Optical Waveguide Arrays Research Articles

Nonlinear topological edge states in a non-Hermitian array of optical waveguides embedded in an atomic gas

We propose a scheme comprising an array of anisotropic optical waveguides, embedded in a gas of cold atoms, which can be tuned from a Hermitian to an odd-PT -- symmetric configuration through the manipulation of control and assistant laser fields. We show that the system can be controlled by tuning intra -- and inter-cell coupling coefficients, enabling the creation of topologically distinct phases and linear topological edge states. The waveguide array, characterized by a quadrimer primitive cell, allows for implementing transitions between Hermitian and odd-PT -symmetric configurations, broken and unbroken PT -symmetric phases, topologically trivial and nontrivial phases, as well as transitions between linear and nonlinear regimes. The introduced scheme generalizes the Rice-Mele Hamiltonian for a nonlinear non-Hermitian quadrimer array featuring odd-PT symmetry and makes accessible unique phenomena and functionalities that emerge from the interplay of non-Hermiticity, topology, and nonlinearity. We also show that in the presence of nonlinearity the system sustains nonlinear topological edge states bifurcating from the linear topological edge states and the modes without linear limit. Each nonlinear mode represents a doublet of odd-PT -conjugate states. In the broken PT phase, the nonlinear edge states may be effectively stabilized when an additional absorption is introduced into the system.

Floquet higher-order topological insulator in a periodically driven bipartite lattice

Floquet higher order topological insulators (FHOTIs) are a novel topological phase that can occur in periodically driven lattices. An appropriate experimental platform to realize FHOTIs has not yet been identified. We introduce a periodically-driven bipartite (two-band) system that hosts FHOTI phases, and predict that this lattice can be realized in experimentally-realistic optical waveguide arrays, similar to those previously used to study anomalous Floquet insulators. The model exhibits interesting phase transitions from first-order to second-order topological matter by tuning a coupling strength parameter, without breaking lattice symmetry. In the FHOTI phase, the lattice hosts corner modes at eigenphase $0$ or $\pi$, which are robust against disorder in the individual couplings.

Asymptotic behaviors of mixed-type vector double-pole solutions for the discrete coupled nonlinear Schrödinger system

In this paper, we analyze the asymptotic behaviors of mixed-type vector double-pole solutions for the discrete coupled nonlinear Schrodinger system with the focusing-focusing or focusing-defocusing nonlinearities applied in optical waveguide arrays. First of all, based on the bright-bright and bright-dark vector two-soliton solutions given by the Hirota method, we construct the mixed-type vector double-pole solutions via the limit technique. Then, through a modified asymptotic analysis method, we obtain the exact expressions of all asymptotic solitons in the vector double-pole solutions. Further, we investigate the characteristics of soliton interactions in the vector double-pole solutions and find some special properties different from the usual vector two-soliton interactions, like each asymptotic soliton is localized in a curve rather than a line, the interacting bright or dark solitons separate from each other in a logarithmical law and the separation acceleration decreases exponentially with the relative distance.

Topological states in arrays of optical waveguides engineered via mode interference

Photonic structures with topologically nontrivial bands are usually designed by arranging simple meta-atoms, ideally, single-mode ones, in a carefully designed photonic lattice with symmetry that guarantees the emergence of topological states. Here we investigate an alternative option that does not require complex lattice geometry but instead relies on the tuning of the parameters of the individual meta-atoms to achieve the degeneracy of the modes with different symmetry. As an illustrative example, we consider a one-dimensional array of equidistant identical periodic nanophotonic waveguides supporting degenerate modes with strongly asymmetric near field profiles giving rise to the coupling modulation. Exploiting this feature, we demonstrate that the proposed system supports topological edge modes and can be viewed as a generalization of the paradigmatic Su-Schrieffer-Heeger model, reducing to it for the suitable parameter choice. Our results thus provide an avenue to engineer topological states via mode interference which further expands the plethora of topological structures available in photonics being especially promising for nonlinear topological systems.

Onset times of long-lived rogue waves in an optical waveguide array.

We study the effects of increasing modulation instability and disorder on the onset times of rogue waves in waveguide arrays as described by the discrete unstable nonlinear Schrödinger equation (UNLSE). We analytically determine regions of instability, where rogue waves are likely to occur in the UNLSE, and then use numerical techniques to study the time evolution of these systems. Only for small modulation instability is the effect of fluctuations prominent on the onset times; otherwise, we find that large modulation instability dominates the onset time behavior.

Universal form of arrays with spectral singularities.

