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Mangini F, Ferraro M, Gemechu WA, Sun Y, Gervaziev M, Kharenko D, Babin S, Couderc V, Wabnitz S. On the maximization of entropy in the process of thermalization of highly multimode nonlinear beams. OPTICS LETTERS 2024; 49:3340-3343. [PMID: 38875615 DOI: 10.1364/ol.521563] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/16/2024] [Accepted: 05/13/2024] [Indexed: 06/16/2024]
Abstract
We present a direct experimental confirmation of the maximization of entropy which accompanies the thermalization of a highly multimode light beam, upon its nonlinear propagation in standard graded-index (GRIN) optical fibers.
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2
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Labaz M, Sidorenko P. Spatial-spectral complexity in Kerr beam self-cleaning. OPTICS LETTERS 2024; 49:2902-2905. [PMID: 38824288 DOI: 10.1364/ol.524367] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/20/2024] [Accepted: 04/29/2024] [Indexed: 06/03/2024]
Abstract
We report on a comprehensive experimental investigation into the spatial-spectral complexity of the laser beam during Kerr-induced beam self-cleaning in graded-index multimode fibers. We demonstrate the self-cleaning of beams using both transform-limited and chirped femtosecond pulses. By utilizing the spectrally resolved imaging technique, we examine variations in beam homogeneity during the beam cleanup process and reveal correlations observed among spatial beam profiles at different wavelengths for the various cleaned pulses. Our results significantly advance our understanding of Kerr-induced self-cleaning with chirped ultrafast pulses and offer new possibilities for diverse applications.
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3
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Deng Y, Li W, Gao Z, Liu W, Ma P, Zhou P, Jiang Z. General error analysis of matrix-operation-mode decomposition technique in few-mode fiber laser. OPTICS EXPRESS 2024; 32:17988-18006. [PMID: 38858966 DOI: 10.1364/oe.523307] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/07/2024] [Accepted: 04/18/2024] [Indexed: 06/12/2024]
Abstract
The mode decomposition based on matrix operation (MDMO) is one of the fastest mode decomposition (MD) techniques, which is important to the few-mode fiber laser characterization and its applications. In this paper, the general error of the MDMO technique was analyzed, where different influencing factors, such as position deviation of the optical imaging system, coordinate deviation of the image acquisition system, aberrations, and mode distortion were considered. It is found that the MDMO technique based on far-field intensity distribution is less affected by optical imaging system position deviation, coordinate deviation of the image acquisition system, and mode distortion than those based on direct near-field decomposition. But far-field decomposition is more affected by aberration than those based on near-field decomposition. In particular, the numerical results show that the deviation of the coordinate axis direction is an important factor limiting the accuracy of MD. In addition, replacing the ideal eigenmode basis with a distorted eigenmode basis can effectively suppress the decrease in mode decomposition accuracy caused by fiber bending. Moreover, based on detailed numerical analysis results, fitting formulas for estimating the accuracy of the MDMO technique with imperfections are also provided, which provides a comprehensive method for evaluating the accuracy of the MDMO technique in practical engineering operations.
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4
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Frahm KM, Shepelyansky DL. Random matrix model of Kolmogorov-Zakharov turbulence. Phys Rev E 2024; 109:044201. [PMID: 38755800 DOI: 10.1103/physreve.109.044201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/21/2024] [Accepted: 03/08/2024] [Indexed: 05/18/2024]
Abstract
We introduce and study a random matrix model of Kolmogorov-Zakharov turbulence in a nonlinear purely dynamical finite-size system with many degrees of freedom. For the case of a direct cascade, the energy and norm pumping takes place at low energy scales with absorption at high energies. For a pumping strength above a certain chaos border, a global chaotic attractor appears with a stationary energy flow through a Hamiltonian inertial energy interval. In this regime, the steady-state norm distribution is described by an algebraic decay with an exponent in agreement with the Kolmogorov-Zakharov theory. Below the chaos border, the system is located in the quasi-integrable regime similar to the Kolmogorov-Arnold-Moser theory and the turbulence is suppressed. For the inverse cascade, the system rapidly enters a strongly nonlinear regime where the weak turbulence description is invalid. We argue that such a dynamical turbulence is generic, showing that it is present in other lattice models with disorder and Anderson localization. We point out that such dynamical models can be realized in multimode optical fibers.
