We experimentally demonstrate the photonic realization of a dispersionless flat-band in a quasi-one-dimensional photonic lattice fabricated by ultrafast laser inscription. In the nearest neighbor tight binding approximation, the lattice supports two dispersive and a non-dispersive (flat) band. We experimentally excite superpositions of flat-band eigen modes at the input of the photonic lattice and show the diffractionless propagation of the input states due to their infinite effective mass. In the future, the use of photonic rhombic lattices, together with the successful implementation of a synthetic gauge field, will enable the observation of Aharonov-Bohm photonic caging.
We demonstrate that a flat-band state in a quasi-one-dimensional rhombic lattice is robust in the presence of external drivings along the lattice axis. The lattice was formed by periodic arrays of evanescently coupled optical waveguides, and the external drivings were realized by modulating the paths of the waveguides. We excited a superposition of flat-band eigenmodes at the input and observed that this state does not diffract in the presence of static as well as high-frequency sinusoidal drivings. This robust localization is due to destructive interference of the analogous wavefunction and i…
We demonstrate experimentally the existence of compact localized states (CLSs) in a quasi-one-dimensional photonic rhombic lattice in presence of two distinct refractive-index gradients (i.e., a driven lattice ribbon) acting as external direct current (dc) electric fields. Such a lattice is composed of an array of periodically arranged evanescently coupled waveguides, which hosts a perfect flatband that touches both remaining dispersive bands when it is not driven. The external driving is realized by modulating the relative writing beam intensity of adjacent waveguides. We find that a y-gradie…
Flatband photonic lattices, i.e. arrays of waveguides or resonators displaying a flat Bloch band, offer new routes for light trapping and distortion-free imaging. Here it is shown that flatland lattices can show stable and cooperative laser emission when optical gain is supplied to the system, despite the large degree of degeneracy of flatland supermodes. By considering a quasi one-dimensional rhombic lattice of coupled semiconductor microrings, selective pumping of the outer sublattices can induce cooperative lasing in a supermode of the flat band
We report on the experimental realization of a uniform synthetic magnetic flux and the observation of Aharonov-Bohm cages in photonic lattices. Considering a rhombic array of optical waveguides, we engineer modulation-assisted tunneling processes that effectively produce non-zero magnetic flux per plaquette. This synthetic magnetic field for light can be tuned at will by varying the phase of the modulation. In the regime where half a flux quantum is realized in each plaquette, all the energy bands dramatically collapse into non-dispersive (flat) bands and all eigenstates are completely localiz…
We show experimentally how a non-diffracting state can be excited in a photonic Lieb lattice. This lattice supports three energy bands, including a perfectly flat middle band, which corresponds to an infinite effective mass with zero dispersion. We show that a suitable optical input state can be prepared so as to only excite the flat band. We analyse, both experimentally and theoretically, the evolution of such photonic flat-band states, and show their remarkable robustness, even in the presence of disorder.
We observe Wannier-Stark localization in curved photonic lattices, realized using arrays of evanescently coupled optical waveguides. By correctly tuning the strength of inter-site coupling in the lattice, we observe that Wannier-Stark states become increasingly localized, and eventually fully localized to one site, as the curvature of the lattice is increased. We then demonstrate that tunneling can be successfully restored in the lattice by applying a sinusoidal modulation to the lattice position, an effect that is a direct analogue of photon-assisted tunneling. This precise tuning of the tunn…
We report on singular and nonsingular flat bands in a Sierpinski fractal-like photonic lattice. We demonstrate that the the lowest two bands, being isolated and degenerate due to geometrical frustration, are nonsingular and thus can be spanned by a complete set of compact localized states. We experimentally prove these states to propagate diffractionless in the photonic lattice. Our results reveal the interplay between geometrical frustration, degenerate flat bands and compact localized states in a single photonic lattice, and pave the way to photonic spin liquid ground states.
Near the band edge of photonic crystal waveguides, localized modes appear due to disorder. We demonstrate a new method to elucidate spatial profile of the localized modes in such systems using precise local tuning. Using deconvolution with the known thermal profile, the spatial profile of a localized mode with quality factor ($Q$) $>10^5$ is successfully reconstructed with a resolution of $2.5 \ μ$m.
