Honeycomb Lattice Photonic Crystals Research Articles

Design of a beam splitter based on an adjustable beam-splitting ratio of a hexagonal star-like topological photonic crystal

We propose a new, to the best of our knowledge, mechanism to realize topological phase transition, that is, in a hexagonal star-like honeycomb lattice photonic crystal (PC), the optical quantum spin Hall effect (QSHE) can be realized by changing the materials of the outer or inner ring dielectric rods in the cells. We calculated the energy band and analyzed the topological phase transition law of a hexagonal star-like honeycomb PC. By changing the permittivity of the PC, the disturbance is introduced to the edge state. It is found that with the decrease of the permittivity of the PC, the gap decreases, the lower boundary state gradually redshifts, and the maximum transmittance in the straight waveguide can reach 98.8%. On this basis, a topological beam splitter was designed and analyzed. Results show that the beam splitting ratio obtained by the system is in the wide range of 0.2–3.5. Our research enriches the implementation of topological photonics, provides potential applications for topological boundary states in terahertz technology, and offers a new avenue for the design of current optical integrated devices.

Large transmittance contrast via 90-degree sharp bends in square lattice glide-symmetric photonic crystal waveguides.

We demonstrate an intriguing transmittance contrast in a glide-symmetric square-lattice photonic crystal waveguide with a 90-degree sharp bend. The glide-symmetry gives rise to a degeneracy point in the band structure and separates a high-frequency and a low-frequency band. Previously, a similar large transmittance contrast between these two bands has been observed in glide-symmetric triangular- or honeycomb-lattice photonic crystals without inversion symmetry, and this phenomenon has been attributed to the valley-photonic effect. In this study, we demonstrate the first example of this phenomenon in square-lattice photonic crystals, which do not possess the valley effect. Our result sheds new light onto unexplored properties of glide-symmetric waveguides. We show that this phenomenon is related to the spatial distribution of circular polarization singularities in glide-symmetric waveguides. This work expands the possible designs of low-loss photonic circuits and provides a new understanding of light transmission via sharp bends in photonic crystal waveguides.

Multiple topological transitions and topological edge states of triple-site honeycomb lattice photonic crystals

We propose a two-dimensional (2D) triple-site honeycomb lattice (TSHL) photonic crystal (PC) by rotating the three dielectric rods six times, forming unit cell, and then arraying the unit cells in the triangular lattice. The TSHL PC structure can achieve topological phase transitions in three ways, which are changing the position or size of the rods, and rotating the rods. By calculating the band structure under different parameters, the law of topological phase transition for TSHL PC is analyzed. The topological edge state can be adjusted by changing the rotation angle of the dielectric rods. Based on this, a frequency-selective beam splitter is designed. Compared with previous studies, this flexible topological system shows more abundant physical phenomena, enriches the implementation of topological photonics , and promotes the research of topological edge states and the development of topological insulators in practical applications. • We propose a two-dimensional triple-site honeycomb lattice photonic crystal, which has the high degrees of freedom. • The triple-site honeycomb lattice unit cell can achieve topological phase transitions in three ways, which are changing the position or size of the cylinders, and rotating the cylinders. • We design a frequency-selective beam splitter, by changing the rotation angle of the dielectric rods.

Fragile topology in double-site honeycomb lattice photonic crystal.

Fragile topology (FT) opens a new direction in topological photonics, but a new type of photonic crystal (PC) with FT remains to be proposed. In this Letter, the double-site honeycomb lattice (DSHL) PC is proposed by rotating the double dielectric rods (DDR) six times, forming unit cell, and then arraying the unit cells in a triangular lattice. Quantum spin Hall effect occurs by manipulating the DDR in the tangential and radial directions of the unit cell. First, the band structures of DSHL PCs with different structural parameters are calculated, and the laws of topological phase transition are analyzed statistically. Then, to prove the FT properties of two groups of topological nontrivial DSHL PCs, the Wannier-center positions of the bulk bands are calculated by the Wilson-Loop method. Finally, the topological edge states and two groups of topological corner states, which are in the same bulk-state bandgap, are realized successfully. The DSHL PC provides good platforms for both the research of topological photonics and the device design and application, which has a broad prospect.

BROKEN SYMMETRY AND TOPOLOGY IN PHOTONIC ANALOG OF GRAPHENE

We review how broken symmetries affect optical properties in photonic analog of graphene, namely, honeycomb-lattice photonic crystals (PhCs). The spatial symmetry of the honeycomb lattice yields Dirac spectra at Brillouin zone corners without fine tuning of physical parameters. In addition, the "Dirac-mass" gap can be introduced by breaking the time-reversal symmetry and/or the space-inversion symmetry. These two symmetries are closely related to the topology of radiation fields in momentum space, and are linked with nontrivial edge states if the system has edges. We show that an effective Hamiltonian for photon obtained with the aid of group theory predicts a modulation of chiral edge states that are hardly implemented in electronic graphene. Numerical simulation of the honeycomb-lattice PhCs of infinitely-long cylinders, confirms the prediction fairly well.

