Dalton's law of partial optical thermodynamic pressures in highly multimoded nonlinear photonic systems.

We show that in highly multimoded nonlinear photonic systems, the optical thermodynamic pressures emerging from different species of the optical field obey Dalton's law of partial pressures. In multimode settings, the optical thermodynamic pressure is defined as the conjugate to the extensive variable associated with the system's total number of modes and is directly related to the actual electrodynamic radiation forces exerted at the physical boundaries of the system. Here, we extend this notion to photonic configuration supporting different species of the optical field. Under thermal equilibrium conditions, we formally derive an equation that establishes a direct link between the partial thermodynamic pressures and the electrodynamic radiation pressures exerted by each polarization species. Our theoretical framework provides a straightforward approach for quantifying the total radiation pressures through the system's thermodynamic variables without invoking the Maxwell stress tensor formalism. In essence, we show that the total electrodynamic pressure in such arrangements can be obtained in an effortless manner from initial excitation conditions, thus avoiding time-consuming simulations of the utterly complex multimode dynamics. To illustrate the validity of our results, we carry out numerical simulations in multimoded nonlinear optical structures supporting two polarization species and demonstrate excellent agreement with the Maxwell stress tensor method.

Bimorphic Floquet topological insulators.

Topological theories have established a unique set of rules that govern the transport properties in a wide variety of wave-mechanical settings. In a marked departure from the established approaches that induce Floquet topological phases by specifically tailored discrete coupling protocols or helical lattice motions, we introduce a class of bimorphic Floquet topological insulators that leverage connective chains with periodically modulated on-site potentials to reveal rich topological features in the system. In exploring a 'chain-driven' generalization of the archetypical Floquet honeycomb lattice, we identify a rich phase structure that can host multiple non-trivial topological phases associated simultaneously with both Chern-type and anomalous chiral states. Experiments carried out in photonic waveguide lattices reveal a strongly confined helical edge state that, owing to its origin in bulk flat bands, can be set into motion in a topologically protected fashion, or halted at will, without compromising its adherence to individual lattice sites.

Coherence properties of light in highly multimoded nonlinear parabolic fibers under optical equilibrium conditions.

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.

Thermalization of the Ablowitz-Ladik lattice in the presence of non-integrable perturbations.

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.

Nature of Optical Thermodynamic Pressure Exerted in Highly Multimoded Nonlinear Systems.

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.

Thermalization Dynamics of Nonlinear Non-Hermitian Optical Lattices.

We develop a rigorous theoretical framework based on principles from statistical mechanics that allows one to predict the equilibrium response of classical non-Hermitian arrangements in the weakly nonlinear regime. In this respect, we demonstrate that a pseudo-Hermitian configuration can always be driven into thermal equilibrium when a proper nonlinear operator is paired with the linear Hamiltonian of the system. We show that, in this case, the system will thermodynamically settle into an irregular pattern that does not resemble any known statistical distribution. Interestingly, this stable equilibrium response is associated with a Rayleigh-Jeans law when viewed within an appropriately transformed space that displays unitary dynamics. By considering a non-Hermitian Su-Schrieffer-Heeger chain, our results indicate that the thermodynamic equilibrium will always favor the edge modes instead of the ground state, in stark contrast to conventional nonlinear Hermitian configurations. Moreover, non-Hermitian lattices are shown to exhibit unusually high heat capacities, potentially acting as optical heat reservoirs to other Hermitian systems, by employing only a small number of sites and low power levels.

Emergence of Type-II Dirac Points in Graphynelike Photonic Lattices.

We theoretically demonstrate that a type-II class of tilted Dirac cones can emerge in generalized two-dimensional anisotropic lattice arrangements. This is achieved by introducing a special set of graphynelike exchange bonds by means of which the complete spectrum of the underlying Weyl Hamiltonian can be realized. Our ab initio calculations demonstrate a unique class of eigensolutions corresponding to a type-II class of Dirac fermionic excitations. Based on our approach, one can systematically synthesize a wide range of strongly anisotropic band diagrams having tilted Dirac cones with variable location and orientation. Moreover, we show that asymmetric conical diffraction, as well as edge states, can arise in these configurations. Our results can provide a versatile platform to observe, for the first time, optical transport around type-II Dirac points in two-dimensional optical settings under linear, nonlinear, and non-Hermitian conditions.

Guiding charged particles in vacuum via Lagrange points.

We propose a method for guiding charged particles such as electrons and protons, in vacuum, by employing the exotic properties of Lagrange points. This leap is made possible by the dynamics unfolding around these equilibrium points, which stably capture such particles, akin to the way Trojan asteroids are held in Jupiter's orbit. Unlike traditional methodologies that allow for either focusing or three-dimensional storage of charged particles, the proposed scheme can guide both non-relativistic and relativistic electrons and protons in small cross-sectional areas in an invariant fashion over long distances without any appreciable loss in energy - in a manner analogous to photon transport in optical fibers. Here, particle guiding is achieved by employing twisted electrostatic potentials that in turn induce stable Lagrange points in vacuum. In principle, guidance can be realized within the fundamental mode of the resulting waveguide, thereby presenting a prospect for manipulating these particles in the quantum domain. Our findings may be useful in a wide range of applications in both scientific and technological pursuits. These applications could encompass electron microscopies and lithographies, particle accelerators, quantum and classical communication/sensing systems, as well as methods for shuttling entangled qubits between nodes within a quantum network.

Thermal control of the topological edge flow in nonlinear photonic lattices.

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.

Complex skin modes in non-Hermitian coupled laser arrays.

From biological ecosystems to spin glasses, connectivity plays a crucial role in determining the function, dynamics, and resiliency of a network. In the realm of non-Hermitian physics, the possibility of complex and asymmetric exchange interactions ([Formula: see text]) between a network of oscillators has been theoretically shown to lead to novel behaviors like delocalization, skin effect, and bulk-boundary correspondence. An archetypical lattice exhibiting the aforementioned properties is that proposed by Hatano and Nelson in a series of papers in late 1990s. While the ramifications of these theoretical works in optics have been recently pursued in synthetic dimensions, the Hatano-Nelson model has yet to be realized in real space. What makes the implementation of these lattices challenging is the difficulty in establishing the required asymmetric exchange interactions in optical platforms. In this work, by using active optical oscillators featuring non-Hermiticity and nonlinearity, we introduce an anisotropic exchange between the resonant elements in a lattice, an aspect that enables us to observe the non-Hermitian skin effect, phase locking, and near-field beam steering in a Hatano-Nelson laser array. Our work opens up new regimes of phase-locking in lasers while shedding light on the fundamental physics of non-Hermitian systems.

Symmetry-controlled edge states in the type-II phase of Dirac photonic lattices.

The exceptional properties exhibited by two-dimensional materials, such as graphene, are rooted in the underlying physics of the relativistic Dirac equation that describes the low energy excitations of such molecular systems. In this study, we explore a periodic lattice that provides access to the full solution spectrum of the extended Dirac Hamiltonian. Employing its photonic implementation of evanescently coupled waveguides, we indicate its ability to independently perturb the symmetries of the discrete model (breaking, also, the barrier towards the type-II phase) and arbitrarily define the location, anisotropy, and tilt of Dirac cones in the bulk. This unique aspect of topological control gives rise to highly versatile edge states, including an unusual class that emerges from the type-II degeneracies residing in the complex space of k. By probing these states, we investigate the topological nature of tilt and shed light on novel transport dynamics supported by Dirac configurations in two dimensions.