Modulation of Photonic Bandgap and Localized States by Dielectric Constant Contrast and Filling Factor in Photonic Crystals

The band structure of 2D photonic crystals (PCs) and localized states resulting from defects are analyzed by finite-difference time-domain (FDTD) technique and Padé approximation.The effect of dielectric constant contrast and filling factor on photonic bandgap (PBG) for perfect PCs and localized states in PCs with point defects are investigated.The resonant frequencies and quality factors are calculated for PCs with different defects.The numerical results show that it is possible to modulate the location,width and number of PBGs and frequencies of the localized states only by changing the dielectric constant contrast and filling factor.

A new photonic bandgap cover for a patch antenna with a photonic bandgap substrate

A new photonic bandgap (PBG) cover for a patch antenna with a photonic bandgap substrate is introduced. The plane wave expansion method and the FDTD method were used to calculate such an antenna system. Numerical re-sults for the input return loss, radiation pattern, surface wave, and the directivity of the antennas are presented. A com-parison between the conventional patch antenna and the new PBG antenna is given. It is shown that the new PBG cover is very efficient for improving the radiation directivity. The physical reasons for the improvement are also given.

Photonic Bandgap Properties of Atom-lattice Photonic Crystals in Polymer

The present paper covers the various photonic crystals（PhCs） structures mimicking real atom-lattice structures in electronic crystals by using the femtosecond laser-induced two-photon photopolymerization of SU-8 resin. The bandgap properties were investigated by varying the crystal orientations in 〈111 〉, 〈110〉 and 〈100〉 of diamond-lattice PhCs. The photonic stop gaps were present at λ=3.88 um in 〈111〉 direction, λ=4.01 um in 〈110〉 direction and λ=5.30 um in 〈100〉 direction, respectively. In addition, defects were introduced in graphite-lattice PhCs and the strong localization of photons in this structure with defects at λ=5 um was achieved. All the above work shows the powerful capability of femtosecond laser fabrication in manufacturing various complicated threedimensional photonic crystals and of controlling photons by inducing defects in the PhCs samples.

Photonic Bandgap Properties of One-Dimensional Photonic Crystal Consisting of Complex Artificial Media

Propagation of electromagnetic waves in one-dimensional (1-D) stratifiedchiral structures is described by the 4X4 transfer-matrix method. The photonic bandgap (PBG)properties in 1-D periodical chiral media are investigated. The relation between PBGand chiralityadmittance has been analyzed. Under proper operating parameters, quite perfect multichannelfiltering properties can be obtained with the periodic structure. The photonic bandgap properties ofone-dimensional layered periodical structures that include of double negative (DNG) medium,so-called backward-wave (BW) medium are investigated. The simulation results show that the width ofthe PBG in the structure composed of chiral medium and BW medium is larger then that composed ofchiral medium and usual medium. Our analysis has shown that the usage of the negative material makesit possible to dramatically widen the band gap of one-dimensional photonic crystal.

Effect of single point defects on the confinement losses of air-guiding photonic bandgap fibers

The confinement losses in air-guiding photonic bandgap fibers （PBGFs） with air hole missing are studied with the full-vector finite-element method. It is confirmed that there are two loss peaks （1.555 and 1.598 μm） if there is a hole missing in the cladding far from the core. The closer to the core the hole missing is, the larger the confinement losses are, and even no mode could propagate in the core. The main power of the fundamental mode leaks from the core to the cladding defect. The quality of PBGFs can be improved through controlling the number and position of defects.

A simple model for approximate bandgap structure calculation of all-solid photonic bandgap fibre based on an array of rings

A simple model for approximate bandgap structure calculation of all-solid photonic bandgap fibre based on an array of rings is proposed. In this model calculated are only the potential modes of a unit cell, which is a high-index ring in the low-index background for this fibre, rather than the whole cladding periodic structure based on Bloch＇s theorem to find the bandgap. Its accuracy is proved by comparing its results with the results obtained by using the accurate full-vector plane-wave method. High speed in computation is its great advantage over the other exact methods, because it only needs to find the roots of one-dimensional analytical expressions. And the results of this model, mode plots, offer an ideal environment to explore the basic properties of photonie bandgap clearly.

Zero dispersion wavelength and dispersion slope control of hollow-core photonic bandgap fibres

This paper investigates the zero dispersion wavelength and dispersion slope control of hollow-core photonic bandgap fibres （PBGFs） by using a full-vector finite element method. By simulation we found that theoretically the zero dispersion wavelength can be tailored by respectively changing the rounded diameter of air holes, pitch, refractive index, normalized thickness of core rings, and hole diameter to pitch ratio. At the same time the tailoring of dispersion slope can also be realized by changing the rounded diameter of air holes or pitch or normalized thickness of core rings. To illustrate the reasonability of fibre designs, this paper also gives the variance of normalized interface field intensity which measures the scattering loss relatively versus wavelength for different designs. From the viewpoint of loss, varying the rounded diameter and the thickness of core ring could shift zero wavelength but it is difficult to get the required parameters within so tiny range in practical drawing of PBGFs, on the other hand, it is possible in practice to respectively alter the pitch and refractive index to shift zero wavelength. But varying hole diameter to pitch ratio is not worthwhile because they each induce large increase of loss and narrowness of transmission bandwidth. The zero dispersion wavelength can be engineered by respectively varying the rounded diameter of air holes, pitch, refractive index, and normalized thickness of core rings without incurring large loss penalties.

Modulated spatial transmission signals in the photonic bandgap

This paper describes the spatial transmission of electromagnetically induced transparency and four-wave mixing signals in the photonic bandgap structure,which are modulated using the adjustable parameters of light fields.The spatial transmission patterns of the relevant signals are experimentally investigated with respect to the optical nonlinear Kerr effect that occurs in the modulation process.The experimental results reveal the spatial transmission patterns of the probe transmission and the four-wave mixing signals,such as focusing,defocusing,shifting,and spatial splitting.This study explains how the tunable parameters of light fields and their interactions with each other can regulate the spatial transmission of the light fields by changing the refractive indices of media,which provides a new research perspective and a degree of experimental technology support for more efficient all-optical communications.

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.

Characteristics of Bragg Gratings in All-Solid Photonic Bandgap Fiber

We report on fiber Bragg gratings in all-solid photonie bandgap fiber that was composed of a triangular array of high-index Ge-doped rods in pure silica background with fluorine-doped index-depressed layer surrounding the Ge-doped rod. Fiber Bragg gratings were photowritten with 193 nm ArF excimer laser and characterized for their response to strain, temperature, bending, and torsion. These gratings couple light from the forward core mode to not only backward core mode but also backward rod modes. This results in multiple resonance peaks in the reflection spectrum. All resonance wavelengths exhibited the same temperature and strain response with coefficient similar to that of Bragg gratings in standard single-mode fiber. The strength of the resonance peaks corresponding to the backward rod modes showed high sensitivity to bending and torsion.

Application of Padé Approximation in Simulating Photonic Crystals

To save finite-difference time-domain（FDTD） computing time, several methods are proposed to convert the time domain FDTD output into frequency domain. The Pad6 approximation with Baker＇s algorithm and the program are introduced to simulate photonic crystal structures. For a simple pole system with frequency 160THz and quality factor of 5000, the intensity spectrum obtained by the Padé approximation from a 2^8-item sequence output is more exact than that obtained by fast Fourier transformation from a 2^20-item sequence output. The mode frequencies and quality factors are calculated at different wave vectors for the photonic crystal slab from a much shorter FDTD output than that required by the FFT method, and then the band diagrams are obatined. In addition, mode frequencies and Q-factors are calculated for photonic crystal microcavity.

A photonic crystal waveguide with silicon on insulator in the near-infrared band

A two-dimensional （2D） photonic crystal waveguide in the Г-K direction with triangular lattice on a silicon-on-insulator （SOI） substrate in the near-infrared band is fabricated by the combination of electron beam lithography and inductively coupled plasma etching. Its transmission characteristics are analysed from the stimulated band diagram by the effective index and the 2D plane wave expansion （PWE） methods. In the experiment, the transmission band edge in a longer wavelength of the photonic crystal waveguide is about 1590 nm, which is in good qualitative agreement with the simulated value. However, there is a disagreement between the experimental and the simulated results when the wavelength ranges from 1607 to 1630 nm, which can be considered as due to the unpolarized source used in the transmission measurement.

