The properties of cutoff frequency in two-dimensional superconductor photonic crystals

In this paper, by means of frequency-dependent plane wave expansion method we investigate the properties of photonic band structures in two-dimensional superconductor photonic crystals. Effects of cut-off frequency are investigated by various parameters such as filling factor, the lattice constant alteration, threshold frequency of the superconductor, and shape of the rods as well. We show that the cut-off frequency can be efficiently tuned by the operating temperature. Moreover, it can be tailored by changing the dielectric constant of the background and the threshold frequency of the superconductor material.     

Enlarged Photonic Band Gap in Heterostructure of Metallic Photonic and Superconducting Photonic Crystals

We show theoretically that the frequency range of photonic band gap of a hetero-structure which is made of a metallic photonic and superconducting photonic crystal can be enlarged due to the combination of the reflection band properties of the superconductor–dielectric (PC1) and metallic–dielectric (PC2) periodic structures. The transmittance and band structure of the considered structures are calculated using simple transfer matrix method and the Bloch theorem. