Two-dimensional Photonic Lattices Research Articles

Edge-dependent anomalous topology in synthetic photonic lattices subject to discrete step walks

Anomalous topological phases, where edge states coexist with topologically trivial Chern bands, can only appear in periodically driven lattices. When the driving is smooth and continuous, the bulk-edge correspondence is guaranteed by the existence of a bulk invariant known as the winding number. However, in lattices subject to periodic discrete step walks the existence of edge states does not only depend on bulk invariants but also on the boundary. This is a consequence of the absence of an intrinsic time dependence or micromotion in discrete step walks. We report the observation of edge states and a simultaneous measurement of the bulk invariants in anomalous topological phases in a two-dimensional synthetic photonic lattice subject to discrete step walks. The lattice is implemented using time multiplexing of light pulses in two coupled fibre rings, in which one of the dimensions displays real-space dynamics and the other one is parametric. The presence of edge states is inherent to the periodic driving and depends on the properties of the boundary in the implemented two-band model with zero Chern number. We provide a suitable expression for the topological invariants whose calculation does not rely on micromotion dynamics. Published by the American Physical Society 2024

Photonic Floquet Skin-Topological Effect.

Non-Hermitian skin effect and photonic topological edge states are of great interest in non-Hermitian physics and optics. However, the interplay between them is largely unexplored. Here, we propose and demonstrate experimentally the non-Hermitian skin effect constructed from the nonreciprocal flow of Floquet topological edge states, which can be dubbed "Floquet skin-topological effect." We first show the non-Hermitian skin effect can be induced by structured loss when the one-dimensional (1D) system is periodically driven. Next, based on a two-dimensional (2D) Floquet topological photonic lattice with structured loss, we investigate the interaction between the non-Hermiticity and the topological edge states. We observe that all the one-way edge states are imposed onto specific corners, featuring both the non-Hermitian skin effect and topological edge states. Furthermore, a topological switch for the skin-topological effect is presented by utilizing the phase-transition mechanism. Our experiment paves the way for realizing non-Hermitian topological effects in nonlinear and quantum regimes.

Topological states switching and group velocity control in two-dimensional non-reciprocal Hermitian photonic lattice

We proposed a model with non reciprocal coupling coefficients, in which the imaginary parts γ indicate the phase delay or exceed term. The distributions of band structure and the group velocity are both characterized as a function of the coupling. we studied the system’s topological states and group velocity control. The results show that the movement and breaking of Dirac points exist in the energy band of the system. By changing the coupling coefficients, the conversion between any topological states corresponds to different Chern number. Topological edge states exist in topological non-trivial systems that correspond to the two different Chern numbers. Besides, it is also found that both the coupling coefficient and the wave vector can cause the oscillation of the pulse group velocity. At the same time, the topological state can suppress the amplitude of the group velocity profiles. Our findings enrich the theory of light wave manipulation in high-dimensional photonic lattices and provide a novel view for realizing linear localization and group velocity regulation of light waves, which has potential application in high-speed optical communication and quantum information fields.

Isolated flat bands in 2D lattices based on a novel path-exchange symmetry

The increased ability to engineer two-dimensional (2D) systems, either using materials, photonic lattices, or cold atoms, has led to the search for 2D structures with interesting properties. One such property is the presence of flat bands. Typically, the presence of these requires long-ranged hoppings, fine-tuning of nearest neighbor hoppings, or breaking time-reversal symmetry by using a staggered flux distribution in the unit cell. We provide a prescription based on carrying out projections from a parent system to generate different flat band systems. We identify the conditions for maintaining the flatness and identify a path-exchange symmetry in such systems that cause the flat band to be degenerate with the other dispersive ones. Breaking this symmetry leads to lifting the degeneracy while still preserving the flatness of the band. This technique does not require changing the topology nor breaking time-reversal symmetry as was suggested earlier in the literature. The prescription also eliminates the need for any fine-tuning. Moreover, it is shown that the subsequent projected systems inherit the precise fine-tuning conditions that were discussed in the literature for similar systems, in order to have and isolate a flat band. As examples, we demonstrate the use of our prescription to arrive at the flat band conditions for popular systems like the Kagomé, the Lieb, and the Dice lattices. Finally, we are also able to show that a flat band exists in a recently proposed chiral spin-liquid state of the Kagomé lattice only if it is associated with a gauge field that produces a flux modulation of the Chern-Simons type.

