The Maryland model was introduced more than 30 years ago as an integrable model of localization by aperiodic order. Even though quite popular and rich of fascinating mathematical properties, this model has so far remained quite artificial, as compared to other models displaying dynamical localization like the periodically-kicked quantum rotator or the Aubry-Andre$^{\prime}$ model. Here we suggest that light propagation in a polygonal optical waveguide lattice provides a photonic realization of the Maryland model and enables to observe a main prediction of this model, namely fragility of wave localization in the commensurate potential limit.
The topological trivial band of a lattice can be driven into a topological phase by disorder in the system. This so-called topological Anderson phase has been predicted and observed for uncorrelated static disorder, while in the presence of correlated disorder conflicting results are found. Here we consider a Su-Schrieffer-Heeger (SSH) waveguide lattice in the trivial topological phase, and show that quasi-periodic disorder in the coupling constants can drive the lattice into a topological non-trivial phase. A method to detect the emergence of the topological Anderson phase, based on light dyn…
Light escape from an optical waveguide side-coupled to a waveguide lattice provides a photonic analogue of the spontaneous emission process of an excited two-level atom in a one-dimensional array of cavities. According to the Fermi golden rule the decay process is prevented when the atomic resonance frequency falls in a stop band of the lattice, while time-reversal symmetry ensures that the spontaneously emitted photon has equal probability to propagate in opposite directions of the array. This scenario is drastically modified when the quantum emitter drifts along the lattice at a constant spe…
We suggest a method for trapping photons in quasi one-dimensional waveguide or coupled-resonator lattices, which is based on an optical analogue of the Aharonov-Bohm cages for charged particles. Light trapping results from a destructive interference of Aharonov-Bohm type induced by a synthetic magnetic field, which is realized by periodic modulation of the waveguide/resonator propagation constants/resonances.
We consider coupled waveguide lattices as an architecture that implement a wide range of multiport transformations. In this architecture, a particular transfer matrix is obtained through setting the step-wise profiles of the propagation constants seen by the field evolving in the lattice. To investigate the transformation capabilities, the implementation of a set of transfer matrices taken at random and particular cases of discrete Fourier transform, Hadamard and permutation matrices have been described. Because the waveguide lattices schemes are more compact than their traditional lumped-para…
A method to realize effective magnetic fields for photons in square lattices of coupled optical waveguides or resonators is suggested, which is inspired by an optical analogue of photon-assisted tunneling of atom optics. It is shown that an artificial magnetic field can be achieved by application of an index gradient and periodic lumped phase shifts or modulation of the propagation constants/resonances, without the need to modulate the coupling strength.
In this work, we propose a completely general method to pump the gapped topological modes of a lattice of optical waveguides by controlling the propagation constant of an auxiliary waveguide and its coupling to the main lattice. In this way, we can transform a single-waveguide excitation on the auxiliary waveguide into a specific mode of the lattice. We also demonstrate the possibility of transferring supermodes between two waveguide lattices using the same method. We illustrate the results by pumping and transferring the topological modes of Su-Schrieffer-Heeger lattices. For both scenarios, …
Time reversal is one of the most intriguing yet elusive wave phenomenon of major interest in different areas of classical and quantum physics. Time reversal requires in principle to flip the sign of the Hamiltonian of the system, leading to a revival of the initial state (Loschmidt echo). Here it is shown that Loschmidt echo of photons can be observed in an optical setting without resorting to reversal of the Hamiltonian. We consider photonic propagation in a binary waveguide lattice and show that, by exchanging the two sublattices after some propagation distance, a Loschmidt echo can be obser…
We study coupling and decoupling of parallel waveguides in two-dimensional square-lattice photonic crystals. We show that the waveguide coupling is prohibited at some wavelengths when there is an odd number of rows between the waveguides. In contrast, decoupling does not take place when there is even number of rows between the waveguides. Decoupling can be used to avoid cross talk between adjacent waveguides.
Recently, it has been suggested that the collective radiative decay of two point-like quantum emitters coupled to a waveguide, separated by a distance comparable to the coherence length of a spontaneously emitted photon, leads to an apparent $^{\prime}$superradiance paradox$^{\prime}$ by which one cannot decide whether independent or collective emission occurs. The resolution of the paradox stems from the strong non-Markovian dynamics arising from the delayed field-mediated atom interaction. Here we suggest an integrated optics platform to emulate the superradiance paradox, based on photon esc…
A general method for flexible control of the path of discretized light beams in homogeneous waveguide lattices, based on longitudinal modulation of the coupling constant, is theoretically proposed. As compared to beam steering and refraction achievable in graded-index waveguide arrays, the proposed approach enables to synthesize rather arbitrary target paths.
A discrete analogue of the dynamical (Kapitza) trapping effect, known for classical and quantum particles in rapidly oscillating potentials, is proposed for light waves in modulated graded-index waveguide lattices. As in the non-modulated waveguide lattice a graded-index potential can confine light at either normal or Bragg angle incidence, periodic modulation of the potential in the longitudinal direction enables to trap optical beams at both normal and Bragg incidence angles.
One-dimensional lattices with chiral symmetry are known to possess quantized Zak phase and nontrivial topological phases. Here it is shown that quantized Zak phase and nontrivial edge states, partially protected by inversion symmetry rather than chiral symmetry, can be observed and probed in the bulk exploiting continuous-time photonic quantum walk in zig-zag waveguide arrays. Averaged beam displacement measurements can detect quantized Zak phase and non-trivial topological phases in the extended Su-Schrieffer-Heeger model with broken chiral symmetry.
Recently, waveguide lattices with non-uniform tunneling amplitudes have been explored due to their myriad tunable properties, many of which arise from the extended nature of their eigenstates in the absence of disorder. Here, we investigate the dynamics, localization, and parity- and time-reversal-($\mP\mT$) symmetry breaking in lattices that support only localized eigenstates in the disorder-free limit. We propose three families of tunneling profiles that lead to qualitatively different single-particle time evolution, and show that the effects of weak disorder contain signatures of the locali…
Artificial gauge fields enable the intriguing possibility to manipulate the propagation of light as if it were under the influence of a magnetic field even though photons possess no intrinsic electric charge. Typically, such fields are engineered via periodic modulations of photonic lattices such that the effective coupling coefficients after one period become complex-valued. In this work, we investigate the possibility to introduce randomness into artificial gauge fields by applying local random phase shifts in the modulation of lattices of optical waveguides. We first study the elemental uni…
We analyze spontaneous parametric down-conversion in various experimentally feasible 1D quadratic nonlinear waveguide arrays, with emphasis on the relationship between the lattice's topological invariants and the biphoton correlations. Nontrivial topology results in a nontrivial "winding" of the array's Bloch waves, which introduces additional selection rules for the generation of biphotons. These selection rules are in addition to, and independent of existing control using the pump beam's spatial profile and phase matching conditions. In finite lattices, nontrivial topology produces single ph…
We investigate the waveguiding properties of the optical interference pattern of two counter-propagating Laguerre-Gaussian beams. The number, helicity, radius, pitch, depth and frequencies of transverse confinement of the waveguides are simply related to the beam parameters. Quantitative connections to the familiar Gaussian optical lattice are made and an application to quantum transport is suggested.
We report the enhancement of the effect of transverse localization of light (TL) in presence of a weak longitudinal modulation of refractive index in disordered waveguide lattices. In our chosen lattices, tunneling inhibition along length favors to achieve the diffraction-free propagation along with the simultaneous presence of transverse disorder. Results will be useful to tune the threshold value of disorder to achieve localized light.
We analyze the impact of loss in lattices of coupled optical waveguides and find that in such case, the hopping between adjacent waveguides is necessarily complex. This results not only in a transition of the light spreading from ballistic to diffusive, but also in a new kind of diffraction that is caused by loss dispersion. We prove our theoretical results with experimental observations.
We present a semi-analytical formulation for calculating the supermodes and corresponding Bloch factors of light in hexagonal lattice photonic crystal waveguide arrays. We then use this formulation to easily calculate dispersion curves and predict propagation in systems too large to calculate using standard numerical methods.
Metamaterials are being used to model various exotic "optical spaces" for such applications as novel lenses and cloaking. While most effort is directed towards engineering of continuously changing dielectric permittivity and magnetic permeability tensors, an alternative approach may be based on lattices of metamaterial waveguides. Here we demonstrate the power of the latter technique by presenting metamaterial lattice models of various 4D spaces.
We investigate the single-particle time evolution and two-particle quantum correlations in a one-dimensional $N$-site lattice with a site-dependent nearest neighbor tunneling function $t_α(k)=t_0[k(N-k)]^{α/2}$. Since the bandwidth and the energy levels spacings for such a lattice both depend upon $α$, we show that the observable properties of a wavepacket, such as its spread and the relative phases of its constitutents, vary dramatically as $α$ is varied from positive to negative values. We also find that the quantum correlations are exquisitely sensitive to the form of the tunneling function…
Quantum random walks are the quantum counterpart of classical random walks, and were recently studied in the context of quantum computation. A quantum random walker is subject to self interference, leading to a remarkably different behavior than that of classical random walks such as ballistic propagation or localization due to disorder. Physical implementations of quantum walks have only been made in very small scale systems severely limited by decoherence. Here we show that the propagation of photons in waveguide lattices, which have been studied extensively in recent years, are essentially …
We measure the next-nearest-neighbour coupling in an array of coupled optical waveguides directly via an integrated eigenmode interferometer. In contrast to light propagation experiments, the technique is insensitive to nearest-neighbour dynamics. Our results show that second-order coupling in a linear configuration can be suppressed well below the level expected from the exponential decay of the guided modes.
