Nonlinear Waveguide Arrays Research Articles

All-optical switching in nonlinear topological waveguide arrays

Photonic topological states are prospective in integrated optical devices due to their robustness to perturbations and defects. When taking into account the nonlinear effects of the system, the functionality of topological photonics can be further enhanced. Here, we investigated the interplay between topological edge states and nonlinear effects based on the Su–Schrieffer–Heeger (SSH) model. Relying on the theory prediction that topological edge states would shift upward under the action of nonlinearity, two types of optical switching are designed and experimentally realized in femtosecond laser direct-write waveguide arrays. This work provides a new, to the best of our knowledge, approach to preparing all-optical switches and offers a new perspective on the application of nonlinearity in topological optical devices.

Coupled Thermal and Power Transport of Optical Waveguide Arrays: Photonic Wiedemann-Franz Law and Rectification Effect.

In isolated nonlinear optical waveguide arrays, simultaneous conservation of longitudinal momentum flow ("internal energy") and optical power ("particle number") of the optical modes enables study of coupled thermal and particle transport in the negative temperature regime. Based on exact numerical simulation and rationale from Landauer formalism, we predict generic photonic version of the Wiedemann-Franz law in such systems, with the Lorenz number L∝|T|^{-2}. This is rooted in the spectral decoupling of thermal and particle current, and their different temperature dependence. In addition, in asymmetric junctions, relaxation of the system toward equilibrium shows apparent asymmetry for positive and negative biases, indicating rectification behavior. This Letter illustrates the possibility of simulate nonequilibrium transport processes using optical networks, in parameter regimes difficult to reach in natural condensed matter or atomic gas systems. It also provides new insights in manipulating power and momentum flow of optical waves in artificial waveguide arrays.

Optimizing biphoton generation via reconfigurable nonlinear waveguide arrays based on scattering tensor

Optimizing biphoton generation via reconfigurable nonlinear waveguide arrays based on scattering tensor

Highly controllable stabilization and switching of multiple colliding soliton sequences with generic Ginzburg–Landau gain–loss

We investigate propagation of J soliton sequences in a nonlinear optical waveguide array with generic weak Ginzburg–Landau (GL) gain–loss and nearest-neighbor (NN) interaction. The propagation is described by a system of J perturbed coupled nonlinear Schrödinger (NLS) equations. The NN interaction property leads to the elimination of collisional three-pulse interaction effects, which prevented the observation of stable multisequence soliton propagation with J>2 sequences in the presence of generic GL gain–loss in all previous studies. We show that the dynamics of soliton amplitudes can be described by a generalized J-dimensional Lotka–Volterra (LV) model. Stability and bifurcation analysis for the equilibrium points of the LV model, which is augmented by an application of the Lyapunov function method, is used to develop setups that lead to robust and scalable transmission stabilization and switching for a general J value. The predictions of the LV model are confirmed by extensive numerical simulations with the perturbed coupled-NLS model with J=3, 4, and 5 soliton sequences. Furthermore, soliton stability and the agreement between the LV model’s predictions and the simulations are not reduced with increasing value of J. Therefore, our study provides the first demonstration of robust control of multiple colliding sequences of NLS solitons in the presence of generic weak GL gain–loss with an arbitrary number of sequences. Due to the robustness and scalability of the results, they can have important applications in stabilization and switching of broadband soliton-based optical waveguide transmission.