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Affiliation(s)
- Klaus M Frahm
- Laboratoire de Physique Théorique, IRSAMC, Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
| | - Dima L Shepelyansky
- Laboratoire de Physique Théorique, IRSAMC, Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
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5
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Ferraro M, Mangini F, Zitelli M, Wabnitz S. On spatial beam self-cleaning from the perspective of optical wave thermalization in multimode graded-index fibers. ADVANCES IN PHYSICS: X 2023; 8. [DOI: 10.1080/23746149.2023.2228018] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2023] [Accepted: 06/16/2023] [Indexed: 09/02/2023] Open
Affiliation(s)
- Mario Ferraro
- Department of Information Engineering, Electronics and Telecommunications, DIET, Sapienza University of Rome, Rome, Italy
- Department of Physics, University of Calabria, Rende, Italy
| | - Fabio Mangini
- Department of Information Engineering, Electronics and Telecommunications, DIET, Sapienza University of Rome, Rome, Italy
- CNR-INO, Istituto Nazionale di Ottica, Pozzuoli, Italy
| | - Mario Zitelli
- Department of Information Engineering, Electronics and Telecommunications, DIET, Sapienza University of Rome, Rome, Italy
| | - Stefan Wabnitz
- Department of Information Engineering, Electronics and Telecommunications, DIET, Sapienza University of Rome, Rome, Italy
- CNR-INO, Istituto Nazionale di Ottica, Pozzuoli, Italy
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6
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Ren H, Pyrialakos GG, Wu FO, Jung PS, Efremidis NK, Khajavikhan M, Christodoulides DN. Nature of Optical Thermodynamic Pressure Exerted in Highly Multimoded Nonlinear Systems. PHYSICAL REVIEW LETTERS 2023; 131:193802. [PMID: 38000401 DOI: 10.1103/physrevlett.131.193802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/05/2023] [Accepted: 10/06/2023] [Indexed: 11/26/2023]
Abstract
The theory of optical thermodynamics provides a comprehensive framework that enables a self-consistent description of the intricate dynamics of nonlinear multimoded photonic systems. This theory, among others, predicts a pressurelike intensive quantity (p[over ^]) that is conjugate to the system's total number of modes (M)-its corresponding extensive variable. Yet at this point, the nature of this intensive quantity is still nebulous. In this Letter, we elucidate the physical origin of the optical thermodynamic pressure and demonstrate its dual essence. In this context, we rigorously derive an expression that splits p[over ^] into two distinct components, a term that is explicitly tied to the electrodynamic radiation pressure and a second entropic part that is responsible for the entropy change. We utilize this result to establish a formalism that simplifies the quantification of radiation pressure under nonlinear equilibrium conditions, thus eliminating the need for a tedious evaluation of the Maxwell stress tensor. Our theoretical analysis is corroborated by numerical simulations carried out in highly multimoded nonlinear optical structures. These results may provide a novel way in predicting and controlling radiation pressure processes in a variety of nonlinear electromagnetic settings.
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Affiliation(s)
- Huizhong Ren
- Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, California 90089, USA
| | - Georgios G Pyrialakos
- Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, California 90089, USA
- CREOL, The College of Optics and Photonics, University of Central Florida, Orlando, Florida 32816, USA
| | - Fan O Wu
- CREOL, The College of Optics and Photonics, University of Central Florida, Orlando, Florida 32816, USA
| | - Pawel S Jung
- CREOL, The College of Optics and Photonics, University of Central Florida, Orlando, Florida 32816, USA
- Faculty of Physics, Warsaw University of Technology, Koszykowa 75, 00-662 Warsaw, Poland
| | - Nikolaos K Efremidis
- Department of Mathematics and Applied Mathematics, University of Crete, Heraklion, Crete 70013, Greece
| | - Mercedeh Khajavikhan
- Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, California 90089, USA
| | - Demetrios N Christodoulides
- Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, California 90089, USA
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7
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Mangini F, Ferraro M, Tonello A, Couderc V, Wabnitz S. High-temperature wave thermalization spoils beam self-cleaning in nonlinear multimode GRIN fibers. OPTICS LETTERS 2023; 48:4741-4744. [PMID: 37707891 DOI: 10.1364/ol.497917] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/13/2023] [Accepted: 08/06/2023] [Indexed: 09/15/2023]
Abstract
In our experiments, we reveal a so-far unnoticed power limitation of beam self-cleaning in graded-index nonlinear multimode optical fibers. As the optical pulse power is progressively increased, we observed that the initial Kerr-induced improvement of the spatial beam quality is eventually lost. Based on a holographic mode decomposition of the output field, we show that beam spoiling is associated with high-temperature wave thermalization, which depletes the fundamental mode in favor of a highly multimode power distribution.
