Nonlinear Photonic Lattices Research Articles

Chiral Bulk Solitons in Photonic Graphene with Decorated Boundaries

AbstractA chiral bulk soliton in a nonlinear photonic lattice with decorated boundaries, presenting a novel approach to manipulate photonic transport without extensive bulk modifications is proposed. Unlike traditional methods that rely on topological edge and corner modes, this strategy leverages the robust chiral propagation of bulk modes. By introducing nonlinearity into the system, a stable bulk soliton, akin to the topological valley Hall effects is found. The chiral bulk soliton exhibits remarkable stability; the energy does not decay even after a long‐distance propagation; and the corresponding Fourier spectrum confirms the absence of inter‐valley scattering indicating a valley‐locking property. The findings not only contribute to the fundamental understanding of nonlinear photonic systems but also hold significant practical implications for the design and optimization of photonic devices.

Effective beam mass of diametrically driven self-accelerating beams in photonic lattices

Optical diametric drive acceleration with positive- and negative-effective mass fields has been realized in nonlinear photonic lattices. By numerically calculating and analyzing the accelerations in different parameters of the interacting beams and in that of the photonic lattices, we demonstrate that the effective beam mass should be defined as the inverse of the Bloch band curvature multiplied by the beam power. The beam acceleration is actually determined by the effective beam mass, and thus long distance diametric drive acceleration can be achieved by adjusting the beam power to match the band curvature. In addition, two beams located in the first and second bands respectively can also achieve diametric drive acceleration and the self-acceleration direction will reverse during propagation.

Topology with Memory in Nonlinear Driven-Dissipative Photonic Lattices

We consider a photonic lattice of nonlinear lossy resonators subjected to a coherent drive, where the system remembers its topological phase. Initially, the system is topologically trivial. After the application of an additional coherent pulse, the intensity is increased, which modifies the couplings in the system and then induces a topological phase transition. However, when the effect of the pulse dies out, the system does not go back to the trivial phase. Instead, it remembers the topological phase and maintains its topology acquired during the pulse application. The pulse can be used as a switch to trigger amplification of the topological modes. We further show that the amplification takes place at a different frequency as well as at a different position from those of the pulse, indicating frequency conversion and intensity transfer. Our work can be useful in triggering the different functionalities of active topological photonic devices.

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.

Emergent Kardar-Parisi-Zhang Phase in Quadratically Driven Condensates.

In bosonic gases at thermal equilibrium, an external quadratic drive can induce a Bose-Einstein condensation described by the Ising transition, as a consequence of the explicitly broken U(1) phase rotation symmetry down to Z_{2}. However, in physical realizations such as exciton polaritons and nonlinear photonic lattices, thermal equilibrium is lost and the state is rather determined by a balance between losses and external drive. A fundamental question is then how nonequilibrium fluctuations affect this transition. Here, we show that in a two-dimensional driven-dissipative Bose system the Ising phase is suppressed and replaced by a nonequilibrium phase featuring Kardar-Parisi-Zhang (KPZ) physics. Its emergence is rooted in a U(1)-symmetry restoration mechanism enabled by the strong fluctuations in reduced dimensionality. Moreover, we show that the presence of the quadratic drive term enhances the visibility of the KPZ scaling, compared to two-dimensional U(1)-symmetric gases, where it has remained so far elusive.

Optical Neural Network Based on Synthetic Nonlinear Photonic Lattices

We reveal that a synthetic photonic lattice based on coupled optical loops can be utilized as a feed-forward neural network for processing of optical pulse sequences in time domain. As a proof of concept, we train the optical system to restore an initial shape of the pulse train from the signal distorted due to linear dispersion in a fiber-optic link. We also show efficient training of the optical network with an intrinsic Kerr-type nonlinearity for the realization of target nonlinear transmission functions and inference functionality for the discrimination of different pulse sequences. The theoretical modeling is performed under practical conditions and can guide future experimental realizations.