We measure the spatial extent of individual localized photonic states in a slow-light photonic crystal waveguide. The size of the states is measured by perturbing each state individually through a local electromagnetic interaction with a near-field probe. We find localized states which are not observed in transmission and show that these states are shorter than the waveguide. We also directly obtain near-field measurements of the participation ratio, from which the size of the states can be derived, in quantitative agreement with the size measured with the perturbation method.
We overview our recent results on the nonlinear localized modes in two-dimensional (2D) photonic crystals and photonic-crystal waveguides. Employing the technique based on the Green function, we describe the existence domains for nonlinear guided modes in photonic crystal waveguides and study their unique properties including bistability. We also show that low-amplitude nonlinear modes near the band edge of a reduced-symmetry 2D square-lattice photonic crystals, which are usually unstable, can be stabilized due to effective long-range linear and nonlinear interactions.
We study a nonlinear Glauber-Fock lattice and the conditions for the excitation of localized structures. We investigate the particular linear properties of these lattices, including linear localized modes. We investigate numerically nonlinear modes centered in each site of the lattice. We found a strong disagreement of the general tendency between the stationary and the dynamical excitation thresholds, and we give a new definition based on both considerations.
Photonic lattices have emerged as a promising approach to localize light in space, for example, through topologically protected edge states and Aharonov-Bohm caging. They are of particular importance in the study of flat band systems via the associated nondiffracting compact localized states. However, such states typically appear static, thus not allowing adaptive or evolutionary features of light localization. Here we report on the first experimental realization of an oscillating compact localized state (OCLS). We observe an oscillatory intensity beating during propagation in a two-dimensiona…
The localization of light in flat-band lattices has been recently proposed and experimentally demonstrated in several configurations, assuming a classical description of light. Here, we study the problem of light localization in the quantum regime. We focus on quasi one-dimensional and two-dimensional lattices which exhibit a perfect flat-band inside their linear spectrum. Localized quantum states are constructed as eigenstates of the interaction Hamiltonian with a vanishing eigenvalue and a well defined total photon number. These are superpositions of Fock states with probability amplitudes g…
A photonic jet (terajet at THz frequencies) commonly denotes a specific spatially localized region in the near-field at the front side of a dielectric particle with diameter comparable with wavelength illuminated with a plane wave from its backside (i.e., the jet emerges from the shadow surface of a dielectric particle). In this paper the formation of photonic is demonstrated using the recently proposed 3D dielectric cuboids working in reflection mode when the specific spatially localized region is localized towards the direction of incidence wavefront. The results of simulations based on Fini…
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.
We investigate the use of guided modes bound to defects in photonic crystals for achieving double resonances. Photoluminescence enhancement by more than three orders of magnitude has been observed when the excitation and emission wavelengths are simultaneously in resonance with the localized guided mode and cavity mode, respectively. We find that the localized guided modes are relatively insensitive to the size of the defect for one of the polarizations, allowing for flexible control over the wavelength combinations. This double resonance technique is expected to enable enhancement of photolum…
A development and an application of the localized function method based on the Galerkin method applying a set of Sine functions to approximate the unknown mode fields of the localized modes propagating along the photonic crystal fibres is proposed. A way for considerably reducing the number of integrals in the case of symmetrical holes shapes with respect to the axes of coordinate systems located at the centers of the holes, circular, elliptical etc., is also presented. The method does not require an expansion of the refractive index and thus inaccuracies of the expansion can be avoided. In th…
We present a numerical study on photonic bandgap and bandedge modes in the golden-angle spiral array of air cylinders in dielectric media. Despite the lack of long-range translational and rotational order, there is a large PBG for the TE polarized light. Due to spatial inhomogeneity in the air hole spacing, the bandedge modes are spatially localized by Bragg scattering from the parastichies in the spiral structure. They have discrete angular momenta that originate from different families of the parastichies whose numbers correspond to the Fibonacci numbers. The unique structural characteristic…
We predict a generic mechanism of wave localization at an interface between uniform gauge fields, arising due to propagation-dependent phase accumulation similar to Aharonov-Bohm phenomenon. We realize experimentally a photonic mesh lattice with real-time control over the vector gauge field, and observe robust localization under a broad variation of gauge strength and direction, as well as structural lattice parameters. This suggests new possibilities for confining and guiding waves in diverse physical systems through the synthetic gauge fields.
