Theoretical study on the photonic band gap in one-dimensional photonic crystals with graded multilayer structure

We theoretically investigate the photonic band gap in one-dimensional photonic crystals with a graded multilayer structure. The proposed structure constitutes an alternating composite layer （metallic nanoparticles embedded in TiO2 film） and an air layer. Regarding the multilayer as a series of capacitance, effective optical properties are derived. The dispersion relation is obtained with the solution of the transfer matrix equation. With a graded structure in the composite layer, numerical results show that the position and width of the photonic band gap can be effectively modulated by varying the number of the graded composite layers, the volume fraction of nanoparticles and the external stimuli.

Frequency bands of negative refraction in finite one-dimensional photonic crystals

We have discussed theoretically the negative refraction in finite one-dimensional （1D） photonic crystals （PCs） composed of alternative layers with high index contrast. The frequency bands of negative refraction are obtained with the help of the photonic band structure, the group velocity and the power transmittance, which are all obtained in analytical expression. There shows negative transverse position shift at the endface when negative refraction occurs, which is analysed in detail.

Ultra-narrow bandwidth optical filters consisting of one-dimensional photonic crystals with anomalous dispersion materials

We present a new type of optical filter with an ultra-narrow bandwidth and a wide field-of-view （FOV）. This kind of optical filter consists of one-dimensional photonic crystal （PC） incorporating an anomalous-dispersion-material （ADM） with, for instance, an anomalous dispersion of 6P3/2←6S1/2 hyperfine structure transition of a caesium atom. The transmission spectra of optical filters are calculated by using the transfer-matrix method. The simulation results show that the designed optical filter has a bandwidth narrower than 0.33GHz and a wide FOV of ±30°as well. The response of transmission spectrum to an external magnetic field is also investigated.

Band structures analysis of one-dimensional photonic crystals using plane wave expansion

A theoretical analysis is made, using plane wave expansion, on how the width of the first three band gaps is influenced by filling ratio, dielectric constant ratio, and periodic width in one-dimensional photonic crystals （PhCs）. From simulation and analysis, there are one, two, and three peak points on the first, second and third band gaps respectively with the changes of filling ratio un- der fixed dielectric constant ratio. When filling ratio is fixed, the bandwidth of the first band gap consistently increases with dielectric constant ratio. However, no similar trend is observed in the second and the third band gaps. Because of scaling properties, varying periodic width does not alter the relative bandwidth.

Thermal tunable one-dimensional photonic crystals containing phase change material

To obtain the adjustable photonic crystals (PCs), we numerically investigate one-dimensional (1D) PCs with alternating VO2 and SiO2 layers through transfer matrix method. The dispersion relation agrees well with the transmittance obtained by the finite element calculation. Tunable band gaps are achieved with the thermal stimuli of VO2, which has two crystal structures. The monoclinic crystal structure VO2 (R) at low temperature exhibits insulating property, and the high temperature square rutile structure VO2 (M) presents metal state. Concretely, the bandwidth is getting narrower and red shift occurs with the higher temperature in VO2 (R)/SiO2 PCs structure. Based on the phase change characteristics of VO2, we can flexibly adjust the original structure as VO2 (R)/VO2 (M)/SiO2. By increasing the phase ratio of VO2 (R) to VO2 (M), the band gap width gradually becomes wider and blue shift occurs. The discrete layers of gradient composites on the dispersion of 1D PCs are also investigated, which enhances the feasibility in practical operation. Thus, our proposed thermal modulation PCs structure paves a new way to realize thermal tunable optical filters and sensors.

Nonreciprocal wide-angle bidirectional absorber based on one-dimensional magnetized gyromagnetic photonic crystals

We propose magnetized gyromagnetic photonic crystals(MGPCs)composed of indium antimonide(InSb)and yttrium iron garnet ferrite(YIGF)layers,which possess the properties of nonreciprocal wide-angle bidirectional absorption.Periodical defects in the MGPCs work as filters.Absorption bands(ABs)for the positive and negative propagations arise from the optical Tamm state and resonance in cavities respectively,and they prove to share no overlaps in the studied frequency range.Givenω=2.0138 THz,for the positive propagation,the ABs in the high-frequency range are localized in the interval between 0.66ωand 0.88ω.In the angular range,the ABs for the TE and TM waves reach 60°and 51°,separately.For the negative propagation,the ABs in the low-frequency range are localized in the interval between 0.13ωand 0.3ω.The AB s extend to 60°for the TE waves and 80.4°for the TM waves.There also exists a narrow frequency band in a lower frequency range.The relevant factors,which include the external temperature,the magnetic fields applied to the YIGF,the refractive index of the impedance matching layer,and the defect thickness,are adjusted to investigate the effects on the ABs.All the numerical simulations are based on the transfer matrix method.This work provides an approach to designs of isolators and so on.