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8
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Biasi A, Evnin O, Malomed BA. Obstruction to ergodicity in nonlinear Schrödinger equations with resonant potentials. Phys Rev E 2023; 108:034204. [PMID: 37849119 DOI: 10.1103/physreve.108.034204] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2023] [Accepted: 08/11/2023] [Indexed: 10/19/2023]
Abstract
We identify a class of trapping potentials in cubic nonlinear Schrödinger equations (NLSEs) that make them nonintegrable, but prevent the emergence of power spectra associated with ergodicity. The potentials are characterized by equidistant energy spectra (e.g., the harmonic-oscillator trap), which give rise to a large number of resonances enhancing the nonlinearity. In a broad range of dynamical solutions, spanning the regimes in which the nonlinearity may be either weak or strong in comparison with the linear part of the NLSE, the power spectra are shaped as narrow (quasidiscrete), evenly spaced spikes, unlike generic truly continuous (ergodic) spectra. We develop an analytical explanation for the emergence of these spectral features in the case of weak nonlinearity. In the strongly nonlinear regime, the presence of such structures is tracked numerically by performing simulations with random initial conditions. Some potentials that prevent ergodicity in this manner are of direct relevance to Bose-Einstein condensates: they naturally appear in 1D, 2D, and 3D Gross-Pitaevskii equations (GPEs), the quintic version of these equations, and a two-component GPE system.
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Affiliation(s)
- Anxo Biasi
- Laboratoire de Physique de l'Ecole Normale Supérieure ENS Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
| | - Oleg Evnin
- Department of Physics, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand
- Theoretische Natuurkunde, Vrije Universiteit Brussel and International Solvay Institutes, Brussels 1050, Belgium
| | - Boris A Malomed
- Department of Physical Electronics, School of Electrical Engineering, Tel Aviv University, Tel Aviv 69978, Israel
- Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7D, Arica, Chile
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9
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Frahm KM, Shepelyansky DL. Nonlinear Perturbation of Random Matrix Theory. PHYSICAL REVIEW LETTERS 2023; 131:077201. [PMID: 37656840 DOI: 10.1103/physrevlett.131.077201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2022] [Revised: 05/17/2023] [Accepted: 07/25/2023] [Indexed: 09/03/2023]
Abstract
We consider a system of linear oscillators, or quantum states, described by random matrix theory and analyze how its time evolution is affected by a nonlinear perturbation. Our numerical results show that above a certain chaos border a weak or moderate nonlinearity leads to a dynamical thermalization of a finite number of degrees of freedom with energy equipartition over linear eigenmodes as expected from the laws of classical statistical mechanics. The system temperature is shown to change in a broad range from positive to negative values, and the dependence of system characteristics on the initial injected energy is determined. Below the chaos border the dynamics is described by the Kolmogorov-Arnold-Moser integrability. Owing to universal features of random matrix theory we argue that the obtained results describe the generic properties of its nonlinear perturbation.
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Affiliation(s)
- Klaus M Frahm
- Laboratoire de Physique Théorique, Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
| | - Dima L Shepelyansky
- Laboratoire de Physique Théorique, Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
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10
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Mangini F, Ferraro M, Sun Y, Gervaziev M, Parra-Rivas P, Kharenko DS, Couderc V, Wabnitz S. Modal phase-locking in multimode nonlinear optical fibers. OPTICS LETTERS 2023; 48:3677-3680. [PMID: 37450723 DOI: 10.1364/ol.494543] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/01/2023] [Accepted: 06/19/2023] [Indexed: 07/18/2023]
Abstract
Spatial beam self-cleaning, a manifestation of the Kerr effect in graded-index multimode fibers, involves a nonlinear transfer of power among modes, which leads to robust bell-shaped output beams. The resulting mode power distribution can be described by statistical mechanics arguments. Although the spatial coherence of the output beam was experimentally demonstrated, there is no direct study of modal phase evolutions. Based on a holographic mode decomposition method, we reveal that nonlinear spatial phase-locking occurs between the fundamental and its neighboring low-order modes, in agreement with theoretical predictions. As such, our results dispel the current belief that the spatial beam self-cleaning effect is the mere result of a wave thermalization process.