Loss Difference Induced Localization in a Non-Hermitian Honeycomb Photonic Lattice.

Non-Hermitian systems with complex-valued energy spectra provide an extraordinary platform for manipulating unconventional dynamics of light. Here, we demonstrate the localization of light in an instantaneously reconfigurable non-Hermitian honeycomb photonic lattice that is established in a coherently prepared atomic system. One set of the sublattices is optically modulated to introduce the absorptive difference between neighboring lattice sites, where the Dirac points in reciprocal space are extended into dispersionless local flat bands, with two shared eigenstates: low-loss (high-loss) one with fields confined at sublattice B (A). When these local flat bands are broad enough due to larger loss difference, the incident beam with its tangential wave vector being at the K point in reciprocal space is effectively localized at sublattice B with weaker absorption, namely, the commonly seen power exchange between adjacent channels in photonic lattices is effectively prohibited. The current work unlocks a new capability from non-Hermitian two-dimensional photonic lattices and provides an alternative route for engineering tunable local flat bands in photonic structures.

Corner states in photonic higher-order Dirac semimetals

The introduction of higher-order topological insulators featuring topological corner states has been an extremely active topic for the generation of confined modes. Recent studies show that corner states are not an exclusive feature of topological insulators but can also exist as bound states in the continuum (BIC). This suggests that corner states may exist in different topological phases that exhibit a higher-order character, beyond the conventional bulk-edge correspondence. In this paper, we show that corner states can appear in a higher-order Dirac semimetal phase of a two-dimensional photonic lattice. Such a lattice displays a dispersion relationship with a fourfold degeneracy, which serves to induce a higher-order topological phase transition, leaving a Dirac point between two edge bands. Just as Dirac modes exist in regular lattice defects, the nonconventional bulk-edge-corner correspondence leads to corner states in the Dirac semimetal phase. Notably, the induced corner state exhibits an algebraic decay characteristic of long-range interactions, predicted by the massless Dirac equation. The analysis of the field profile and quality factors indicates that the state is not a BIC, but rather a corner-Dirac state. We show that if the photonic lattice does not present a higher-order phase transition the existence of the corner-Dirac state does not arise. The results obtained in this paper indicate that corner states can exist throughout the entire topological phase transition process, even in the semimetal phase, and pave the way to generate light-matter interactions with such a photonic bath.

Photonic quadrupole topological insulator using orbital-induced synthetic flux

The rich physical properties of multiatomic crystals are determined, to a significant extent, by the underlying geometry and connectivity of atomic orbitals. The mixing of orbitals with distinct parity representations, such as s and p orbitals, has been shown to be useful for generating systems that require alternating phase patterns, as with the sign of couplings within a lattice. Here we show that by breaking the symmetries of such mixed-orbital lattices, it is possible to generate synthetic magnetic flux threading the lattice. We use this insight to experimentally demonstrate quadrupole topological insulators in two-dimensional photonic lattices, leveraging both s and p orbital-type modes. We confirm the nontrivial quadrupole topology by observing the presence of protected zero-dimensional states, which are spatially confined to the corners, and by confirming that these states sit at mid-gap. Our approach is also applicable to a broader range of time-reversal-invariant synthetic materials that do not allow for tailored connectivity, and in which synthetic fluxes are essential.