Tunable topological edge state in plasma photonic crystals

In this study, we found a kind of edge state located at the interface between plasma photonic crystals(PPCs) and traditional photonic crystals, which depends on the property of the photonic band gap rather than the surface defect. Simulation and theoretical analysis show that by adjusting the plasma density, we can change the topological characteristics of the photonic band gap of PPCs. This makes it different from the photonic band gap of traditional PCs, and thus excites or closes the topological edge states. We further discussed the influence of plasma parameters on edge state characteristics, and the results showed that as the plasma density increased, the first photonic band gap(PBG) of the PPCs closed and then reopened, resulting in band inversion and a change in the PBG properties of the PPCs. We can control the generation of edge states through plasma and adjust the frequency and strength of the edge states. After the appearance of edge states, as the plasma density further increases, the first PBG of the PPCs will shift towards high frequencies and deepen. The frequency of edge states will shift towards higher frequencies, and their strength will also increase. We increased the first PBG depth of the PPCs by increasing the number of arrays and found that when the number of the PPCs arrays increased, only the intensity of the edge states would increase while the frequency remained unchanged. Therefore, flexible adjustment of edge state frequency and intensity can be achieved through plasma density and array quantity parameters. Our study demonstrates the properties of topological edge states in plasma photonic crystals, which we believe can provide some guidance for applications based on edge states.

Reconfigurable(4, 6^(2)) and(4, 8^(2)) Archimedean plasma photonic crystals in dielectric barrier discharge

Archimedean photonic crystal has become a research area of great interest due to its various unique properties. Here, we experimentally demonstrate the realization of reconfigurable(4, 6^(2))and(4, 8^(2)) Archimedean plasma photonic crystals(APPCs) by use of dielectric barrier discharges in air. Dynamical control on both the macrostructures including the lattice symmetry and the crystal orientation, and the microstructures including the fine structures of scattering elements has been achieved. The formation mechanisms of APPCs are studied by time-resolved measurements together with numerical simulations. Large omnidirectional band gaps of APPCs have been obtained. The tunable topology of APPCs may offer new opportunities for fabricating multi-functional and highly-integrated microwave devices.

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.

Properties of single and multiple defect modes in one-dimensional photonic crystals containing left-handed metamaterials

Wave propagation is studied in structures consisting of alternate left- and right-handed layers. Bragg gap and zero-n gap appear in different frequency regions of the structure. The periodicity of the structure is broken by simply reversing the order of the layers in one half of the structure, resulting in defect modes located inside the zero-n gap and Bragg gap. These modes can be made very narrow by adding more layers in the structure. The defect mode located inside the zero-n gap is sensitive to the symmetry of the structure and insensitive to the angle of incidence of the incoming radiation. Multiple modes are also generated inside the gaps by repeating the structural pattern. Thus, a simple structure can be used for single and multiple modes that are imDortant for different applications.

Method of measuring one-dimensional photonic crystal period-structure-film thickness based on Bloch surface wave enhanced Goos–H?nchen shift

This paper puts forward a novel method of measuring the thin period-structure-film thickness based on the Bloch surface wave(BSW) enhanced Goos–Hanchen(GH) shift in one-dimensional photonic crystal(1DPC). The BSW phenomenon appearing in 1DPC enhances the GH shift generated in the attenuated total internal reflection structure. The GH shift is closely related to the thickness of the film which is composed of layer-structure of 1DPC. The GH shifts under multiple different incident light conditions will be obtained by varying the wavelength and angle of the measured light, and the thickness distribution of the entire structure of 1DPC is calculated by the particle swarm optimization(PSO) algorithm.The relationship between the structure of a 1DPC film composed of TiO_(2) and SiO_(2) layers and the GH shift, is investigated.Under the specific photonic crystal structure and incident conditions, a giant GH shift, 5.1 × 10^(3) times the wavelength of incidence, can be obtained theoretically. Simulation and calculation results show that the thickness of termination layer and periodic structure bilayer of 1DPC film with 0.1-nm resolution can be obtained by measuring the GH shifts. The exact structure of a 1DPC film is innovatively measured by the BSW-enhanced GH shift.

