2D Photonic Lattices Research Articles

Coupling of photonic topological states and their dynamical control based on liquid crystal.

Optical field manipulation inspired by topology theory has recently drawn great research attention in nanophotonic. For flexible and programmable light management, the capacity to dynamically regulate the photonic topological states in fixed optical artificial microstructures is essential. Here, we propose a dynamic light manipulation of a two-dimensional (2D) photonic lattice aided by liquid crystals, which is composed of all-dielectric photonic crystals with distinct topological phases. In brief, by submerging the well-designed photonic lattice into a liquid crystal (LC), the topological edge and corner states can be actively modulated by applying external bias voltage, which offers an electrically switchable tuning capability, enabling the coupling between higher-order topological states in a structurally deterministic photonic structure. As a proof-of-principle, we use the 1D topological edge states and 0D topological corner states in one sample, respectively, to mimic line-waveguides and corner-cavities, and demonstrate their selective couplings with Fano-like profile driven by electric bias. Our work offers an effective and flexible way for light control in the potential active topological photonic devices.

Noncontractible loop states from a partially flat band in a photonic borophene lattice

Abstract Flat band systems are commonly associated with compact localized states (CLSs) that arise from the macroscopic degeneracy of eigenstates at the flat band energy. However, in the case of singular flat bands, conventional localized flat band states are incomplete, leading to the existence of noncontractible loop states (NLSs) with nontrivial real-space topology. In this study, we experimentally and analytically demonstrate the existence of NLSs in a 2D photonic borophene lattice without a CLS counterpart, owing to a band that is flat only along high-symmetry lines and dispersive along others. Our findings challenge the conventional notion that NLSs are necessarily linked to robust boundary modes due to a bulk-boundary correspondence. Protected by the band flatness that originates from band touching, NLSs play a significant role in investigating the fundamental physics of flat band systems.

Design and performance analysis of eight channel demultiplexer using 2D photonic crystal with trapezium cavity

In this work, an eight-channel dense wavelength division multiplexing demultiplexer is designed with a 2D photonic crystal triangular lattice. The proposed demultiplexer consists of a centre bus waveguide, an isosceles trapezium resonant cavity, and an eight-circular ring cavity (CR1, CR2, CR3, CR4, CR5, CR6, CR7, and CR8). The point defect resonant cavity consists of seven rods to drop different wavelengths from eight cavities, each of eight drop waveguides. The design is very simple to realise. The finite difference time domain and plane wave expansion method methods were used to analyse the proposed design’s band structure and transmission spectrum. The resonant wavelengths are 1.5441 μm, 1.5443 μm, 1.544 49 μm, 1.5447 μm, 1.5449 μm, 1.5451 μm, 1.5453 μm, and 1.5455 μm respectively. The proposed device provides a high-quality factor, transmission efficiency, and low crosstalk. The device’s footprint is 490.0 μm2, which can be easily incorporated into photonic integrated circuits.

Open investigation on the interaction length between a terahertz wave and an embedded dielectric ZRIM structure, and also phase tuning.

In this paper, we have focused on the near field behaviour of 2D Photonic Crystal-based dielectric zero refractive index metamaterial lattices with cylindrical silicon rods embedded in THz waveguides having PMC sidewalls. An "interaction length" is expected in both input and output sides of a ZRIM lattice, after illumination of a TE polarized THz electromagnetic wave. In other words, by getting closer than a specific distance to the ZRIM lattice area from both input and output sides, which is called the interaction length, the wave profile will be affected significantly. Studying the field profile variation in the output side of the ZRIM lattice, we have considered two separate cascaded 2D PC-based ZRIM lattices in a THz waveguide with the same conditions and computed spatial phase shifts, and also the transmission and reflection coefficients versus the displacement between the two ZRIM lattices. This small limited distance led us to an almost 34° phase shift tuning between THz waves in two (multiple) THz waveguide systems.