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11
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Zitelli M, Ferraro M, Mangini F, Wabnitz S. Characterization of the Modal Distribution from Linear and Nonlinear Mode Coupling in Multimode Fibers. 2023 23RD INTERNATIONAL CONFERENCE ON TRANSPARENT OPTICAL NETWORKS (ICTON) 2023. [DOI: 10.1109/icton59386.2023.10207275] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/02/2023]
Affiliation(s)
- Mario Zitelli
- Università Degli Studi di Roma Sapienza,Department of Information Engineering, Electronics and Telecommunications,Rome,Italy,00184
| | - Mario Ferraro
- Università Degli Studi di Roma Sapienza,Department of Information Engineering, Electronics and Telecommunications,Rome,Italy,00184
| | - Fabio Mangini
- Università Degli Studi di Roma Sapienza,Department of Information Engineering, Electronics and Telecommunications,Rome,Italy,00184
| | - Stefan Wabnitz
- Università Degli Studi di Roma Sapienza,Department of Information Engineering, Electronics and Telecommunications,Rome,Italy,00184
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12
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Selim MA, Pyrialakos GG, Wu FO, Musslimani Z, Makris KG, Khajavikhan M, Christodoulides D. Thermalization of the Ablowitz-Ladik lattice in the presence of non-integrable perturbations. OPTICS LETTERS 2023; 48:2206-2209. [PMID: 37058678 DOI: 10.1364/ol.489165] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/06/2023] [Accepted: 03/26/2023] [Indexed: 06/19/2023]
Abstract
We investigate the statistical mechanics of the photonic Ablowitz-Ladik lattice, the integrable version of the discrete nonlinear Schrödinger equation. In this regard, we demonstrate that in the presence of perturbations, the complex response of this system can be accurately captured within the framework of optical thermodynamics. Along these lines, we shed light on the true relevance of chaos in the thermalization of the Ablowitz-Ladik system. Our results indicate that when linear and nonlinear perturbations are incorporated, this weakly nonlinear lattice will thermalize into a proper Rayleigh-Jeans distribution with a well-defined temperature and chemical potential, in spite of the fact that the underlying nonlinearity is non-local and hence does not have a multi-wave mixing representation. This result illustrates that in the supermode basis, a non-local and non-Hermitian nonlinearity can in fact properly thermalize this periodic array in the presence of two quasi-conserved quantities.
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13
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Deng Y, Chang Q, Chang H, Liu W, Ma P, Zhou P, Jiang Z. Analysis of an image noise sensitivity mechanism for matrix-operation-mode-decomposition and a strong anti-noise method. OPTICS EXPRESS 2023; 31:12299-12310. [PMID: 37157392 DOI: 10.1364/oe.482552] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/10/2023]
Abstract
Mode decomposition (MD) based on the matrix operation (MDMO) is one of the fastest mode decomposition methods in fiber laser which has great potential for optical communications, nonlinear optics and spatial characterization applications. However, we found that the image noise sensitivity is the main limit to the accuracy of the original MDMO method, but improving the decomposition accuracy by using conventional image filtering methods is almost ineffective. By using the norm theory of matrices, the analysis result shows that both the image noise and the coefficient matrix condition number determine the total upper-bound error of the original MDMO method. Besides, the greater the condition number, the more sensitive of MDMO method is to noise. In addition, it is found that the local error of each mode information solution in the original MDMO method is different, which depends on the L2-norm of each row vector of the inverse coefficient matrix. Moreover, a more noise-insensitive MD method is achieved by screening out the information corresponding to large L2-norm. In particular, selecting the higher accuracy among the original MDMO method and such noise-insensitive method as the result in a single MD process, a strong anti-noise MD method was proposed in this paper, which displays high MD accuracy in strong noise for both near-filed and far-filed MD cases.
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14
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Selim MA, Wu FO, Pyrialakos GG, Khajavikhan M, Christodoulides D. Coherence properties of light in highly multimoded nonlinear parabolic fibers under optical equilibrium conditions. OPTICS LETTERS 2023; 48:1208-1211. [PMID: 36857250 DOI: 10.1364/ol.483282] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/09/2022] [Accepted: 01/24/2023] [Indexed: 06/18/2023]
Abstract
We study the coherence characteristics of light propagating in nonlinear graded-index (GRIN) multimode fibers after attaining optical thermal equilibrium conditions. The role of optical temperature on the spatial mutual coherence function and the associated correlation area is systematically investigated. In this respect, we show that the coherence properties of the field at the output of a multimode nonlinear fiber can be controlled through its optical thermodynamic properties.
