Waveguide Lattices Research Articles

Integrated photonic fractional convolution accelerator

An integrated photonic circuit architecture to perform a modified-convolution operation based on the discrete fractional Fourier transform (DFrFT) is introduced. This is accomplished by utilizing two nonuniformly coupled waveguide lattices with equally spaced eigenmode spectra, the lengths of which are chosen so that the DFrFT and its inverse operations are achieved. A programmable modulator array is interlaced so that the required fractional convolution operation is performed. Numerical simulations demonstrate that the proposed architecture can effectively perform smoothing and edge detection tasks even for noisy input signals, which is further verified by electromagnetic wave simulations. Notably, mild lattice defects do not jeopardize the architecture performance, showing its resilience to manufacturing errors.

Higher‐Order Topological Corner States in a Specially Distorted Photonic Kagome Lattice

AbstractKagome lattices have garnered significant interest over the decades due to their rich physics and implications for exotic superconductors and topological materials. In particular, the so‐called “breathing Kagome lattice” (BKL) is often used as a prototypical model to understand higher‐order topological insulators. Here it is demonstrated that higher‐order corner states exist in a specially distorted Kagome lattice, resembling the “Inverse Hexagram” lattice distortion originally introduced in the study of charge density waves in Kagome metals. Importantly, it is found that such an Inverse Hexagram‐like Kagome lattice with C6 rotational symmetry hosts two types of in‐gap corner states, in contrast to a flat‐cutting BKL of C3 symmetry that supports only one type of corner state under the tight‐binding condition. It is shown that the nontrivial corner states exhibit a fractional corner anomaly, revealing the feature of higher‐order topology. Using laser‐written waveguide lattices as a photonic platform, these two types of corner states are experimentally observed, along with a direct comparison with the corner excitation at their trivial counterparts. Experimental observations are further corroborated by numerical simulations and stability analysis under random perturbation. These results may prove relevant and applicable to similar phenomena in other Kagome platforms beyond photonics.

Interplay of Luminophores and Photoinitiators during Synthesis of Bulk and Patterned Luminescent Photopolymer Blends.

Four-dimensional printing with embedded photoluminescence is emerging as an exciting area in additive manufacturing. Slim polymer films patterned with three-dimensional lattices of multimode cylindrical waveguides (waveguide-encoded lattices, WELs) with enhanced fields of view can be fabricated by localizing light as self-trapped beams within a photopolymerizable formulation. Luminescent WELs have potential applications as solar cell coatings and smart planar optical components. However, as luminophore-photoinitiator interactions are expected to change the photopolymerization kinetics, the design of robust luminescent photopolymer sols is nontrivial. Here, we use model photopolymer systems based on methacrylate-siloxane and epoxide homopolymers and their blends to investigate the influence of the luminophore Lumogen Violet (LV) on the photolysis kinetics of the Omnirad 784 photoinitiator through UV-vis absorbance spectroscopy. Initial rate analysis with different bulk polymers reveals differences in the pseudo-first-order rate constants in the absence and presence of LV, with a notable increase (∼40%) in the photolysis rate for the 1:1 blend. Fluorescence quenching studies, coupled with density functional theory calculations, establish that these differences arise due to electron transfer from the photoexcited LV to the ground-state photoinitiator molecules. We also demonstrate an in situ UV-vis absorbance technique that enables real-time monitoring of both waveguide formation and photoinitiator consumption during the fabrication of WELs. The in situ photolysis kinetics confirm that LV-photoinitiator interactions also influence the photopolymerization process during WEL formation. Our findings show that luminophores play a noninnocent role in photopolymerization and highlight the necessity for both careful consideration of the photopolymer formulation and a real-time monitoring approach to enable the fabrication of high-quality micropatterned luminescent polymeric films.