Thermal control of the topological edge flow in nonlinear photonic lattices

The chaotic evolution resulting from the interplay between topology and nonlinearity in photonic systems generally forbids the sustainability of optical currents. Here, we systematically explore the nonlinear evolution dynamics in topological photonic lattices within the framework of optical thermodynamics. By considering an archetypical two-dimensional Haldane photonic lattice, we discover several prethermal states beyond the topological phase transition point and a stable global equilibrium response, associated with a specific optical temperature and chemical potential. Along these lines, we provide a consistent thermodynamic methodology for both controlling and maximizing the unidirectional power flow in the topological edge states. This can be achieved by either employing cross-phase interactions between two subsystems or by exploiting self-heating effects in disordered or Floquet topological lattices. Our results indicate that photonic topological systems can in fact support robust photon transport processes even under the extreme complexity introduced by nonlinearity, an important feature for contemporary topological applications in photonics.

Higher-order topological biphoton corner states in two-dimensional photonic lattices

Higher-order topological insulators have attracted great interest for their unconventional bulk-boundary correspondence especially gapless corner states. Here, we realize topological biphoton corner states in two-dimensional lattices. In addition to the striking state localization, the correlations in topologically nontrivial cases are more than 60 times higher than those in trivial cases and the visibility of Hong-Ou-Mandel interference for output topological corner-entangled states is higher than 90.3%. We confirm that the second-order photonic topological insulators support stable biphoton states that can maintain spatial distributions in high-dimensional Hilbert space, which have potential applications in quantum algorithms, simulation, and computation.

Numerical methods for generation and characterization of disordered aperiodic photonic lattices.

We introduce numerical modeling of two different methods for the deterministic randomization of two-dimensional aperiodic photonic lattices based on Mathieu beams, optically induced in a photorefractive media. For both methods we compare light transport and localization in such lattices along the propagation, for various disorder strengths. A disorder-enhanced light transport is observed for all disorder strengths. With increasing disorder strength light transport becomes diffusive-like and with further increase of disorder strength the Anderson localization is observed. This trend is more noticeable for longer propagation distances. The influence of input lattice intensity on the localization effects is studied. The difference in light transport between two randomization methods is attributed to various levels of input lattice intensity. We observe more pronounced localization for one of the methods. Localization lengths differ along different directions, due to the crystal and lattice anisotropy. We analyze localization effects comparing uniform and on-site probe beam excitation positions and different probe beam widths.

Observing two-particle Anderson localization in linear disordered photonic lattices.

We theoretically and systematically investigate Anderson localization of two bosons with nearest-neighbor interaction in one dimension under short- and long-time scales, two types of disorders, and three types of initial states, which can be directly observed in linear disordered photonic lattices via two experimentally measurable physical quantities, participation ratio and spatial correlation. We find that the behavior of localization characterized by the participation ratio depends on the strength of interaction and the type of disorder and initial condition. Two-boson spatial correlation reveals more novel and unique features. In the ordered case, two types of two-boson bindings and bosonic "fermionization" are shown, which are intimately attributed to the band structure of the system. In the disordered case, the impact of interaction on the two-boson Anderson localization is reexamined and the joint effect of disorder and interaction is addressed. We further demonstrate that the independence of the participation ratio or spatial correlation on the sign of interaction can be eliminated by employing an initial state that breaks one of two specific symmetries. Finally, we elucidate the relevant details of the experimental implementation in a two-dimensional linear photonic lattice.

Linearized theory of the fluctuation dynamics in two-dimensional topological lasers

We theoretically study the collective excitation modes of a topological laser device operating in a single-mode steady-state with monochromatic emission. We consider a model device based on a two-dimensional photonic Harper-Hofstadter lattice including a broadband gain medium localized on the system edge. Different regimes are considered as a function of the value of the optical nonlinearity and of the gain relaxation time. The dispersion of the excitation modes is calculated via a full two-dimensional Bogoliubov approach and physically interpreted in terms of an effective one-dimensional theory. Depending on the system parameters, various possible physical processes leading to dynamical instabilities are identified and characterized. On this basis, strategies to enforce a stable single-mode topological laser operation are finally pointed out.