Area scalable and period manipulable three-dimensional optically induced photorefractive photonic periodic crystal or aperiodic quasicrystal

Abstract We experimentally investigate the formation of area-scalable three-dimensional (3D) photonic periodic crystal and aperiodic quasicrystal in an iron doped lithium niobate photorefractive material by multi-wedge prisms assisted compact and versatile single step optical induction approach. The induced large-area lattice microstructures are analyzed and verified by plane wave guiding, Brillouin-zone spectroscopy, far field diffraction pattern imaging, angle-dependent transmission spectra. Our technique can be easily expanded for the larger area of photonic periodic crystal or aperiodic quasicrystal microstructures. We also demonstrate experimentally and theoretically the manipulation to the period of 3D photorefractive photonic lattices by engineered vertex angle of multi-wedge prisms. The intensity analyses of interference light fields show that (1) the 3D photonic lattice has not only different Z-axis longitudinal structure, but also different X–Y front structure to the corresponding 2D photonic lattice, and (2) there exist three sets of sub-lattices which are mutually nested to form the 3D triangle photonic crystal.

Topological Edge States and Gap Solitons in the Nonlinear Dirac Model

AbstractTopological photonics has emerged recently as a novel approach for realizing robust optical circuitry, and the study of nonlinear effects in topological photonics is expected to open the door for tunability of photonic structures with topological properties. Here, the topological edge states and topological gap solitons which reside in the same band gaps described by the nonlinear Dirac model are studied, in both one and two dimensions. Strong nonlinear interactions between these dissimilar topological modes, manifested in the efficient excitation of topological edge states by scattered traveling gap solitons are revealed. Nonlinear tunability of localized states is explicated with exact analytical solutions for the two‐component spinor wave function. Our studies are complemented by spatiotemporal numerical modeling of the nonlinear scattering in 1D and 2D photonic lattices.

Topological phases and the bulk-edge correspondence in 2D photonic microring resonator lattices.

We show that 2D photonic lattices consisting of coupled microring resonators can emulate quantum systems driven by periodic Hamiltonians and can thus be used to realize photonic Floquet topological insulators. By transforming a 2D microring lattice into an equivalent array of coupled waveguides with periodic boundary conditions, we explicitly derive the Floquet-Bloch Hamiltonian of the system and determine the winding numbers characterizing the band topology and bulk-edge correspondence of the lattice. By varying the coupling strengths between adjacent resonators, we show that a 2D microring lattice can support both anomalous Floquet insulator edge modes and Chern insulator edge modes over a wide range of coupling parameters.

Line nodes, Dirac points, and Lifshitz transition in two-dimensional nonsymmorphic photonic crystals

Topological phase transitions, which have fascinated generations of physicists, are always demarcated by gap closures. In this work, we propose very simple 2D photonic crystal lattices with gap closure points, i.e. band degeneracies protected by nonsymmorphic symmetry. Our photonic structures are relatively easy to fabricate, consisting of two inequivalent dielectric cylinders per unit cell. Along high symmetry directions, they exhibit line degeneracies protected by glide reflection symmetry, which we explicitly demonstrate for $pg,pmg,pgg$ and $p4g$ nonsymmorphic groups. In the presence of time reversal symmetry, they also exhibit point degeneracies (Dirac points) protected by a $Z_2$ topological number associated with crystalline symmetry. Strikingly, the robust protection of $pg$-symmetry allows a Lifshitz transition to a type II Dirac cone across a wide range of experimentally accessible parameters, thus providing a convenient route for realizing anomalous refraction. Further potential applications include a stoplight device based on electrically induced strain that dynamically switches the lattice symmetry from $pgg$ to the higher $p4g$ symmetry. This controls the coalescence of Dirac points and hence the group velocity within the crystal.

Non-diffracting optical Bloch oscillations in hexagonal photonic lattices.

Light beams undergoing optical Bloch oscillations (OBOs) in two-dimensional (2D) photonic lattices suffer from severe diffraction along the perpendicular direction to the oscillation plane. In this paper, we propose and demonstrate that such diffraction could be suppressed in hexagonal photonic lattices via sophisticated managements of the discrete diffraction. By positioning the Fourier spectrum of the beam to a special region in the Brillouin zone, the light driven by the OBO experiences normal and anomalous diffractions alternatively, leading to a non-diffracting propagation for a long distance. We show that non-diffracting OBOs can be implemented not only for Gaussian beam but also for other complex 2D beams including self-accelerating Airy beams and vortex beams. Our results provide novel insights into the diffraction or dispersion engineering of waves in periodic structures.

