The presence of topological edge modes at the interface of two perturbed honeycomb photonic crystals with $C_6$ symmetry is often attributed to the different signs of Berry curvature at the K and K$'$ valleys. In contrast to the electronic counterpart, the Chern number defined in photonic valley Hall effect is not a quantized quantity but can be tuned to finite values including zero simply by changing geometrical perturbations. Here, we argue that the edge modes in photonic valley Hall effect can exist even when Berry curvature vanishes. We numerically demonstrate the presence of the zero-Berry-curvature edge modes in triangular lattice photonic crystal slab structures in which $C_3$ symmetry is maintained but inversion symmetry is broken. We investigate the evolution of the Berry curvature from the honeycomb-lattice photonic crystal slab to the triangular-lattice photonic crystal slab and show that the triangular-lattice photonic crystals still support edge modes in a very wide photonic bandgap. Additionally, we find that the edge modes with zero Berry curvature can propagate with extremely low bending loss.
We apply gain/loss to honeycomb photonic lattices and show that the dispersion relation is identical to tachyons - particles with imaginary mass that travel faster than the speed of light. This is accompanied by PT-symmetry breaking in this structure. We further show that the PT-symmetry can be restored by deforming the lattice.
We explore the effects of random link removal on the photonic band gaps of honeycomb networks. Missing or incomplete links are expected to be common in practical realizations of this class of connected network structures due to unavoidable flaws in the fabrication process. We focus on the collapse of the photonic band gap due to the defects induced by the link removal. We show that the photonic band gap is quite robust against this type of random decimation and survives even when almost 58% of the network links are removed.
The field energy distributions and effective mode areas of silica-based photonic bandgap fibers with a honeycomb airhole structure in the cladding and an extra airhole defining the core are investigated. We present a generalization of the common effective area definition, suitable for the problem at hand, and compare the results for the photonic bandgap fibers with those of index-guiding microstructured fibers. While the majority of the field energy in the honeycomb photonic bandgap fibers is found to reside in the silica, a substantial fraction (up to ~30%) can be located in the airholes. Thi…
In an atomic vapor, a honeycomb lattice can be constructed by utilizing the three-beam interference method. In the method, the interference of the three beams splits the dressed energy level periodically, forming a periodic refractive index modulation with the honeycomb profile. The energy band topology of the honeycomb lattice can be modulated by frequency detunings, thereby affecting the appearance (and disappearance) of Dirac points and cones in the momentum space. This effect can be usefully exploited for the generation and manipulation of topological insulators.
We consider an air-silica honeycomb lattice and demonstrate a new approach to the formation of a core defect. Typically, a high or low-index core is formed by adding a high-index region or an additional air-hole (or other low-index material) to the lattice, but here we discuss how a core defect can be formed by manipulating the cladding region rather than the core region itself. Germanium-doping of the honeycomb lattice has recently been suggested for the formation of a photonic band-gap guiding silica-core and here we experimentally demonstrate how an index-guiding silica-core can be formed b…
In this paper, the photonic quantum spin Hall effect (PQSHE) is realized in dielectric two-dimensional (2D) honeycomb lattice photonic crystal (PC) by stretching and shrinking the honeycomb unit cell. Combining two honeycomb lattice PCs with a common photonic band gap (PBG) but different band topologies can generate a topologically protected edge state at the combined junction. The topological edge states and their unidirectional transmission as the scatterers with triangular, pentagonal, and heptagonal shapes are researched. Meanwhile, the unidirectional transmission in an inverted Ω-shaped w…
We introduce a small-core air-guiding photonic crystal fiber whose cladding is made of improved air-silica photonic crystal with non-circular air holes placed in triangular lattice. The fiber achieves un-disturbed bandgap guidance over 350nm wavelength range.
We report on transport properties of the super-honeycomb lattice, the band structure of which possesses a flat band and Dirac cones, according to the tight-binding approximation. This super-honeycomb model combines the honeycomb lattice and the Lieb lattice and displays the properties of both. The super-honeycomb lattice also represents a hybrid fermionic and bosonic system, which is rarely seen in nature. By choosing the phases of input beams properly, the flat-band mode of the super-honeycomb will be excited and the input beams will exhibit strong localization during propagation. On the othe…
We theoretically investigate the flow of electromagnetic waves in complex honeycomb photonic lattices with local PT symmetries. Such PT structure is introduced via a judicious arrangement of gain or loss across the honeycomb lattice, characterized by a gain/loss parameter γ. We found a new class of conical diffraction phenomena where the formed cone is brighter and travels along the lattice with a transverse speed proportional to Sqrt (γ).
