Entropic thermodynamics of nonlinear photonic chain networks

Abstract

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.

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

“…where A = 2κ µ . The quantity |A| is always less than unity [28] and can be regarded as the zero temperature limit of the system since, as we will see in the upcoming sections, when |A| approaches unity, the power in the nonlinear waveguide array system tends to occupy the lowest or the highest-order mode. To explicitly evaluate the sum in Eq.…”

“…On the other hand, as the number of modes becomes very large (M 1) the quantity A can be analytically obtained using the procedure in ref. [28]…”

“…limit |A| = 1, and hence, the function ζ(A, M ) can be ignored. In fact, the ζ(A, M ) term reflects the contribution of discreetness in the kinetic energy U arising at low temperatures whenever the number of modes is very low, an aspect that was unimportant and hence ignored in [28]. Figure 3 depicts the logarithm of the function ζ(A, M ), which itself represents a departure from Eq.…”

“…As such, of interest will be to develop a formalism that could capture the macroscopic behavior of these weakly nonlinear waveguide arrays using notions from statistical mechanics. Along these lines, previous studies have shown that an optical Sackur-Tetrode equation can be utilized to describe nonlinear chain networks under thermal equilibrium conditions-an equation that explicitly provides in closed form the optical temperature and chemical potential of such systems [28,29]. In general, this formalism is based on the assumption that these networks are highly multimoded-an aspect that is not always met in deploying such a statistical approach.…”

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

“…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.…”