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.

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.

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 ra 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.

Photonic band structures of two-dimensional photonic crystals with deformed lattices

Using the plane-wave expansion method, we have calculated and analysed the changes of photonic band structures arising from two kinds of deformed lattices, including the stretching and shrinking of lattices. The square lattice with square air holes and the triangular lattice with circular air holes are both studied. Calculated results show that the change of lattice size in some special ranges can enlarge the band gap, which depends strongly on the filling factor of air holes in photonic crystals; and besides, the asymmetric band edges will appear with the broken symmetry of lattices.

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.

Main Factors for Affecting Photonic Bandgap of Photonic Crystals

The factors affecting one dimensional （1D） and two dimensional （2D） photonic crystals （PhCs） are systemically analyzed in this paper by numerical simulation. Transfer matrix method （TMM） is employed for 1D PCs, both finite difference time domain method （FDTD） and plane wave expansion method （PWE） are employed for 2D PCs. The result shows that the photonic bandgaps （PBG） are directly affected by crystal type, crystal lattice constant, modulation of refractive index and periodicity, and it is should be useful for design of different type photonic crystals with the required PBG and functional devices. Finally, as an example, a near-IR 1D PCs narrow filter was designed.

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.

Behavior of exciton in direct−indirect band gap Al_(x)Ga_(1−x)As crystal lattice quantum wells

Excitons have significant impacts on the properties of semiconductors.They exhibit significantly different properties when a direct semiconductor turns in to an indirect one by doping.Huybrecht variational method is also found to influence the study of exciton ground state energy and ground state binding energy in Al_(x)Ga_(1−x)As semiconductor spherical quantum dots.The Al_(x)Ga_(1−x)As is considered to be a direct semiconductor at AI concentration below 0.45,and an indirect one at the concentration above 0.45.With regards to the former,the ground state binding energy increases and decreases with AI concentration and eigenfrequency,respectively;however,while the ground state energy increases with AI concentration,it is marginally influenced by eigenfrequency.On the other hand,considering the latter,while the ground state binding energy increases with AI concentration,it decreases with eigenfrequency;nevertheless,the ground state energy increases both with AI concentration and eigenfrequency.Hence,for the better practical performance of the semiconductors,the properties of the excitons are suggested to vary by adjusting AI concentration and eigenfrequency.

Photonic band structure of three-dimensional colloidal crystals with field-induced lattice structure transformation

By utilizing the electrorheological effect, three-dimensional colloidal crystals can be produced, whose lattice structure can be changed from the body-centered-tetragonal lattice to other lattices under the application of electric fields. This paper calculates photonic band structures of such crystals with lattice structure transformation, and demonstrates the existence of complete band gaps for some intermediate lattices. Thus, it becomes possible to use the electrorheological effect to achieve photonic crystals with desired photonic gap properties resulting from tunable structures.

Existing conditions of full bandgaps and absolute negative refraction in metallic-dielectric photonic crystal

This paper has theoretically studied the characteristic frequencies of band structures in two-dimensional metallic- dielectric photonic crystals. It is demonstrated that a large filling fraction benefits the existence of absolute photonic band gap, while a smaller filling fraction benefits an absolute negative refraction band. In addition, it also finds that the relation between the cut-off frequency of E-polarized wave and the filling fraction exceeding 10% is content with a linear increasing function, whose coefficients are exponential to the normalized lattice constant. These investigations have significant implications for tuning the operational frequencies to desired applications and manufacturing photonic crystals.

The features of band structures for woodpile three-dimensional photonic crystals with plasma and function dielectric constituents

The features of the band structures of woodpile three-dimensional （3D） photonic crystals composed of plasma and function dielectric constituents, referred to as function plasma photonic crystals （FPPCs）, are theoretically studied by a modified plane wave expansion method, and the formulas for computing the band structures are derived. The arrangement for the proposed FPPCs is that the function dielectric columns are surrounded by plasma, and the embedded dielectric columns are stacked according to the woodpile lattices, which are arrayed with facecentered-tetragonal symmetry. The relative permittivity of function dielectric rods depends on the function coefficient and space coordinates. The relationships between the parameters for inserted function dielectric rods and plasma and the band structures are also investigated. The computed results illustrate that the obtained PBG can be tuned by those parameters as mentioned above. Compared to dielectric-air PCs, function dielectric PCs and plasma dielectric PCs with the same topology, a wider bandwidth of the photonic band gap can be observed in the proposed FPPCs. The calculated results also show us another alternative way to realize reconfigurable applications with 3D FPPCs.

Differences of Band Gap Characteristics of Square and Triangular Lattice Photonic Crystals in Terahertz Range

Band gap characteristics of the photonic crystals in terahertz range with square lattice and triangular lattice of GaAs cylinders are comparatively studied by means of plane wave method （PWM）. The influence of the radius on the band gap width is analyzed and the critical values where the band gap appears are put forward. The results show that the maximum band gap width of photonic crystal with triangular lattice of GaAs cylinders is much wider than that of photonic crystal with square lattice. The research provides a theoretic basis for the development of terahertz （THz） devices.