Dynamics of the Berezinskii–Kosterlitz–Thouless transition in a photon fluid

In addition to enhancing confinement, restricting optical systems to two dimensions gives rise to new photonic states, modified transport and distinct nonlinear effects. Here we explore these properties in combination and experimentally demonstrate a Berezinskii–Kosterlitz–Thouless phase transition in a nonlinear photonic lattice. In this topological transition, vortices are created in pairs and then unbind, changing the dynamics from that of a photonic fluid to that of a plasma-like gas of free (topological) charges. We explicitly measure the number and correlation properties of free vortices, for both repulsive and attractive interactions (the photonic equivalent of ferromagnetic and antiferromagnetic conditions), and confirm the traditional thermodynamics of the Berezinskii–Kosterlitz–Thouless transition. We also suggest a purely fluid interpretation, in which vortices are nucleated by inhomogeneous flow and driven by seeded instability. The results are fundamental to optical hydrodynamics and can impact two-dimensional photonic devices if temperature and interactions are not controlled properly. A topological transition in a nonlinear photonic lattice results in new vortex dynamics and a change from photonic fluid behaviour to that of a plasma-like gas.

Hidden order in quantum many-body dynamics of driven-dissipative nonlinear photonic lattices

We study the dynamics of nonlinear photonic lattices driven by two-photon parametric processes. By means of matrix-product-state based calculations, we show that a quantum many-body state with long-range hidden order can be generated from the vacuum. This order resembles that characterizing the Haldane insulator. A possible explanation highlighting the role of the symmetry of the drive, and the effect of photon loss are discussed. An implementation based in superconducting circuits is proposed and analyzed

Quantum Critical Regime in a Quadratically Driven Nonlinear Photonic Lattice.

We study an array of coupled optical cavities in the presence of two-photon driving and dissipation. The system displays a critical behavior similar to that of a quantum Ising model at finite temperature. Using the corner-space renormalization method, we compute the steady-state properties of finite lattices of varying size, both in one and two dimensions. From a finite-size scaling of the average of the photon number parity, we highlight the emergence of a critical point in regimes of small dissipations, belonging to the quantum Ising universality class. For increasing photon loss rates, a departure from this universal behavior signals the onset of a quantum critical regime, where classical fluctuations induced by losses compete with long-range quantum correlations.

Strongly correlated photon transport in nonlinear photonic lattices with disorder: Probing signatures of the localization transition

We study the transport of few-photon states in an open disordered nonlinear photonic lattice. More specifically, we consider a waveguide quantum electrodynamics (QED) setup where photons are scattered from a chain of nonlinear resonators with onsite Bose-Hubbard interaction in the presence of an incommensurate potential. Applying our recently developed diagrammatic technique that represents scattering matrix (S-matrix) with scattering diagrams and associated propagators, we compute the two-photon transmission probability and show that it carries signatures of the underlying many-body localization transition of the system. We compare the calculated probability to the participation ratio of the eigenstates and find close agreement for a range of interaction strengths. We analyze the robustness of the transmission signatures against local dissipation and briefly discuss possible implementation using current superconducting circuit technology.

Controlled mobility of compact discrete solitons in nonlinear Lieb photonic lattices

Controlled mobility of compact discrete solitons in nonlinear Lieb photonic lattices

Geometrical frustration in nonlinear photonic lattices

Geometrical frustration in either classical or quantum lattice systems is a phenomenon in which the impossibility of satisfying simultaneously all constraints of the system Hamiltonian leads to complex structures with degeneracy of the ground state. We show that geometrical frustration can be observed in a simple setup consisting of classical light propagating along a regular array of evanescently coupled photonic nonlinear waveguides arranged in a honeycomb geometry. Here, geometrical frustration emerges as competition between the number of waveguides and the need to satisfy the stationary constraints of the system. The phenomenology that exhibits these photonic arrays mimics the behavior observed in graphene-related spin lattices. Our results show that two-dimensional arrays of coupled photonic waveguides can be used as a proxy to study geometry frustration in diverse lattice systems.

Ring Dirac solitons in nonlinear topological systems

We study solitons of the two-dimensional nonlinear Dirac equation with asymmetric cubic nonlinearity. We show that, with the nonlinearity parameters specifically tuned, a high degree of localization of both spinor components is enabled on a ring of certain radius. Such ring Dirac soliton can be viewed as a self-induced nonlinear domain wall and can be implemented in nonlinear photonic graphene lattice with Kerr-like nonlinearities. Our model could be instructive for understanding localization mechanisms in nonlinear topological systems.