We show that point defects in two-dimensional photonic crystals can support bound states in the continuum (BICs). The mechanism of confinement is a symmetry mismatch between the defect mode and the Bloch modes of the photonic crystal. These BICs occur in the absence of bandgaps and therefore provide an alternative mechanism to confine light. Furthermore, we show that such BICs can propagate in a fiber geometry and exhibit arbitrarily small group velocity which could serve as a platform for enhancing non-linear effects and light-matter interactions in structured fibers.
Light localization due to random imperfections in periodic media is paramount in photonics research. The group index is known to be a key parameter for localization near photonic band edges, since small group velocities reinforce light interaction with imperfections. Here, we show that the size of the smallest localized mode that is formed at the band edge of a one-dimensional periodic medium is driven instead by the effective photon mass, i.e. the flatness of the dispersion curve. Our theoretical prediction is supported by numerical simulations, which reveal that photonic-crystal waveguides c…
We predict the coexistence of both TE- and TM-polarized localized electromagnetic waves that can propagate \emph{in the same frequency range} along a graphene layer inserted in a photonic crystal. In addition, we studied the excitation of these modes by an external wave and have shown that the resonance peaks of the sample transmissivity should be observed due to the excitation of the localized waves, independently of the polarization of the exciting wave. The simplicity of the derived dispersion relations for the localized modes and the possibility to excite waves of both polarizations provid…
Optical nanostructures have proven to be meritorious for tailoring the emission properties of quantum emitters. However, unavoidable fabrication imperfections may represent a nuisance. Quite remarkably, disorder offers new opportunities since light can be efficiently confined by random multiple scattering leading to Anderson localization. Here we investigate the effect of such disorder-induced cavities on the emission dynamics of single quantum dots embedded in disordered photonic-crystal waveguides. We present time-resolved measurements of both the total emission from Anderson-localized cavit…
We demonstrate lasing in GaAs photonic crystal waveguides with InAs quantum dots as gain medium. Structural disorder is present due to fabrication imperfection and causes multiple scat- tering of light and localization of light. Lasing modes with varying spatial extend are observed at random locations along the guide. Lasing frequencies are determined by the local structure and occur within a narrow frequency band which coincides with the slow light regime of the waveguide mode. The three-dimensional numerical simulation reveals that the main loss channel for lasing modes located away from the…
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…
Wannier function expansions are well suited for the description of photonic- crystal-based defect structures, but constructing maximally localized Wannier functions by optimizing the phase degree of freedom of the Bloch modes is crucial for the efficiency of the approach. We systematically analyze different locality criteria for maximally localized Wannier functions in two- dimensional square and triangular lattice photonic crystals, employing (local) conjugate-gradient as well as (global) genetic-algorithm-based, stochastic methods. Besides the commonly used second moment (SM) locality measur…
We investigate analytically and numerically the formation of temporal localized structures in all photonic crystal fiber resonator. These dissipative structures consist of isolated or randomly distributed peaks in an uniform background of the intensity profile. The number of peaks and their temporal distribution are determined solely by initial conditions. They exhibit multistability behavior in a finite range of parameters. A weakly nonlinear analysis is performed in the neighborhood of the first threshold associated with the modulational instability. We consider the regime where the instabil…
A general analysis of undistorted propagation of localized wavepackets in photonic crystals based on a Wannier-function expansion technique is presented. Different kinds of propagating and stationary spatio-temporal localized waves are found from an asymptotic analysis of the Wannier function envelope equation.
