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Akakpo EK, Haelterman M, Leo F, Parra-Rivas P. Emergence of collapsed snaking related dark and bright Kerr dissipative solitons with quartic-quadratic dispersion. Phys Rev E 2023; 108:014203. [PMID: 37583153 DOI: 10.1103/physreve.108.014203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2023] [Accepted: 05/23/2023] [Indexed: 08/17/2023]
Abstract
We theoretically investigate the dynamics, bifurcation structure, and stability of dark localized states emerging in Kerr cavities in the presence of positive second- and fourth-order dispersion. In this previously unexplored regime, dark states form through the locking of uniform wave fronts, or domain walls, connecting two coexisting stable uniform states, and undergo a generic bifurcation structure known as collapsed homoclinic snaking. We characterize the robustness of these states by computing their stability and bifurcation structure as a function of the main control parameter of the system. Furthermore, we show that by increasing the dispersion of fourth order, bright localized states can be also stabilized.
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Affiliation(s)
- Edem Kossi Akakpo
- OPERA-photonics, Université libre de Bruxelles, 50 Avenue F. D. Roosevelt, CP 194/5, B-1050 Bruxelles, Belgium
| | - Marc Haelterman
- OPERA-photonics, Université libre de Bruxelles, 50 Avenue F. D. Roosevelt, CP 194/5, B-1050 Bruxelles, Belgium
| | - Francois Leo
- OPERA-photonics, Université libre de Bruxelles, 50 Avenue F. D. Roosevelt, CP 194/5, B-1050 Bruxelles, Belgium
| | - Pedro Parra-Rivas
- OPERA-photonics, Université libre de Bruxelles, 50 Avenue F. D. Roosevelt, CP 194/5, B-1050 Bruxelles, Belgium
- Dipartimento di Ingegneria dell'Informazione, Elettronica e Telecomunicazioni, Sapienza Universitá di Roma, via Eudossiana 18, 00184 Rome, Italy
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Skryabin DV. Sech-squared Pockels solitons in the microresonator parametric down-conversion. OPTICS EXPRESS 2021; 29:28521-28529. [PMID: 34614980 DOI: 10.1364/oe.432670] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/27/2021] [Accepted: 08/05/2021] [Indexed: 06/13/2023]
Abstract
We present an explicit sech-squared-soliton solution associated with the optical Pockels effect, achieved through the generation of the frequency combs via parametric down-conversion in optical microresonators with quadratic nonlinearity. This soliton contrasts the parametric sech-soliton describing the half-harmonic field in the limit of the large index mismatch, and associated with the cascaded-Kerr effect. We predict differences in the spectral profiles and powers of the Pockels and cascaded-Kerr solitons, and report that the pump power threshold of the former agree with the recent experimental observations.
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Mas Arabí C, Parra-Rivas P, Hansson T, Gelens L, Wabnitz S, Leo F. Localized structures formed through domain wall locking in cavity-enhanced second-harmonic generation. OPTICS LETTERS 2020; 45:5856-5859. [PMID: 33057302 DOI: 10.1364/ol.399658] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/08/2020] [Accepted: 09/22/2020] [Indexed: 06/11/2023]
Abstract
We analyze the formation of localized structures in cavity-enhanced second-harmonic generation. We focus on the phase-matched limit, and consider that fundamental and generated waves have opposite signs of group velocity dispersion. We show that these states form due to the locking of domain walls connecting two stable homogeneous states of the system, and undergo collapsed snaking. We study the impact of temporal walk-off on the stability and dynamics of these localized states.