Multiple nonlinear Bragg diffraction of femtosecond laser pulses in a photonic lattice with hexagonal domains

The frequency doubling of femtosecond laser pulses in a two-dimensional (2D) rectangular nonlinear photonic lattice with hexagonal domains is studied experimentally and theoretically. The broad fundamental spectrum enables frequency conversion under nonlinear Bragg diffraction for a series of transverse orders at a fixed longitudinal quasi-phase-matching order. The consistent nonstationary theory of the frequency doubling of femtosecond laser pulses is developed using the representation based on the reciprocal lattice of the structure. The calculated spatial distribution of the second-harmonic spectral intensity agrees well with the experimental data. The condition for multiple nonlinear Bragg diffraction in a 2D nonlinear photonic lattice is offered. The hexagonal shape of the domains contributes to multibeam second harmonic excitation. The maximum conversion efficiency for a series of transverse orders in the range 0.01%–0.03% is obtained.

Asimetrični nasuprot simetričnim defektima u jedno-dimenzionalnoj fotonskoj rešetki

Light propagation in one-dimensional photonic lattice is numerically analyzed. Two linear or nonlinear different widths asymmetric defects separated by a waveguide are located within the linear or nonlinear photonic lattice. We have found various types of localized modes located at the asymmetric defect position and at the waveguide between asymmetric defects. The results are compared with the ones obtained for light propagation in the system with the appropriate symmetric defects located within the linear or nonlinear photonic lattice.

Spatial algebraic solitons at the Dirac point in optically induced nonlinear photonic lattices.

The discovery of a new type of soliton occurring in periodic systems is reported. This type of nonlinear excitation exists at a Dirac point of a photonic band structure, and features an oscillating tail that damps algebraically. Solitons in periodic systems are localized states traditionally supported by photonic bandgaps. Here, it is found that besides photonic bandgaps, a Dirac point in the band structure of triangular optical lattices can also sustain solitons. Apart from their theoretical impact within the soliton theory, they have many potential uses because such solitons are possible in both Kerr material and photorefractive crystals that possess self-focusing and self-defocusing nonlinearities. The findings enrich the soliton family and provide information for studies of nonlinear waves in many branches of physics.

Spontaneous symmetry breaking in a quadratically driven nonlinear photonic lattice

We investigate the occurrence of a phase transition, characterized by the spontaneous breaking of a discrete symmetry, in a driven-dissipative Bose-Hubbard lattice in presence of two-photon coherent driving. The driving term does not lift the original $U(1)$ symmetry completely and a discrete $\mathbb{Z}_2$ symmetry is left. When driving the bottom of the Bose-Hubbard band, a mean-field analysis of the steady state reveals a second-order transition from a symmetric phase to a quasi-coherent state with a finite expectation value of the Bose field. For larger driving frequency, the phase diagram shows a third region, where both phases are stable and the transition becomes of first order.

Pearcey solitons in curved nonlinear photonic caustic lattices

Controlling artificial Pearcey and swallowtail beams allows the realization of caustic lattices in nonlinear photosensitive media at very low light intensities. We examine their functionality as 2D and 3D waveguiding structures and show the potential of exploiting these lattices as linear beam splitters, which we name a ‘Pearcey-Y-splitter’. For symmetrized Pearcey beams as auto-focusing beams, the formation of solitons in focusing nonlinearity is observed. Our original approach represents the first realization of caustic photonic lattices and can directly be applied in signal processing, microscopy and material lithography.

The influence of a geometric defect on the light propagation through two one-dimensional nonlinear photonic lattices

The influence of a geometric defect on the light propagation through two one-dimensional nonlinear photonic lattices

Observation of spatially oscillating solitons in photonic lattices

We report on the experimental observation of spatially oscillating solitons in two-dimensional nonlinear photonic lattices, realized by optical induction using a continuous nondiffracting Weber beam. Thereby, we introduce and demonstrate a new type of transverse soliton dynamics originating from the unique parabolic geometry of the photonic lattice. First, we numerically calculate the fundamental soliton solution for this lattice and experimentally demonstrate its existence. Afterwards, we experimentally launch the soliton with an additional transverse momentum and observe harmonic spatial oscillation during propagation.