We study theoretically light propagations at the zigzag edge of a honeycomb photonic crystal consisting of dielectric rods in air, analogous to graphene. Within the photonic band gap of the honeycomb photonic crystal, a unimodal edge state may exist with a sharp confinement of optical fields. Its dispersion can be tuned simply by adjusting the radius of the edge rods. For the edge rods with a graded variation in radius along the edge direction, we show numerically that light beams of different frequencies can be trapped sharply in different spatial locations, rendering wideband trapping of lig…
We study topological states of honeycomb photonic crystals in absence of inversion symmetry using plane wave expansion and finite element methods. The breaking of inversion symmetry in honeycomb lattice leads to contrasting topological valley indices, i.e., the valley-dependent Chern numbers in momentum space. We find that the topological corner states appear for 60$^\circ$ degree corners, but absent for other corners, which can be understood as the sign flip of valley Chern number at the corner. Our results provide an experimentally feasible platform for exploring valley-dependent higher-orde…
We describe the formation of highly degenerate, Landau-level-like amplified states in a strained photonic honeycomb lattice in which amplification breaks the sublattice symmetry. As a consequence of the parity anomaly, the zeroth Landau level is localized on a single sublattice and possesses an enhanced or reduced amplification rate. The spectral properties of the higher Landau levels are constrained by a generalized time-reversal symmetry. In the setting of two-dimensional photonic crystal lasers, the anomaly directly affects the mode selection and lasing threshold while in three-dimensional …
We study, theoretically and experimentally, optical properties of different types of honeycomb photonic structures, known also as `photonic graphene'. First, we employ the two-photon polymerization method to fabricate the honeycomb structures. In experiment, we observe a strong diffraction from a finite number of elements, thus providing a unique tool to define the exact number of scattering elements in the structure by a naked eye. Then, we study theoretically the transmission spectra of both honeycomb single layer and 2D structures of parallel dielectric circular rods. When the dielectric co…
We consider light propagation through a ballistic amplifying photonic honeycomb lattice below the lasing threshold. Two sublattices of the system are formed by the wave-guides with different complex dielectric permittivities, which results in the non-Hermitian Dirac equation for electromagnetic field. We reveal that there exists a critical length of the amplifying region for which the photonic lattice exhibits an amplifier to generator transition. The transmission and reflection probabilities at the normal angle of incidence are strongly enhanced at a critical length of the system. We also com…
We experimentally reveal the emergence of edge states in a photonic lattice with orbital bands. We use a two-dimensional honeycomb lattice of coupled micropillars whose bulk spectrum shows four gapless bands arising from the coupling of $p$-like photonic orbitals. We observe zero-energy edge states whose topological origin is similar to that of conventional edge states in graphene. Additionally, we report novel dispersive edge states that emerge not only in zigzag and bearded terminations, but also in armchair edges. The observations are reproduced by tight-binding and analytical calculations.…
We report the realization of a synthetic magnetic field for photons and polaritons in a honeycomb lattice of coupled semiconductor micropillars. A strong synthetic field is induced in both the s and p orbital bands by engineering a uniaxial hopping gradient in the lattice, giving rise to the formation of Landau levels at the Dirac points. We provide direct evidence of the sublattice symmetry breaking of the lowest-order Landau level wavefunction, a distinctive feature of synthetic magnetic fields. Our realization implements helical edge states in the gap between n=0 and n=1 Landau levels, expe…