Fundamental and vortex gap solitons in quasiperiodic photonic lattices.

We address the existence and stability of fundamental, single-charged vortex, and double-charged vortex gap solitons in two-dimensional quasiperiodic photonic lattices imprinted in a Kerr-type medium. Fundamental and vortex gap solitons can bifurcate from linear localized states or their combination supported by quasiperiodic lattices for both defocusing and focusing nonlinearities. We find that the three types of solitons mentioned above are stable in the entire existence domain for defocusing nonlinearities, and that they can also be stable at a lower power level for focusing nonlinearities. At higher power, unstable solitons are characterized by a ring-shaped symmetry-breaking distribution, and the unique spot profile formed is repeatedly observed with changes in propagation distance.

Diffraction propagation of light wave and image distortionless transmission in ten-fold symmetric photonic quasicrystal lattices

Linear propagation behavior of light wave in two-dimensional ten-fold symmetric photonic quasicrystal lattices was studied numerically by using beam propagation method. The influences of structural characteristics and parameter changes of the quasicrystal lattices on the propagation and suppression of light wave diffraction are analyzed, and the results are also compared with those in periodic square lattices. We investigate the linear transverse light localization in the quasicrystal lattices without defects. The results indicate that the quasicrystal lattices are easier to achieve linear light localization than the periodic lattices. In addition, we demonstrate the distortionless transmission of light-spot images can be achieved in the quasicrystal lattices by numerical simulation. In this way, more complex light-spot images can be transmitted in photonic quasicrystal arrays which are consisting of multiple basic units of quasicrystal lattices. It has potential applications for optical information transmission and all optical signal processing.

Fundamental entropic processes in the theory of optical thermodynamics

We study the statistical behavior of multimoded optical systems under equilibrium conditions. We investigate the role of variations of the system parameters in the thermodynamic description and derive, an optical analogue of the first law of thermodynamics, a generic expression for the work done to the system, and an optical Gibbs-Duhem equation. To demonstrate these effects, we focus in the case of two-dimensional photonic lattices. We study the conditions under which the entropy in such waveguide arrays can be considered as extensive. In this respect, small deviations from the extensive character of the entropy give rise to stress and strain terms. We examine how the conservation laws in such array configurations are affected by variations in the system parameters, and furthermore, we analyze the respective thermodynamic processes (isentropic and Joule-type expansions).

Dimensional Transformations of Guided-Mode Resonant Photonic Lattices

Reflection spectra based on guided-mode resonance (GMR) are simulated and discussed with transformation between one-dimensional (1-D) and two-dimensional (2-D) photonic lattices by introducing intermediate structures consisting of vertically-stacked 1-D and 2-D gratings. Dependences of reflection spectra on a 2-D fractional ratio are investigated for two examples of narrowband and broadband resonance elements. Observed complicated spectrum transformations for the narrowband example are successfully explained by combining simple models with guided-mode indices and multilayer reflection. The understanding of the fundamental transformation dynamics will aid in the reflection band engineering for development of new optical components.

Polarization independent enhancement of zeroth order diffracted second harmonic from multilayer gallium selenide on a silicon resonant metasurface.

We demonstrate polarization-independent resonant-enhancement of second harmonic generation (SHG) from multilayer Gallium Selenide (GaSe) on a silicon-based resonant metasurface. Two-dimensional hexagonal photonic lattice with circularly symmetric silicon meta-atoms are designed to achieve resonant field enhancement at the fundamental wavelength independent of the incident polarization direction. Such structures are however found to exhibit strong resonant field depolarization effects at the fundamental excitation fields resulting in modified nonlinear polarization components when compared to the native GaSe layer. Furthermore, the sub-wavelength metasurface designed to have resonances at the fundamental wavelengths act as a higher order diffraction grating at the second harmonic wavelength. Nonlinear wave propagation simulations show that the higher order diffracted SHG exhibit strong polarization dependent enhancement with characteristics very different from the native GaSe layer. In this context, polarization independent enhancement of the second harmonic signal is achieved only for the zeroth order diffracted component. Experimental study of second harmonic generation from the GaSe layer integrated with the silicon metasurface shows maximum nonlinear signal enhancement on-resonance with polarization dependence identical to the native GaSe layer by selectively detecting the zeroth-order diffracted component. This work shows that it is not sufficient to use symmetric meta-atoms in such 2D material integrated resonant metasurfaces for achieving polarization independent nonlinear optical enhancement. Depolarization of the resonant fields and higher-order diffraction at the nonlinear signal wavelength need to be considered as well.

