The single-longitudinal-mode operation of a ridge waveguide laser based on two-dimensional photonic crystals

An electrically driven, single-longitudinal-mode GaAs based photonic crystal (PC) ridge waveguide (RWG) laser emitting at around 850 nm is demonstrated. The single-longitudinal-mode lasing characteristic is achieved by introducing the PC to the RWG laser. The triangle PC is etched on both sides of the ridge by photolithography and inductive coupled plasma (ICP) etching. The lasing spectra of the RWG lasers with and without the PC are studied, and the result shows that the PC purifies the longitudinal mode. The power per facet versus current and current-voltage characteristics have also been studied and compared.

Germanium Based Two-Dimensional Photonic Crystals: The Hexagonal and Honeycomb Lattices

The properties of two-dimensional (2D) photonic crystals (PCs) composed of germanium (Ge) are discussed. We investigate polarization-dependent photonic band diagrams (transverse electric and transverse magnetic polarizations), gap maps, surface plots, contour maps, etc. for 2D PCs with Ge rods in air and vice versa for two different lattices geometries, namely hexagonal and honeycomb lattices. The obtained graphs for the four possible combinations are presented in this paper. All the graphs depict clear photonic band gaps. The conditions for the largest TE and TM band gaps are described. The honeycomb lattice of Ge rods in air background offers a large complete photonic band gap Δω/ωm greater than 8% (for rod radius of r = 0.2 μm). Using these data, new Ge based photonic devices can be fabricated to confine, control and manipulate light in a more useful way.

Application of Fourier Series Expansion Method with PMLs to the Microcavities on Two-Dimensional Photonic Crystals

By using a Fourier series expansion method combined with Chew's perfectly matched layers (PMLs), we analyze the frequency and quality factor of a micro-cavity on a two-dimensional photonic crystal is analyzed. Compared with the results by the method without PML and finite-difference time-domain (FDTD) based on supercell approximation, it can be shown that by the present method with PMLs, the resonant frequency and the quality factor values can be calculated satisfyingly and the characteristics of the micro-cavity can be obtained by changing the size and permittivity of the point defect in the micro-cavity.

Topological edge and corner states of valley photonic crystals with zipper-like boundary conditions

We present a stable valley photonic crystal(VPC)unit cell with C_(3v)symmetric quasi-ring-shaped dielectric columns and realize its topological phase transition by breaking mirror symmetry.Based on this unit cell structure,topological edge states(TESs)and topological corner states(TCSs)are realized.We obtain a new type of wave transmission mode based on photonic crystal zipper-like boundaries and apply it to a beam splitter assembled from rectangular photonic crystals(PCs).The constructed beam splitter structure is compact and possesses frequency separation functions.In addition,we construct a box-shaped triangular PC structures with zipper-like boundaries and discover phenomena of TCSs in the corners,comparing its corner states with those formed by other boundaries.Based on this,we explore the regularities of the electric field patterns of TESs and TCSs,explain the connection between the characteristic frequencies and locality of TCSs,which helps better control photons and ensures low power consumption of the system.

High-efficiency ultra-fast all-optical photonic crystal diode based on the lateral-coupled nonlinear elliptical defect

An all-optical Fano-like diode featuring a nonlinear lateral elliptical micro-cavity and a reflecting column in the photonic crystal waveguide is proposed.The asymmetric micro-cavity is constructed by removing one rod and changing the shape of the lateral rod from a circle to an ellipse.A reflecting pillar is also introduced into the waveguide to construct an F-P cavity with the elliptical defect and enhance the asymmetric transmission for the incident light wave transmitting rightwards and leftwards,respectively.By designing the size of the ellipse and optimizing a reflecting rod at a suitable position,a maximum forward light transmittance of-1.14 dB and a minimum backward transmittance of-57.66 dB are achieved at the working wavelength of 1550.47 nm.The corresponding response time is about 10 ps when the intensity of the pump light beam resonant at 637 nm is 3.97 W/μm2.