An array of non-Hermitian optical waveguides can operate as a laser or as a coherent perfect absorber, which corresponds to a spectral singularity of the underlying discrete complex potential. We show that all lattice potentials with spectral singularities are characterized by the universal form of the gain-and-loss distribution. Using this result, we systematically construct potentials characterized by several spectral singularities at arbitrary wavelengths, as well as potentials with second-order spectral singularities in their spectra. Higher-order spectral singularities demonstrate a greatly enhanced response to incident beams, resulting in the excitation of high-intensity lasing modes.

Unidirectional flow of discrete solitons in optical waveguide arrays with nonlinearity management

We propose a mechanism for realising a unidirectional flow of discrete solitons in optical waveguide arrays. Modulating the nonlinear interaction strength in each waveguide according to a double reflectionless potential well with slight difference in the depths of its two wells, we achieve a unidirectional flow of the soliton propagation. We verify clearly, through the transport coefficients as in terms of the speed of the incident soliton, that an incident soliton velocity window of finite width exists where unidirectional flow can be realised. We discuss the physics underlying this behaviour on the basis of energy exchange between the soliton's kinetic and interaction energies.

Circular Optical Arrays Using Waveguide Fed 45° Angled Mirrors

An array of optical waveguide fed 45° metal-coated mirrors are proposed and validated by simulation, for generating optical scalar and vector vortices. Subwavelength element-to-element spacings are achieved, which is not possible in traditional grating-based phased arrays. This vortex source can be superior over other methods like phase masks which are not planar process integrable with lasers and phase modulators. A simple plane wave reflection model is used to analyze the mirror and the results are matched with reasonable tolerance against simulation results. The spin and orbital angular momentum charges are directly calculated from the field values for quantifying the performance. Four- and eight-element arrays are studied. The matching of prediction with simulation has been good for linear, azimuthal and radial polarization. Good angular momentum conversion efficiencies are obtained for up to orbital angular momentum charges ${l}$ = ±2. Important aspects of generating vortices with circular polarization are brought out. Directional beams with >10 dB gains are achieved. This is the first report in which a planar dielectric optical waveguide array with subwavelength spacing has achieved good angular momentum control for linearly, azimuthally, radially and circularly polarized beams, in the same geometry.

Fabrication and transmission of optical polymer waveguide backplane for high - performance computers.

In this paper, a high-speed, large-capacity and compact optical backplane architecture for high-performance computers (HPC) is proposed and designed. The MT couplers is designed without additional mirror to divert the light from vertical cavity surface emitting laser (VCSEL) array by 90°. The light is then coupled into the optical waveguide through the MT. A bidirectional 8 channels polymer optical waveguide array with low insertion loss is designed and fabricated. The waveguides are embedded in the printed circuit board. We test the performance of 8 channels for the optical waveguide backplane. In the entire optical backplane, the averaged insertion loss of optical backplane with 50 μm input fiber is 1.62 dB with 850 nm VCSEL. The misalignment loss is 0.5 dB when the misalignment between waveguide and multi-mode fiber is 8.5 μm. Then, the transmission performances of 4 channels with different speed signals is demonstrated by off-line experiment. The optical backplane network can achieve 15 G data error-free transmission in the range of [-2 dBm, -10 dBm] received optical power (ROP). Based on VCSEL arrays, the optical interconnection network system can achieve 8 channels parallel signal transmission. In the optical backplane, the 10 Gbit / s data generated / processed by field programmable gate array (Xilinx Kintex-7) chips can realize error-free transmission. In large-capacity, high-speed parallel HPC, the designed optical backplane system can facilitate the establishment of a large number of parallel transmissions.

Unstaggered-staggered solitons on one- and two-dimensional two-component discrete nonlinear Schrödinger lattices

We study coupled unstaggered-staggered soliton pairs emergent from a system of two coupled discrete nonlinear Schrödinger (DNLS) equations with the self-attractive on-site self-phase-modulation nonlinearity, coupled by the repulsive cross-phase-modulation interaction, on 1D and 2D lattice domains. These mixed modes are of a “symbiotic” type, as each component in isolation may only carry ordinary unstaggered solitons. While most work on DNLS systems addressed symmetric on-site-centered fundamental solitons, these models give rise to a variety of other excited states, which may also be stable. The simplest among them are antisymmetric states in the form of discrete twisted solitons, which have no counterparts in the continuum limit. In the extension to 2D lattice domains, a natural counterpart of the twisted states are vortical solitons. We first introduce a variational approximation (VA) for the solitons, and then correct it numerically to construct exact stationary solutions, which are then used as initial conditions for simulations to check if the stationary states persist under time evolution. Two-component solutions obtained include (i) 1D fundamental-twisted and twisted-twisted soliton pairs, (ii) 2D fundamental-fundamental soliton pairs, and (iii) 2D vortical-vortical soliton pairs. We also highlight a variety of other transient dynamical regimes, such as breathers and amplitude death. The findings apply to modeling binary Bose-Einstein condensates, loaded in a deep lattice potential, with identical or different atomic masses of the two components, and arrays of bimodal optical waveguides.