Localized modes in a two-dimensional lattice with a pluslike geometry.

We investigate analytically and numerically the existence and dynamical stability of different localized modes in a two-dimensional photonic lattice comprising a square plaquette inscribed in the dodecagon lattices. The eigenvalue spectrum of the underlying linear lattice is characterized by a net formed of one flat band and four dispersive bands. By tailoring the intersite coupling coefficient ratio, opening of gaps between two pairs of neighboring dispersive bands can be induced, while the fully degenerate flat band characterized by compact eigenmodes stays nested between two inner dispersive bands. The nonlinearity destabilizes the compact modes and gives rise to unique families of localized modes in the newly opened gaps, as well as in the semi-infinite gaps. The governing mechanism of mode localization in that case is the light energy self-trapping effect. We have shown the stability of a few families of nonlinear modes in gaps. The suggested lattice model may serve for probing various artificial flat-band systems such as ultracold atoms in optical lattices, periodic electronic networks, and polariton condensates.

A quantum chaos study on the localization of light in a resonator-based photonic crystal

We explore the issue of eigenstate localization in a two-dimensional photonic resonator lattice. In the system of our purpose, by harmonically modulating coupling constants between the resonators an effective magnetic field is imposed on the motion of a photon. From the study on the spectral fluctuantions and participation ration of eigenstates we proceed our aim. We find that the localization properties of the studied system do not change significantly in the region of small phases. In this regime a strong delocalized character is revealed. Conversely, for larger phases a great tendency to localization is seen.

Localization and delocalization of light in photonic moiré lattices.

Moiré lattices consist of two superimposed identical periodic structures with a relative rotation angle. Moiré lattices have several applications in everyday life, including artistic design, the textile industry, architecture, image processing, metrology and interferometry. For scientific studies, they have been produced using coupled graphene-hexagonal boron nitride monolayers1,2, graphene-graphene layers3,4 and graphene quasicrystals on a silicon carbide surface5. The recent surge of interest in moiré lattices arises from the possibility of exploring many salient physical phenomena in such systems; examples include commensurable-incommensurable transitions and topological defects2, the emergence of insulating states owing to band flattening3,6, unconventional superconductivity4 controlled by the rotation angle7,8, the quantum Hall effect9, the realization of non-Abelian gauge potentials10 and the appearance of quasicrystals at special rotation angles11. A fundamental question that remains unexplored concerns the evolution of waves in the potentials defined by moiré lattices. Here we experimentally create two-dimensional photonic moiré lattices, which-unlike their material counterparts-have readily controllable parameters and symmetry, allowing us to explore transitions between structures with fundamentally different geometries (periodic, general aperiodic and quasicrystal). We observe localization of light in deterministic linear lattices that is based on flat-band physics6, in contrast to previous schemes based on light diffusion in optical quasicrystals12, where disorder is required13 for the onset of Anderson localization14 (that is, wave localization in random media). Using commensurable and incommensurable moiré patterns, we experimentally demonstrate the two-dimensional localization-delocalization transition of light. Moiré lattices may feature an almost arbitrary geometry that is consistent with the crystallographic symmetry groups of the sublattices, and therefore afford a powerful tool for controlling the properties of light patterns and exploring the physics of periodic-aperiodic phase transitions and two-dimensional wavepacket phenomena relevant to several areas of science, including optics, acoustics, condensed matter and atomic physics.