The interaction of optical and acoustic waves via stimulated Brillouin scattering (SBS) has recently reached on-chip platforms, which has opened new fields of applications ranging from integrated microwave photonics and on-chip narrow-linewidth lasers, to phonon-based optical delay and signal processing schemes. Since SBS is an effect that scales exponentially with interaction length, on-chip implementation on a short length scale is challenging, requiring carefully designed waveguides with optimized opto-acoustic overlap. In this work, we use the principle of Brillouin optical correlation dom…
What is the role of topology in the propagation of quantum light in photonic lattices? We address this question by studying the propagation of squeezed states in a topological one-dimensional waveguide array, benchmarking our results with those for a topologically trivial localized state, and studying their robustness against disorder. Specifically, we study photon statistics, one-mode and two-mode squeezing, and entanglement generation when the localized state is excited with squeezed light. These quantum properties inherit the shape of the localized state but, more interestingly, and unlike …
Mechanical motion of photonic devices driven by optical forces provides a profound means of coupling between optical fields. The current focus of these optomechanical effects has been on cavity optomechanics systems in which co-localized optical and mechanical modes interact strongly to enable wave-mixing between photons and phonons and backaction cooling of mechanical modes. Alternatively, extended mechanical modes can also induce strong nonlocal effects on propagating optical fields or multiple localized optical modes at distances. Here, we demonstrate a novel multi-cavity optomechanical dev…
Efficient on-chip integration of single-photon emitters imposes a major bottleneck for applications of photonic integrated circuits in quantum technologies. Resonantly excited solid-state emitters are emerging as near-optimal quantum light sources, if not for the lack of scalability of current devices. Current integration approaches rely on cost-inefficient individual emitter placement in photonic integrated circuits, rendering applications impossible. A promising scalable platform is based on two-dimensional (2D) semiconductors. However, resonant excitation and single-photon emission of waveg…
A localized defect mode in a photonic-layered structure develops nodal points. Placing a thin metallic layer at such a nodal point results in the phenomenon of induced transparency. We demonstrate that if this nodal point is not a point of symmetry, then even a tiny alteration of the permittivity in the vicinity of the defect suppresses the localized mode along with the resonant transmission; the layered structure becomes highly reflective within a broad frequency range. Applications of this hypersensitive transport for optical limiting and switching are discussed.
A major challenge in quantum optics and quantum information technology is to enhance the interaction between single photons and single quantum emitters. Highly engineered optical cavities are generally implemented requiring nanoscale fabrication precision. We demonstrate a fundamentally different approach in which disorder is used as a resource rather than a nuisance. We generate strongly confined Anderson-localized cavity modes by deliberately adding disorder to photonic crystal waveguides. The emission rate of a semiconductor quantum dot embedded in the waveguide is enhanced by a factor of 1…
In non-Hermitian quasicrystals, mobility edges (ME) separating localized and extended states in complex energy plane can arise as a result of non-Hermitian terms in the Hamiltonian. Such ME are of topological nature, i.e. the energies of localized and extended states exhibit distinct topological structures in the complex energy plane. However, depending on the origin of non-Hermiticity, i.e. asymmetry of hopping amplitudes or complexification of the incommensurate potential phase, different winding numbers are introduced, corresponding to different transport features in the bulk of the lattice…
We present, theoretically and experimentally, amorphous photonic lattices exhibiting a band-gap yet completely lacking Bragg diffraction: 2D waveguides distributed randomly according to a liquid-like model responsible for the absence of Bragg peaks as opposed to ordered lattices containing disorder, which always exhibit Bragg peaks. In amorphous lattices the bands are comprised of localized states, but we find that defect states residing in the gap are more localized than the Anderson localization length. Finally, we show how the concept of effective mass carries over to amorphous lattices.
