Thermodynamic theory of highly multimoded nonlinear optical systems

Abstract

The quest for ever higher information capacities has brought about a renaissance in multimode optical waveguide systems. This resurgence of interest has recently initiated a flurry of activities in nonlinear multimode fiber optics. The sheer complexity emerging from the presence of a multitude of nonlinearly interacting modes has led not only to new opportunities in observing a host of novel optical effects that are otherwise impossible in single-mode settings, but also to new theoretical challenges in understanding their collective dynamics. In this Article, we present a consistent thermodynamical framework capable of describing in a universal fashion the exceedingly intricate behavior of such nonlinear highly multimoded photonic configurations at thermal equilibrium. By introducing pertinent extensive variables, we derive new equations of state and show that both the "internal energy" and optical power in many-mode arrangements always flow in such a way so as to satisfy the second law of thermodynamics. The laws governing isentropic processes are derived and the prospect for realizing Carnot-like cycles is also presented.In addition to shedding light on fundamental issues, our work may pave the way towards a new generation of high power multimode optical structures and could have ramifications in other manystate nonlinear systems, ranging from Bose-Einstein condensates to optomechanics.

Entropic thermodynamics of nonlinear photonic chain networks

“…These include, for example, the prospect for beam cooling (leading to an improvement in beam quality) as well as Joule expansion and aspects associated with the photo-capacity and thermal conductivity of such chain networks. As opposed to previous works that were foundational in nature 18,20 , the results reported here (applicable to large-scale nonlinear tight-binding lattices) establish a tangible theoretical model through which many of these abstract ideas can be conceptually grasped and further developed.…”

“…This relation is given through a global equation of state, given by U À μP ¼ MT that explicitly involves the total number of modes M (ref. 18 ). Here, the optical temperature is associated with the optical field itself and has nothing to do with the actual temperature of the environment the system is embedded in.…”

“…Quite recently, an optical thermodynamic theory was put forward, that can self-consistently describe by means of statistical mechanics the utterly complex processes of energy exchange in nonlinear multimode systems at thermal equilibrium 18 . In accord with the axioms of thermodynamics 19 , the entropy of these systems was appropriately defined in terms of other extensive variables and a global equation of state was derived 18,20 . Moreover, the laws governing isentropic processes were obtained and the prospect for Carnot cycles was suggested.…”

Wave condensation with weak disorder versus beam self-cleaning in multimode fibers

“…lmnp + (8∆β) 2 δ K (∆ω lmnp ). (43) Proceeding as in section III, we obtain the discrete kinetic equation…”

“…Recent works indicate that this phenomenon of beam self-cleaning can be interpreted as a consequence of wave thermalization and condensation [41][42][43]. In particular, in Ref.…”