One-way Edge Modes Research Articles

Tunable all-optical microwave logic gates based on nonreciprocal topologically protected edge modes

All-optical logic gates have been studied intensively owing to their potential to enable broadband, low-loss and high-speed communications. However, poor tunability has remained a key challenge in this field. In this work, we propose a Y-shaped structure composed of Yttrium Iron Garnet (YIG) layers that can serve as tunable all-optical logic gates, including, but not limited to, OR, AND and NOT gates, by applying external magnetic fields to magnetize the YIG layers. Our findings reveal that these logic gates are founded on protected one-way edge modes, where by tuning the wavenumber k of the operating mode to a sufficiently small (or even zero) value, the gates can become nearly immune to nonlocal effects. This not only enhances their reliability but also allows for maintaining extremely high precision in their operations. Furthermore, the operating band itself of the logic gates is also shown to be tunable. We introduce a straightforward and practical method for controlling and switching these gates between "work", "skip", and "stop" modes. These findings have potentially significant implications for the design of high-performance and robust all-optical microwave communication systems.

Frequency band-selected one-way topological edge mode via acoustic metamaterials and metasurface

Single functionality and fixed operating bands maintain the key drawbacks in existing acoustic topological insulators. Here, we report an acoustic system to realize the frequency band-selected one-way topological edge state transmission. The system is combined with a double-layer sonic crystal and a lossy acoustic metasurface. The topological insulators enable the frequency band-selected effect by separating and nesting the two layers of the sonic crystals. The sound one-way transmission effect is ensured by the metasurface. Consequently, the one-way topological edge state transmission is realized, and the operating band of the system can be shifted between two distinct ranges. Our work may have potential in the areas where multiple frequency bands are required, such as sound isolation, acoustic switch, mechanical imaging, acoustic split, and integrated acoustic communications.

Modeling Reflection-Free One-Way Edge Modes Using Foldy-Lax Multiple Scattering Theory

The Foldy-Lax multiple scattering theory is applied to compute the reflection-free topological one-way edge modes induced by wave interactions with periodic gyromagnetic scatterers. The electromagnetic field response arising from a point source at the interface of two photonic crystals, one comprised of gyromagnetic scatterers, - yttrium-iron-garnet (YIG) scatterers, and the other of alumina scatterers, is studied. The T-matrices of a single cylindrical scatterer of circular cross-section, of both YIG and alumina materials, are derived and utilized to formulate the Foldy-Lax multiple scattering equations. The fields inside and outside the scatterers are derived. Field results of both single-scatterer scattering and multiple-scatterer scattering are compared with results from the method of moments (MoM) and from COMSOL simulations. The comparisons confirm the accuracy of the proposed method and show that the Foldy-Lax multiple-scattering theory is far more efficient than MoM and COMSOL. The proposed approach can be a useful tool for topological wave device analysis and design.

Nonequilibrium edge transport in quantum Hall based Josephson junctions

We study the transport properties of a voltage-biased Josephson junction where the BCS superconducting leads are coupled via the edges of a quantum Hall sample. In this scenario, an out of equilibrium Josephson current develops, which is numerically studied within the Floquet-Keldysh Green's function formalism. We particularly focus on the time-averaged current as a function of both the bias voltage and the magnetic flux threading the sample and analyze the resonant multiple Andreev reflection processes that lead to an enhancement of the quasiparticle transmission. We find that a full tomography of the dc current in the voltage-flux plane allows for a complete spectroscopy of the one-way edge modes and could be used as a hallmark of chiral edge mediated transport in these hybrid devices.

Zero GVD slow-light originating from a strong coupling of one-way modes in double-channel magneto-optical photonic crystal waveguides.