We address Anderson localization in disordered honeycomb photonic lattices and show that the localization process is strongly affected by the spectral position of the input wavepacket within the first Brillouin zone of the lattice. In spite of the fact that in regular lattice the expansion of the beam is much stronger for the excitation near the Dirac points, where light exhibits conical diffraction, than for the excitation at the center of the Brillouin zone, where the beam exhibits normal diffraction, we found that disorder leads to pronounced Anderson localization even around the Dirac poin…
We establish experimentally a photonic super-honeycomb lattice (sHCL) by use of a cw-laser writing technique, and thereby demonstrate two distinct flatband line states that manifest as noncontractible-loop-states in an infinite flatband lattice. These localized states (straight and zigzag lines) observed in the sHCL with tailored boundaries cannot be obtained by superposition of conventional compact localized states because they represent a new topological entity in flatband systems. In fact, the zigzag-line states, unique to the sHCL, are in contradistinction with those previously observed in…
We clarify theoretically that the topological ring-cavity (TRC) modes propagating along the interface between two honeycomb-type photonic crystals distinct in topology can be exploited for achieving stable single-mode lasing, with the maximal intensity larger than a whispering-gallery-mode counterpart by order of magnitude. Especially, we show that the TRC modes located at the bulk bandgap center benefit maximally from the gain profile since they are most concentrated and uniform along the ring cavity, and that, inheriting from the Dirac-like dispersion of topological interface states, they ar…
The Fano resonance with a distinctive ultra-sharp, asymmetric line shape and high quality factor Q, is a widely occurring phenomena that has a large variety of optical, plasmonic and microwave manifestations. In this paper, we explore the characteristic robustness of the Fano resonance mode, which is topologically protected by manufacturing band inversion induced by breaking the mirror symmetry of a two-dimensional honeycomb photonic crystal (HPC), associated with C_6 point group symmetry. So the dark and bright topological edge modes appear in the band gap made by opening of the Dirac cone. D…
According to a recent proposal [S. Takayama et al., Appl. Phys. Lett. 87, 061107 (2005)], the triangular lattice of triangular air holes may allow to achieve a complete photonic band gap in two-dimensional photonic crystal slabs. In this work we present a systematic theoretical study of this photonic lattice in a high-index membrane, and a comparison with the conventional triangular lattice of circular holes, by means of the guided-mode expansion method whose detailed formulation is described here. Photonic mode dispersion below and above the light line, gap maps, and intrinsic diffraction los…
The toolbox quantities used for manipulating the flow of light include typically amplitude, phase, and polarization. Pseudospins, such as those arising from valley degrees of freedom in photonic structures, have recently emerged as an excellent candidate for this toolbox, in parallel with rapid development of spintronics and valleytronics in condensed-matter physics. Here, by employing symmetry-broken honeycomb photonic lattices, we demonstrate valley-dependent wavepacket self-rotation manifested in spiraling intensity patterns, which occurs without any initial orbital angular momentum. Theore…
A scalable approach for integrated photonic networks in single-crystal diamond using triangular etching of bulk samples is presented. We describe designs of high quality factor (Q=2.51x10^6) photonic crystal cavities with low mode volume (Vm=1.062x(λ/n)^3), which are connected via waveguides supported by suspension structures with predicted transmission loss of only 0.05 dB. We demonstrate the fabrication of these structures using transferred single-crystal silicon hard masks and angular dry etching, yielding photonic crystal cavities in the visible spectrum with measured quality factors in ex…
We demonstrate theoretically and experimentally a topological transition of classical light in "photonic graphene": an array of waveguides arranged in the honeycomb geometry. As the system is uniaxially strained (compressed), the two unique Dirac points (present in the spectrum of conventional graphene) merge and annihilate each other, and a band gap forms. As a result, edge states are created on the zig-zag edge and destroyed on the bearded edge. These results are applicable for any 2D honeycomb-type structure, from carbon-based graphene to photonic lattices and crystals.
