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.

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.

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.

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

Polarization characteristics of chiral photonic crystal fibers with an elliptical hollow core

The theoretical study of dielectric-chiral photonic crystal fiber （PCF） with an elliptical hollow core is presented. The band structure of chiral photonic crystal （PhC） is calculated by using a modified plane-wave expansion （PWE） method. By examining the out-of-plane photonic bandgaps （PBGs） of chiral PhC, a kind of chiral PCF with a hollow core is designed and their eigenstates are calculated. The distributions of mode field and polarization state are demonstrated, and how the structural asymmetry of the core together with the chirality in the background affects the modal polarization is discussed. The dependences of birefringence on chirality for different ellipticities of core are investigated.

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.

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.

Investigation of Photonic Band Gap in Si-Based One-Dimensional Photonic Crystal

A one-dimensional silicon based photonic crystal with nonlinear defect layers is examined. The linear and nonlinear optical properties are analyzed. The transmission spectrum was obtained by applying the optical transfer matrix formalism to the photonic crystal. The various transmittance peaks obtained with the defect layers are investigated. The nature of the transmittance peak is analyzed with the number of defect layers.

Investigation of the guided-mode characteristics of hollow-core photonic band-gap fibre with interstitial holes

This paper investigates the guided-mode characteristics of hollow-core photonic band-gap fibre （HC-PBGF） with interstitial holes fabricated by an improved twice stack-and-draw technique at visible wavelengths. Based on the simulation model with interstitial holes, the influence of glass interstitial apexes on photonic band-gaps is discussed. The existing forms of guided-mode in part band gaps are shown by using the full-vector plane-wave method. In the experiment, the observed transmission spectrum corresponds to the part band gaps obtained by simulation. The fundamental and second-order guided-modes with mixture of yellow and green light are observed through choosing appropriate fibre length and adjusting coupling device. The loss mechanism of guided-modes in HC-PBGF is also discussed.

Modification of spontaneous emission rate of micrometer-sized light sources using hollow-core photonic crystal fibers

We investigate numerically and experimentally the modification of the spontaneous emission rate for micrometersized light sources embedded in a hollow-core photonic crystal fiber （HCPCF）. The diameter of the light source is deliberately chosen such that they could be easily introduced into the central hole of the hollow-core photonic crystal fiber by capillary force. The photoluminescence from the microparticles is measured by using an inverted microscope in combination with a spectrometer. The modification of the spontaneous emission rate is observed in a wavelength region where there is no band gap. The experimental observations are consistent with the simulation results obtained by the plane wave expansion and finite-difference time-domain techniques.

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.

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.

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.

Highly efficient Cherenkov radiation generation in the irregular point of hollow-core photonic crystal fiber

Highly efficient Cherenkov radiation （CR） is generated by the soliton self-frequency shift （SSFS） in the irregular point of a hollow-core photonic crystal fiber （HC-PCF） in our laboratory. The impacts of pump power and wavelength on the CR are investigated, and the corresponding nonlinear processes are discussed. When the average power of the 120 fs pump pulse increases from 500 mW to 700 mW, the Raman soliton shifts from 2210 nm to 2360 nm, the output power of the CR increases by 2.3 times, the maximum output power ratio of the CR at 539 nm to that of the residual pump is calculated to be 24.32：1, the width of the output optical spectrum at the visible wavelength broadens from 35 nm to 62 nm, and the conversion efficiency η of the CR in the experiment can be above 32%.

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.

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.

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.

Tunable Reflection Bands and Defect Modes in One-Dimensional Tilted Photonic Crystal Structure

We show theoretically that range of reflection bands and defect modes inside the band gap can be tuned by using a one-dimensional tilted photonic crystal (TPC) structure. A TPC structure is similar to the conventional PC structure with the only difference that in this case alternate layers are inclined at certain angle in the direction of periodicity of the structure. In order to obtain the reflectance spectra of the proposed structure transfer matrix method (TMM) has been employed. From the analysis of the reflectance curve, it is found that 100% reflectance range can be varied and enhanced by using TPC structure for both (TE- and TM-) polarizations. The enhancement in reflection bands increases as the tilt angle increases for both the polarizations and hence the enlarged omni-reflectance bands are obtained. Further, we study the properties of the defect modes in TPC structure by introducing the tilted defect at the different tilt angle. The results show that defect modes (tunneling modes) can be tuned at different wavelengths by changing the tilt angle of the structure without changing other parameters. Finally, the effect of variation thickness of defect layers on the tunneling mode has been studied for both TPC and conventional PC structure. The proposed model might be used as a tunable broadband omnidirectional reflector as well as tunable tunneling or transmission mode, which has potential applications in the field of photonics and optoelectronics.

Polarization-dependent efficient Cherenkov radiation at visible wavelengths in hollow-core photonic crystal fiber cladding

Efficient Cherenkov radiation （CR） is experimentally generated by a soliton self-frequency shift （SSFS） in a knot of hollow-core photonic crystal fiber （HC-PCF）. When the angle of the half-wave plate is rotated from 0° to 45°, the Raman soliton shifts from 2227 to 2300 nm, the output power of the CR increases 8.15 times, and the maximum output power ratio of the CR at 556 nm to the residual pump is estimated to be 20：1. The width of the output optical spectrum at visible wavelengths broadens from 25 to 45 nm, and the conversion efficiency of the CR can be above 28%. Moreover, the influences of the pump polarization and wavelength on the CR are studied, and the corresponding nonlinear processes are discussed.