Chiral Domain-Wall States in a Quadratic Hamiltonian

In two-dimensional lattice systems, the effective Hamiltonian around a doubly degenerate point at the Brillouin-zone center can be of a similar form to the d-wave Bogoliubov–Nambu Hamiltonian. A band gap opens there if a perturbation of time-reversal-symmetry breaking is introduced. In such a system, two domain-wall states with the same chirality emerge around the interface between two domains having the gap parameters of opposite signs. The domain-wall states have asymptotically quadratic dispersions, in contrast to the domain-wall state of the Dirac fermion, which has a linear dispersion irrespective of the domain-wall profile. As an explicit example, we numerically study the domain-wall states of photons in a honeycomb-lattice photonic crystal. The results are in agreement with those obtained using the effective theory based on the quadratic Hamiltonian.

OPTIMIZATION AND DESIGN OF 2D HONEYCOMB LATTICE PHOTONIC CRYSTAL MODULATED BY LIQUID CRYSTALS

Photonic crystals (PCs) with infiltrating liquid crystals (LCs) have many potential applications because of their ability to continuously modulate the band-gaps. Using the plane-wave expansion method (PWM), we simulate the band-gap distribution of 2D honeycomb lattice PC with different pillar structures (circle, hexagonal and square pillar) and with different filling ratios, considering both when the LC is used as filling pillar material and semiconductors ( Si , Ge ) are used in the substrate, and when the semiconductors ( Si , Ge ) are pillar material and the LC is the substrate. Results show that unlike LC-based triangle lattice PC, optimized honeycomb lattice PC has the ability to generate absolute photonic band-gaps for fabricating optical switches. We provide optimization parameters for LC infiltrating honeycomb lattice PC structure based on simulation results and analysis.

Unusual Surface-Plasmon-Polaritons-Induced Multiflatbands From Usual Two-Dimensional Honeycomb Lattice Photonic Crystals Composed of Plasma-Coated Cylinders

In the presence of dispersion and dissipation, we deduce a modified plane wave expansion method to calculate photonic bands in 2-D honeycomb lattice photonic crystals (PCs) composed of plasma-coated layers. A linearization technique of the generalized eigenvalue problem for a complex matrix of wave expansion is used to obtain the photonic band structures. In the transverse magnetic mode, when plasma-coating thickness increases to a critical value, most of the dielectric-plasma (DP) photonic bands are the same as photonic bands generated by pure plasma cylinders. This property provides us a way to replace plasma PCs with DP PCs that save energy and materials. In the transverse electric mode, multiflatbands below the plasma frequency also occupy a large frequency range when the plasma coating is sufficiently large. Given that these multiflatbands are caused by surface plasmon polaritons, the region of flatbands depends not on the geometry of the photonic lattice but on the filling factor of the plasma coating. The numerical results validate the correctness of our prediction.

Free-Standing GaN-Based Photonic Crystal Band-Edge Laser

We report the fabrication of a GaN-based membrane-type photonic crystal (PC) band-edge laser (BEL) that requires a smaller PC active area than previous designs due to strong field confinement. A honeycomb-lattice PC was designed such that the Γ1 monopole band-edge mode fell within the emission band of InGaN quantum wells. The BEL exhibited pulsed lasing at room-temperature when optically pumped above its threshold pump energy density of ~ 15.5 mJ/cm2. Based on polarization angle analysis, we confirmed that the BEL indeed lased at the Γ1 monopole band-edge mode.

Low crosstalk waveguide intersections in honeycomb lattice photonic crystals forTM-polarized light

We present the design of a low crosstalk, high throughput waveguide intersection fortransverse-magnetic-polarized light. The design is based on two orthogonal photonic crystalwaveguides and a resonant photonic crystal cavity in honeycomb lattice geometry. Theresults of our numerical simulation validate the concept of the design and demonstrate acrosstalk smaller than 0.1% and throughput transmission of more than 80% for bothorthogonal waveguide branches.

Near-field and far-field analysis of an azimuthally polarized slow Bloch mode microlaser

We report on the near- and far-field investigation of the slow Bloch modes associated with the Γ point of the Brillouin zone, for a honeycomb lattice photonic crystal, using near-field scanning optical microscopy (NSOM) and infra-red CCD camera. The array of doughnut-shaped monopolar mode (mode M) inside each unit cell, predicted previously by numerical simulation, is experimentally observed in the near-field by means of a metal-coated NSOM tip. In far-field, we detect the azimuthal polarization of the doughnut laser beam due to destructive and constructive interference of the mode radiating from the surface (mode TEM(01*)). A divergence of 2° for the laser beam and a mode size of (12.8 ± 1) µm for the slow Bloch mode at the surface of the crystal are also estimated.

