Engineering isospectrality in multidimensional photonic systems
Selective manipulation of energy levels plays an essential role in realizing multichannel wave devices. One of the representative examples is to utilize the concept of quasi-isospectrality: a family of wave systems with an almost identical spectrum except for a part of energy levels. Most approaches...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2023-03-01
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| Series: | Nanophotonics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/nanoph-2022-0740 |
| _version_ | 1826841690671939584 |
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| author | Lee Dayeong Park Hyungchul Yu Sunkyu |
| author_facet | Lee Dayeong Park Hyungchul Yu Sunkyu |
| author_sort | Lee Dayeong |
| collection | DOAJ |
| description | Selective manipulation of energy levels plays an essential role in realizing multichannel wave devices. One of the representative examples is to utilize the concept of quasi-isospectrality: a family of wave systems with an almost identical spectrum except for a part of energy levels. Most approaches toward quasi-isospectrality have employed analytical methods based on symmetry or tridiagonalization, such as supersymmetry, Householder, or Lanczos transformations. Although such analytical approaches provide deterministic and stable designs based on operator factorizations, the mathematical strictness in the factorizations, at the same time, hinders isospectral engineering in a given multidimension. Here we develop the semi-analytical method for engineering isospectrality in multidimensional photonic systems. The method provides the systematic perturbation for the target energy level shifts by decomposing the allowed form of system changes into the perturbation basis. We demonstrate the isospectrality of lower-, higher-, and random-order states while imposing the designed shifts on the other states. The stability analysis shows that the accuracy of the method is determined by the ranges of isospectral state numbers and perturbation strength. The systematic, free-form, and multidimensional natures of the proposed method show great potential for the platform-transparent design of multichannel devices. |
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| format | Article |
| id | doaj.art-803764b734ac4f99a6b21912c5d400db |
| institution | Directory Open Access Journal |
| issn | 2192-8614 |
| language | English |
| last_indexed | 2025-02-16T13:06:13Z |
| publishDate | 2023-03-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Nanophotonics |
| spelling | doaj.art-803764b734ac4f99a6b21912c5d400db2025-02-02T15:46:12ZengDe GruyterNanophotonics2192-86142023-03-0112132593260110.1515/nanoph-2022-0740Engineering isospectrality in multidimensional photonic systemsLee Dayeong0Park Hyungchul1Yu Sunkyu2Intelligent Wave Systems Laboratory, Department of Electrical and Computer Engineering, Seoul National University, Seoul08826, KoreaIntelligent Wave Systems Laboratory, Department of Electrical and Computer Engineering, Seoul National University, Seoul08826, KoreaIntelligent Wave Systems Laboratory, Department of Electrical and Computer Engineering, Seoul National University, Seoul08826, KoreaSelective manipulation of energy levels plays an essential role in realizing multichannel wave devices. One of the representative examples is to utilize the concept of quasi-isospectrality: a family of wave systems with an almost identical spectrum except for a part of energy levels. Most approaches toward quasi-isospectrality have employed analytical methods based on symmetry or tridiagonalization, such as supersymmetry, Householder, or Lanczos transformations. Although such analytical approaches provide deterministic and stable designs based on operator factorizations, the mathematical strictness in the factorizations, at the same time, hinders isospectral engineering in a given multidimension. Here we develop the semi-analytical method for engineering isospectrality in multidimensional photonic systems. The method provides the systematic perturbation for the target energy level shifts by decomposing the allowed form of system changes into the perturbation basis. We demonstrate the isospectrality of lower-, higher-, and random-order states while imposing the designed shifts on the other states. The stability analysis shows that the accuracy of the method is determined by the ranges of isospectral state numbers and perturbation strength. The systematic, free-form, and multidimensional natures of the proposed method show great potential for the platform-transparent design of multichannel devices.https://doi.org/10.1515/nanoph-2022-0740coupled mode theorycoupled resonatorsdisordered systemisospectralityperturbationpseudo-inverse |
| spellingShingle | Lee Dayeong Park Hyungchul Yu Sunkyu Engineering isospectrality in multidimensional photonic systems Nanophotonics coupled mode theory coupled resonators disordered system isospectrality perturbation pseudo-inverse |
| title | Engineering isospectrality in multidimensional photonic systems |
| title_full | Engineering isospectrality in multidimensional photonic systems |
| title_fullStr | Engineering isospectrality in multidimensional photonic systems |
| title_full_unstemmed | Engineering isospectrality in multidimensional photonic systems |
| title_short | Engineering isospectrality in multidimensional photonic systems |
| title_sort | engineering isospectrality in multidimensional photonic systems |
| topic | coupled mode theory coupled resonators disordered system isospectrality perturbation pseudo-inverse |
| url | https://doi.org/10.1515/nanoph-2022-0740 |
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