In this article, silica based triangular lattice PCF has been investigated towards both narrowband and broadband dispersion compensation for application in the communication wavelength. A dual core structure is obtained by introducing two different air-hole diameters in the cladding of the PCF. Dependence of individual structural parameters towards high negative dispersion (both narrowband and broadband) has been investigated in details with multipole mode based solver. The numerical investigation exhibits narrowband of very large negative dispersion of -37,300 ps/nm/km around the wavelength o…
We demonstrate the photonic Floquet topological insulator (PFTI) in an atomic vapor with nonlinear susceptibilities. The interference of three coupling fields splits the energy levels periodically to form a periodic refractive index structure with honeycomb symmetry that can be adjusted by the choice of frequency detunings and intensities of the coupling fields, which all affect the appearance of Dirac cones in the momentum space. When the honeycomb lattice sites are helically ordered along the propagation direction, we obtain a PFTI in the atomic vapor in which an obliquely incident beam move…
Triangular cross-section SiC photonic devices have been studied as an efficient and scalable route for integration of color centers into quantum hardware. In this work, we explore efficient collection and detection of color center emission in a triangular cross-section SiC waveguide by introducing a photonic crystal mirror on its one side and a superconducting nanowire single photon detector (SNSPD) on the other. Our modeled triangular cross-section devices with a randomly positioned emitter have a maximum coupling efficiency of 89 % into the desired optical mode and a high coupling efficiency…
We develop a class of supercell photonic crystals supporting complete photonic bandgaps based on breaking spatial symmetries of the underlying primitive photonic crystal. One member of this class based on a two-dimensional honeycomb structure supports a complete bandgap for an index-contrast ratio as low as $n_{high}/n_{low} = 2.1$, making this the first such 2D photonic crystal to support a complete bandgap in lossless materials at visible frequencies. The complete bandgaps found in such supercell photonic crystals do not necessarily monotonically increase as the index-contrast in the system …
Diamond photonics provides an attractive architecture to explore room temperature cavity quantum electrodynamics and to realize scalable multi-qubit computing. Here we review the present state of diamond photonic technology. The design, fabrication and characterization of a novel triangular cross section nanobeam cavity produced in a single crystal diamond is demonstrated. The present cavity design, based on a triangular cross section allows vertical confinement and better signal collection efficiency than that of slab-based nanocavities, and eliminates the need for a pre-existing membrane. Th…
We present Floquet fractal topological insulators: photonic topological insulators in a fractal-dimensional lattice consisting of helical waveguides. The helical modulation induces an artificial gauge field and leads to the trivial-to-topological transition. The quasienergy spectrum shows the existence of topological edge states corresponding to real-space Chern number 1. We study the propagation of light along the outer edges of the fractal lattice and find that wavepackets move along the edges without penetrating into the bulk or backscattering even in the presence of disorder. In a similar …
Two-dimensional (2D) coupled resonant optical waveguide (CROW), exhibiting topological edge states, provides an efficient platform for designing integrated topological photonic devices. In this paper, we propose an experimentally feasible design of 2D honeycomb CROW photonic structure. The characteristic optical system possesses two-fold and three-fold Dirac points at different positions in the Brillouin zone. The effective gauge fields implemented by the intrinsic pseudo-spin-orbit interaction open up topologically nontrivial bandgaps through the Dirac points. Spatial lattice geometries allow…
Silicon carbide is evolving as a prominent solid-state platform for the realization of quantum information processing hardware. Angle-etched nanodevices are emerging as a solution to photonic integration in bulk substrates where color centers are best defined. We model triangular cross-section waveguides and photonic crystal cavities using Finite-Difference Time-Domain and Finite-Difference Eigensolver approaches. We analyze optimal color center positioning within the modes of these devices and provide estimates on achievable Purcell enhancement in nanocavities with applications in quantum com…
Silicon carbide is among the leading quantum information material platforms due to the long spin coherence and single-photon emitting properties of its color center defects. Applications of silicon carbide in quantum networking, computing, and sensing rely on the efficient collection of color center emission into a single optical mode. Recent hardware development in this platform has focused on angle-etching processes that preserve emitter properties and produce triangularly shaped devices. However, little is known about the light propagation in this geometry. We explore the formation of photo…
We experimentally demonstrate topological edge states arising from the valley-Hall effect in twodimensional honeycomb photonic lattices with broken inversion symmetry. We break inversion symmetry by detuning the refractive indices of the two honeycomb sublattices, giving rise to a boron nitride-like band structure. The edge states therefore exist along the domain walls between regions of opposite valley Chern numbers. We probe both the armchair and zig-zag domain walls and show that the former become gapped for any detuning, whereas the latter remain ungapped until a cutoff is reached. The val…