We have studied the coupling effect of topological photonic states in a double-channel magneto-optical photonic crystal waveguide by introducing a two-stranded ordinary Al2O3 photonic crystal as the coupling layer. There exist both M1 (odd) and M2 (even) one-way modes simultaneously in the bandgap. Interestingly, M1 mode is always a fast-light mode with large group velocity (vg) and large group velocity dispersion (GVD) regardless what the radius (RA) of Al2O3 rods is. However, when RA is appropriate, M2 mode becomes a very slow-light mode exhibiting near-zero vg and zero GVD simultaneously. The physical reason of such slow-light is attributed to the strong coupling effect between the one-way edge modes in both sub-waveguides. Furthermore, the simulation results show that the robustness of both the fast- and slow-light modes are extremely strong against perfect electric conductor defect and the one-way transmittance is close to 100%. Besides, the PEC defect can cause significant phase delay. These results hold promise for many fields such as signal processing, optical modulation, and the design of various topological devices.

Single-Photon Transport in a Topological Waveguide from a Dynamically Modulated Photonic System

The topologically protected one-way edge modes for light show a way to manipulate the interaction between a single photon and a quantum emitter. We systematically study single-photon quantum optics in a topological waveguide supporting the frequency-dependent one-way edge mode at the boundary of a dynamically modulated photonic system, and compare the results of the single-photon interacting dynamics with the quantum emitter in a unidirectional waveguide. As a major difference, a photon in a topological waveguide propagates around the resonant site coupled to the quantum emitter due to the topological protection. Our results show that, despite different subtleties, photon-emitter interactions for one photon at the edge mode and for one photon propagating in a unidirectional waveguide hold similar features. In addition, we consider the interaction between the photon and a $\mathrm{\ensuremath{\Lambda}}$-type three-level quantum emitter in the topological waveguide, where we show the nonlocal correlated photon-state generation as well as the single-photon reflection with the frequency conversion. Our work provides insight for understanding the interaction between the topologically protected unidirectional-propagating photon and the quantum emitter, which holds promise for potential applications in quantum-information processing.

Nonlinear one-way edge-mode interactions for frequency mixing in topological photonic crystals

Topological photonics aims to utilize topological photonic bands and corresponding edge modes to implement robust light manipulation, which can be readily achieved in the linear regime of light-matter interaction. Importantly, unlike solid state physics, the common test bed for new ideas in topological physics, topological photonics provide an ideal platform to study wave mixing and other nonlinear interactions. These are well-known topics in classical nonlinear optics but largely unexplored in the context of topological photonics. Here, we investigate nonlinear interactions of one-way edge-modes in frequency mixing processes in topological photonic crystals. We present a detailed analysis of the band topology of two-dimensional photonic crystals with hexagonal symmetry and demonstrate that nonlinear optical processes, such as second- and third-harmonic generation can be conveniently implemented via one-way edge modes of this setup. Moreover, we demonstrate that more exotic phenomena, such as slow-light enhancement of nonlinear interactions and harmonic generation upon interaction of backward-propagating (left-handed) edge modes can also be realized. Our work opens up new avenues towards topology-protected frequency mixing processes in photonics.

Photonic states on Möbius band

Exotic electronic states have been studied with different boundary conditions and on various geometries, especially topological states. However, geometries, including the boundary conditions in photonic crystals, have not drawn sufficient attention and have rarely been investigated. Here, we propose photonic crystals on a Möbius band, which is topologically equivalent to the lattice on cylinder with reflection symmetries. Through this mapping, we can obtain some exotic phenomena in magnetic and all-dielectric photonic systems, such as two photonic carrier channels, one-way edge modes and interface states. Along this line, the photonic states on more complex geometries can be raised and studied based on the topological equivalence principle for exploring the richer edge and interface physics, even topological physics.