Experimental observation of anomalous topological edge modes in a slowly driven photonic lattice

Topological quantum matter can be realized by subjecting engineered systems to time-periodic modulations. In analogy with static systems, periodically driven quantum matter can be topologically classified by topological invariants, whose non-zero value guarantees the presence of robust edge modes. In the high-frequency limit of the drive, topology is described by standard topological invariants, such as Chern numbers. Away from this limit, these topological numbers become irrelevant, and novel topological invariants must be introduced to capture topological edge transport. The corresponding edge modes were coined anomalous topological edge modes, to highlight their intriguing origin. Here we demonstrate the experimental observation of these topological edge modes in a 2D photonic lattice, where these propagating edge states are shown to coexist with a quasi-localized bulk. Our work opens an exciting route for the exploration of topological physics in time-modulated systems operating away from the high-frequency regime.

Analytical approximation for photonic array modes in two-dimensional photonic crystal lattices.

We presented here a comprehensive analytical approximation, describing array modes (both the modal fields and their associated propagation constants) in 2D photonic lattices (i.e., arrays of identical coupled waveguides/lasers). Our approximation is a vectorial approach, accounting for the TE and TM polarizations. It is applicable to both the low-contrast and high-contrast photonic devices. The model of standing waves of a membrane was used for analytical evaluation of envelopes of the array modes and the total modal fields. Combination of this model with the coupled-mode formalism for 2D infinite photonic lattices allowed for evaluation of propagation constants of the array modes. Both the computations required only a few seconds. Still, the results, acquired with the analytical approximation, are in close agreement with those acquired with well-established approaches. Moreover, for the first time, analytical expressions for the modal fields and propagation constants become available.

Self-trapping and oscillation of quadruple beams in high band gap of 2D photonic lattices

Higher-band self-trapping and oscillation (rotation) of nonlinear quadruple beams in two-dimensional (2D) square photonic lattices are numerically demonstrated. Under appropriate conditions of nonlinearity, a quadruple-like beam can self-trap into localized modes that reside in the second Bragg reflection gap through single-site excitation. By changing the initial orientation of the incident quadruple beam related to the lattices, periodic oscillations of the localized quadruple mode may be obtained. The localized quadruple state becomes a rotating doubly charged optical vortex (DCV) during rotation and should undergo charge-flipping when the rotating direction is reversed.

Talbot Effect from Rotational Symmetry Gratings: Application to 3D Refractive Grating Formation

We report the first observation of Talbot effect – diffraction grating images self-replications at regular distances, from 1D annular grating with the period of d = 30 ± 1 μm. Up to 20 high contrast revivals of the grating were observed by the green laser beam at λ = 532 nm with Talbot distance ZT = d2/λ = 1.57 ± 0.01 mm. The grating self imaging with half period of the original grating at ZT/2 was also observed. Using the annular grating as a mask, the recording of refractive index photonic lattice in 2 mm thick Fe doped lithium niobate crystal was performed by 532 nm laser beam. The replication of the grating images due to Talbot effect provides the recording of two refractive replicas of the grating with the periods of d and d/2 inside the 2 mm crystal checked by phase microscope depth scan observations. The obtained results show the possibility of the use of 2D masks for the creation of 3D photonic lattices in photorefractive materials, which can be used as photonic crystals.

Silicon-based photonic crystals fabricated using proton beam writing combined with electrochemical etching method

A method for fabrication of three-dimensional (3D) silicon nanostructures based on selective formation of porous silicon using ion beam irradiation of bulk p-type silicon followed by electrochemical etching is shown. It opens a route towards the fabrication of two-dimensional (2D) and 3D silicon-based photonic crystals with high flexibility and industrial compatibility. In this work, we present the fabrication of 2D photonic lattice and photonic slab structures and propose a process for the fabrication of 3D woodpile photonic crystals based on this approach. Simulated results of photonic band structures for the fabricated 2D photonic crystals show the presence of TE or TM gap in mid-infrared range.