Engineering of the orbital angular momentum (OAM) of light due to interaction with photonic lattices reveals rich physics and motivates potential applications. We report the experimental creation of regularly-distributed quantized vortex arrays in momentum space by probing the honeycomb and hexagonal photonic lattices with a single focused Gaussian beam. For the honeycomb lattice, the vortices are associated with Dirac points and mimic the Berry curvature sources. However, we show that the resulting spatial patterns of vortices are strongly defined by the symmetry of the wave packet evolving i…
Spin-momentum locking of polariton edge states in honeycomb lattices
Universidad Autónoma de Madrid（马德里自治大学）；Università di Padova（帕多瓦大学）；Indian Institute of Technology Bombay（孟买印度理工学院）；Indian Institute of Technology Dharwad（达尔瓦德印度理工学院）；Julius-Maximilians-Universität Würzburg（维尔茨堡朱利叶斯-马克西米利安大学）
In this paper, we theoretically study the Floquet engineering of two dimensional photonic waveguide arrays in three types of lattices: honeycomb lattice with Kekule distortion, breathing square lattice and breathing Kagome lattice. The Kekule distortion factor or the breathing factor in the corresponding lattice is periodically changed along the axial direction of the photonic waveguide with frequency $ω$. Within certain ranges of $ω$, the Floquet corner states in the Floquet band gap of quasi-energy spectrum are found, which are localized at the corner of the finite two-dimensional arrays. Du…
We study the dynamics of coherent waves in nonlinear honeycomb lattices and show that nonlinearity breaks down the Dirac dynamics. As an example, we demonstrate that even a weak nonlinearity has major qualitative effects one of the hallmarks of honeycomb lattices: conical diffraction. Under linear conditions, a circular input wave-packet associated with the Dirac point evolves into a ring, but even a weak nonlinearity alters the evolution such that the emerging beam possesses triangular symmetry, and populates Bloch modes outside of the Dirac cone region. Our results are presented in the conte…
We predict the existence and study properties of the valley Hall edge solitons in a composite photonic graphene with a domain wall between two honeycomb lattices with broken inversion symmetry. Inversion symmetry in our system is broken due to detuning introduced into constituent sublattices of the honeycomb structure. We show that nonlinear valley Hall edge states with sufficiently high amplitude bifurcating from the linear valley Hall edge state supported by the domain wall, can split into sets of bright spots due to development of the modulational instability, and that such an instability i…
Consider electromagnetic waves in two-dimensional {\it honeycomb structured media}. The properties of transverse electric (TE) polarized waves are determined by the spectral properties of the elliptic operator $\LA=-\nabla_\bx\cdot A(\bx) \nabla_\bx$, where $A(\bx)$ is $Λ_h-$ periodic ($Λ_h$ denotes the equilateral triangular lattice), and such that with respect to some origin of coordinates, $A(\bx)$ is $\mathcal{P}\mathcal{C}-$ invariant ($A(\bx)=\overline{A(-\bx)}$) and $120^\circ$ rotationally invariant ($A(R^*\bx)=R^*A(\bx)R$, where $R$ is a $120^\circ$ rotation in the plane). We first ob…
Beam combiners are important components of an optical/infrared astrophysical interferometer, with many variants as to how to optimally combine two or more beams of light to fringe-track and obtain the complex fringe visibility. One such method is the use of an integrated optics chip that can instantaneously provide the measurement of the visibility without temporal or spatial modulation of the optical path. Current asymmetric planar designs are complex, resulting in a throughput penalty, and so here we present developments into a three dimensional triangular tricoupler that can provide the req…
We study the driven-dissipative steady-state of a coherently-driven Bose field in a honeycomb lattice geometry. In the presence of a suitable spatial modulation of the hopping amplitudes, a valley-dependent artificial magnetic field appears and the low-energy eigenmodes have the form of relativistic Landau levels. We show how the main properties of the Landau levels can be extracted by observing the peaks in the absorption spectrum of the system and the corresponding spatial intensity distribution. Finally, quantitative predictions for realistic lattices based on photonic or microwave technolo…
We study the spin-orbit coupling induced by the splitting between TE and TM optical modes in a photonic honeycomb lattice. Using a tight-binding approach, we calculate analytically the band structure. Close to the Dirac point,we derive an effective Hamiltonian. We find that the local reduced symmetry ($\mathrm{D_{3h}}$) transforms the TE-TM effective magnetic field into an emergent field with a Dresselhaus symmetry. As a result, particles become massive, but no gap opens. The emergent field symmetry is revealed by the optical spin Hall effect.
We derive in the present work topological photonic states purely based on silicon, a conventional dielectric material, by deforming a honeycomb lattice of silicon cylinders into a triangular lattice of cylinder hexagons. The photonic topology is associated with a pseudo time reversal (TR) symmetry constituted by the TR symmetry respected in general by the Maxwell equations and the $C_6$ crystal symmetry upon design, which renders the Kramers doubling in the present photonic system with the role of pseudo spin played by the circular polarization of magnetic field in the transverse magnetic mode…
