Photonic Waveguide Arrays Research Articles

Landau-Zener-Stückelberg interferometry in PT -symmetric non-Hermitian models

We systematically investigate the non-Hermitian generalisations of the Landau-Zener (LZ) transition and the Landau-Zener-St\"{u}ckelberg (LZS) interferometry. The LZ transition probabilities, or band populations, are calculated for a generic non-Hermitian model and their asymptotic behaviour analysed. We then focus on non-Hermitian systems with a real adiabatic parameter and study the LZS interferometry formed out of two identical avoided level crossings. Four distinctive cases of interferometry are identified and the analytic formulae for the transition probabilities are calculated for each case. The differences and similarities between the non-Hermitian case and its Hermitian counterpart are emphasised. In particular, the geometrical phase originated from the sign change of the mass term at the two level crossings is still present in the non-Hermitian system, indicating its robustness against the non-Hermiticity. We further apply our non-Hermitian LZS theory to describing the Bloch oscillation in one-dimensional parity-time $(\mathcal{PT})$ reversal symmetric non-Hermitian Su-Schrieffer-Heeger model and propose an experimental scheme to simulate such dynamics using photonic waveguide arrays. The Landau-Zener transition, as well as the LZS interferometry, can be visualised through the beam intensity profile and the transition probabilitiess measured by the centre of mass of the profile.

Distinguishing the Topological Zero Mode and Tamm Mode in a Microwave Waveguide Array

AbstractThe Su–Schrieffer–Heeger (SSH) model has been the subject of extensive experimental research in the context of topological photonics. Ideally, the on‐site potential and hopping strength are sufficiently accurate for implementation in photonic coupled waveguide arrays. Here, two localized edge modes, the topological zero mode and trivial Tamm mode, are proposed and demonstrated in the modified SSH model using a microwave photonic waveguide array. The system used is composed of an array of evanescently coupled ultrathin corrugated metallic “H‐bar” waveguides. Furthermore, the differences between the zero mode and Tamm mode are clearly demonstrated by microwave near‐field experiments on the coupling behavior along the propagation direction for 40 cm at the excitation frequency of 17 GHz. These findings should deepen the understanding of localized edge mode confinement mechanisms, both in coupled waveguide array systems and other topological or quantum systems.

Quantum Network Transfer and Storage with Compact Localized States Induced by Local Symmetries.

We propose modulation protocols designed to generate, store, and transfer compact localized states in a quantum network. Induced by parameter tuning or local reflection symmetries, such states vanish outside selected domains of the complete system and are therefore ideal for information storage. Their creation and transfer is here achieved either via amplitude phase flips or via optimal temporal control of intersite couplings. We apply the concept to a decorated, locally symmetric Lieb lattice where one sublattice is dimerized, and also demonstrate it for more complex setups. The approach allows for a flexible storage and transfer of states along independent paths in lattices supporting flat energetic bands. We further demonstrate a method to equip any network featuring static perfect state transfer of single-site excitations with compact localized states, thus increasing the storage ability of these networks. We show that these compact localized states can likewise be perfectly transferred through the corresponding network by suitable, time-dependent modifications. The generic network and protocols proposed can be utilized in various physical setups such as atomic or molecular spin lattices, photonic waveguide arrays, and acoustic setups.

Electromagnetic‐Dual Metasurfaces for Topological States along a 1D Interface

AbstractThe discovery of topological insulators was rapidly followed by the advent of their photonic analogues, motivated by the prospect of backscattering‐immune light propagation. So far, however, implementations have mainly relied on engineering bulk modes in photonic crystals and waveguide arrays in two‐dimensional (2D) systems, which closely mimic their electronic counterparts. In addition, metamaterials‐based implementations subject to electromagnetic duality and bianisotropy conditions suffer from intricate designs and narrow operating bandwidths. Here, it is shown that symmetry‐protected topological states akin to the quantum spin‐Hall effect can be realized in a straightforward manner by coupling surface modes over metasurfaces of complementary electromagnetic responses. Specifically, stacking unit cells of such metasurfaces directly results in double Dirac cones of degenerate transverse‐electric (TE) and transverse‐magnetic (TM) modes, which break into a wide nontrivial bandgap at small interlayer separation. Consequently, the ultrathin structure supports robust gapless edge states, which are confined along a one‐dimensional (1D) line rather than a surface interface, as demonstrated at microwave frequencies by near‐field imaging. The simplicity and versatility of the proposed approach proves attractive as a tabletop platform for the study of classical topological phases, as well as for applications benefiting the compactness of metasurfaces and the potential of topological insulators.