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15
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Baudin K, Garnier J, Fusaro A, Berti N, Michel C, Krupa K, Millot G, Picozzi A. Observation of Light Thermalization to Negative-Temperature Rayleigh-Jeans Equilibrium States in Multimode Optical Fibers. PHYSICAL REVIEW LETTERS 2023; 130:063801. [PMID: 36827573 DOI: 10.1103/physrevlett.130.063801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/22/2022] [Accepted: 01/03/2023] [Indexed: 06/18/2023]
Abstract
Although the temperature of a thermodynamic system is usually believed to be a positive quantity, under particular conditions, negative-temperature equilibrium states are also possible. Negative-temperature equilibriums have been observed with spin systems, cold atoms in optical lattices, and two-dimensional quantum superfluids. Here we report the observation of Rayleigh-Jeans thermalization of light waves to negative-temperature equilibrium states. The optical wave relaxes to the equilibrium state through its propagation in a multimode optical fiber-i.e., in a conservative Hamiltonian system. The bounded energy spectrum of the optical fiber enables negative-temperature equilibriums with high energy levels (high-order fiber modes) more populated than low energy levels (low-order modes). Our experiments show that negative-temperature speckle beams are featured, in average, by a nonmonotonic radial intensity profile. The experimental results are in quantitative agreement with the Rayleigh-Jeans theory without free parameters. Bringing negative temperatures to the field of optics opens the door to the investigation of fundamental issues of negative-temperature states in a flexible experimental environment.
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Affiliation(s)
- K Baudin
- Laboratoire Interdisciplinaire Carnot de Bourgogne, CNRS, Université de Bourgogne, Dijon, France
- CMAP, CNRS, Ecole Polytechnique, Institut Polytechnique de Paris, 91128 Palaiseau Cedex, France
| | - J Garnier
- CMAP, CNRS, Ecole Polytechnique, Institut Polytechnique de Paris, 91128 Palaiseau Cedex, France
| | - A Fusaro
- CEA, DAM, DIF, F-91297 Arpajon Cedex, France
| | - N Berti
- Laboratoire Interdisciplinaire Carnot de Bourgogne, CNRS, Université de Bourgogne, Dijon, France
| | - C Michel
- Université Côte d'Azur, CNRS, Institut de Physique de Nice, Nice, France
| | - K Krupa
- Institute of Physical Chemistry Polish Academy of Sciences, Warsaw, Poland
| | - G Millot
- Laboratoire Interdisciplinaire Carnot de Bourgogne, CNRS, Université de Bourgogne, Dijon, France
- Institut Universitaire de France (IUF), 1 rue Descartes, 75005 Paris, France
| | - A Picozzi
- Laboratoire Interdisciplinaire Carnot de Bourgogne, CNRS, Université de Bourgogne, Dijon, France
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16
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Universality of light thermalization in multimoded nonlinear optical systems. Nat Commun 2023; 14:370. [PMID: 36690636 PMCID: PMC9871037 DOI: 10.1038/s41467-023-35891-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/28/2022] [Accepted: 01/05/2023] [Indexed: 01/24/2023] Open
Abstract
Recent experimental studies in heavily multimoded nonlinear optical systems have demonstrated that the optical power evolves towards a Rayleigh-Jeans (RJ) equilibrium state. To interpret these results, the notion of wave turbulence founded on four-wave mixing models has been invoked. Quite recently, a different paradigm for dealing with this class of problems has emerged based on thermodynamic principles. In this formalism, the RJ distribution arises solely because of ergodicity. This suggests that the RJ distribution has a more general origin than was earlier thought. Here, we verify this universality hypothesis by investigating various nonlinear light-matter coupling effects in physically accessible multimode platforms. In all cases, we find that the system evolves towards a RJ equilibrium-even when the wave-mixing paradigm completely fails. These observations, not only support a thermodynamic/probabilistic interpretation of these results, but also provide the foundations to expand this thermodynamic formalism along other major disciplines in physics.