Anomalous refractive effects in honeycomb lattice photonic crystals formed by holographic lithography

We have investigated for the first time the anomalous refractive effects of a photonic crystal (PhC) formed by holographic lithography (HL) with triangular rods arranged in a honeycomb lattice in air. Possibilities of left-handed negative refraction and superlens are discussed for the case of TM2 band with the index contrast n = 3.4:1. In contrast to the conventional honeycomb PhC made of regular rods in air, the HL PhCs show left-handed negative refraction over a wider and higher frequency range with high transmissivity (>90%), and the effective indices quite close to -1 for a wide range of incident angles with a larger all-angle left-handed negative refraction (AALNR) frequency range (Deltaomega/omega approximately 14.8%). Calculations and FDTD simulations demonstrate the high-performance negative refraction properties can happen in the holographic structures for a wide filling ratio and can be modulated by changing the filling ratio easily.

Topological properties of bulk and edge states in honeycomb lattice photonic crystals: thecase of TE polarization

Topological properties of bulk and edge states in honeycomb lattice photonic crystals areinvestigated theoretically for transverse-electric (TE) polarization. Breaking ofspace-inversion and time-reversal symmetries is considered at optical frequencies. The bulkband structure exhibits a topological phase transition by changing the degree of the brokensymmetries. The resulting phase diagram correlates with zigzag and armchair edge states,and the so-called bulk–edge correspondence is verified. The effects of flat interfaces near theedges are also discussed.

Photonic analog of graphene model and its extension: Dirac cone, symmetry, and edge states

This paper investigates the topological phase transition in honeycomb lattice photonic crystals with and without time-reversal and space-inversion symmetries through extensive analysis on bulk and edge states. In the system with both the symmetries, there appear multiple Dirac cones in the photonic band structure, and the mass gaps are controllable via symmetry breaking. The zigzag and armchair edges of the photonic crystals can support novel edge states that reflect the symmetries of the photonic crystals. The dispersion relation and the field configuration of the edge states are analyzed in detail in comparison to electronic edge states. Leakage of the edge states to free space, which is inherent in photonic systems, is fully taken into account in the analysis. A topological relation between bulk and edge states, which has been discussed in the context of electronic quantum Hall effect, is also examined in the photonic system with leaky edge states.

High-power and large-alignment-tolerance fiber coupling of honeycomb-lattice photonic crystal Γ-point band-edge laser

Butt-end fiber coupling is a compact and efficient scheme especially suitable for a surface-emitting photonic crystal (PC) band-edge laser. The honeycomb-lattice PC offers a relatively large intact area without air-holes, and therefore, a high optical gain. The use of a Γ-point band-edge mode allows vertical laser emission, yielding a fiber-coupled output power of more than 30 μW. The system is virtually alignment-free in the lateral directions; however, it exhibits oscillatory decay in the vertical direction, which can be significantly suppressed by using an angle-cleaved fiber tip.

Correspondence between Andreev reflection and Klein tunneling in bipolar graphene

Andreev reflection at a superconductor and Klein tunneling through an n-p junction in graphene are two processes that couple electrons to holes -- the former through the superconducting pair potential Delta and the latter through the electrostatic potential U. We derive that the energy spectra in the two systems are identical, at low energies E<<Delta and for an antisymmetric potential profile U(-x,y)=-U(x,y). This correspondence implies that bipolar junctions in graphene may have zero density of states at the Fermi level and carry a current in equilibrium, analogously to superconducting Josephson junctions. It also implies that nonelectronic systems with the same band structure as graphene, such as honeycomb-lattice photonic crystals, can exhibit pseudo-superconducting behavior.

Far-field focusing properties of two-dimensional honeycomb photonic crystals and the effect of the interface

The far-field focusing properties of two dimensional rod-type honeycomb lattice photonic crystals are investigated by using finite difference time domain method，and it was found that it explicitly follows the wave-beam negative refraction law with relative refractive index of -1. But the image qualities are limited by low transmission at large incident angles. The image qualities can be improved by modifying the radius of rods near the surface of photonic crystals slab.

Negative refraction in a honeycomb-lattice photonic crystal

In this paper we theoretically investigate a photonic crystal with dielectric rods in a honeycomb lattice. Two left-handed frequency regions are found in the second and third photonic band by using the plane wave expansion method to analyze the photonic band structure and equifrequency contours. Subwavelength imaging by the photonic crystal flat lens are systematically studied by numerical simulations using the multiple scattering method. Different from the photonic crystals with noncircular dielectric rods in air, this structure is almost isotropic at the optimal frequency for superlensing. As a comparison, flat slab focusing is also demonstrated at other frequencies in the two left-handed regions.