Topologically protected edge states of elastic waves in phononic crystal plates

<sec> The topologically protected edge states of elastic waves in phononic crystal plates have the outstanding characteristics in wave manipulation such as the strong suppression of back-scattering and defect immunity, which can be used for controlling vibration and noise, detecting the structural damage, conducting the material nondestructive test and other engineering practices, and therefore have received much attention. But for plate structures, the propagation of elastic waves is complicated due to the coexistence and coupling of different types of wave modes, resulting in a challenge in designing topologically protected states. </sec><sec>In this paper, a simple phononic crystal plate with triangular holes is designed for elastic wave manipulation based on topologically protected edge states. The band structure characteristics of the unit cell are studied by varying the rotation angle <i>θ</i> of the triangular holes around their geometric centers from the initial positions. It is found that the band structure of the initial unit cell with rotation angle <i>θ</i> = 0° has two pairs of degenerate modes. At <inline-formula><tex-math id="M6">\begin{document}$ \theta = \pm 33^\circ $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="15-20200542_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="15-20200542_M6.png"/></alternatives></inline-formula>, a double Dirac cone appears at the center <i>Γ</i> point of the Brillouin zone without requiring the lattices to fold, and a band inversion occurs on both sides of <inline-formula><tex-math id="M7">\begin{document}$ \pm 33^\circ $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="15-20200542_M7.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="15-20200542_M7.png"/></alternatives></inline-formula> which can be characterized as a topological phase transition. </sec><sec>The elastic band gap and two kinds of pseudospin states with clockwise or counterclockwise circulating mechanical energy flux patterns in the band structure are found by calculating the projected band structures of a supercell which is composed of phononic crystals with different topological phases. Based on this finding, different constructions of phononic waveguide are used for implementing the numerical analysis to demonstrate the back-scattering immunity of the edge states when disorder, tortuosity and cavity are introduced into the waveguide. Unidirectional robust propagation and multichannel waveguide switch due to the pseudospin-dependent one-way edge modes are also validated with numerical models. The phononic crystal plate presented in this paper provides a simple realizable method of designing the topologically protected elastic edge states. </sec>

Topological kink plasmons on magnetic-domain boundaries

Two-dimensional topological materials bearing time reversal-breaking magnetic fields support protected one-way edge modes. Normally, these edge modes adhere to physical edges where material properties change abruptly. However, even in homogeneous materials, topology still permits a unique form of edge modes – kink modes – residing at the domain boundaries of magnetic fields within the materials. This scenario, despite being predicted in theory, has rarely been demonstrated experimentally. Here, we report our observation of topologically-protected high-frequency kink modes – kink magnetoplasmons (KMPs) – in a GaAs/AlGaAs two-dimensional electron gas (2DEG) system. These KMPs arise at a domain boundary projected from an externally-patterned magnetic field onto a uniform 2DEG. They propagate unidirectionally along the boundary, protected by a difference of gap Chern numbers (pm1) in the two domains. They exhibit large tunability under an applied magnetic field or gate voltage, and clear signatures of nonreciprocity even under weak-coupling to evanescent photons.

Achievement of unidirectional air waveguide with extra-broad operation bandwidth in magneto-optical photonic crystals with a triangle lattice

We have presented a coupling structure of two-dimensional (2D) magneto-optical photonic crystals (MOPCs) with a triangular lattice. The numerical calculation of photonic band structure is performed based on the finite element method. The result shows that photonic band gap of 2D MOPCs with a triangular lattice is much larger than that of 2D MOPCs with a square lattice or a honeycomb lattice under the same applied external magnetic field, i.e., working bandwidth of 2D MOPCs with a triangular lattice is much larger than that of the other two MOPCs. We have studied the coupling effect of one-way edge modes in 2D MOPCs with a triangle lattice, and achieved a unidirectional air waveguide with high-transmission, strong nonreciprocity and extra-broad operation bandwidth. Furthermore, we have qualitatively analyzed waveguide transmission characteristics based on S-parameter method, and illustrated the effective operating bandwidth and the optimum operating frequency for optical waveguide nonreciprocity devices according to different transmission losses in application.

Self-Guiding Backscattering Immune Transportation of Light in the Visible Range

The implementation of topological photonic systems at optical frequency is of great significance for practical applications. In this work, we extend the study of unidirectional transmission to the visible light range with a relatively simple structure. We theoretically demonstrated the existence of self-guiding one-way edge modes at the interface between air and a hexagonal lattice of rods with a layered plasmo-semiconductor-gyroelectric metamaterial as the background medium. The inherent loss in metals can be compensated by the incorporation of the semiconductor layers with optical gain. Our simulation result shows that the self-guiding transmission remains 82% over a distance of about 30 wavelengths. In addition, it renders the light travel on such an interface insensitive to obstacles or impurities either on-purposely introduced or caused by manufacturing imperfections or variations. We show that the power transmission remains around 80% even in the presence of deliberately introduced obstacles. By exploiting the robust self-guiding unidirectional transport feature, we have designed a shape-independent cavity that can tolerate sharp corners in different angles, which eliminates the reflection and relaxes the geometrical constraint in design of integrated photonic devices.