Collision dynamics of a discrete soliton in uniform waveguide arrays

We investigate the collision dynamics of a discrete soliton (DS) pair in a realistic semi-infinite nonlinear waveguide array (WA) in the context of diffractive resonant radiation (DifRR). Depending on the initial amplitude ( A 0 ) and wavenumber ( k 0 ), a co-moving pair of identical DSs either collide elastically or merge to form a discrete breather. For a large amplitude and small wavenumber, DSs do not interact to form a bound state. We map the domain of interaction by iterative simulation and present a phase plot in ( A 0 − k 0 ) parameter space. To grasp the collision dynamics, we develop an analytical treatment based on a variational method that leads us to a set of ordinary differential equations describing the collision mechanism. Our analytical results corroborate our numerical data. We further investigate the role of initial phase detuning between two identical DSs and observe a periodic energy exchange during their interaction. A varied degree of energy exchange occurs when two DSs with different wavenumbers collide, which results in three distinct output states accompanied by DifRR generation. Extending our investigation to a more generalized condition by taking a nonidentical DS pair, we find unique secondary radiation in -space that originates due to the interaction of DSs during collision. The nature of this collision mediated secondary radiation is found to be different from usual DifRR. Our results shed light on the interesting aspects of the collision dynamics of a DS pair in a nonlinear WA and are useful in understanding the complex mechanism.

Spatially entangled states of light in nonlinear waveguide arrays - INVITED

We demonstrate a nonlinear AlGaAs photonic chip generating biphotons with nonclassical spatial correlations. Photon pairs are generated by parametric down conversion in a waveguide array and simultaneously spread through quantum walks along the various waveguides. This concept implements a compact and versatile source of spatially entangled states, operating at room temperature and telecom wavelength, that could serve as a workbench for simulating condensed matter problems on-chip.

Thresholds between modulational stability, rogue waves and soliton regimes in saturable nonlinear media

We study a third-order nonlinear Schrödinger equation for saturable nonlinear media, which can represent either optical pulse propagation in 1D nonlinear waveguide arrays or electron dynamics in one-dimensional lattices. Here, we describe how stable uniform solutions can evolve into regimes in which they are localized and the influence of saturation on this transition. We observed regular and chaotic-like breathing dynamics as intermediate regimes, which have their domain of existence significantly altered by the saturation parameter. Critical nonlinear strengths separating the existing regimes are shown in phase diagrams, evidencing the role played by saturation. Numerical data and analytical approach show the nonlinear strength above which uniform solutions become breather solutions increasing with the saturation parameter. In the regular breathing regime, we reveal the breathing frequency for media with saturable nonlinearity displaying faster growth as it moves away from the critical point of uniform solutions. Furthermore, critical nonlinear strength separating the regimes of regular and chaotic-like breather solutions exhibits a decreasing behavior as the saturation parameter increases. The latter ones present clear signatures of emerging rogue waves, such as peaks showing long-tailed statistics. Thresholds of this regime are increased by the saturable nonlinearity. Thus, the regime of localized solutions, which we have shown to be well-described by bright soliton-like structures, becomes less accessible with increasing saturation.

Mode-locking in quadratically nonlinear waveguide arrays.

A two-dimensional theoretical model is constructed to describe optical mode-locking (ML) in quadratically nonlinear waveguide arrays (QWGAs). Steady-state solutions of the considered model are obtained by a modified pseudo-spectral renormalization algorithm, and the mode-locking dynamics of the model are investigated through direct simulation of the nonlinear evolution and a linear stability analysis of the solutions. It is shown that stable mode-locking of elliptic steady-state solutions in quadratically nonlinear waveguide arrays are possible for a wide range of parameters, suggesting that quadratically nonlinear materials are well suited for producing stable mode-locked states for a wide range of applications.

Quantum-state creation in nonlinear-waveguide arrays

Many photonic quantum information tasks employ single photons and linear transformations to create and manipulate quantum states of light to process information. Integrated optical systems have become useful platforms to perform these tasks. New technologies introduce new possible processes available for multimode quantum operations. Here we explore one such setup, motivated by current experiments, which is a nonlinear-waveguide array system operating in a regime of nondegenerate-frequency down-converted photons. This allows one photon to act as a herald for the other photon, which is created in a superposition of the individual waveguide channels. We demonstrate this setup's ability to generate highly nonclassical states, such as $N$-photon Fock states and NOON states.