Influence of different disorder types on Aharonov-Bohm caging in the diamond chain

The linear diamond chain with fine-tuned effective magnetic flux has a completely flat energy spectrum and compactly-localized eigenmodes, forming an Aharonov-Bohm cage. We study numerically how this localization is affected by different types of disorder (static and time-evolving) relevant to recent realizations of Aharonov-Bohm cages in periodically-modulated optical waveguide arrays. We demonstrate robustness of localization under static and periodically-evolving disorder, while in contrast non-quenched (time-dependent) disorder leads to wavepacket spreading and delocalization.

Modeling and control of a reconfigurable photonic circuit using deep learning

The complexity of experimental quantum information processing devices is increasing rapidly, requiring new approaches to control them. In this paper, we address the problems of practically modeling and controlling an integrated optical waveguide array chip—a technology expected to have many applications in telecommunications and optical quantum information processing. This photonic circuit can be electrically reconfigured, but only the output optical signal can be monitored. As a result, the conventional control methods cannot be naively applied. Characterizing such a chip is challenging for three reasons. First, there are uncertainties associated with the Hamiltonian model describing the chip. Second, we expect distortions of the control voltages caused by the chip’s electrical response, which cannot be directly observed. And third, there are imperfections in the measurements caused by losses from coupling the chip externally to optical fibers. We have developed a deep neural network (NN) approach to solve these problems. The architecture is designed specifically to overcome the aforementioned challenges using a gated recurrent unit -based network as the central component. The Hamiltonian is estimated as a blackbox, while the rules of quantum mechanics such as state evolution is embedded in the structure as a whitebox. The resulting overall graybox model of the chip shows good performance both quantitatively in terms of the mean square error and qualitatively in terms of the shape of the predicted waveforms We use this NN to solve a classical and a quantum control problem. In the classical application we find a control sequence to approximately realize a time-dependent output power distribution. For the quantum application we obtain the control voltages to realize a target set of quantum gates. The method we propose is generic and can be applied to other systems that can only be probed indirectly.

Topological bound modes in optical waveguide arrays with alternating positive and negative couplings

We investigate the topological bound modes in a binary waveguide array with alternating positive and negative couplings. The negative coupling is realized by incorporating additional waveguides into the bare array and suitably tuning the refractive index. We show the band structures close and Dirac point emerges at the Brillouin zone center when the absolute values of real and negative couplings are equal, indicating topological phase transition. The topological bound modes emerge at the edge of topological non-trivial arrays or at the interface of two arrays with different topologies. Moreover, we show the topological bound mode can be isolated from the trivial defect mode by tuning the coupling strength, which is reflected from wave propagation. The study provides a promising approach to realizing robust light transport.

Robust and Broadband Optical Coupling by Topological Waveguide Arrays

AbstractPhotonic topological states have been exploited to give rise to robust optical behaviors that are quite insensitive to local defects or perturbations, which provide a promising solution for robust photonic integrations. Specifically, for example, optical coupling between waveguides is a universal function in integrated photonics. However, the coupling performance usually suffers from high structure‐sensitivity and challenges current manufacturing for massive production. Here, the topological edge state in a finite Su–Schriffer–Heeger modeled optical waveguide array is explored and robust optical coupling (e.g., directional coupling and beam splitting) is demonstrated, which is quite insensitive to structural variations. It is experimentally proved that even a large discrepancy (21–26% structural deviation) in silicon waveguides gaps has little influence on optical coupling (>90% performance), while conventional counterparts totally break down. Moreover, thanks to such a topological design, the devices show much broader working bandwidth (≈10 times performance improvement) than the conventional ones, greatly favoring the photonic integrations. This work would inspire new families of optical devices with robust and broadband properties that can excite more interesting and useful exploration in both fields, and possibly open a new avenue toward topological devices with unique properties and functionalities.

2D Solitons in PT-Symmetric Photonic Lattices.