The Goldilocks principle of learning unitaries by interlacing fixed operators with programmable phase shifters on a photonic chip

Programmable photonic integrated circuits represent an emerging technology that amalgamates photonics and electronics, paving the way for light-based information processing at high speeds and low power consumption. Programmable photonics provides a flexible platform that can be reconfigured to perform multiple tasks, thereby holding great promise for revolutionizing future optical networks and quantum computing systems. Over the past decade, there has been constant progress in developing several different architectures for realizing programmable photonic circuits that allow for realizing arbitrary discrete unitary operations with light. Here, we systematically investigate a general family of photonic circuits for realizing arbitrary unitaries based on a simple architecture that interlaces a fixed intervening layer with programmable phase shifter layers. We introduce a criterion for the intervening operator that guarantees the universality of this architecture for representing arbitrary N×N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N \ imes N$$\\end{document} unitary operators with N+1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N+1$$\\end{document} phase layers. We explore this criterion for different photonic components, including photonic waveguide lattices and meshes of directional couplers, which allows the identification of several families of photonic components that can serve as the intervening layers in the interlacing architecture. Our findings pave the way for efficiently designing and realizing novel families of programmable photonic integrated circuits for multipurpose analog information processing.

Selecting mode by the complex Berry phase in non-Hermitian waveguide lattices

Bloch oscillations (BOs) in a parity-time (PT)-symmetric Su–Schrieffer–Heeger (SSH) waveguide array are theoretically investigated. We show that the BOs are amplified or damped even for the systems to exhibit entirely real energy bands. The amplified and damped BOs stem from the complex Berry phase and closely relate to the topological properties of the lattice. For the topological nontrivial lattice, the amplification and attenuation of BOs are much more prominent than the trivial case and the output Bloch mode can be selected. Furthermore, we propose an experimental scheme and perform a numerical simulation based on a bent waveguide array. Our work uncovers the impact of the topological properties on the dynamics of the bulk Bloch modes and unveils a horizon in the study of non-Hermitian physics. The mode selection induced by the complex Berry phase may also find application in integrated photonic devices such as the mode filter.

Light switching between localized and delocalized states in chiral moiré-like photonic lattice

Abstract We constructed a chiral moiré-like lattice pattern by the interference between two sets of plane waves and two circular polarized beams. The study shows that the intensity distributions of the lattice pattern are a moiré-like structure in the transverse direction and a spiral structure in the longitudinal direction. By tuning the relative rotation angle between two sets of beams, moiré-like lattice pattern can be switched between periodic to aperiodic systems. Further, we numerically study the impacts of relative rotation angle, the screw pitch of the lattice waveguide, the width and incident direction of the probe beam on the light behavior in chiral moiré-like photonic lattice fabricated with photon-induction method. It turns out that light propagation can be switched between localization and delocalization. Our study enriches the physical content of moiré-like lattice patterns and paves a novel way to the light modulation in photonic lattices.

Optical mode-controlled topological edge state in waveguide lattice

Abstract Topological edge state (TES) has emerged as a significant research focus in photonics due to its unique property of unidirectional transmission. This feature provides immunity to certain structural disorders or perturbations, greatly improving the robustness of photonic systems and enabling various applications such as optical isolation and topological lasers. Nevertheless, most of current researches focus on the fixed generated TES with no means to control, leaving untapped potential for manipulating the TES through specific methods. In this work, we propose a topological Su–Schriffer–Heeger (SSH) waveguides-lattice scheme that enables the controllable TES without changing the topological phase of the system. Light is selectively localized at the edges of the SSH waveguide lattice, which is determined by the special waveguide modes. Eventually, achieving an effective mode splitter. To validate our proposal, we further demonstrate such mode-controlled TES with a fabricated on-chip device in experiment. The experimentally tested results confirm a successful separation of the waveguide modes with the mode extinction ratio of approximately 10 dB in each channel near the wavelength of 1550 nm. This scheme presents a promising approach for manipulating the TES in photonic systems, thereby facilitating the design of optical controllable topological photonic devices.

Improvement of Output Extraction Efficiency by Optimizing Edge Structure of Circular Defect in Photonic Crystal Laser

We aim to achieve wavelength division multiplexing with a circular defect in two‐dimensional photonic crystal (CirD) laser that has an orthogonal lattice waveguide (OLW). In a simulation, we calculate the output extraction efficiency to discover a structure in which stronger optical output can be extracted for the CirD laser with OLW. Consequently, adjusting the edge face position and applying a semicircular port can strengthen the energy extracted from the edge face. This appears to be caused by changing the positional relationship between the standing wave mode and the edge face. Furthermore, the OLW‐W1 structure proposed in this report can achieve higher output extraction efficiency than the conventional OLW. The transmittance is enhanced by changing the structure near the edge face because this improves the matching of light speed in different media.