Asymmetric localized states in periodic potentials with a domain-wall-like Kerr nonlinearity

We study the existence of one-dimensional localized states supported by linear periodic potentials and a domain-wall-like Kerr nonlinearity. The model gives rise to several new types of asymmetric localized states, including single- and double-hump soliton profiles, and multihump structures. Exploiting the linear stability analysis and direct simulations, we prove that these localized states are exceptional stable in the respective finite band gaps. The model applies to Bose–Einstein condensates loaded onto optical lattices, and in optics with period potentials, e.g., the photonic crystals and optical waveguide arrays, thereby the predicted solutions can be implemented in the state-of-the-art experiments.

Photonic topological boundary pumping as a probe of 4D quantum Hall physics.

When a two-dimensional (2D) electron gas is placed in a perpendicular magnetic field, its in-plane transverse conductance becomes quantized; this is known as the quantum Hall effect. It arises from the non-trivial topology of the electronic band structure of the system, where an integer topological invariant (the first Chern number) leads to quantized Hall conductance. It has been shown theoretically that the quantum Hall effect can be generalized to four spatial dimensions, but so far this has not been realized experimentally because experimental systems are limited to three spatial dimensions. Here we use tunable 2D arrays of photonic waveguides to realize a dynamically generated four-dimensional (4D) quantum Hall system experimentally. The inter-waveguide separation in the array is constructed in such a way that the propagation of light through the device samples over momenta in two additional synthetic dimensions, thus realizing a 2D topological pump. As a result, the band structure has 4D topological invariants (known as second Chern numbers) that support a quantized bulk Hall response with 4D symmetry. In a finite-sized system, the 4D topological bulk response is carried by localized edge modes that cross the sample when the synthetic momenta are modulated. We observe this crossing directly through photon pumping of our system from edge to edge and corner to corner. These crossings are equivalent to charge pumping across a 4D system from one three-dimensional hypersurface to the spatially opposite one and from one 2D hyperedge to another. Our results provide a platform for the study of higher-dimensional topological physics.

On-Chip Positionable Waveguides for Submicrometric Photonic Alignment

In this paper, we present positionable photonic waveguide arrays that are developed for optical chip-to-chip alignment. Partly suspended photonic structures, based on the Si3N4/SiO2 material platform, are equipped with thermal actuators enabling the free end of the structures to be positioned with submicrometer accuracy. A finite-element model is developed to provide insight in the way the design of the system affects the performance. The modeling results show that the expected vertical deflection and rotation are highly dependent on the array design. Measurements of fabricated devices confirm the trends that follow from the model and are used to assess the positioning performance. Moreover, the finite-element analysis gives guidelines for the design parameters of an optimal positionable photonic waveguide array. By following these guidelines, all the requirements for the intended photonic alignment can be fulfilled, which is validated by measurements. The stability over time of the positioning system is experimentally determined and is also sufficient. Measured mode field profiles of partly suspended waveguide beams with 1 $\mu \text{m} \,\, \times 220$ nm (width $\times $ thickness) sized waveguide cores show correct waveguiding functionality. Finally, an alignment experiment demonstrates how three adjacent waveguide beams within a positionable waveguide array can be actively aligned with the channels of another photonic chip. [2017-0046]

A Review of Three-Dimensional Scanning Near-Field Optical Microscopy (3D-SNOM) and Its Applications in Nanoscale Light Management

In this article, we present an overview of aperture and apertureless type scanning near-field optical microscopy (SNOM) techniques that have been developed, with a focus on three-dimensional (3D) SNOM methods. 3D SNOM has been undertaken to image the local distribution (within ~100 nm of the surface) of the electromagnetic radiation scattered by random and deterministic arrays of metal nanostructures or photonic crystal waveguides. Individual metal nanoparticles and metal nanoparticle arrays exhibit unique effects under light illumination, including plasmon resonance and waveguiding properties, which can be directly investigated using 3D-SNOM. In the second part of this article, we will review a few applications in which 3D-SNOM has proven to be useful for designing and understanding specific nano-optoelectronic structures. Examples include the analysis of the nano-optical response phonetic crystal waveguides, aperture antennae and metal nanoparticle arrays, as well as the design of plasmonic solar cells incorporating random arrays of copper nanoparticles as an optical absorption enhancement layer, and the use of 3D-SNOM to probe multiple components of the electric and magnetic near-fields without requiring specially designed probe tips. A common denominator of these examples is the added value provided by 3D-SNOM in predicting the properties-performance relationship of nanostructured systems.