The role of a prominent photonic bandgap (PBG) on the phenomenon of transverse localization of light in a semi-infinite lossless waveguide lattice consisting of evanescently coupled disordered one-dimensional optical waveguides has been investigated numerically. The interplay between the underlying photonic bandgap due to inherent periodicity of the optical system and various levels of deliberately induced transverse disorder in its refractive index periodicity has been studied. We show that the PBG indeed plays an important role and its simultaneous presence could catalyze realization of loca…
We investigate the propagation of Gaussian beams through optical waveguide lattices characterized by correlated non-Hermitian disorder. In the framework of coupled mode theory, we demonstrate how the imaginary part of the refractive index needs to be adjusted to achieve perfect beam transmission, despite the presence of disorder. Remarkably, the effects of both diagonal and off-diagonal disorder in the waveguides and their couplings can be efficiently eliminated by our non-Hermitian design. Waveguide arrays thus provide an ideal platform for the experimental realization of non-Hermitian phenom…
We predict that stable mobile spatio-temporal solitons can exist in arrays of periodically curved optical waveguides. We find two-dimensional light bullets in one-dimensional arrays with harmonic waveguide bending and three-dimensional bullets in square lattices with helical waveguide bending using variational formalism. Stability of the light bullet solutions is confirmed by the direct numerical simulations which show that the light bullets can freely move across the curved arrays. This mobility property is a distinguishing characteristic compared to previously considered discrete light bulle…
We investigate the influence of the phase-front curvature of an input light beam on the transverse localization of light by choosing an evanescently coupled disordered one-dimensional semi-infinite waveguide lattice as an example. Our numerical study reveals that a finite phase front curvature of the input beam indeed plays an important role and it could degrade the quality of light localization in a disordered dielectric structure. More specifically, a faster transition from ballistic mode of beam propagation due to diffraction to a characteristic localized state is observed in case of a cont…
We propose a feasible waveguide design optimized for harnessing Stimulated Brillouin Scattering with long-lived phonons. The design consists of a fully suspended ridge waveguide surrounded by a 1D phononic crystal that mitigates losses to the substrate while providing the needed homogeneity for the build-up of the optomechanical interaction. The coupling factor of these structures was calculated to be 0.54 (W.m)$^{-1}$ for intramodal backward Brillouin scattering with its fundamental TE-like mode and 4.5(W.m)$^{-1}$ for intramodal forward Brillouin scattering. The addition of the phononic crys…
Quantum Hall system possesses topologically protected edge states which have enormous theoretical and practical implications in both fermionic and bosonic systems. Harnessing the quantum Hall effect in optical platforms with lower dimensionality is highly desirable with synthetic dimensions and has attracted broad interests in the photonics society. Here, we introduce an alternative way to realize the artificial magnetic field in a frequency dimension, which is achieved in a pump-probe configuration with cross-phase modulations in a one-dimensional four waveguide array. The dynamics of the top…
We study a one-dimensional photonic resonator lattice with Kerr nonlinearity under the dynamic modulation. With an appropriate choice of the modulation frequency and phase, we find that this system can be used to create anyons from photons. By coupling the resonators with external waveguides, the anyon characteristics can be explored by measuring the transport property of the photons in the external waveguides.
In this paper, we theoretically study the Floquet engineering of two dimensional photonic waveguide arrays in three types of lattices: honeycomb lattice with Kekule distortion, breathing square lattice and breathing Kagome lattice. The Kekule distortion factor or the breathing factor in the corresponding lattice is periodically changed along the axial direction of the photonic waveguide with frequency $ω$. Within certain ranges of $ω$, the Floquet corner states in the Floquet band gap of quasi-energy spectrum are found, which are localized at the corner of the finite two-dimensional arrays. Du…
We reveal and observe experimentally significant modifications undertaken by discrete solitons in waveguide lattices upon the continuous transformation of the lattice structure from one-dimensional to two-dimensional. Light evolution and soliton excitation in arrays with a gradually increasing number of rows are investigated, yielding solitons with an effective reduced dimensionality residing at the edge and in the bulk of the lattice.