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17
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Chen J, Hong W, Luo A. Nonlinear dynamics of beam self-cleaning on LP 11 mode in multimode fibers. OPTICS EXPRESS 2022; 30:43453-43463. [PMID: 36523042 DOI: 10.1364/oe.474238] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/30/2022] [Accepted: 10/28/2022] [Indexed: 06/17/2023]
Abstract
We investigate the modal energy flow of the femtosecond-pulsed beam self-cleaning on LP11 mode with the influence of different factors such as the initial fraction of LP11 mode, initial peak power, distribution of high-order modes and the numerical aperture of the fiber. It is interesting that there is a critical value of the initial peak power, Pcr, which is the watershed, not only in the quantitatively dominant transverse mode converting from LP11 mode to LP01 mode, but also in the behavior of HOMs of the transition from Attractor to chaos. Our simulation results may provide a novel perspective to understanding the beam self-cleaning on LP11 mode.
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18
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Berti N, Baudin K, Fusaro A, Millot G, Picozzi A, Garnier J. Interplay of Thermalization and Strong Disorder: Wave Turbulence Theory, Numerical Simulations, and Experiments in Multimode Optical Fibers. PHYSICAL REVIEW LETTERS 2022; 129:063901. [PMID: 36018655 DOI: 10.1103/physrevlett.129.063901] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/04/2022] [Accepted: 07/07/2022] [Indexed: 06/15/2023]
Abstract
We address the problem of thermalization in the presence of a time-dependent disorder in the framework of the nonlinear Schrödinger (or Gross-Pitaevskii) equation with a random potential. The thermalization to the Rayleigh-Jeans distribution is driven by the nonlinearity. On the other hand, the structural disorder is responsible for a relaxation toward the homogeneous equilibrium distribution (particle equipartition), which thus inhibits thermalization (energy equipartition). On the basis of the wave turbulence theory, we derive a kinetic equation that accounts for the presence of strong disorder. The theory unveils the interplay of disorder and nonlinearity. It unexpectedly reveals that a nonequilibrium process of condensation and thermalization can take place in the regime where disorder effects dominate over nonlinear effects. We validate the theory by numerical simulations of the nonlinear Schrödinger equation and the derived kinetic equation, which are found in quantitative agreement without using any adjustable parameter. Experiments realized in multimode optical fibers with an applied external stress evidence the process of thermalization in the presence of strong disorder.
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Affiliation(s)
- Nicolas Berti
- Laboratoire Interdisciplinaire Carnot de Bourgogne, CNRS, Université Bourgogne Franche-Comté, 21000 Dijon, France
| | - Kilian Baudin
- Laboratoire Interdisciplinaire Carnot de Bourgogne, CNRS, Université Bourgogne Franche-Comté, 21000 Dijon, France
| | | | - Guy Millot
- Laboratoire Interdisciplinaire Carnot de Bourgogne, CNRS, Université Bourgogne Franche-Comté, 21000 Dijon, France
- Institut Universitaire de France (IUF), 1 Rue Descartes, 75005 Paris, France
| | - Antonio Picozzi
- Laboratoire Interdisciplinaire Carnot de Bourgogne, CNRS, Université Bourgogne Franche-Comté, 21000 Dijon, France
| | - Josselin Garnier
- CMAP, CNRS, Ecole Polytechnique, Institut Polytechnique de Paris, 91128 Palaiseau Cedex, France
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19
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Jung PS, Pyrialakos GG, Wu FO, Parto M, Khajavikhan M, Krolikowski W, Christodoulides DN. Thermal control of the topological edge flow in nonlinear photonic lattices. Nat Commun 2022; 13:4393. [PMID: 35906224 PMCID: PMC9338248 DOI: 10.1038/s41467-022-32069-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2022] [Accepted: 07/18/2022] [Indexed: 11/29/2022] Open
Abstract
The chaotic evolution resulting from the interplay between topology and nonlinearity in photonic systems generally forbids the sustainability of optical currents. Here, we systematically explore the nonlinear evolution dynamics in topological photonic lattices within the framework of optical thermodynamics. By considering an archetypical two-dimensional Haldane photonic lattice, we discover several prethermal states beyond the topological phase transition point and a stable global equilibrium response, associated with a specific optical temperature and chemical potential. Along these lines, we provide a consistent thermodynamic methodology for both controlling and maximizing the unidirectional power flow in the topological edge states. This can be achieved by either employing cross-phase interactions between two subsystems or by exploiting self-heating effects in disordered or Floquet topological lattices. Our results indicate that photonic topological systems can in fact support robust photon transport processes even under the extreme complexity introduced by nonlinearity, an important feature for contemporary topological applications in photonics. The nonlinear evolution dynamics in topological photonic lattices is systematically investigated within the framework of optical thermodynamics. This approach allows for the precise prediction of topological currents even under the extreme complexity introduced by nonlinearity.