Investigation on photonic crystal nanobeam cavity based on mixed diamond–circular holes

A photonic crystal nanobeam cavity(M-PCNC)with a structure incorporating a mixture of diamond-shaped and circular air holes is pro-posed.The performance of the cavity is simulated and studied theoretically.Using thefinite-difference time-domain method,the parameters of the M-PCNC,including cavity thickness and width,lattice constant,and radii and numbers of holes,are optimized,with the quality factor Q and mode volume Vm as performance indicators.Mutual modulation of the lattice constant and hole radius enable the proposed M-PCNC to realize outstanding performance.The optimized cavity possesses a high quality factor Q 1.45105 and an ultra-small mode=×volume Vm 0.01(λ/n)[Zeng et al.,Opt Lett 2023:48;3981–3984]in the telecommunications wavelength range.Light can be progres-=sively squeezed in both the propagation direction and the perpendicular in-plane direction by a series of interlocked anti-slots and slots in the diamond-shaped hole structure.Thereby,the energy can be confined within a small mode volume to achieve an ultra-high Q/Vm ratio.

Comment on “Band gaps structure and semi-Dirac point of two-dimensional function photonic crystals” by Si-Qi Zhang et al.

Recently, Zhang et al.(Chin. Phys. B 26 024208(2017)) investigated the band gap structures and semi-Dirac point of two-dimensional function photonic crystals, and the equations for the plane wave expansion method were induced to obtain the band structures. That report shows the band diagrams with the effects of function coefficient k and medium column r_a under TE and TM waves. The proposed results look correct at first glance, but the authors made some mistakes in their report. Thus, the calculated results in their paper are incorrect. According to our calculations, the errors in their report are corrected, and the correct band structures also are presented in this paper.

Band gaps structure and semi-Dirac point of two-dimensional function photonic crystals

Two-dimensional function photonic crystals, in which the dielectric constants of medium columns are the functions of space coordinates , are proposed and studied numerically. The band gaps structures of the photonic crystals for TE and TM waves are different from the two-dimensional conventional photonic crystals. Some absolute band gaps and semiDirac points are found. When the medium column radius and the function form of the dielectric constant are modulated, the numbers, width, and position of band gaps are changed, and the semi-Dirac point can either occur or disappear. Therefore,the special band gaps structures and semi-Dirac points can be achieved through the modulation on the two-dimensional function photonic crystals. The results will provide a new design method of optical devices based on the two-dimensional function photonic crystals.

Tunability of Photonic Band Gaps in One- and Two-dimensional Photonic Crystals Based on ZnS Particles Embedded in TiO2 Matrix

用 Maxwell-Garnett 理论，钛二氧化物(TiO2 ) 的折射索引的进化与锌做了硫化物(ZnS ) 粒子被介绍。在主人矩阵的 nano 反对的存在允许我们与悦耳的光性质获得新合成材料。我们发现 ZnS nanoparticles 的充满的因素极大地改变 photonic 乐队差距(PBG ) 。我们也为在由有限差别时间领域(FDTD ) 在六角形的 2D 和方形的格子被空气壳层盖住的 ZnS 杆组成的结构宣传的电磁波计算了 photonic 乐队结构方法。杆与一个高绝缘的常数在 TiO2 背景媒介被嵌入。在场的如此的 photonic 格子完成 photonic 乐队差距(CPBG ) 。我们的结果证明空气壳层的存在导致更大的完全的 photonic 差距。我们相信现在的结果是重要的增加可能性让试验者认识到可观、更大的 CPBG。

Numerical study on characteristic of two-dimensional metal/dielectric photonic crystals

An improved plan-wave expansion method is adopted to theoretically study the photonic band diagrams of twodimensional(2D) metal/dielectric photonic crystals.Based on the photonic band structures,the dependence of flat bands and photonic bandgaps on two parameters(dielectric constant and filling factor) are investigated for two types of 2D metal/dielectric(M/D) photonic crystals,hole and cylinder photonic crystals.The simulation results show that band structures are affected greatly by these two parameters.Flat bands and bandgaps can be easily obtained by tuning these parameters and the bandgap width may reach to the maximum at certain parameters.It is worth noting that the hole-type photonic crystals show more bandgaps than the corresponding cylinder ones,and the frequency ranges of bandgaps also depend strongly on these parameters.Besides,the photonic crystals containing metallic medium can obtain more modulation of photonic bands,band gaps,and large effective refractive index,etc.than the dielectric/dielectric ones.According to the numerical results,the needs of optical devices for flat bands and bandgaps can be met by selecting the suitable geometry and material parameters.

