Statistical mechanics of weakly nonlinear optical multimode gases

Makris, Konstantinos G.; Wu, Fan O.; Jung, Paweł S.; Christodoulides, Demetrios N.

doi:10.1364/ol.387863

Cited by 48 publications

(24 citation statements)

References 26 publications

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“…Moreover, the laws governing isentropic processes were obtained and the prospect for Carnot cycles was suggested. Similar results were derived from the perspective of the grand canonical ensemble along with the expected statistical fluctuations in these systems 21,22 .…”

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confidence: 79%

Entropic thermodynamics of nonlinear photonic chain networks

Jung

Parto

et al. 2020

Commun Phys

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The convoluted nonlinear behaviors of heavily multimode photonic structures have been recently the focus of considerable attention. The sheer complexity associated with such multimode systems, allows them to display a host of phenomena that are otherwise impossible in few-mode settings. At the same time, however, it introduces a set of fundamental challenges in terms of comprehending and harnessing their response. Here, we develop an optical thermodynamic approach capable of describing the thermalization dynamics in large scale nonlinear photonic tight-binding networks. For this specific system, an optical Sackur-Tetrode equation is obtained that explicitly provides the optical temperature and chemical potential of the photon gas. Processes like isentropic expansion/compression, Joule expansion, as well as aspects associated with beam cleaning/cooling and thermal conduction effects in such chain networks are discussed. Our results can be used to describe in an effortless manner the exceedingly complex dynamics of highly multimoded nonlinear bosonic systems.

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confidence: 79%

Entropic thermodynamics of nonlinear photonic chain networks

Jung

Parto

et al. 2020

Commun Phys

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“…Developments using the microcanonical ensemble can be found in [36]. In the field of nonlinear optics some interesting work has been done at equilibrium for a finite number of modes, see [37][38][39][40]. Our approach, being based on a theory that makes use of the random phase approximation both for positive and negative temperatures, cannot be applied in the presence of coherent structures such as solitons or breathers.…”

Section: Introductionmentioning

confidence: 99%

Equilibrium and nonequilibrium description of negative temperature states in a one-dimensional lattice using a wave kinetic approach

et al. 2022

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We predict negative temperature states in the Discrete Nonlinear Schödinger (DNLS) equation as exact solutions of the associated Wave Kinetic equation. Within the wave kinetic approach, we define an entropy that results monotonic in time and reaches a stationary state, that is consistent with classical equilibrium statistical mechanics. We also perform a detailed analysis of the fluctuations of the actions at fixed wave numbers around their mean values. We give evidence that such fluctuations relax to their equilibrium behaviour on a shorter time scale than the one needed for the spectrum to reach the equilibrium state. Numerical simulations of the DNLS equation are shown to be in agreement with our theoretical results. The key ingredient for observing negative temperatures in lattices characterized by two invariants is the boundedness of the dispersion relation. THE WAVE KINETIC THEORY FOR THE DNLS EQUATIONThe DNLS equation reads i ψm + (ψ m+1 + ψ m−1 − 2ψ m ) + ν|ψ m | 2 ψ m = 0, (1)

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“…Quite recently, a thermodynamic formalism has been developed that can describe in an effortless manner the classical behavior of highly multimode weakly nonlinear bosonic systems whose dynamics involve two conserved quantities [14,15]. This approach is universal and applicable to both multimode waveguide and cavity arrangements, irrespective of the type of nonlinearity used, as long as ergodicity is at play [16].…”

Section: Introductionmentioning

confidence: 99%

A thermodynamic description of the near- and far-field intensity patterns emerging from multimode nonlinear waveguide arrays

Selim,

Wu,

Ren

et al. 2022

Preprint

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Nonlinear highly multimode photonic systems are ubiquitous in optics. Yet, the sheer complexity arising from the action of nonlinearity in multimode environments has posed theoretical challenges in describing these systems. In this work, we deploy concepts from optical thermodynamics to investigate the near-and far-field emission intensity patterns emerging from nonlinear waveguide arrays. An exact equation dictating the response of a nonlinear array is derived in terms of the system's invariants that act as extensive thermodynamic variables. In this respect, the near-and farfield characteristics emerging from a weakly nonlinear waveguide lattice are analytically addressed. We show that statistically, these patterns and the resulting far-field brightness are governed by the optical temperature and its corresponding chemical potential. The extensivity associated with the entropy of such configurations is discussed. The thermodynamic results presented here were found to be in good agreement with numerical simulations obtained from nonlinear coupled-mode theory.

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Statistical mechanics of weakly nonlinear optical multimode gases

Cited by 48 publications

References 26 publications

Entropic thermodynamics of nonlinear photonic chain networks

Entropic thermodynamics of nonlinear photonic chain networks

Equilibrium and nonequilibrium description of negative temperature states in a one-dimensional lattice using a wave kinetic approach

A thermodynamic description of the near- and far-field intensity patterns emerging from multimode nonlinear waveguide arrays

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