One-way edge modes in truncated semiconductor photonic crystal at terahertz frequencies

Terahertz one-way edge modes in truncated photonic crystals (PhCs) are investigated theoretically. The PhC consists of a square array of air columns in a semiconductor. By applying an external dc magnetic field in the PhC, a band gap is generated by lifting the degeneracy point of the lowest two bands. Based on this band gap, the edge mode always exists in the truncated PhC for any boundary cutting, and it may propagate unidirectionally or bidirectionally, closely depending on the PhC boundary shape. It is shown that for the one-way edge mode, the PhC boundary cutting has a remarkable influence on the propagation length when the semiconductor loss is taken into account. A boundary structure is introduced into the PhC system for weakening the loss effect, and the propagation length of the one-way edge mode can be increased nearly by twice by optimizing the boundary parameters.

Realization of Hofstadter's butterfly and a one-way edge mode in a polaritonic system

We present a scheme to generate an artificial gauge field for the system of neutral bosons, represented by polaritons in micropillars arranged into a square lattice. The splitting between the two polarizations of the micropillars breaks the time-reversal symmetry (TRS) and results in the effective phase-dependent hopping between cavities. This can allow for engineering a nonzero flux on the plaquette, corresponding to an artificial magnetic field. Changing the phase, we observe a characteristic Hofstadter's butterfly pattern and the appearance of chiral edge states for a finite-size structure. For long-lived polaritons, we show that the propagation of wave packets at the edge is robust against disorder. Moreover, given the inherent driven-dissipative nature of polariton lattices, we find that the system can exhibit topological lasing, recently discovered for active ring cavity arrays. The results point to a static way to realize artificial magnetic field in neutral spinful systems, avoiding the periodic modulation of the parameters or strong spin-orbit interaction. Ultimately, the described system can allow for high-power topological single-mode lasing which is robust to imperfections.

A unidirectional air waveguide basing on coupling of two self-guiding edge modes

Nonreciprocal waveguide plays the key role in optical communication devices because of the robustness of one-way transport along the edge. We present a 2D honeycomb magnetic-optical photonic crystal frame and realize a unidirectional air waveguide based on the coupling effect of two self-guiding one-way edge modes in proper the waveguide width. A great ideal nonreciprocal air waveguide with condensed-energy, strong stability, great nonreciprocity is achieved, and its transmission features of superiority over others configuration are demonstrated.

One-way edge modes in a photonic crystal of semiconductor at terahertz frequencies

Electromagnetic edge mode in a photonic crystal (PhC), which is a square array of semiconductor rods in air, is theoretically investigated for terahertz frequencies. In the PhC, gyroelectric anisotropy is introduced in the semiconductor rods by applying an external magnetic field and consequently, a degeneracy point, at which two dispersion surfaces intersect, is lifted and a new band gap is created. The edge mode sustained by the PhC possesses the character of one-way propagation, and it even can be immune to backscattering at large defect on the wavelength scale and 90° sharp bend. The properties of the one-way mode are closely dependent on the cladding layer structure of the PhC.

Model for topological phononics and phonon diode

The quantum anomalous Hall effect, an exotic topological state first theoretically predicted by Haldane and recently experimentally observed, has attracted enormous interest for low-power-consumption electronics. In this work, we derived a Schr{\"o}dinger-like equation of phonons, where topology-related quantities, time reversal symmetry and its breaking can be naturally introduced similar as for electrons. Furthermore, we proposed a phononic analog of the Haldane model, which gives the novel quantum (anomalous) Hall-like phonon states characterized by one-way gapless edge modes immune to scattering. The topologically nontrivial phonon states are useful not only for conducting phonons without dissipation but also for designing highly efficient phononic devices, like an ideal phonon diode, which could find important applications in future phononics.

