Two-dimensional Waveguide Arrays Research Articles

Investigating the effects of various input beam profiles on the propagations of light in two-dimensional interfaced binary

In this work, we numerically study how various input beam profiles influence the linear and nonlinear light propagation at the interface of two-dimensional (2D) binary waveguide arrays. It is revealed that, due to the presence of the central homogeneous interfaced waveguides, light beams are effectively steered into the preferred direction. Interestingly, the formation of discretely localized states in nonlinear modes can be intentionally utilized to optimize the stability and intensity of the signals at the central interfaced channels. This study thus opens alternative possibilities to achieve reliable distant beam propagation through discrete optical systems.

Talbot effect in arrays of helical waveguides.

We demonstrate that periodic self-imaging of light patterns with certain input periods can be effectively realized in one-dimensional and two-dimensional helical waveguide arrays. The band structure is drastically dependent on the helix radius and period, and the complete collapse of quasi-energy bands occurs for a certain helix radius and period, which strongly affects the intensity carpet and the Talbot length of the Talbot self-imaging effect. Talbot length would extend to infinity, as the helix radius and period approach the corresponding critical values corresponding to the band collapse, where the inversion of intensity distribution between even and odd waveguides is observed for the binary input pattern with π/2 phase shift between the adjacent waveguides.

Dirac equation on a square waveguide lattice with site-dependent coupling strengths and the gravitational Aharonov-Bohm effect

The main objective of this work is to present a theoretical proposal for an implementation of the $(2 + 1)$-dimensional Dirac equation in classical gravitational and electromagnetic backgrounds in a two-dimensional waveguide array. For this, a framework for achieving site-dependent effective coupling constants in two-dimensional waveguide arrays is developed. Implementability of the Dirac equation under the proposed scheme puts minor demands on gauge and spacetime backgrounds; however, a wide array of physical spacetimes, such as all vacuum and static solutions, prove to be implementable. As an interesting and instructive example, we discuss a tabletop realization of the gravitational Aharonov-Bohm effect: After devising a thought experiment in which signatures of the gravitational Aharonov-Bohm effect could be detected, we briefly discuss how the analogue of such a setting can in principle be implemented using the proposed waveguide setup.

Localized vortex beams in anisotropic Lieb lattices.

We address the issue of nonlinear modes in a two-dimensional waveguide array, spatially distributed in the Lieb lattice geometry, and modeled by a saturable nonlinear Schrödinger equation. In particular, we analyze the existence and stability of vortex-type solutions finding localized patterns with symmetric and asymmetric profiles, ranging from topological charge S=1 to S=3. By taking into account the presence of anisotropy, which is inherent to experimental realization of waveguide arrays, we identify different stability behaviors according to their topological charge. Our findings might give insight into experimental feasibility to observe these kinds of vortex states.

Topological plasmonic modes in graphene-coated nanowire arrays

We investigate the topological edge modes of surface plasmonic polaritons (SPPs) in a two-dimensional waveguide array composed of graphene-coated nanowires. The system experiences topological phase transition by tuning the inter-layer spacing between adjacent unit cells. The topological modes emerge at the edge of topological non-trivial nanowire arrays when the intra-layer spacing is larger than the inter-layer spacing. Thanks to the strong confinement of graphene SPPs, the modal wavelength of topological edge modes can be squeezed as small as 1/20 of incident wavelength. The study provides a promising approach to realizing robust light transport beyond diffraction limit.

Stable discrete soliton molecules in two-dimensional waveguide arrays

Stable discrete soliton molecules in two-dimensional waveguide arrays

Modulation instability in two-dimensional waveguide arrays with alternating signs of refractive index

We consider the propagation of coupled forward and backward waves in two-dimensional arrays of alternating waveguides with positive and negative refractive indices. The array has a cross section in the form of a face-centered square lattice. The unit cell consists of three different waveguides with different optical properties. We obtain the condensate solutions for electromagnetic pulse propagation in such an array of waveguides. The base equations describing this model have solutions that correspond to the static and homogeneous intensity distribution on the waveguides. The stability of these solutions in both normal and anomalous dispersion regimes is also investigated using modulation instability analysis.

