Dynamically Encircling Exceptional Points: Exact Evolution and Polarization State Conversion
We show that a two-level non-Hermitian Hamiltonian with constant off-diagonal exchange elements can be analyzed exactly when the underlying exceptional point is perfectly encircled in the complex plane. The state evolution of this system is explicitly obtained in terms of an ensuing transfer matrix,...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2017
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| Online Access: | http://hdl.handle.net/1721.1/107202 https://orcid.org/0000-0002-7572-4594 https://orcid.org/0000-0002-7184-5831 |
| _version_ | 1811083556133273600 |
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| author | Hassan, Absar U. Khajavikhan, Mercedeh Christodoulides, Demetrios N. Zhen, Bo Soljacic, Marin |
| author2 | Massachusetts Institute of Technology. Research Laboratory of Electronics |
| author_facet | Massachusetts Institute of Technology. Research Laboratory of Electronics Hassan, Absar U. Khajavikhan, Mercedeh Christodoulides, Demetrios N. Zhen, Bo Soljacic, Marin |
| author_sort | Hassan, Absar U. |
| collection | MIT |
| description | We show that a two-level non-Hermitian Hamiltonian with constant off-diagonal exchange elements can be analyzed exactly when the underlying exceptional point is perfectly encircled in the complex plane. The state evolution of this system is explicitly obtained in terms of an ensuing transfer matrix, even for large encirclements, regardless of adiabatic conditions. Our results clearly explain the direction-dependent nature of this process and why in the adiabatic limit its outcome is dominated by a specific eigenstate—irrespective of initial conditions. Moreover, numerical simulations suggest that this mechanism can still persist in the presence of nonlinear effects. We further show that this robust process can be harnessed to realize an optical omnipolarizer: a configuration that generates a desired polarization output regardless of the input polarization state, while from the opposite direction it always produces the counterpart eigenstate. |
| first_indexed | 2024-09-23T12:34:56Z |
| format | Article |
| id | mit-1721.1/107202 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T12:34:56Z |
| publishDate | 2017 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/1072022022-10-01T09:54:03Z Dynamically Encircling Exceptional Points: Exact Evolution and Polarization State Conversion Hassan, Absar U. Khajavikhan, Mercedeh Christodoulides, Demetrios N. Zhen, Bo Soljacic, Marin Massachusetts Institute of Technology. Research Laboratory of Electronics Zhen, Bo Soljacic, Marin We show that a two-level non-Hermitian Hamiltonian with constant off-diagonal exchange elements can be analyzed exactly when the underlying exceptional point is perfectly encircled in the complex plane. The state evolution of this system is explicitly obtained in terms of an ensuing transfer matrix, even for large encirclements, regardless of adiabatic conditions. Our results clearly explain the direction-dependent nature of this process and why in the adiabatic limit its outcome is dominated by a specific eigenstate—irrespective of initial conditions. Moreover, numerical simulations suggest that this mechanism can still persist in the presence of nonlinear effects. We further show that this robust process can be harnessed to realize an optical omnipolarizer: a configuration that generates a desired polarization output regardless of the input polarization state, while from the opposite direction it always produces the counterpart eigenstate. United States. Army Research Office. Institute for Soldier Nanotechnologies (Grant W911NF-13-D-0001) United States-Israel Binational Science Foundation (Grant 2013508) 2017-03-06T21:55:55Z 2017-03-06T21:55:55Z 2017-03 2016-11 2017-03-03T23:00:04Z Article http://purl.org/eprint/type/JournalArticle 0031-9007 1079-7114 http://hdl.handle.net/1721.1/107202 Hassan, Absar U. et al. “Dynamically Encircling Exceptional Points: Exact Evolution and Polarization State Conversion.” Physical Review Letters 118.9 (2017): n. pag. © 2017 American Physical Society https://orcid.org/0000-0002-7572-4594 https://orcid.org/0000-0002-7184-5831 en http://dx.doi.org/10.1103/PhysRevLett.118.093002 Physical Review Letters Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. American Physical Society application/pdf American Physical Society American Physical Society |
| spellingShingle | Hassan, Absar U. Khajavikhan, Mercedeh Christodoulides, Demetrios N. Zhen, Bo Soljacic, Marin Dynamically Encircling Exceptional Points: Exact Evolution and Polarization State Conversion |
| title | Dynamically Encircling Exceptional Points: Exact Evolution and Polarization State Conversion |
| title_full | Dynamically Encircling Exceptional Points: Exact Evolution and Polarization State Conversion |
| title_fullStr | Dynamically Encircling Exceptional Points: Exact Evolution and Polarization State Conversion |
| title_full_unstemmed | Dynamically Encircling Exceptional Points: Exact Evolution and Polarization State Conversion |
| title_short | Dynamically Encircling Exceptional Points: Exact Evolution and Polarization State Conversion |
| title_sort | dynamically encircling exceptional points exact evolution and polarization state conversion |
| url | http://hdl.handle.net/1721.1/107202 https://orcid.org/0000-0002-7572-4594 https://orcid.org/0000-0002-7184-5831 |
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