A compact T-branch beam splitter based on anomalous reflection in two-dimensional photonic crystals

We project a compact T-branch beam splitter with a micron scale using a two-dimensional(2D)photonic crystal(PC).For TE polarization,one light beam can be split into two sub-beams along opposite directions. The propagating directions of the two splitting beams remain unchanged when the incident angle varies in a certain range.Coupled-mode theory is used to analyze the truncating interface structure in order to investigate the energy loss of the splitter.Simulation results and theoretical analysis show that choosing an appropriate location of the truncating interface(PC-air interface)is very important for obtaining high efficiency due to the effect of defect modes.The most advantage of this kind of beam splitter is being fabricated and integrated easily.

The Absorbing Properties of Two-Dimensional Plasma Photonic Crystals

Plasma photonic crystals composed of periodic plasma and dielectric materials have attracted considerable attention because of their tunable photonic band gaps,but only their band structures or negative refractive index properties have been addressed in previous works.In this paper,through studying the transmission and reflection characteristics of two types of twodimensional plasma photonic crystals,it is found that plasma photonic crystals play an important role in absorbing waves,and they show broader band and higher amplitude absorption characteristics than bulk plasmas.Also,the absorption of plasma photonic crystals can be tuned via plasma parameters;varying the collision frequency can make the bandwidth and amplitude tunable,but cannot change the central frequency,whereas varying the plasma frequency would control both the location and the amplitude of the absorbers.These features of plasma photonic crystals have potential for terahertz tunable absorber applications.

Low Frequency Dispersion Law for Two-Dimensional Metallic Photonic Crystals

Using the rigorous multiple-scattering theory, we study the dispersion relation of electromagnetic (EM) waves in two di- mensional dielectric photonic crystals (PCs) and metallic photonic crystals (MPCs) in the low-frequency limit. Analytic formula for the effective velocity of EM waves in PCs and MPCs is obtained. Accuracy of our formula is checked by comparing the results with rigorous calculations. For PCs, our result is exactly the same as the coherent potential approximation (CPA), which is accurate even when the filling fraction is high. But for MPCs, our approach demonstrates special advantages, while the CPA theory fails, in predicting the effective velocity of EM waves in MPCs at low frequency.

The Photonic Band Gaps in the Two-Dimensional Plasma Photonic Crystals with Rhombus Lattice

In this paper,under two different electromagnetic modes,the photonic band gaps(PBGs) in the two-dimensional plasma photonic crystals(PPCs) are theoretically investigated based on the plane wave expansion method.The proposed PPCs are arranged in rhombus lattices,in which the homogeneous unmagnetized plasma rods are immersed in the isotropic dielectric background.The computed results showed that PBGs can be easily tuned by the angle of rhombus lattices,and a cutoff frequency and a flatbands region can be observed under the TM and TE polarized waves,respectively.The relationships between the relative bandwidths of first PBGs and the parameters of PPCs in two such cases also are discussed.The numerical simulations showed that the PBGs can be manipulated obviously by the parameters as mentioned above.The proposed results can be used to design the waveguide and filter based on the PPCs.

Research Progress in Preparation and Application of Photonic Crystals

Photonic crystals are periodic structural materials that have an impact on the propagation properties of photons.Due to their excellent optical,electrical and magnetic properties,their advantages and potential for applications in the above areas are gradually emerging.Therefore,an increasing number of researchers have focused on photonic crystals.In this paper,the characteristics of biological photonic crystal structures,such as those found in butterfly wings,sea mouse bristles,peacock feathers,melon jellyfish epidermal cells,and weevil exoskeletons,are described.The preparation methods of photonic crystals are systematically summarized(including the template method,self-assembly technology,electron beam evaporation coating technology,chemical vapor deposition technology,femtosecond laser two-photon technology,spin coating technology,and a variety of technology mixing),and the characteristics,advantages,and disadvantages of the different methods are compared.Furthermore,the development of photonic crystals in the field of sensors,solar cells,filters,and infrared stealth is discussed,demonstrateing the great development potential of photonic crystals.It is concluded that the realization of photonic crystals with high precision,high sensitivity,angle independence,and large-area uniform preparation is a key problem requiring urgent solution.Moreover,photonic crystals have potential development prospects in the fields of equipment stealth,new concept weapons,production,an daily life.

