Symmetry, stability, and computation of degenerate lasing modes
Name
PhysRevA.95.023835.pdf
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1.83 MB
Format
Adobe PDF
Checksum (MD5)
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Author(s)
Ge, Li
Pick, Adi
Burkhardt, Stephan
Liertzer, Matthias
Rotter, Stefan
Liu, David
Zhen, Bo
Hernandez, Felipe
Johnson, Steven G
Date Issued
February 2017
Journal
Physical Review A
Publisher
American Physical Society
Citation
Liu, David et al. “Symmetry, Stability, and Computation of Degenerate Lasing Modes.” Physical Review A 95.2 (2017): n. pag. © 2017 American Physical Society
Version
Final published version
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Massachusetts Institute of Technology. Department of Physics
Massachusetts Institute of Technology. Research Laboratory of Electronics
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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.
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DOI of Published Version
https://doi.org/10.1103/PhysRevA.95.023835