Nonlinear signatures of Floquet band topology

We study how the nonlinear propagation dynamics of bulk states may be used to distinguish topological phases of slowly driven Floquet lattices. First, we show how instabilities of nonlinear Bloch waves may be used to populate Floquet bands and measure their Chern number via the emergence of nontrivial polarization textures in a similar manner to static (undriven) lattices. Second, we show how the nonlinear dynamics of nonstationary superposition states may be used to identify dynamical symmetry inversion points in the intracycle dynamics, thereby allowing anomalous Floquet phases to be distinguished from the trivial phase. The approaches may be readily implemented using light propagation in nonlinear waveguide arrays.

Nonlinear compact localized modes in flux-dressed octagonal-diamond lattice

Tuning the values of artificial flux in the two-dimensional octagonal-diamond lattice drives topological phase transitions, including between singular and non-singular flatbands. We study the dynamical properties of nonlinear compact localized modes that can be continued from linear flatband modes. We show how the stability of the compact localized modes can be tuned by the nonlinearity strength or the applied artificial flux. Our model can be realized using ring resonator lattices or nonlinear waveguide arrays.

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

Nonlinear highly multimode photonic systems are ubiquitous in optics. Yet, the sheer complexity arising from the action of nonlinearity in multimode environments has posed theoretical challenges in describing these systems. In this work, we deploy concepts from optical thermodynamics to investigate the near- and far-field emission intensity patterns emerging from nonlinear waveguide arrays. An exact equation dictating the response of a nonlinear array is derived in terms of the systems invariants that act as extensive thermodynamic variables. In this respect, the near- and far-field characteristics emerging from a weakly nonlinear waveguide lattice are analytically addressed. We show that statistically, these patterns and the resulting far-field brightness are governed by the optical temperature and its corresponding chemical potential. The extensivity associated with the entropy of such configurations is discussed. The thermodynamic results presented here were found to be in good agreement with numerical simulations obtained from nonlinear coupled-mode theory.

Biphoton topology in a quadratic nonlinear waveguide array under the Su-Schrieffer-Heeger model

We demonstrate the generation of a stable topologically nontrivial biphoton state with a high degree of quantum entanglement by the bosonic Bogoliubov Hamiltonian in a quadratic nonlinear waveguide array (QNWA) under the Su-Schrieffer-Heeger model. Analysis of its energy spectrum and eigenmode spectra verifies that this biphoton state is a topological nontrivial edge state characterized by the nonzero Berry phase at 1/4 and 3/4 fillings. The changes of Berry phase at 1/4 and 3/4 fillings indicate the topological quantum transition. The topological robustness of the biphoton edge state can be demonstrated by the spatial correlation under random disorders in propagation constant of the QNWA. It is also shown that the R\'enyi entanglement entropy of this topologically nontrivial biphoton state can approach high values. The robustness of this topologically nontrivial property suggests the promising application of this highly entangled biphoton state in quantum computing and information.

Floquet defect solitons.

We consider an array of straight nonlinear waveguides constituting a two-dimensional square lattice, with a few central layers tilted with respect to the rest of the structure. It is shown that such a configuration represents a line defect in the lattice plane, which is periodically modulated along the propagation direction. In the linear limit, such a system sustains line defect modes, whose number coincides with the number of tilted layers. In the presence of nonlinearity, the branches of defect solitons propagating along the defect line bifurcate from each of the linear defect modes. Depending on the effective dispersion induced by the Floquet spectrum of the system, the bifurcating solitons can be either bright or dark. Dynamics and stability of such solitons are studied numerically.

Squeezed states generation in an array of Linear and Nonlinear Waveguides

We demonstrate the generation of squeezed states of light due to the second harmonic generation and Kerr effect in an array of nonlinear waveguides mediated through a linear one. We characterized the electromagnetic field by a quantum mechanical Hamiltonian and the density operator time evolution is obtained from the Von-Neumann equation of motion. Using the quasiprobability positive P of phase space representation, the classical Fokker-Planck equation is obtained from the master equation and translated to its classical matching set of nonlinear differential equations. We showed that because of the new possibilities of correlation between the linear and nonlinear channel waveguides, highly nonclassical light may be produced.