Over the last few years, parity-time (PT) symmetry has been the focus of considerable attention. Ever since, pseudo-Hermitian notions have permeated a number of fields ranging from optics to atomic and topological physics, as well as optomechanics, to mention a few. Unlike their Hermitian counterparts, nonconservative systems do not exhibit apriori real eigenvalues and hence unitary evolution. However, once PT symmetry is introduced, such dissipative systems can surprisingly display a real eigenspectrum, thus ensuring energy conservation during evolution. In optics, PT symmetry can be readily established by incorporating, in a balanced way, regions having an equal amount of optical gain and loss. However, thus far, all optical realizations of such PT symmetry have been restricted to a single transverse dimension (1D), such as arrays of optical waveguides or active coupled cavity arrangements. In most cases, only the loss function was modulated-a restrictive aspect that is only appropriate for linear systems. Here, we present an experimental platform for investigating the interplay between PT symmetry and nonlinearity in two-dimensional (2D) environments, where nonlinear localization and soliton formation can be observed. In contrast to typical dissipative solitons, we demonstrate a one-parameter family of soliton solutions that are capable of displaying attributes similar to those encountered in nonlinear conservative arrangements. For high optical powers, this new family of PT solitons tends to collapse on a discrete network-thus giving rise to an amplified, self-accelerating structure.

Effect of loss on transverse localization of light in 1D optical waveguide array in the presence of Kerr-type nonlinearity

In this paper we have comprehensive study on the interplay among radiation loss, transverse disorder (diagonal and off-diagonal) and Kerr-type nonlinearity on the light propagation in 1D array of optical waveguides. Our numerical results demonstrate the presence of three distinguished regimes of transverse light expansion at different propagation distances. At short propagation distance, the Kerr-type nonlinearity are dominated and results in the transverse localization of light through the self-trapping mechanism. Radiation loss, causes the light escape from the injected guides, affect the light expansion in middle distance via broadening the light beam width. At longer distance the disorder terms led to the transverse localization of light, again. Also, we compared the propagation of light in edge and middle modes in the presence of the above effects. Our results show that the propagation distance of first localized regime for edge modes is larger than the middle modes since the edge modes can exchange energy with one of the left or right waveguides, while for middle modes there are two ways for energy exchange. Therefore the discrete diffraction can be diminished the nonlinear effects in middle modes faster than the edge modes.

Bosonic discrete supersymmetry for quasi-two-dimensional optical arrays

We apply the notion of discrete supersymmetry based on matrix factorization to quantum systems consisting of coupled bosonic oscillators to construct isospectral bosonic quantum networks. By using the algebra that arises due to the indistinguishability of bosonic particles, we write down the Schrodinger equations for these oscillators in the different boson-number sectors. By doing so, we obtain, for every partner quantum network, a system of coupled differential equations that can be emulated by classical light propagation in optical waveguide arrays. This mathematical scheme allows us to build quasi-two-dimensional optical arrays that are either isospectral or share only a subset of their spectrum after deliberately omitting some chosen eigenstates from the spectrum. As an example, we use this technique (which we call bosonic discrete supersymmetry or BD-SUSY) to design two optical, silica-based waveguide arrays consisting of six and three elements, respectively, with overlapping eigenspectrum.

Manipulation of multimode squeezing in a coupled waveguide array

We present a scheme for generating and manipulating three-mode squeezed states with genuine tripartite entanglement by injecting single-mode squeezed light into an array of coupled optical waveguides. We explore the possibility to selectively generate single-mode squeezing or multimode squeezing at the output of an elliptical waveguides array, determined solely by the input light polarization. We study the effect of losses in the waveguides array and show that quantum correlations and squeezing are preserved for realistic parameters. Our results show that arrays of optical waveguides are suitable platforms for generating multimode quantum light, which could lead to novel applications in quantum metrology.

Experimental realization of a Weyl exceptional ring

Weyl points are isolated degeneracies in reciprocal space that are monopoles of the Berry curvature. This topological charge makes them inherently robust to Hermitian perturbations of the system. However, non-Hermitian effects, usually inaccessible in condensed matter systems, are an important feature of photonics systems, and when added to an otherwise Hermitian Weyl material have been predicted to spread the Berry charge of the Weyl point out onto a ring of exceptional points, creating a Weyl exceptional ring and fundamentally altering its properties. Here, we observe the implications of the Weyl exceptional ring using real-space measurements of an evanescently-coupled bipartite optical waveguide array by probing its effects on the Fermi arc surface states, the bulk diffraction properties, and the output power ratio of the two constituent sublattices. This is the first realization of an object with topological Berry charge in a non-Hermitian system.

Topological bound modes in anti-PT-symmetric optical waveguide arrays.

We investigate the topological bound modes in a binary optical waveguide array with anti-parity-time (PT) symmetry. The anti-PT-symmetric arrays are realized by incorporating additional waveguides to the bare arrays, such that the effective coupling coefficients are imaginary. The systems experience two kinds of phase transition, including global topological order transition and quantum phase transition. As a result, the system supports two kinds of robust bound modes, which are protected by the global topological order and the quantum phase, respectively. The study provides a promising approach to realizing robust light transport by utilizing mediating components.