A ministop band in a single-defect photonic crystal waveguide based on silicon on insulator

This paper reports that a two-dimensional single-defect photonic crystal waveguide in the Г-K direction with triangular lattice on a silicon-on-insulator substrate is fabricated by the combination of electron beam lithography and inductively coupled plasma etching. A ministop band （MSB） is observed by the measurement of transmission characteristics. It results from the coupling between the two modes with the same symmetry, which is analysed from the stimulated band diagram by the effective index and the two-dimensional plane wave expansion methods. The parameter working on the MSB is the ratio of the radius of air holes to the lattice constant, fla. It is obtained that the critical τ/a value determining the occurrence or disappearance of MSB is 0.36. When τ/a is larger than or equal to 0.36, the MSB occurs. However, when τ/a is smaller than 0.36, the MSB disappears.

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.

Amplitude and phase controlled absorption and dispersion of coherently driven five-level atom in double-band photonic crystal

The absorption–dispersion properties of a microwave-driven five-level atom embedded in an isotropic photonic bandgap(PBG) have been studied. Due to the singular density of modes(DOM) in the isotropic PBG and the dynamically coherence induced by the coupling fields, modified reservoir-induced transparency and quantum interference-induced transparency emerge simultaneously. Their interaction leads to ultra-narrow spectral structure. As a result of closed-loop configuration, these features can be manipulated by the amplitudes and relative phase of the coherently driven fields. The position and width of PBG also have an influence on the spectra. The theoretical studies can provide us with more efficient methods to control the atomic absorption–dispersion properties, which have applications in optical switching and slow light.

Applied electric field to fabricate colloidal crystals with the photonic band-gap in communication waveband

The macropore silica colloidal crystal templates were assembled orderly in a capillary glass tube by an applied electric field method to control silica deposition. In order to achieve the photonic band gap （PBG） of colloidal crystal in optical communication waveband, the diameter of silica microspheres is selected by Bragg diffraction formula. An experiment was designed to test the bandgap of the silica crystal templates. This paper discusses the formation process and the close-packed fashion of the silica colloidal crystal templates was discussed. The surface morphology of the templates was also analyzed. The results showed that the close-packed fashion of silica array templates was face-centered cubic （FCC） structure： The agreement is very good between the experimental data and the theoretical calculation.

Photonic crystal structures:Beam deflector and beam router

We investigate the optical characteristic,transverse magnetic（TM） and transverse electric（TE） band of twodimensional（2 D） square lattice photonic crystal structure,which is composed of cylindrical air regions positioned at the corners of the square shaped dielectric rods.We obtain the wide photonic bandwidths between TM1–TM2 and TM3–TM4 bands.According to the results,we demonstrate the band gaps close to each other in the TM and TE frequencies for proposed structures.The resulting photonic gaps are formed to be about 8% at the higher frequencies of TE modes（TE4–TE5）and TM modes（TM7–TM8 and TM9–TM10）.In addition,we examine isotropically generated structures for light guiding properties and observe that the light is directed in a particular route without using any deflection.We also investigate the self-collimation effect with the designed structure.The obtained results reveal the influences of the radius of cylindrical air holes and the angle between these air holes on absolute and partial photonic band gaps.Moreover,we observe the TM and TE band gaps that overlap.It is thought that the obtained band overlap will provide an easy way to produce the photonic crystals in practical applications like photonic insensitive waveguide.It is also believed that these results can provide the photonic crystal structures to work as a beam deflecting and beam router in integrated optical circuit applications.

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.

基于FDTD的波导介质层PBG结构的研究

该文提出了波导中介质层式的PBG结构,并对其阻带特性进行了数值分析,其中包括PBG 结构的设计;周期长度、周期个数、单元尺寸等几个方面对阻带特性的影响等,并给出了结论。利用介质层 PBG结构来制作波导滤波器具有设计简单、易于实现的显著优点。

PBG光子晶体光纤的色散特性研究

光子晶体光纤(PCF)是一种具有特殊包层结构的光纤,它是利用光子禁带效应(PBG)来导光的。利用时域有限差分法(FDTD)来分析光波在PCF中传输的色散特性,结果表明,PBG光子晶体光纤的色散值和色散斜率比常规的通信光纤要小。