Scalable multimode entanglement based on efficient squeezing of propagation eigenmodes

Continuous-variable encoding of quantum information in the optical domain has recently yielded large temporal and spectral entangled states instrumental for quantum computing and quantum communication. We introduce a protocol for the generation of spatial multipartite entanglement based on phase-matching of a propagation eigenmode in a monolithic photonic device: the array of quadratic nonlinear waveguides. We theoretically demonstrate in the spontaneous parametric downconversion regime the generation of large multipartite entangled states useful for multimode quantum networks. Our protocol is remarkably simple and robust as it does not rely on specific values of coupling, nonlinearity or length of the sample.

Coherent optical processes with an all-optical atomic simulator.

We show how novel photonic devices such as broadband quantum memory and efficient quantum frequency transduction can be implemented using three-wave mixing processes in a 1D array of nonlinear waveguides evanescently coupled to nearest neighbors. We do this using an analogy of an atom interacting with an external optical field using both classical and quantum models of the optical fields and adapting well-known coherent processes from atomic optics, such as electromagnetically induced transparency and stimulated Raman adiabatic passage to design. This approach allows the implementation of devices that are very difficult or impossible to implement by conventional techniques.

Versatile Photonic Entanglement Synthesizer in the Spatial Domain

Multimode entanglement is an essential resource for quantum information in continuous-variable systems. Light-based quantum technologies will arguably not be built upon table-top bulk setups, but will presumably rather resort to integrated optics. Sequential bulk optics-like proposals based on cascaded integrated interferometers are not scalable with the current state-of-the-art low-loss materials used for continuous variables. We analyze the multimode continuous-variable entanglement capabilities of a compact currently-available integrated device without bulk-optics analog: the array of nonlinear waveguides. We theoretically demonstrate that this simple and compact structure, together with a reconfigurable input pump distribution and multimode coherent detection of the output modes, is a versatile entanglement synthesizer in the spatial domain. We exhibit this versatility through analytical and numerically optimized multimode squeezing, entanglement, and cluster state generation in different encodings. Our results re-establish spatial encoding as a contender in the game of continuous-variable quantum information processing.

Quantum state engineering in arrays of nonlinear waveguides

In the current quest for efficient and experimentally feasible platforms for implementation of multimode squeezing and entanglement in the continuous variable regime, we underpin and complement our results on the generation of versatile multimode entanglement and cluster states in nonlinear waveguide arrays presented by Barral et al., Phys. Rev. Appl. $\bf{14}$, 044025 (2020). We present detailed derivations of the equations that describe the propagation of light through this system, and then we focus on parameter regimes where these equations can be solved analytically. These analytical solutions build an intuition for the wide landscape of quantum states that are accessible through the activation of pumping, coupling and measurement schemes. Furthermore, we showcase the acquired insights by using one of the identified analytical solutions to exhibit the generation, optimization and scalability of spatial linear cluster states.

Dynamic diffractive resonant radiation in a linearly chirped nonlinear waveguide array

We theoretically and numerically investigate the evolution of discrete soliton in a 1D linearly chirped nonlinear waveguide array (WA). The discrete soliton is self-accelerated inside the transversely chirped WA and emits a \textit{dynamic diffractive resonant radiation} (DifRR). The radiation appears when soliton wave-number matched with linear radiation wave. Unlike uniform WA, the DifRR can be excited even for zero wave-number of input soliton when the waveguide channels are chirped. The transverse modulation due to chirp conceptually imposes a linear potential which acts as a perturbation to soliton dynamics and leads to a monotonous wave-number shift of the propagating wave. Exploiting perturbative variational analysis we determine the equation of motion of soliton wave-number and use it to establish a modified phase-matching condition which takes into account the soliton wave-number shift and efficiently predicts the dynamic DifRR. A startling effect like generation of dual DifRR occurs as a result of the interplay between self-accelerated soliton and its initial wave-number. We exploit the modified phase matching relation to understand this unique phenomenon of dual radiation and find a satisfactory agreement with numerical result in radiation wave-number calculation.