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.

Mode coupling with Fabry-Perot modes in photonic crystal slabs

Fabry–Perot(FP)modes are a class of fundamental resonances in photonic crystal(PhC)slabs.Owing to their low quality factors,FP modes are frequently considered as background fields with their resonance nature being neglected.Nevertheless,FP modes can play important roles in some phenomena,as exemplified by their coupling with guided resonance(GR)modes to achieve bound states in the continuum(BIC).Here,we further demonstrate the genuine resonance mode capability of FP modes PhC slabs.Firstly,we utilize temporal coupled-mode theory to obtain the transmittance of a PhC slab based on the FP modes.Secondly,we construct exceptional points(EPs)in both momentum and parameter spaces through the coupling of FP and GR modes.Furthermore,we identify a Fermi arc connecting two EPs and discuss the far-field polarization topology.This work elucidates that the widespread FPs in PhC slabs can serve as genuine resonant modes,facilitating the realization of desired functionalities through mode coupling.

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.

Some New Band Characteristics in One-Dimensional Plasma Dielectric Photonic Crystals

Propagation of electromagnetic waves in one-dimensional plasma dielectric photonic crystals, the superlattice structure consisting of alternating plasma and dielectric materials, is studied theoretically for oblique incidence by using the transfer matrix method. Our results show that complete photonic band gaps for all polarizations can be obtained in one-dimensional plasma dielectric photonic crystals. These structures can exhibit a new type of band or gap, for the incidence other than the normal one, near frequencies where the electric permittivity of the plasma layer changes sign. This new band or gap arises, from the dispersive properties of the plasma layer, only for transverse magnetic polarized waves, and its width increases with the increase in incident angle. This differential behavior under polarization can be utilized in the design of an efficient polarization splitter. The existence of both photonic gaps and resonance transmission bands is demonstrated for experimentally realizable structures such as double electromagnetic barriers.

Microwave transmittance characteristics in different uniquely designed one-dimensional plasma photonic crystals

Plasma photonic crystals(PPCs)are emerging as a powerful instrument for the dynamical control of the electromagnetic properties of a propagating wave.Here we demonstrate several one-dimensional(1 D)PPCs with uniquely designed superlattice structures,annular structures or with incorporation of the third material into the primitive unit cell.The influences of the properties of the third material as well as the structural configurations of suplerlattices on the transmittance characteristics of PPCs have been investigated by use of the finite element method.The optimal design strategy for producing PPCs that have more and larger band gaps is provided.These new schemes can potentially be extended to 2 D or 3 D plasma crystals,which may find broad applications in the manipulation of microwaves and terahertz waves.

One-Dimensional InP-Based Photonic Crystal Quantum Cascade Laser Emitting at 5.36μm

An InP-based one-dimensional photonic crystal quantum cascade laser is realized. With photo lithography instead of electron beam lithography and using inductively coupled plasma etching, four-period air-semiconductor couples are defined as Bragg reflectors at one end of the resonator. The spectral measurement at 80K shows the quasi-continuous-wave operation with the wavelength of 5.36μm for a 22gm-wide and 2mm-long epilayer-up bonded device.

Controlling the Bandgaps of One-Dimensional TiO2/SiO2, TiO2/SnO2, and SiO2/SnO2 Photonic Crystals Using the Transfer Matrix Method

One-dimensional photonic crystals (1D PhCs) have a unique ability to control the propagation of light waves, however certain classes of 1D oxides remain relatively unexplored for use as PhCs. Specifically, there has not been a comparative study of the three different 1D PhC structures to compare the influence of layer thickness, number, and refractive index on the ability of the PhCs to control light transmission. Herein, we use the transfer matrix method (TMM) to theoretically examine the transmission of 1D PhCs composed of layers of TiO2/SiO2, TiO2/SnO2, SiO2/SnO2, and combinations of the three with various top and bottom layer thicknesses to cover a substantial region of the electromagnetic spectrum (UV to NIR). With increasing layer numbers for TiO2/SiO2 and SiO2/SnO2, the edges became sharper and wider and the photonic bandgap width increased. Moreover, we demonstrated that PhCs with significantly thick TiO2/SiO2 layers had a high transmittance for a wide bandgap, allowing for wide-band optical filter applications. These different PhC architectures could enable a variety of applications, depending on the properties needed.

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.

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.