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Affiliation(s)
- Pawel S Jung
- College of Optics & Photonics-CREOL, University of Central Florida, Orlando, FL, 32816, USA.,Faculty of Physics, Warsaw University of Technology, Koszykowa 75, 00-662, Warsaw, Poland
| | - Georgios G Pyrialakos
- College of Optics & Photonics-CREOL, University of Central Florida, Orlando, FL, 32816, USA
| | - Fan O Wu
- College of Optics & Photonics-CREOL, University of Central Florida, Orlando, FL, 32816, USA
| | - Midya Parto
- College of Optics & Photonics-CREOL, University of Central Florida, Orlando, FL, 32816, USA
| | - Mercedeh Khajavikhan
- College of Optics & Photonics-CREOL, University of Central Florida, Orlando, FL, 32816, USA.,Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, CA, USA
| | - Wieslaw Krolikowski
- Laser Physics Centre, Research School of Physics and Engineering, Australian National University, Canberra, ACT, 0200, Australia.,Science Program, Texas A&M University at Qatar, Doha, Qatar
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20
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Podivilov EV, Mangini F, Sidelnikov OS, Ferraro M, Gervaziev M, Kharenko DS, Zitelli M, Fedoruk MP, Babin SA, Wabnitz S. Thermalization of Orbital Angular Momentum Beams in Multimode Optical Fibers. PHYSICAL REVIEW LETTERS 2022; 128:243901. [PMID: 35776459 DOI: 10.1103/physrevlett.128.243901] [Citation(s) in RCA: 15] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/28/2021] [Revised: 04/20/2022] [Accepted: 05/31/2022] [Indexed: 06/15/2023]
Abstract
We report on the thermalization of light carrying orbital angular momentum in multimode optical fibers, induced by nonlinear intermodal interactions. A generalized Rayleigh-Jeans distribution of asymptotic mode composition is obtained, based on the conservation of the angular momentum. We confirm our predictions by numerical simulations and experiments based on holographic mode decomposition of multimode beams. Our work establishes new constraints for the achievement of spatial beam self-cleaning, giving previously unforeseen insights into the underlying physical mechanisms.
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Affiliation(s)
- E V Podivilov
- Novosibirsk State University, Novosibirsk 630090, Russia
- Institute of Automation and Electrometry SB RAS, 1 academician Koptyug avenue, Novosibirsk 630090, Russia
| | - F Mangini
- Department of Information Engineering, University of Brescia, Via Branze 38, 25123 Brescia, Italy
- Department of Information Engineering, Electronics, and Telecommunications, Sapienza University of Rome, Via Eudossiana 18, 00184 Rome, Italy
| | - O S Sidelnikov
- Novosibirsk State University, Novosibirsk 630090, Russia
| | - M Ferraro
- Department of Information Engineering, Electronics, and Telecommunications, Sapienza University of Rome, Via Eudossiana 18, 00184 Rome, Italy
| | - M Gervaziev
- Novosibirsk State University, Novosibirsk 630090, Russia
| | - D S Kharenko
- Novosibirsk State University, Novosibirsk 630090, Russia
- Institute of Automation and Electrometry SB RAS, 1 academician Koptyug avenue, Novosibirsk 630090, Russia
| | - M Zitelli
- Department of Information Engineering, Electronics, and Telecommunications, Sapienza University of Rome, Via Eudossiana 18, 00184 Rome, Italy
| | - M P Fedoruk
- Novosibirsk State University, Novosibirsk 630090, Russia
| | - S A Babin
- Novosibirsk State University, Novosibirsk 630090, Russia
- Institute of Automation and Electrometry SB RAS, 1 academician Koptyug avenue, Novosibirsk 630090, Russia
| | - S Wabnitz
- Novosibirsk State University, Novosibirsk 630090, Russia
- Department of Information Engineering, Electronics, and Telecommunications, Sapienza University of Rome, Via Eudossiana 18, 00184 Rome, Italy
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