Programmable high-dimensional Hamiltonian in a photonic waveguide array

Waveguide lattices offer a compact and stable platform for a range of applications, including quantum walks, condensed matter system simulation, and classical and quantum information processing. However, to date, waveguide lattice devices have been static and designed for specific applications. We present a programmable waveguide array in which the Hamiltonian terms can be individually electro-optically tuned to implement various Hamiltonian continuous-time evolutions on a single device. We used a single array with 11 waveguides in lithium niobate, controlled via 22 electrodes, to perform a range of experiments that realized the Su-Schriffer-Heeger model, the Aubrey-Andre model, and Anderson localization, which is equivalent to over 2500 static devices. Our architecture’s micron-scale local electric fields overcome the cross-talk limitations of thermo-optic phase shifters in other platforms such as silicon, silicon-nitride, and silica. Electro-optic control allows for ultra-fast and more precise reconfigurability with lower power consumption, and with quantum input states, our platform can enable the study of multiple condensed matter quantum dynamics with a single device.

Tunable Localization of Higher‐Order Bound States in Non‐Hermitian Optical Waveguide Lattices

AbstractHigher‐order corner‐bound states in a 2D structure have been found to possess robust and exotic properties beyond the “ordinary” topological edge states, giving rise to a promising applicative potential. For example, the topological nanocavity designed based on the corner states exhibits much better performance than that of the conventional photonic crystal cavity. However, the corner states in the finite Hermitian system are usually coupled with each other, which results in the weakening of their localization. As such, the contradiction between the performance and footprint of topological devices is vexing. Here, it shows that introducing non‐Hermiticity in the higher‐order topological insulators is an effective strategy to enhance the localization of corner states in finite systems. By designing and analyzing the 2D finite Su‐Schriffer‐Heeger optical lattices with two types of non‐Hermitian configuration, the localization degree of higher‐order corner states is found to depend on the gain/loss strength. This is experimentally demonstrated by observing the distribution of corner states in the femtosecond‐laser‐writing loss‐controlled waveguide arrays. This scheme tuning localization of higher‐order corner‐bound states by non‐Hermiticity may offer a new avenue to design robust and compact devices, such as topological nano‐lasers with an ultra‐low threshold.

Exact envelope solitons in topological Floquet insulators.

The existence of new types of four-wave mixing Floquet solitons were recently realized numerically through a resonant phase matching in a photonic lattice of type-I Dirac cones; specifically, a honeycomb lattice of helical array waveguides imprinted on a weakly birefringent medium. We present a wide class of exact solutions in this system for the envelope solitons in dark-bright pairs and a "molecular" form of bright-dark combinations. Some of the solutions, red or blue detuned, are mode-locked in their momenta, while the others offer a spectrum of allowed momenta subject to constraints amongst the system and solution parameters. We show that the characteristically different solutions exist at and away from the band edge, with the exact band edge possessing a periodic pair of sinusoidal excitations akin to that of two-level systems apart from localized solitons. These could have possible applications for designing quantum devices.

Edge-to-edge topological spectral transfer in diamond photonic lattices

The transfer of information between topological edge states is a robust way of spatially manipulating spatial states in lattice environments. This method is particularly efficient when the edge modes are kept within the topological gap of the lattice during the transfer. In this work, we show experimentally the transfer of photonic modes between topological edge states located at opposite ends of a dimerized one-dimensional photonic lattice. We use a diamond lattice of coupled waveguides and show that the topological transfer is insensitive to the presence of a high density of states in the form of a flat band at an energy close to that of the edge states and prevails in the presence of a hopping impurity. We explore the dynamics in the waveguide lattice using a wavelength-scan method, where different input wavelengths translate into different effective lattice lengths. Our results offer an alternative way to the implementation of efficient transfer protocols based on active driving mechanisms.