In this article, localized linear defect modes due to bandgap guidance in two-dimensional photonic lattices with localized or non-localized defects are investigated theoretically. First, when the defect is localized and weak, eigenvalues of defect modes bifurcated from edges of Bloch bands are derived analytically. It is shown that in an attractive (repulsive) defect, defect modes bifurcate out from Bloch-band edges with normal (anomalous) diffraction coefficients. Furthermore, distances between defect-mode eigenvalues and Bloch-band edges are exponentially small functions of the defect streng…
We present a framework for the construction of solvable models of optical settings with genuinely two-dimensional landscapes of refractive index. The solutions of the associated non-separable Maxwell equations in paraxial approximation are found with the use of the time-dependent supersymmetry. We discuss peculiar theoretical aspects of the construction. Sufficient conditions for existence of localized states are discussed. Localized solutions vanishing for large $|\vec{x}|$, that we call light dots, as well as the guided modes that vanish exponentially outside the wave guides are constructed.…
We demonstrate theoretically and experimentally a novel type of localized beams supported by the combined effects of total internal and Bragg reflection in nonlinear two-dimensional square periodic structures. Such localized states exhibit strong anisotropy in their mobility properties, being highly mobile in one direction and trapped in the other, making them promising candidates for optical routing in nonlinear lattices.
Light transport in a dilute photonic crystal is considered. The analytical expression for the transmission coefficient is derived.Straightening of light under certain conditions in a one-dimensional photonic crystal is predicted. Such behavior is caused by the formation of a localized state in transversal motion. The main contribution to the central diffracted wave transmission coefficient is due to states, that either close to the conductance bands bottom or deeply localized in the forbidden gap. Both these states suppress mobility in the transverse direction and force light to be straightene…
Periodically structured materials can sustain both optical and mechanical modes. Here we investigate and observe experimentally the optomechanical properties of a conventional two-dimensional suspended photonic crystal defect cavity with a mode volume of $\sim$$3(λ/n)^{3}$. Two families of mechanical modes are observed: flexural modes, associated to the motion of the whole suspended membrane, and localized modes with frequencies in the GHz regime corresponding to localized phonons in the optical defect cavity of diffraction-limited size. We demonstrate direct measurements of the optomechanical…
The field of topological photonics was initiated with the realization of a Chern insulator phase in a gyromagnetic photonic crystal (PhC) with broken time-reversal symmetry (T), hosting chiral edge states that are topologically protected propagating modes. Recent advances in higher-order band topology have discovered another type of topological state, as manifested by those modes localized at the corners of a sample, which are known as corner states. Here we report the realization of a quadrupole higher-order topological insulator phase in a gyromagnetic PhC, induced by a topological phase tra…
We measure localized and extended mode profiles at the band edge of slow-light photonic-crystal waveguides using phase-sensitive near-field microscopy. High-resolution band structures are obtained and interpreted, allowing the retrieval of the optical density of states (DOS). This constitutes a first observation of the DOS of a periodic system with weak disorder. The Van Hove singularity in the DOS expected at the band edge of an ideal 1D periodic structure is removed by the disorder. The Anderson-localized states form a "tail" in the density of states, as predicted by Lifshitz for solid-state…
Flatband systems typically host "compact localized states"(CLS) due to destructive interference and macroscopic degeneracy of Bloch wave functions associated with a dispersionless energy band. Using a photonic Lieb lattice(LL), we show that conventional localized flatband states are inherently incomplete, with the missing modes manifested as extended line states which form non-contractible loops winding around the entire lattice. Experimentally, we develop a continuous-wave laser writing technique to establish a finite-sized photonic LL with specially-tailored boundaries, thereby directly obse…
In disordered two dimensional Chern insulators, a single bulk extended mode is predicted to exist per band, up to a critical disorder strength; all the other bulk modes are localized. This behavior contrasts strongly with topologically trivial two-dimensional phases, whose modes all become localized in the presence of disorder. Using a tight-binding model of a realistic photonic Chern insulator, we show that delocalized bulk eigenstates can be observed in an experimentally realistic setting. This requires the selective use of resonator losses to suppress topological edge states, and acquiring …
Localized crystallization of Ce:YIG thin films on Si using CO2 laser annealing for integrated nonreciprocal photonic device applications
National Engineering Research Centre of Electromagnetic Radiation Control Materials, University of Electronic Science and Technology of China（电磁辐射控制材料工程技术研究中心，电子科技大学）；State Key Laboratory of Electronic Thin-Films and Integrated Devices, University of Electronic Science and Technology of China（电子薄膜与集成器件国家重点实验室，电子科技大学）