We study the propagation of non-classical light through arrays of coupled linear photonic waveguides and introduce some sets of refractive indices and coupling parameters that provide a closed form propagator in terms of orthogonal polynomials. We present propagation examples of non-classical states of light: single photon, coherent state, path-entangled state and two-mode squeezed vacuum impinging into two-waveguide couplers and a photonic lattice producing coherent transport.
A method for realizing asymmetric (one-way) transmission of discretized light in modulated, linear and purely passive optical lattices is suggested, which exploits the idea of unidirectional coherent perfect absorption. The system consists of a linear photonic lattice of coupled resonators or waveguides, side coupled to a chain of lossy elements, in which light can avoid the occupation of the dissipative sites when propagating in one way, but not in the opposite one. Non-reciprocity requires modulation of the resonator/waveguide parameters, realizing a dissipative optical Aharonov-Bohm diode w…
We review both theoretical and experimental advances in the recently emerged physics of modulated photonic lattices. Artificial periodic dielectric media, such as photonic crystals and photonic lattices, provide a powerful tool for the control of the fundamental properties of light propagation in photonic structures. Photonic lattices are arrays of coupled optical waveguides, where the light propagation becomes effectively discretized. Such photonic structures allow one to study many useful optical analogies with other fields, such as the physics of solid state and electron theory. In particul…
We present a numerical study on the light transport properties which are modulated by the disorder strength in quasi-one-dimensional disordered waveguide which consists of periodically arranged scatterers with random dielectric constant. The transport mean free path is found to stay inversely proportional to the square of the relative fluctuation of the dielectric constant as in the 1D and 2D cases but with . The transport properties of light through a sample with a fixed size can be modulated from ballistic to localized regime as well, and a generalized scaling function is defined to determin…
In this article we use the method of shortcuts to adiabaticity to design a photonic lattice (array of waveguides) which can drive the input light to a controlled location at the output. The output position in the array is determined by functions of the propagation distance along the waveguides, which modulate the lattice characteristics (index of refraction, first and second neighbor couplings). The proposed coupler is expected to posses the robustness properties of the design method, coming from its adiabatic nature, and also to have a smaller footprint than purely adiabatic couplers. The pre…
An 'optical ratchet' for discretized light in photonic lattices, which enables to observe rectification of light refraction at any input beam conditions, is theoretically presented, and a possible experimental implementation based on periodically-curved zigzag waveguide arrays is proposed.
In recent years, there has been considerable interest in the study of wave propagation in nonlinear photonic lattices. The interplay between nonlinearity and periodicity has led researchers to manipulate light and discover new and interesting phenomena such as new classes of localized modes, usually referred to as solitons, and novel surface states that propagate robustly. A field where both nonlinearity and periodicity arises naturally is nonlinear optics. But there are other areas where waves propagating on background lattices play an important role, including photonic crystal fibers and Bos…
Topological insulators are studied via tight-binding approximations of longitudinally driven photonic lattices with three lattice sites per unit cell. Two cases are considered in detail: Lieb and Kagome lattices. The lattice is decomposed into three sublattices each of which are allowed move independently of one another. Emphasis is placed on periodic driving induced by laser-etched helical coils along the direction of propagation. The linear Floquet bands are constructed for various inter-sublattice rotation patterns such as: different radii, different frequency, phase offset and quasi one-di…
By means of a systematic numerical analysis, we demonstrate that hexagonal lattices of parallel linearly-coupled waveguides, with the intrinsic cubic self-focusing nonlinearity, give rise to three species of stable semi-discrete complexes (which are continuous in the longitudinal direction), with embedded vorticity S: triangular modes with S=1, hexagonal ones with S=2, both centered around an empty central core, and compact triangles with S=1, which do not not include the empty site. Collisions between stable triangular vortices are studied too. These waveguiding lattices can be realized in op…
We report experimental observations of large Bragg reflection from arrays of cold atoms trapped near a one-dimensional nanoscale waveguide. By using an optical lattice in the evanescent field surrounding a nanofiber with a period nearly commensurate with the resonant wavelength, we observe a reflectance of up to 75% for the guided mode. Each atom behaves as a partially-reflecting mirror and an ordered chain of about 2000 atoms is sufficient to realize an efficient Bragg mirror. Measurements of the reflection spectra as a function of the lattice period and the probe polarization are reported. T…