A Study of Properties of the Photonic Band Gap of Unmagnetized Plasma Photonic Crystal

In this study, the propagation of electromagnetic waves in one-dimensional plasma photonic crystals （PPCs）, namely, superlattice structures consisting alternately of a homogeneous unmagnetized plasma and dielectric material, is simulated numerically using the finite-difference time-domain （FDTD） algorithm. A perfectly matched layer （PML） absorbing technique is used in this simulation. The reflection and transmission coefficients of electromagnetic （EM） waves through PPCs are calculated. The characteristics of the photonic band gap （PBG） are discussed in terms of plasma density, dielectric constant ratios, number of periods, and introduced layer defect. These may provide some useful information for designing plasma photonic crystal devices.

Improve the Efficiency of Scintillation Detectors Using Reflectors Based on Photonic Crystals Arrays

In the present work, we designed the new type of photonic crystals (PCs) as reflectors. Reflections from single layer of Al2O3/MgO PC help us in recapturing the light that does escape from the scintillation surface. Photonic crystals in one dimension array of Al2O3 and MgO with silver at periodicities N = 1, 2 and 3 were used as a reflector around the surface of the scintillation volume. Scintillation detectors are widely used in nuclear medicine. The efficiency is an important parameter for characterizing the capability of the detectors. The counting efficiency of the detectors depends on the light emission induced by radiation. The light then was converted by the photomultiplier tube into electrical pulses. The efficiency may increase by an amount of 1.64% if MgO-Ag photonic crystals are used at periodicity N = 1 as a reflector.

Comparative Study of the One Dimensional Dielectric and Metallic Photonic Crystals

The optical transmission properties of two types of photonic crystals have been analyzed by using the transfer matrix method. The first one is the dielectric photonic crystal (DPC), and the second is the metallic photonic crystal (MPC). We found the dielectric and metallic photonic crystals have different transmission spectra. The effect of the most prameters on the transmission spectra of the dielectric and metallic photonic crystals has been studied.

Analysis on Band Gaps of MCM-41 Type of Materials

The concept and analysis method of photonic crystals and band gaps are introduced into one-dimensional(1D) ordered mesoporous materials. MCM-41 type of materials are treated theoretically as photonic crystals. The formation of band gaps is exhibited and confirmed by a calculation of transfer matrix technique. PBG was found around 9-42 nm in soft X-ray region. The photonic band-gap was predicted to be dependent on incident direction, pore size and lattice constant. The mesoporous materials with different pore sizes and different lattice constants have different band-gap widths.

Studies of Optical Properties of Symmetrical Quasi-Periodic Photonic Crystals

Using the transfer matrix method approach (TMM), the present paper attempts to determine the optical properties of quasi-periodic symmetric one-dimensional photonic systems. In addition, it studies hybrid hetero-structure systems constructed by using periodic and quasi-periodic multilayer systems. The effect of symmetry applied to symmetric multilayer systems results in the appearance of optical windows at the photonic band gaps (PBG) of the system. The use of hybrid symmetric systems, at normal incidence in the visible range, show that the complete photonic band gap is the sum of bands from individual systems. The results show also that the width of the PBG depends on the parameters and nature of the built system.

Theoretical investigation of band-gap and mode characteristics of anti-resonance guiding photonic crystal fibres

With the full-vector plane-wave method （FVPWM） and the full-vector beam propagation method （FVBPM）, the dependences of the band-gap and mode characteristics on material index and cladding structure parameter in anti- resonance guiding photonic crystal fibres （ARGPCFs） are sufficiently analysed. An ARGPCF operating in the near- infrared wavelength is shown. The influences of the high index cylinders, glass interstitial apexes and silica structure on the characteristics of band-gaps and modes are deeply investigated. The equivalent planar waveguide theory is used for analysing such an ARGPCF filled by the isotropic materials, and the resonance and the anti-resonance characteristics r：~n h~ w~｜] r^r~dlrtpd

Transmission spectra characteristics of 1D photonic crystals with complex dielectric constant

The characteristics of photonic forbidden bands, transmission gain and absorption of one-dimensional （ID） dual-periodical photonic crystals （PC） with a complex dielectric layer were studied by using the optical transfer matrix （TM） method. The results show that the photonic band gap （PBG） of this structure is enlarged and many transmission resonance peaks appear in PBG. Large transmission gain for transmission peaks is obtained if the imaginary part of dielectric constant is negative. With the increase of the absolute value of the imaginary part, the transmission gain increases firstly and the transmittance gain gets to an apex. The imaginary parts of dielectric constant corresponding to transmission gain apex are different according to wavelength. However, the transmission ratio of resonance peaks is less than 1 if the imagi- nary part of dielectric constant is positive. The properties might be used to design multi-narrow-channel band filters and optical amplification devices synchronously.

Intensity Dependent Nonlinear Absorption in Direct and Indirect Band Gap Crystals under Nano and Picosecond Z-Scan

The nonlinear absorption properties of direct (GaN) and indirect (CdI2) band gap crystals have been studied by using an open aperture Z-scan technique under fundamental (1064 nm) and frequency doubled (532 nm) wavelength respectively with 10 ns or 60 ps pulse durations. Direct band gap crystal exhibits two and three photon absorption at all input irradiances. On the other hand, at low input irradiance the indirect band gap crystal exhibits saturable absorption (SA). At higher input irradiances two and three photon absorption becomes dominant. A monotonic increase of the nonlinear absorption coefficients with increasing laser pulse duration from 60 ps to 10 ns is observed for GaN and CdI2 crystals.