Interacting quantum fluid in a polariton Chern insulator

We study Bogoliubov excitations of a spinor Bose Einstein condensate in a honeycomb periodic potential, in the presence of a Zeeman field and of a spin-orbit coupling specific for photonic systems, which is due to the energy splitting between TE and TM polarized eigenstates. We also consider spin-anisotropic interactions typical for cavity polaritons. We show that the non-trivial topology of the single particle case is also present for the interacting system. At low condensate density, the topology of the single-particle bands is transferred to the bogolon dispersion. At a critical value, the self-induced Zeeman field at the Dirac points of the dispersion becomes equal to the real Zeeman field and then exceeds it. The gap is thus closed and then re-opened with inverted Chern numbers. This change of topology is accompanied by a change of the propagation directions of the one-way edge modes. This result demonstrates that the chirality of a topological insulator can be reversed by collective effects in a Bose-Einstein condensate.

Localized surface plasmon resonance and the size effects of magneto-optic rods

Localized surface plasmon resonance of cylindrical magneto optical particles provides an important mechanism for the formation of chiral edge states in two-dimensional magneto-optical photonic crystals. These states are an electromagnetic analogy of the so-called chiral edge state's (CESs) in a quantum Hall system where the power transmission is unidirectional due to particular topological properties of the bands. Just like their electronic counterpart, the number of optical CESs in the band gap opened by an applied magnetic field is determined by the sum of the Chern numbers of the lower bands. For a two-dimensional photonic crystal composed of ferrite rods magnetized along their axis, the coupling of the localized surface plasmon resonance states of each rod results in a narrow flat band-gap, which contains one-way edge modes arising from the circulation of the energy flow around each rod excited by the resonance with broken time-reversal symmetry. So far the interpretation of the resonance-related chiral edge states are based on the long-wavelength approximation of the localized surface plasmon resonance of an individual magneto-optical particle. Though the results agree with the experimental results qualitatively, an obvious quantitative deviation is still obvious. In this work we apply the scattering theory to analyze the resonance condition and the features of both the far-field and the near-field at resonance for cylindrical magneto-optical particles. Our calculation shows that the splitting of scattering peaks of different orders will occur due to the magneto-optical effect. Such a split is observed between an (+n)-peak and an (-n) peak, as a sign of the broken time-reversal symmetry, and also between peaks of lower-order and higher-order. Another important feature is the simultaneous occurring of the far-field resonance and the near-field resonance, where the latter is characterized by a peak of energy-flow circulation around the particle. Based on this model the effects of particle size on the resonance peaks are discussed. It is shown that the resonance peaks are moved and broadened with the particle size increasing. The results explain the obvious deviation of the position of the resonance band-gap from the predicted frequency according to the previous long-wavelength approximation. Furthermore, the calculation of a particle of moderately-large size (nearly one-tenth of the incident wavelength) demonstrates the appearance of higher-order modes up to n=4 circling around the particle surface. This implies that these higher-order modes may also make non-trivial contribution to the formation of the flat band-gap observed in a photonic crystal of ferrite-rods and affect the behaviours of the chiral-edge state existing in such a gap. Particularly, it may be helpful in realizing the multimodes of chiral edge states in magneto-optical photonic crystals.

Topologically nontrivial Floquet band structure in a system undergoing photonic transitions in the ultrastrong-coupling regime

We consider a system of dynamically-modulated photonic resonator lattice undergoing photonic transition, and show that in the ultra-strong coupling regime such a lattice can exhibit non-trivial topological properties, including topologically non-trivial band gaps, and the associated topologically-robust one-way edge states. Compared with the same system operating in the regime where the rotating wave approximation is valid, operating the system in the ultra-strong coupling regime results in one-way edge modes that has a larger bandwidth, and is less susceptible to loss. Also, in the ultra-strong coupling regime, the system undergoes a topological insulator-to-metal phase transition as one varies the modulation strength. This phase transition has no counter part in systems satisfying the rotating wave approximation, and its nature is directly related to the non-trivial topology of the quasi-energy space.