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Gao X, He H, Sobolewski S, Cerjan A, Hsu CW. Dynamic gain and frequency comb formation in exceptional-point lasers. Nat Commun 2024; 15:8618. [PMID: 39366982 DOI: 10.1038/s41467-024-52957-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2024] [Accepted: 09/26/2024] [Indexed: 10/06/2024] Open
Abstract
Exceptional points (EPs)-singularities in the parameter space of non-Hermitian systems where two nearby eigenmodes coalesce-feature unique properties with applications such as sensitivity enhancement and chiral emission. Existing realizations of EP lasers operate with static populations in the gain medium. By analyzing the full-wave Maxwell-Bloch equations, here we show that in a laser operating sufficiently close to an EP, the nonlinear gain will spontaneously induce a multi-spectral multi-modal instability above a pump threshold, which initiates an oscillating population inversion and generates a frequency comb. The efficiency of comb generation is enhanced by both the spectral degeneracy and the spatial coalescence of modes near an EP. Such an "EP comb" has a widely tunable repetition rate, self-starts without external modulators or a continuous-wave pump, and can be realized with an ultra-compact footprint. We develop an exact solution of the Maxwell-Bloch equations with an oscillating inversion, describing all spatiotemporal properties of the EP comb as a limit cycle. We numerically illustrate this phenomenon in a 5-μm-long gain-loss coupled AlGaAs cavity and adjust the EP comb repetition rate from 20 to 27 GHz. This work provides a rigorous spatiotemporal description of the rich laser behaviors that arise from the interplay between the non-Hermiticity, nonlinearity, and dynamics of a gain medium.
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Affiliation(s)
- Xingwei Gao
- Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, CA, 90089, USA.
| | - Hao He
- Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, CA, 90089, USA
| | - Scott Sobolewski
- Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, CA, 90089, USA
| | - Alexander Cerjan
- Center for Integrated Nanotechnologies, Sandia National Laboratories, Albuquerque, NM, 87185, USA.
| | - Chia Wei Hsu
- Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, CA, 90089, USA
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Guria C, Zhong Q, Ozdemir SK, Patil YSS, El-Ganainy R, Harris JGE. Resolving the topology of encircling multiple exceptional points. Nat Commun 2024; 15:1369. [PMID: 38355733 PMCID: PMC10867139 DOI: 10.1038/s41467-024-45530-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2023] [Accepted: 01/26/2024] [Indexed: 02/16/2024] Open
Abstract
Non-Hermiticity has emerged as a new paradigm for controlling coupled-mode systems in ways that cannot be achieved with conventional techniques. One aspect of this control that has received considerable attention recently is the encircling of exceptional points (EPs). To date, most work has focused on systems consisting of two modes that are tuned by two control parameters and have isolated EPs. While these systems exhibit exotic features related to EP encircling, it has been shown that richer behavior occurs in systems with more than two modes. Such systems can be tuned by more than two control parameters, and contain EPs that form a knot-like structure. Control loops that encircle this structure cause the system's eigenvalues to trace out non-commutative braids. Here we consider a hybrid scenario: a three-mode system with just two control parameters. We describe the relationship between control loops and their topology in the full and two-dimensional parameter space. We demonstrate this relationship experimentally using a three-mode mechanical system in which the control parameters are provided by optomechanical interaction with a high-finesse optical cavity.
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Affiliation(s)
- Chitres Guria
- Department of Physics, Yale University, New Haven, CT, 06520, USA
| | - Qi Zhong
- Department of Physics, Michigan Technological University, Houghton, MI, 49931, USA
- Department of Engineering Science and Mechanics, and Materials Research Institute, The Pennsylvania State University, University Park, PA, 16802, USA
| | - Sahin Kaya Ozdemir
- Department of Engineering Science and Mechanics, and Materials Research Institute, The Pennsylvania State University, University Park, PA, 16802, USA
| | - Yogesh S S Patil
- Department of Physics, Yale University, New Haven, CT, 06520, USA
| | - Ramy El-Ganainy
- Department of Physics, Michigan Technological University, Houghton, MI, 49931, USA.
- Henes Center for Quantum Phenomena, Michigan Technological University, Houghton, MI, 49931, USA.
| | - Jack Gwynne Emmet Harris
- Department of Physics, Yale University, New Haven, CT, 06520, USA.
- Department of Applied Physics, Yale University, New Haven, CT, 06520, USA.
- Yale Quantum Institute, Yale University, New Haven, CT, 06520, USA.
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