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Clerc MG, Coulibaly S, Parra-Rivas P, Tlidi M. Nonlocal Raman response in Kerr resonators: Moving temporal localized structures and bifurcation structure. CHAOS (WOODBURY, N.Y.) 2020; 30:083111. [PMID: 32872794 DOI: 10.1063/5.0007350] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2020] [Accepted: 07/13/2020] [Indexed: 06/11/2023]
Abstract
A ring resonator made of a silica-based optical fiber is a paradigmatic system for the generation of dissipative localized structures or dissipative solitons. We analyze the effect of the non-instantaneous nonlinear response of the fused silica or the Raman response on the formation of localized structures. After reducing the generalized Lugiato-Lefever to a simple and generic bistable model with a nonlocal Raman effect, we investigate analytically the formation of moving temporal localized structures. This reduction is valid close to the nascent bistability regime, where the system undergoes a second-order critical point marking the onset of a hysteresis loop. The interaction between fronts allows for the stabilization of temporal localized structures. Without the Raman effect, moving temporal localized structures do not exist, as shown in M. G. Clerc, S. Coulibaly, and M. Tlidi, Phys. Rev. Res. 2, 013024 (2020). The detailed derivation of the speed and the width associated with these structures is presented. We characterize numerically in detail the bifurcation structure and stability associated with the moving temporal localized states. The numerical results of the governing equations are in close agreement with analytical predictions.
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Affiliation(s)
- M G Clerc
- Departamento de Física and Millennium Institute for Research in Optics, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 487-3, Santiago, Chile
| | - S Coulibaly
- Univ. Lille, CNRS, UMR 8523 - PhLAM - Physique des Lasers Atomes et Molécules, F-59000 Lille, France
| | - P Parra-Rivas
- OPERA-photonique, Université libre de Bruxelles, 50 Avenue F. D. Roosevelt, CP 194/5, B-1050 Bruxelles, Belgium
| | - M Tlidi
- Faculté des Sciences, Université Libre de Bruxelles (U.L.B), CP 231, Campus Plaine, B-1050 Bruxelles, Belgium
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Nie M, Huang SW. Symbiotic quadratic soliton mode-locked non-degenerate optical parametric oscillators. OPTICS LETTERS 2020; 45:4184-4187. [PMID: 32735254 DOI: 10.1364/ol.398265] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/21/2020] [Accepted: 06/26/2020] [Indexed: 06/11/2023]
Abstract
We analytically and numerically unveil the existence condition of symbiotic solitons in doubly resonant non-degenerate optical parametric oscillators. Resonant signal and idler with terahertz comb bandwidth and femtosecond pulse duration in the mid-infrared are attainable through this symbiotic soliton mode-locking technique. The group velocity mismatches between the three interacting waves are the dominant cause of the symbiotic soliton perturbation, and their effects are numerically investigated in detail. The principle can be applied to commonly used mid-infrared material platforms, making it a competitive ultrashort pulse and broadband comb source architecture.
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Nie M, Huang SW. Quadratic soliton mode-locked degenerate optical parametric oscillator. OPTICS LETTERS 2020; 45:2311-2314. [PMID: 32287221 DOI: 10.1364/ol.389568] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/04/2020] [Accepted: 03/07/2020] [Indexed: 06/11/2023]
Abstract
We examine the existence condition of the quadratic soliton mode-locked degenerate optical parametric oscillator in the previously unexplored parameter space. We study the nature of the quadratic solitons and divide their dynamics into two distinctive branches, depending on the system parameters. Origin of the quadratic soliton perturbation is identified, and strategy to mitigate its detrimental effect is developed. Frequency comb with terahertz bandwidth and femtosecond pulse duration are attainable in an example periodically poled lithium niobate waveguide resonator. Design rules of the quadratic soliton mode-locking are summarized. The principle can be further extended to other material platforms, making it a competitive ultrashort pulse and broadband comb source architecture at the mid-infrared.
