/9/1583 |
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| author | Sara Cruz y Cruz Alejandro Romero-Osnaya Oscar Rosas-Ortiz |
| author_facet | Sara Cruz y Cruz Alejandro Romero-Osnaya Oscar Rosas-Ortiz |
| author_sort | Sara Cruz y Cruz |
| collection | DOAJ |
| description | The construction of exactly solvable refractive indices allowing guided TE modes in optical waveguides is investigated within the formalism of Darboux–Crum transformations. We apply the finite-difference algorithm for higher-order supersymmetric quantum mechanics to obtain complex-valued refractive indices admitting all-real eigenvalues in their point spectrum. The new refractive indices are such that their imaginary part gives zero if it is integrated over the entire domain of definition. This property, called condition of zero total area, ensures the conservation of optical power so the refractive index shows balanced gain and loss. Consequently, the complex-valued refractive indices reported in this work include but are not limited to the parity-time invariant case. |
| first_indexed | 2024-03-10T07:10:53Z |
| format | Article |
| id | doaj.art-baea7380806843db947375fa4a6eb7e5 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T07:10:53Z |
| publishDate | 2021-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-baea7380806843db947375fa4a6eb7e52023-11-22T15:26:58ZengMDPI AGSymmetry2073-89942021-08-01139158310.3390/sym13091583Balanced Gain-and-Loss Optical Waveguides: Exact Solutions for Guided Modes in Susy-QMSara Cruz y Cruz0Alejandro Romero-Osnaya1Oscar Rosas-Ortiz2Instituto Politécnico Nacional, UPIITA, Av I.P.N 2580, México City 07340, MexicoPhysics Department, Cinvestav, AP 14-740, México City 07000, MexicoPhysics Department, Cinvestav, AP 14-740, México City 07000, MexicoThe construction of exactly solvable refractive indices allowing guided TE modes in optical waveguides is investigated within the formalism of Darboux–Crum transformations. We apply the finite-difference algorithm for higher-order supersymmetric quantum mechanics to obtain complex-valued refractive indices admitting all-real eigenvalues in their point spectrum. The new refractive indices are such that their imaginary part gives zero if it is integrated over the entire domain of definition. This property, called condition of zero total area, ensures the conservation of optical power so the refractive index shows balanced gain and loss. Consequently, the complex-valued refractive indices reported in this work include but are not limited to the parity-time invariant case.https://www.mdpi.com/2073-8994/13/9/1583optical waveguidesDarboux methodsupersymmetric quantum mechanicsPT symmetrynon-Hermitian systems |
| spellingShingle | Sara Cruz y Cruz Alejandro Romero-Osnaya Oscar Rosas-Ortiz Balanced Gain-and-Loss Optical Waveguides: Exact Solutions for Guided Modes in Susy-QM Symmetry optical waveguides Darboux method supersymmetric quantum mechanics PT symmetry non-Hermitian systems |
| title | Balanced Gain-and-Loss Optical Waveguides: Exact Solutions for Guided Modes in Susy-QM |
| title_full | Balanced Gain-and-Loss Optical Waveguides: Exact Solutions for Guided Modes in Susy-QM |
| title_fullStr | Balanced Gain-and-Loss Optical Waveguides: Exact Solutions for Guided Modes in Susy-QM |
| title_full_unstemmed | Balanced Gain-and-Loss Optical Waveguides: Exact Solutions for Guided Modes in Susy-QM |
| title_short | Balanced Gain-and-Loss Optical Waveguides: Exact Solutions for Guided Modes in Susy-QM |
| title_sort | balanced gain and loss optical waveguides exact solutions for guided modes in susy qm |
| topic | optical waveguides Darboux method supersymmetric quantum mechanics PT symmetry non-Hermitian systems |
| url | https://www.mdpi.com/2073-8994/13/9/1583 |
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