Nonlocal discrete continuity and invariant currents in locally symmetric effective Schrödinger arrays

We develop a formalism relating nonlocal current continuity to spatial symmetries of subparts in discrete Schrödinger systems. Breaking of such local symmetries hereby generates sources or sinks for the associated nonlocal currents. The framework is applied to locally inversion-(time-) and translation-(time-) symmetric one-dimensional photonic waveguide arrays with Hermitian or non-Hermitian effective tight-binding Hamiltonians. For stationary states the nonlocal currents become translationally invariant within symmetric domains, exposing different types of local symmetry. They are further employed to derive a mapping between wave amplitudes of symmetry-related sites, generalizing also the global Bloch and parity mapping to local symmetry in discrete systems. In scattering setups, perfectly transmitting states are characterized by aligned invariant currents in attached symmetry domains, whose vanishing signifies a correspondingly symmetric density. For periodically driven arrays, the invariance of the nonlocal currents is retained on period average for quasi-energy eigenstates. The proposed theory of symmetry-induced continuity and local invariants may contribute to the understanding of wave structure and response in systems with localized spatial order.

Crystalline metamaterials for topological properties at subwavelength scales

The exciting discovery of topological condensed matter systems has lately triggered a search for their photonic analogues, motivated by the possibility of robust backscattering-immune light transport. However, topological photonic phases have so far only been observed in photonic crystals and waveguide arrays, which are inherently physically wavelength scaled, hindering their application in compact subwavelength systems. In this letter, we tackle this problem by patterning the deep subwavelength resonant elements of metamaterials onto specific lattices, and create crystalline metamaterials that can develop complex nonlocal properties due to multiple scattering, despite their very subwavelength spatial scale that usually implies to disregard their structure. These spatially dispersive systems can support subwavelength topological phases, as we demonstrate at microwaves by direct field mapping. Our approach gives a straightforward tabletop platform for the study of photonic topological phases, and allows to envision applications benefiting the compactness of metamaterials and the amazing potential of topological insulators.

Chiral Light in Helically Twisted Photonic Lattices

The propagation of chiral light in optically induced helical photonic waveguide arrays is investigated. Manifested in their chiral interaction, the system's selectivity to optical orbital angular momentum is demonstrated. In order to realize twisted refractive index waveguide arrays, 3D modulated light fields are tailored to nonlinearly inscribe these helical waveguides in photosensitive material. Additionally, it is shown that this functional system provides controllable output states by optically changing the waveguides' potential depths or the nonlinearity's sign.

Topological phase transitions and Thouless pumping of light in photonic waveguide arrays (Laser Photonics Rev. 10(6)/2016)

Topological phase transitions and Thouless pumping of light in photonic waveguide arrays (Laser Photonics Rev. 10(6)/2016)

Topological phase transitions and Thouless pumping of light in photonic waveguide arrays

AbstractPhotonic waveguide arrays provide an excellent platform for simulating conventional topological systems, and they can also be employed for the study of novel topological phases in photonics systems. However, a direct measurement of bulk topological invariants remains a great challenge. Here we study topological features of generalized commensurate Aubry‐André‐Harper (AAH) photonic waveguide arrays and construct a topological phase diagram by calculating all bulk Chern numbers, and then explore the bulk‐edge correspondence by analyzing the topological edge states and their winding numbers. In contrast to incommensurate AAH models, diagonal and off‐diagonal commensurate AAH models are not topologically equivalent. In particular, there appear nontrivial topological phases with large Chern numbers and topological phase transitions. By implementing Thouless pumping of light in photonic waveguide arrays, we propose a simple scheme to measure the bulk Chern numbers. image

Non-Abelian Braiding of Light.

Many topological phenomena first proposed and observed in the context of electrons in solids have recently found counterparts in photonic and acoustic systems. In this work, we demonstrate that non-Abelian Berry phases can arise when coherent states of light are injected into "topological guided modes" in specially fabricated photonic waveguide arrays. These modes are photonic analogues of topological zero modes in electronic systems. Light traveling inside spatially well-separated topological guided modes can be braided, leading to the accumulation of non-Abelian phases, which depend on the order in which the guided beams are wound around one another. Notably, these effects survive the limit of large photon occupation, and can thus also be understood as wave phenomena arising directly from Maxwell's equations, without resorting to the quantization of light. We propose an optical interference experiment as a direct probe of this non-Abelian braiding of light.

