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.

Non-Hermitian exceptional points (EPs) represent a special type of degeneracy where not only the eigenvalues coalesce, but also the eigenstates tend to collapse on each other. Recent studies have shown that, in the presence of an EP, light–matter interactions are profoundly modified, leading to a host of unexpected optical phenomena ranging from enhanced sensitivity to chiral light transport. Here we introduce a family of unidirectional resonators based on a novel type of broadband exceptional points. In active settings, the resulting unidirectionality exhibits resilience to perturbations, thus, providing a robust and tunable approach for directly generating beams with distinct orbital angular momenta (OAM). This work could open up new possibilities for manipulating OAM degrees of freedom in applications pertaining to telecommunications and quantum information sciences, while at the same time may expand the notions of non-Hermiticity in the orbital angular momentum space.

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We show that, in general, any complex weakly nonlinear highly multimode system can reach thermodynamic equilibrium that is characterized by a unique temperature and chemical potential. The conditions leading to either positive or negative temperatures are explicitly obtained in terms of the linear spectrum of the system, the input power, and the corresponding Hamiltonian invariant. Pertinent examples illustrating these results are provided in various scenarios.

By utilizing notions from statistical mechanics, we develop a general and self-consistent theoretical framework capable of describing any weakly nonlinear optical multimode system involving conserved quantities. We derive the fundamental relations that govern the grand canonical ensemble through maximization of the Gibbs entropy at equilibrium. In this classical picture of statistical photo-mechanics, we obtain analytical expressions for the probability distribution, the grand partition function, and the relevant thermodynamic potentials. Our results universally apply to any other weakly nonlinear multimode bosonic system.

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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We provide a systematic analysis of geometric parametric instabilities in nonlinear graded-index multimode fibers. Our approach implicitly accounts for self-focusing effects and considers dispersion processes to all orders. It is shown that the resulting parametric problem takes the form of a Hill’s equation that can be systematically addressed using a Floquet approach. The theory developed indicates that the unstable spectral domains associated with such geometric parametric instabilities can be significantly altered as the power levels injected in a parabolic multimode fiber increase. These predictions are in excellent agreement with experimental data gathered from graded-index multimode structures.