Photonic Weyl phase transition in dynamically modulated brick-wall waveguide arrays

We investigate the topological phase transition between Type-I and Type-II Weyl points (WPs) in a composite three-dimensional lattice composed of a two-dimensional brick-wall waveguide array and a synthetic frequency dimension created by dynamic modulation. By imposing different modulation amplitudes and phases in the two sublattices, we can break either parity or time-reversal symmetry and realize the phase transition between Type-I and Type-II WPs. As the array is truncated to have two edges, two Fermi-arc surface states will emerge, which propagate in opposite directions for Type-I WPs while in same directions for Type-II WPs, accompanied by bidirectional and unidirectional frequency shifts for the optical modes. Particularly at the phase transition point, we find that one of two bands becomes flat with a vanished group velocity along frequency axis in the vicinity of WPs. The study paves a way towards realizing different topological phases in the same photonic structure, which offers new opportunities to control wave transportation both in spatial and frequency domains.

Enhanced mobility of discrete solitons in anisotropic two-dimensional waveguide arrays with modulated separations

We consider two-dimensional waveguide arrays with anisotropic coupling coefficients. We show using numerical and variational calculations that four stationary soliton types exist: Site-Centered, Bond-Centered, Hybrid-X and Hybrid-Y. For the isotropic case the last two modes become identical and equivalent to the known hybrid soliton. With a variational calculation using a gaussian trial function and six variational parameters corresponding to the soliton's position, width, and velocity components, the four stationary soliton types are reproduced and their equilibrium widths are accounted for accurately for a wide range of anisotropy ratios. We obtained using the variational calculation the Peierls-Nabarro potential and barrier heights for the four soliton types and different anisotropy ratios. We have also obtained a phase diagram showing regions of soliton stability against collapse and subregions of mobility in terms of the initial kick-in speed and anisotropy ratio. The phase diagram shows that 2D solitons become highly mobile for anisotropy ratios larger than some critical values that depend on the initial kick-in speed. This fact was then exploited to design tracks within the 2D waveguide array along which the soliton can be accelerated and routed. We have calculated the actual waveguide separations needed to realist the proposed guided trajectories of 2D solitons.

Discrete Talbot effect in two-dimensional waveguide arrays.

We theoretically study discrete Talbot self-imaging in hexagonal, square, and irregular two-dimensional waveguide arrays. Different from its counterpart in a continuous system, the periods of the input fields must belong to {1, 2, 3, 4, 6} for Talbot self-imaging. Also, the combinations of the input periods cannot be 3 & 4, or 4 & 6 along two different directions, which distinguishes itself from the one-dimensional discrete Talbot effect.

Mimicking photon propagation through two-dimensional waveguide array by a one-dimensional waveguide array.

Photon propagation through 1D and 2D waveguide arrays has been explored for various applications in the fields of quantum optics and quantum information. In this paper, we show that an appropriately designed 1D waveguide array can mimic the photon propagation through a 2D array. This alternative design is enticing since fabrication of 1D arrays is relatively less burdensome than 2D arrays.

Subwavelength focusing by a sheltered metallic waveguide array

We propose a new subwavelength focusing scheme in a limited number of two-dimensional (2D) metallic waveguide arrays. The entrances of middle waveguides are sheltered and only the waveguides on both sides of the array are open. Simulation results show that this structure can focus a plane wave (λ=632.8nm) to a point in the middle waveguide. The full width at half-maximum of the focusing spot is about 54nm, whereas the FWHM without the shelter is about 150nm. We analyze the supermode propagation of SPPs in the MWGA and find that the focusing behavior can be explained by the superposition of the supermode of SPPs. The theoretical results show a good agreement with numerical simulation results. We discuss the power loss arising from the shelter and find that the shelter in middle waveguides has little effect on the energy of the focus in the waveguide.

Anderson localization of multichannel excitations in disordered two-dimensional waveguide arrays

We considered the transfer of multi-spot optical patterns through disordered two-dimensional waveguide arrays with shallow refractive index modulation. In computer simulations, it was uncovered that statistically averaged output intensity distributions of complex inputs retain their structural features for suitable disorder strengths due to the Anderson-like localization of light. To characterize the quality of the input-output pattern similarity, we introduced corresponding criteria and analyzed their variations with the disorder level.