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Ricciardi I, Mosca S, Parisi M, Leo F, Hansson T, Erkintalo M, Maddaloni P, De Natale P, Wabnitz S, De Rosa M. Optical Frequency Combs in Quadratically Nonlinear Resonators. MICROMACHINES 2020; 11:E230. [PMID: 32102284 PMCID: PMC7074798 DOI: 10.3390/mi11020230] [Citation(s) in RCA: 21] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/17/2020] [Revised: 02/17/2020] [Accepted: 02/19/2020] [Indexed: 11/17/2022]
Abstract
Optical frequency combs are one of the most remarkable inventions in recent decades. Originally conceived as the spectral counterpart of the train of short pulses emitted by mode-locked lasers, frequency combs have also been subsequently generated in continuously pumped microresonators, through third-order parametric processes. Quite recently, direct generation of optical frequency combs has been demonstrated in continuous-wave laser-pumped optical resonators with a second-order nonlinear medium inside. Here, we present a concise introduction to such quadratic combs and the physical mechanism that underlies their formation. We mainly review our recent experimental and theoretical work on formation and dynamics of quadratic frequency combs. We experimentally demonstrated comb generation in two configurations: a cavity for second harmonic generation, where combs are generated both around the pump frequency and its second harmonic and a degenerate optical parametric oscillator, where combs are generated around the pump frequency and its subharmonic. The experiments have been supported by a thorough theoretical analysis, aimed at modelling the dynamics of quadratic combs, both in frequency and time domains, providing useful insights into the physics of this new class of optical frequency comb synthesizers. Quadratic combs establish a new class of efficient frequency comb synthesizers, with unique features, which could enable straightforward access to new spectral regions and stimulate novel applications.
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Affiliation(s)
- Iolanda Ricciardi
- CNR-INO, Istituto Nazionale di Ottica, Via Campi Flegrei 34, I-80078 Pozzuoli (NA), Italy; (I.R.); (S.M.); (M.P.); (P.M.); (S.W.)
- INFN, Istituto Nazionale di Fisica Nucleare, Sez. di Napoli, Complesso Universitario di M.S. Angelo, Via Cintia, 80126 Napoli, Italy
| | - Simona Mosca
- CNR-INO, Istituto Nazionale di Ottica, Via Campi Flegrei 34, I-80078 Pozzuoli (NA), Italy; (I.R.); (S.M.); (M.P.); (P.M.); (S.W.)
| | - Maria Parisi
- CNR-INO, Istituto Nazionale di Ottica, Via Campi Flegrei 34, I-80078 Pozzuoli (NA), Italy; (I.R.); (S.M.); (M.P.); (P.M.); (S.W.)
| | - François Leo
- OPERA-photonics, Université libre de Bruxelles, 50 Avenue F. D. Roosevelt, CP 194/5, B-1050 Bruxelles, Belgium;
| | - Tobias Hansson
- Department of Physics, Chemistry and Biology, Linköping University, SE-581 83 Linköping, Sweden;
| | - Miro Erkintalo
- The Dodd-Walls Centre for Photonic and Quantum Technologies, Auckland 1142, New Zealand;
- Physics Department, The University of Auckland, Auckland 1142, New Zealand
| | - Pasquale Maddaloni
- CNR-INO, Istituto Nazionale di Ottica, Via Campi Flegrei 34, I-80078 Pozzuoli (NA), Italy; (I.R.); (S.M.); (M.P.); (P.M.); (S.W.)
- INFN, Istituto Nazionale di Fisica Nucleare, Sez. di Napoli, Complesso Universitario di M.S. Angelo, Via Cintia, 80126 Napoli, Italy
| | - Paolo De Natale
- CNR-INO, Istituto Nazionale di Ottica, Largo E. Fermi 6, I-50125 Firenze, Italy;
| | - Stefan Wabnitz
- CNR-INO, Istituto Nazionale di Ottica, Via Campi Flegrei 34, I-80078 Pozzuoli (NA), Italy; (I.R.); (S.M.); (M.P.); (P.M.); (S.W.)
- Dipartimento di Ingegneria dell’Informazione, Elettronica e Telecomunicazioni, Sapienza Università di Roma- Via Eudossiana 18, I-00184 Roma, Italy
- Department of Physics, Novosibirsk State University, 1 Pirogova Street, Novosibirsk 630090, Russia
| | - Maurizio De Rosa
- CNR-INO, Istituto Nazionale di Ottica, Via Campi Flegrei 34, I-80078 Pozzuoli (NA), Italy; (I.R.); (S.M.); (M.P.); (P.M.); (S.W.)
- INFN, Istituto Nazionale di Fisica Nucleare, Sez. di Napoli, Complesso Universitario di M.S. Angelo, Via Cintia, 80126 Napoli, Italy
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