We propose an exactly solvable waveguide lattice incorporating inhomogeneous coupling coefficient. This structure provides a classical analogue to the squeezed number and squeezed coherent intensity distribution in quantum optics where the propagation length plays the role of squeezed amplitude. The intensity pattern is obtained in a closed form for an arbitrary distribution of the initial beam profile. We have also investigated the phase transition to the spatial Bloch-like oscillations by adding a linear gradient to the propagation constant of each waveguides ($ α$). Our analytical results s…
We present an analysis of modulational instability of diffractionless waves in a face-centered square lattice of waveguides featuring non-Kerr nonlinearity, which are constituted by a combination of positive and negative refractive indices. The unit cell of the lattice consists of three different waveguides with different optical properties. The dispersion curve of the lattice supports flat bands and thereby the base equations describing the model have particular solutions that correspond to the diffractionless waves propagating along the waveguides. We also observe a unique ramification of no…
We report on the experimental observation of two-dimensional surface solitons residing at the interface between a homogeneous square lattice and a superlattice that consists of alternating "deep" and "shallow" waveguides. By exciting single waveguides in the first row of the superlattice, we show that solitons centered on deep sites require much lower powers than their respective counterparts centered on shallow sites. Despite the fact that the average refractive index of the superlattice waveguides is equal to the refractive index of the homogeneous lattice, the interface results in clearly a…
Two-dimensional (2D) coupled resonant optical waveguide (CROW), exhibiting topological edge states, provides an efficient platform for designing integrated topological photonic devices. In this paper, we propose an experimentally feasible design of 2D honeycomb CROW photonic structure. The characteristic optical system possesses two-fold and three-fold Dirac points at different positions in the Brillouin zone. The effective gauge fields implemented by the intrinsic pseudo-spin-orbit interaction open up topologically nontrivial bandgaps through the Dirac points. Spatial lattice geometries allow…
We study the cooperative optical coupling between regularly spaced atoms in a one-dimensional waveguide using decompositions to subradiant and superradiant collective excitation eigenmodes, direct numerical solutions, and analytical transfer-matrix methods. We illustrate how the spectrum of transmitted light through the waveguide including the emergence of narrow Fano resonances can be understood by the resonance features of the eigenmodes. We describe a method based on superradiant and subradiant modes to engineer the optical response of the waveguide and to store light. The stopping of light…
Co-existence and interplay between mesoscopic light dynamics with singular optics in spatially random but temporally coherent disordered waveguide lattices is reported. Two CW light beams of 1.55 micron operating wavelength are launched as inputs to 1D waveguide lattices with controllable weak disorder in refractive index profile. Direct observation of phase singularities in the speckle pattern along the length is numerically demonstrated. Quantitative analysis of onset of such singular behavior and diffusive wave propagation is analyzed for the first time.
In the present work, we examine "binary" waveguide arrays, where the coupling between adjacent sites alternates between two distinct values $C_1$ and $C_2$ and a saturable nonlinearity is present on each site. Motivated by experimental investigations of this type of system in fabricated LiNbO$_3$ arrays, we proceed to analyze the nonlinear wave excitations arising in the self-defocusing nonlinear regime, examining, in particular, dark solitons and bubbles. We find that such solutions may, in fact, possess a reasonably wide, experimentally relevant parametric interval of stability, while they m…
Kagome lattice is a two-dimensional network of corner-sharing triangles and is often associated with geometrical frustration. In particular, the frustrated coupling between waveguide modes in a kagome array leads to a dispersionless flat band consisting of spatially localized modes. Here we propose a complex photonic lattice by placing $\mathcal{PT}$-symmetric dimers at the kagome lattice points. Each dimer corresponds to a pair of strongly coupled waveguides. With balanced arrangement of gain and loss on individual dimers, the system exhibits a $\mathcal{PT}$-symmetric phase for finite gain/l…
We propose a novel geometry for integrated photonic devices that can be used as isolators and polarization splitters based on engineered photonic lattices. Starting from optical waveguide arrays that mimic Fock space representation of a non-interacting two-site Bose Hubbard Hamiltonian, we show that introducing magneto-optic nonreciprocity to these structures leads to a superior optical isolation performance. In the forward propagation direction, an input TM polarized beam experiences a perfect state transfer between the input and output waveguide channels while surface Bloch oscillations bloc…
Waveguide arrays offer enormous potential to design circuit elements essential to fabricate optical devices capable to processing information codified by light. In this work we study the existence and stability of localized beams in one dimensional photonic lattices composed by a Kerr type waveguide array. We analyzed the case where discrete translation symmetry is broken in as much as one of the waveguides lacks a nonlinear response. Specifically, we determined the space of parameters where a coherent and robust mobility across the lattice is achieved. Moreover, we calculate the reflection an…