2D Jackiw–Rebbi and trivial localized states in square interfaced binary waveguide lattices

We investigate optical analogs of two-dimensional (2D) Jackiw–Rebbi (JR) states and 2D trivial localized states in square interfaced binary waveguide lattices in the linear and nonlinear regimes of Kerr type. The 2D JR states can be formed in the square interfaced binary lattice during propagation of optical beams and turn out to be quite robust, especially in the linear and defocusing nonlinearity regime where established 2D JR state profiles are well conserved during propagation. The established profiles of nonlinear 2D JR states formed during propagation agree well with exact solutions obtained by using the Newton–Raphson method. The 2D nonlinear trivial localized states found by the successive approximation method are much broader than 2D JR states with the same peak amplitudes. The 2D JR states can also be well trapped within the central interface of the lattices even in the presence of an initial tilt of the input beam which can easily displace 2D trivial localized states in square interfaced binary waveguide lattices, 2D Dirac solitons in perfectly periodic binary waveguide lattices and other solitonic structures in the continuous media.

Observation of Generalized Dynamic Localizations in Arbitrary‐Wave Driven Synthetic Temporal Lattices

AbstractDynamic localization (DL) refers to a wavefunction confinement effect of electrons in periodic lattices under an ac electric field driving. Recent studies have transplanted DLs from electronic to photonic systems using periodically curved waveguide lattices, where the ac electric field is mimicked by the waveguide's bending curvature. However, due to the severe limitations of bending losses and poor tunability for highly curved, arbitrarily shaped waveguides, present studies mainly focus on DL under the simplest sinusoidal‐wave driving; its extension to an arbitrary‐wave driving remains challenging. Here, by constructing a synthetic temporal lattice with a coupled fiber‐loop circuit, the limitations of spatially curved waveguides are circumvented and generalized DLs are experimentally demonstrated under arbitrary‐wave driving. First, by applying band‐collapse criteria, the general conditions for the driving field's symmetry to achieve DLs are revealed. Then, two representative even‐function driving fields of square‐ and triangle‐waveforms are chosen, and wave‐packet revivals are observed as signatures of DLs. As a counter‐example, the breakdown of DL is also verified using odd‐function driving field of sawtooth‐waveform. The work reveals the conditions for realizing generalized DLs and experimentally verifies them using synthetic lattice schemes. This paradigm may find potential applications in versatile temporal‐waveform reshaping, pulse manipulations for optical communications, and signal processing.

Fluorescent Waveguide Lattices for Enhanced Light Harvesting and Solar Cell Performance.

We present the properties and performance of fluorescent waveguide lattices as coatings for solar cells, designed to address the significant mismatch between the solar cell's spectral response range and the solar spectrum. Using arrays of microscale visible light optical beams transmitted through photoreactive polymer resins comprising acrylate and silicone monomers and fluorescein o,o'-dimethacrylate comonomer, we photopolymerize well-structured films with single and multiple waveguide lattices. The materials exhibited bright green-yellow fluorescence emission through down-conversion of blue-UV excitation and light redirection from the dye emission and waveguide lattice structure. This enables the films to collect a broader spectrum of light, spanning UV-vis-NIR over an exceptionally wide angular range of ±70°. When employed as encapsulant coatings on commercial silicon solar cells, the polymer waveguide lattices exhibited significant enhancements in solar cell current density. Below 400 nm, the primary mode of enhancement is through down-conversion and light redirection from the dye emission and collection by the waveguides. Above 400 nm, the primary modes of enhancement were a combination of down-conversion, wide-angle light collection, and light redirection from the dye emission and collection by the waveguides. Waveguide lattices with higher dye concentrations produced more well-defined structures better suited for current generation in encapsulated solar cells. Under standard AM 1.5 G irradiation, we observed nominal average current density increases of 0.7 and 1.87 mA/cm2 for single waveguide lattices and two intersecting lattices, respectively, across the full ±70° range and reveal optimal dye concentrations and suitable lattice structures for solar cell performance. Our findings demonstrate the significant potential of incorporating down-converting fluorescent dyes in polymer waveguide lattices for improving the current spectral and angular response of solar cell technologies toward increasing clean energy in the energy grid.

