Symmetry, stability, and computation of degenerate lasing modes
We present a general method to obtain the stable lasing solutions for the steady-state ab initio lasing theory (SALT) for the case of a degenerate symmetric laser in two dimensions (2D). We find that under most regimes (with one pathological exception), the stable solutions are clockwise and counter...
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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/1721.1/107481 https://orcid.org/0000-0002-2312-8483 https://orcid.org/0000-0002-7572-4594 https://orcid.org/0000-0001-7327-4967 |
| _version_ | 1811083812978819072 |
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| author | Ge, Li Pick, Adi Burkhardt, Stephan Liertzer, Matthias Rotter, Stefan Liu, David Zhen, Bo Hernandez, Felipe Johnson, Steven G |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Ge, Li Pick, Adi Burkhardt, Stephan Liertzer, Matthias Rotter, Stefan Liu, David Zhen, Bo Hernandez, Felipe Johnson, Steven G |
| author_sort | Ge, Li |
| collection | MIT |
| description | We present a general method to obtain the stable lasing solutions for the steady-state ab initio lasing theory (SALT) for the case of a degenerate symmetric laser in two dimensions (2D). We find that under most regimes (with one pathological exception), the stable solutions are clockwise and counterclockwise circulating modes, generalizing previously known results of ring lasers to all 2D rotational symmetry groups. Our method uses a combination of semianalytical solutions close to lasing threshold and numerical solvers to track the lasing modes far above threshold. Near threshold, we find closed-form expressions for both circulating modes and other types of lasing solutions as well as for their linearized Maxwell-Bloch eigenvalues, providing a simple way to determine their stability without having to do a full nonlinear numerical calculation. Above threshold, we show that a key feature of the circulating mode is its “chiral” intensity pattern, which arises from spontaneous symmetry breaking of mirror symmetry, and whose symmetry group requires that the degeneracy persists even when nonlinear effects become important. Finally, we introduce a numerical technique to solve the degenerate SALT equations far above threshold even when spatial discretization artificially breaks the degeneracy. |
| first_indexed | 2024-09-23T12:39:45Z |
| format | Article |
| id | mit-1721.1/107481 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T12:39:45Z |
| publishDate | 2017 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/1074812022-09-28T09:17:11Z Symmetry, stability, and computation of degenerate lasing modes Ge, Li Pick, Adi Burkhardt, Stephan Liertzer, Matthias Rotter, Stefan Liu, David Zhen, Bo Hernandez, Felipe Johnson, Steven G Massachusetts Institute of Technology. Department of Mathematics Massachusetts Institute of Technology. Department of Physics Massachusetts Institute of Technology. Research Laboratory of Electronics Liu, David Zhen, Bo Hernandez, Felipe Johnson, Steven G We present a general method to obtain the stable lasing solutions for the steady-state ab initio lasing theory (SALT) for the case of a degenerate symmetric laser in two dimensions (2D). We find that under most regimes (with one pathological exception), the stable solutions are clockwise and counterclockwise circulating modes, generalizing previously known results of ring lasers to all 2D rotational symmetry groups. Our method uses a combination of semianalytical solutions close to lasing threshold and numerical solvers to track the lasing modes far above threshold. Near threshold, we find closed-form expressions for both circulating modes and other types of lasing solutions as well as for their linearized Maxwell-Bloch eigenvalues, providing a simple way to determine their stability without having to do a full nonlinear numerical calculation. Above threshold, we show that a key feature of the circulating mode is its “chiral” intensity pattern, which arises from spontaneous symmetry breaking of mirror symmetry, and whose symmetry group requires that the degeneracy persists even when nonlinear effects become important. Finally, we introduce a numerical technique to solve the degenerate SALT equations far above threshold even when spatial discretization artificially breaks the degeneracy. United States. Army Research Office. Institute for Soldier Nanotechnologies (Grant W911NF-07-D-0004) Austrian Science Fund (Project SFB NextLite F49-P10) United States. Air Force Research Laboratory (Agreement FA8650-15-2-5220) 2017-03-17T20:33:42Z 2017-03-17T20:33:42Z 2017-02 2016-11 2017-02-23T23:00:05Z Article http://purl.org/eprint/type/JournalArticle 1050-2947 1094-1622 http://hdl.handle.net/1721.1/107481 Liu, David et al. “Symmetry, Stability, and Computation of Degenerate Lasing Modes.” Physical Review A 95.2 (2017): n. pag. © 2017 American Physical Society https://orcid.org/0000-0002-2312-8483 https://orcid.org/0000-0002-7572-4594 https://orcid.org/0000-0001-7327-4967 en http://dx.doi.org/10.1103/PhysRevA.95.023835 Physical Review A 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 | Ge, Li Pick, Adi Burkhardt, Stephan Liertzer, Matthias Rotter, Stefan Liu, David Zhen, Bo Hernandez, Felipe Johnson, Steven G Symmetry, stability, and computation of degenerate lasing modes |
| title | Symmetry, stability, and computation of degenerate lasing modes |
| title_full | Symmetry, stability, and computation of degenerate lasing modes |
| title_fullStr | Symmetry, stability, and computation of degenerate lasing modes |
| title_full_unstemmed | Symmetry, stability, and computation of degenerate lasing modes |
| title_short | Symmetry, stability, and computation of degenerate lasing modes |
| title_sort | symmetry stability and computation of degenerate lasing modes |
| url | http://hdl.handle.net/1721.1/107481 https://orcid.org/0000-0002-2312-8483 https://orcid.org/0000-0002-7572-4594 https://orcid.org/0000-0001-7327-4967 |
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