Subwavelength Line Imaging Using Plasmonic Waveguides

We investigate the subwavelength imaging capacity of a two-dimensional fanned-out plasmonic waveguide array, formed by air channels surrounded by gold metal layers for operation at near-infrared wavelengths, via finite element simulations. High resolution is achieved on one side of the device by tapering down the channel width while simultaneously maintaining propagation losses of a few dB. On the other, low-resolution side, output couplers are designed to optimize coupling to free space and to minimize channel cross talk via surface plasmons. Point sources separated by {\lambda}/15 can still be clearly distinguished. Moreover, up two 90% of the power of a point dipole is coupled to the device. Applications are high-resolution linear detector arrays and, by operating the device in reverse, high-resolution optical writing.

Quantum walks of correlated photon pairs in two-dimensional waveguide arrays.

We demonstrate quantum walks of correlated photons in a two-dimensional network of directly laser written waveguides coupled in a "swiss cross" arrangement. The correlated detection events show high-visibility quantum interference and unique composite behavior: strong correlation and independence of the quantum walkers, between and within the planes of the cross. Violations of a classically defined inequality, for photons injected in the same plane and in orthogonal planes, reveal nonclassical behavior in a nonplanar structure.

Probing the effect of interaction in Anderson localization using linear photonic lattices

We show how two-dimensional waveguide arrays can be used to probe the effect of on-site interaction on Anderson localization of two interacting bosons in one dimension. It is shown that classical light and linear elements are sufficient to experimentally probe the interplay between interaction and disorder in this setting. For experimental relevance, we evaluate the participation ratio and the intensity correlation function as measures of localization for two types of disorder (diagonal and off-diagonal), for two types of interaction (repulsive and attractive), and for a variety of initial input states. Employing a commonly used set of initial states, we show that the effect of interaction on Anderson localization is strongly dependent on the type of disorder and initial conditions, but is independent of whether the interaction is repulsive or attractive. We then analyze a certain type of entangled input state where the type of interaction is relevant and discuss how it can be naturally implemented in waveguide arrays. We conclude by laying out the details of the two-dimensional photonic lattice implementation including the required parameter regime.

Observation of Discrete, Vortex Light Bullets

Light bullets, solitarily propagating spatiotemporal waves recently observed in a two-dimensional waveguide array, are complex solitons. For the first time, scientists observe and investigate vortex light bullets---stably bound and propagating triplets of light bullets with an energy vortex at their centers.

Simultaneous measurement of curvature and strain based on fiber Bragg grating in two-dimensional waveguide array fiber.

We report on the fabrication of a fiber Bragg grating (FBG) with multiple resonances in a two-dimensional waveguide array microstructured optical fiber containing 91 cores. Theoretical investigation reveals that these resonances originate from the identical and nonidentical mode couplings between forward-propagating and backward-propagating LP0m-like (m=1, 2, 3; LP refers to linearly polarized) supermodes. Since both the central wavelength and minimum transmission of these resonant dips respond differently to curvature and axial strain, this FBG can be applied in the simultaneous measurement of curvature and axial strain.

Anderson cross-localization

We report Anderson localization in two-dimensional optical waveguide arrays with disorder in waveguide separation introduced along one axis of the array, in an uncorrelated fashion for each waveguide row. We show that the anisotropic nature of such disorder induces a strong localization along both array axes. The degree of localization in the cross-axis remains weaker than that in the direction in which disorder is introduced. This effect is illustrated both theoretically and experimentally.

Bending sensor based on intermodal interference properties of two-dimensional waveguide array fiber

We propose a highly sensitive bending sensor based on the intermodal interference properties of a strongly coupled two-dimentional waveguide array fiber (WAF). The interference resonance peaks formed by the SMF-WAF-SMF Mach-Zehnder interferometer are intrinsically the result of interference between the LP(01)-like supermode and other higher order supermodes, displaying supernormal sensitivity to bending in a wide curvature range. The bending sensitivity of the intermodal MZI is a quadratic function of curvature, and the resonance wavelength shift is up to 100 nm within a curvature range 0-10 m(-1). The fabrication reveals briefness, and temperature response shows little impact on the bend sensing precision. The high bending sensitivity and wide sensing range can make this device a candidate for bending discrimination and measurement in widespread areas.