Topological Landau–Zener nanophotonic circuits

Topological edge states (TESs), arising from topologically nontrivial phases, provide a powerful toolkit for the architecture design of photonic integrated circuits, since they are highly robust and strongly localized at the boundaries of topological insulators. It is highly desirable to be able to control TES transport in photonic implementations. Enhancing the coupling between the TESs in a finite-size optical lattice is capable of exchanging light energy between the boundaries of a topological lattice, hence facilitating the flexible control of TES transport. However, existing strategies have paid little attention to enhancing the coupling effects between the TESs through the finite-size effect. Here, we establish a bridge linking the interaction between the TESs in a finite-size optical lattice using the Landau–Zener model so as to provide an alternative way to modulate/control the transport of topological modes. We experimentally demonstrate an edge-to-edge topological transport with high efficiency at telecommunication wavelengths in silicon waveguide lattices. Our results may power up various potential applications for integrated topological photonics.

Inverse design of a photonic moiré lattice waveguide towards improved slow light performances.

Slow light waveguides in photonic crystals are engineered using a conventional method or a deep learning (DL) method, which is data-intensive and suffers from data inconsistency, and both methods result in overlong computation time with low efficiency. In this paper, we overcome these problems by inversely optimizing the dispersion band of a photonic moiré lattice waveguide using automatic differentiation (AD). The AD framework allows the creation of a definite target band to which a selected band is optimized, and a mean square error (MSE) as an objective function between the selected and the target bands is used to efficiently compute gradients using the autograd backend of the AD library. Using a limited-memory Broyden-Fletcher-Goldfarb-Shanno minimizer algorithm, the optimization converges to the target band, with the lowest MSE value of 9.844×10-7, and a waveguide that produces the exact target band is obtained. The optimized structure supports a slow light mode with a group index of 35.3, a bandwidth of 110nm, and a normalized-delay-bandwidth-product of 0.805, which is a 140.9% and 178.9% significant improvement if compared to conventional and DL optimization methods, respectively. The waveguide could be utilized in slow light devices for buffering.

Coherent Control of Topological States in an Integrated Waveguide Lattice.

Topological photonics holds the promise for enhanced robustness of light localization and propagation enabled by the global symmetries of the system. While traditional designs of topological structures rely on lattice symmetries, there is an alternative strategy based on accidentally degenerate modes of the individual meta-atoms. Using this concept, we experimentally realize topological edge state in an array of silicon nanostructured waveguides, each hosting a pair of degenerate modes at telecom wavelengths. Exploiting the hybrid nature of the topological mode, we implement its coherent control by adjusting the phase between the degenerate modes and demonstrating selective excitation of bulk or edge states. The resulting field distribution is imaged via third harmonic generation showing the localization of topological modes as a function of the relative phase of the excitations. Our results highlight the impact of engineered accidental degeneracies on the formation of topological phases, extending the opportunities stemming from topological nanophotonic systems.

Localization effects from local phase shifts in the modulation of waveguide arrays

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 of introducing randomness into artificial gauge fields by applying local random phase shifts in the modulation of lattices of optical waveguides. We first study the elemental unit consisting of two coupled single-mode waveguides and determine the effective complex-valued coupling coefficient after one period of modulation as a function of the phase shift, modulation amplitude, and modulation frequency. Thereby we identify the regime where varying the modulation phase yields sufficiently large changes of the effective coupling coefficient to induce Anderson localization. Using these results, we demonstrate numerically the onset of Anderson localization in 1D and 2D lattices of x- and helically modulated waveguides via randomly choosing the modulation phases of individual waveguides. Besides further fundamental investigations of wave propagation in the presence of random gauge fields, our findings enable the engineering of coupling coefficients without changing the footprint of the overall lattice. As a proof of concept, we demonstrate how to engineer out-of-phase modulated lattices that exhibit dynamic localization and defect-free surface states. Therefore, we anticipate that the modulation phase will play an important role in the judicious design of functional waveguide lattices.

Mode pumping in photonic lattices using a single tailored auxiliary waveguide

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, we show that purities above 99% can be achieved with parameter values within experimental reach. Additionally, we demonstrate how the technique can be used to pump the bulk modes of the lattice for low number of waveguides or enable mode conversion between waveguide lattices.