Spontaneous emission fromΛ-type three-level atom driven by bichromatic field in anisotropic double-band photonic crystals

The spontaneous emission property ofΛ-type three-level atom driven by the bichromatic field in the anisotropic double-band photonic crystal is calculated by n-times iteration method.The influence of different parameters on atomic spontaneous emission is studied,and the phenomena of atomic spontaneous emission are explained in the dressed state representation.It is found that the spontaneous emission spectra of the atom driven by the bichromatic field presents a multi-peak comb structure.The position of the emission peak is determined by the initial state of the atom,and the interval between the neighboring emission peaks is the detuningδof the bichromatic field.When the ratio between Rabi frequency intensity and the detuningδof the bichromatic field remains unchanged,the intensity of each emitted peak remains invariant.The spontaneously emitted peak can be annihilated in the band gap and enhanced near the band edge in the anisotropic photonic crystals.Meanwhile,we also observe the fluorescence quenching phenomenon in the spontaneous emission spectra.The research in this paper provides the theoretical guidance for the control of atomic spontaneous emission.

Valley-dependent topological edge states in plasma photonic crystals

Plasma photonic crystals designed in this paper are composed of gas discharge tubes to control the flow of electromagnetic waves.The band structures calculated by the finite element method are consistent with the experimental results which have two distinct attenuation peaks in the ranges of 1-2.5 GHz and 5-6 GHz.Electromagnetic parameters of the plasma are extracted by the Nicolson-Ross-Weir method and effective medium theory.The measured electron density is between 1×1011 cm-3 and1×1012 cm-3,which verifies the correctness of the parameter used in the simulation,and the collision frequency is near 1.5×1010 Hz.As the band structures are corroborated by the measured scattering parameters,we introduce the concept of photonic topological insulator based on the quantum Valley Hall effect into the plasma photonic crystal.A valley-dependent plasma photonic crystal with hexagonal lattice is constructed,and the phase transition of the valley K(K’)occurs by breaking the spatial inversion symmetry.Valley-spin locked topological edge states are generated and excited by chiral sources.The frequency of the non-bulk state can be dynamically regulated by the electron density.This concept paves the way for novel,tunable topological edge states.More interestingly,the Dirac cone is broken when the electron density increases to 3.1×1012 cm-3,which distinguishes from the methods of applying a magnetic field and changing the symmetry of the point group.

Controllable and tunable plasma photonic crystals through a combination of photonic crystal and dielectric barrier discharge patterns

We report five types of patterns with square symmetry,including three novel types obtained by inserting a specially designed grid photonic crystal(PC)into a dielectric barrier discharge system.They are studied using an intensified charge-coupled device camera and photomultiplier tubes.The three novel types of patterns are a square pattern with one structure,a square superlattice pattern with four sublattices and a(1/4)K_(grid)(K_(grid)is the basic wave vector of the grid),and another square pattern with a complex inversion discharge sequence.From the application viewpoint,the five types of patterns can be used as plasma photonic crystals(PPCs).Their band diagrams under a transverse-magnetic wave simulated by the finite element method show that there are a large number of band gaps.Compared with the original PC with only a unidirectional band gap,the five types of PPCs have tunable and omnidirectional band gaps,which is very important in controlling the propagation of electromagnetic waves in the mm-wave region.The experimental results enrich the pattern types in the dielectric barrier discharge system and provide a method for obtaining PPCs with symmetry controllability and bandgap tunability.

Topological resonators based on hexagonal-star valley photonic crystals

In valley photonic crystals, topological edge states can be gained by breaking the spatial inversion symmetry without breaking time-reversal symmetry or creating pseudo-spin structures, making highly unidirectional light transmission easy to achieve. This paper presents a novel physical model of a hexagonal-star valley photonic crystal. Simulations based on the finite element method(FEM) are performed to investigate the propagation of TM polarized mode and its application to ring resonators. The results show that such a topologically triangular ring resonator exhibits an optimum quality factor Q of about 1.25×104, and Q has a maximum value for both frequency and the cavity length L. Our findings are expected to have significant implications for developing topological lasers and wavelength division multiplexers.