Disorder-induced localization of light in one- and two-dimensional photonic lattices

We study Anderson localization of light in one-dimensional (1D) and 2D photonic lattices. The influence of nonlinearity and disorder on Anderson localization in both systems is studied numerically. A sharp difference between localization in the linear and the nonlinear regimes is observed. Localization in the linear regime is more pronounced in the 2D lattice than in the 1D lattice. In the nonlinear regime, the coexistence of nonlinearity and disorder leads us to different conclusions. There are different nonlinear regimes in which 1D localization is more pronounced than 2D localization.

Reconfigurable 3D photonic lattices by optical induction for optical control of beam propagation

We report on our recent theoretical and experimental studies of three-dimensional (3D) photonic lattice structures which are established in a bulk nonlinear crystal by employing different optical induction techniques. These 3D photonic lattices bring about new opportunities for controlling the flow of light via coupling engineering originated from the lattice modulation along the beam propagation direction. By fine tuning the lattice parameters, we observe a host of unusual behaviors of beam propagation in such reconfigurable 3D lattices, including enhanced discrete diffraction, light tunneling inhibition—better known as coherent destruction of tunneling (CDT), anomalous diffraction, negative refraction, as well as CDT-based image transmission. In addition, we propose and demonstrate a new way of creating 3D ionic-type photonic lattices by controlled Talbot effect.

All-optical switching using nonlinear subwavelength Mach-Zehnder on silicon

We report on the experimental demonstration of ultrafast all-optical switching and wavelength down-conversion based on a novel nonlinear Mach-Zehnder interferometer with subwavelength grating and wire waveguides. Unlike other periodic waveguides such as line-defects in a 2D photonic crystal lattice, a subwavelength grating waveguide confines the light as a conventional index-guided structure and does not exhibit optically resonant behaviour. Since the device had no dedicated port to input optical signal to control switching a new approach was also implemented for all-optical switching control.

Berezinskii-Kosterlitz-Thouless crossover in a photonic lattice

We show that a periodic two-dimensional (2D) photonic lattice with Kerr nonlinearity exhibits a Berezinskii-Kosterlitz-Thouless (BKT) crossover associated with a vortex-unbinding transition. We find that averaging over random initial conditions is equivalent to Boltzmann thermal averaging with the discrete nonlinear Schr$\stackrel{\mathrm{\ifmmode\cdot\else\textperiodcentered\fi{}\ifmmode\cdot\else\textperiodcentered\fi{}}}{\mathrm{o}}$dinger Hamiltonian. By controlling the initial randomness we can continuously vary the effective temperature. Since this Hamiltonian is in the 2D $\mathit{XY}$ universality class, a BKT transition ensues. We verify this prediction using experimentally accessible observables and find good agreement between theory and simulations. This opens the possibility of experimental access to interesting phase transitions known in condensed matter using nonlinear optics.

Subwavelength grating periodic structures in silicon-on-insulator: a new type of microphotonic waveguide

We report on the experimental demonstration and analysis of a new waveguide principle using subwavelength gratings. Unlike other periodic waveguides such as line-defects in a 2D photonic crystal lattice, a subwavelength grating waveguide confines the light as a conventional index-guided structure and does not exhibit optically resonant behaviour. Subwavelength grating waveguides in silicon-on-insulator are fabricated with a single etch step and allow for flexible control of the effective refractive index of the waveguide core simply by lithographic patterning. Experimental measurements indicate a propagation loss as low as 2.1 dB/cm for subwavelength grating waveguides with negligible polarization and wavelength dependent loss, which compares favourably to conventional microphotonic silicon waveguides. The measured group index is nearly constant n(g) ~1.5 over a wavelength range exceeding the telecom C-band.

Nonlinear waves in optical media

In nonlinear optical systems quasi-monochromatic waves satisfy the classical, constant dispersion and dispersion managed nonlocal, nonlinear Schrödinger equations, both of which exhibit localized pulse solutions. Current research has shown that mode-locked lasers are also described by dispersion managed equations. In spatial systems recent developments have attracted considerable interest in 2D photonic lattices. A computational method is introduced to find these and other localized waves in nonlinear optical media with vanishing and non-vanishing boundary conditions.