Stripe states in photonic honeycomb ribbon.

We reveal new stripe states in deformed hexagonal array of photonic wave guides when the array is terminated to have a ribbon-shaped geometry. Unlike the well-known zero energy edge modes of honeycomb ribbon, the new one-dimensional states are shown to originate from high-energy saddle-shaped photonic bands of the ribbon's two-dimensional counterpart. We find that the strain field deforming the ribbon generates pseudo-electric fields in contrast to pseudo-magnetic fields in other hexagonal crystals. Thus, the stripe states experience Bloch oscillation without any actual electric field so that the spatial distributions of stripes have a singular dependence on the strength of the field. The resulting stripe states are located inside the bulk and their positions depend on their energies.

Photonic lattice simulation of dissipation-induced correlations in bosonic systems.

We propose an optical simulation of dissipation-induced correlations in one-dimensional (1D) interacting bosonic systems, using a two-dimensional (2D) array of linear photonic waveguides and only classical light. We show that for the case of two bosons in a 1D lattice, one can simulate on-site two-body dissipative dynamics using a linear 2D waveguide array with lossy diagonal waveguides. The intensity distribution of the propagating light directly maps out the wave function, allowing one to observe the dissipation-induced correlations with simple measurements. Beyond the on-site model, we also show that a generalised model containing nearest-neighbour dissipative interaction can be engineered and probed in the proposed set-up.

Topological pumping over a photonic Fibonacci quasicrystal

Quasiperiodic lattices have recently been shown to be a nontrivial topological phase of matter. Charge pumping---one of the hallmarks of topological states of matter---was recently realized for photons in a one-dimensional off-diagonal Harper model implemented in a photonic waveguide array. However, if the relationship between topological pumps and quasiperiodic systems is generic, one might wonder how to observe it in the canonical and most studied quasicrystalline system in one dimension---the Fibonacci chain. This chain is expected to facilitate a similar phenomenon, yet its discrete nature hinders the experimental study of such topological effects. Here, we overcome this obstacle by utilizing the topological equivalence of a family of quasiperiodic models which ranges from the Fibonacci chain to the Harper model. Implemented in photonic waveguide arrays, we observe the topological properties of this family, and perform a topological pumping of photons across a Fibonacci chain.

Parity-dependent localization inNstrongly coupled chains

Anderson localization of wave-functions at zero energy in quasi-1D systems of $N$ disordered chains with inter-chain coupling $t$ is examined. Localization becomes weaker than for the 1D disordered chain ($t=0$) when $t$ is smaller than the longitudinal hopping $t'=1$, and localization becomes usually much stronger when $t\gg t'$. This is not so for all $N$. We find "immunity" to strong localization for open (periodic) lateral boundary conditions when $N$ is odd (a multiple of four), with localization that is weaker than for $t=0$ and rather insensitive to $t$ when $t \gg t'$. The peculiar $N$-dependence and a critical scaling with $N$ is explained by a perturbative treatment in $t'/t$, and the correspondence to a weakly disordered effective chain is shown. Our results could be relevant for experimental studies of localization in photonic waveguide arrays.

PERTURBATIVE APPROACH TO DIATOMIC LATTICES

By using a small rotation approach, we show that it is possible to obtain well behaved perturbed solutions for the amplitude of the electromagnetic field propagating in a photonic waveguide array. This array mimics the propagation of a quasiparticle among the sites of an infinite one-dimensional chain.

Silicon nanomembrane based photonic crystal waveguide array for wavelength-tunable true-time-delay lines

We demonstrate a four-channel on-chip true-time-delay module based on a photonic crystal waveguide array. Using the photonic crystal taper to minimize the coupling loss, the delay lines with 1–3 mm long photonic crystal waveguides can operate up to a group index ng ∼ 23 without significant loss. The large group velocity dispersion enables continuous and wavelength-tunable time delays. Measurements show a highly linear phase-frequency relation, highest time delay up to 216.7 ps, and large tuning ranges of 58.28 ps, 115.74 ps, and 194.16 ps for 1–3 mm delay lines. The chip-scale true-time-delay module occupies only 0.18 mm2 area and can provide ±44.38° steering for an X-band phased-array-antenna.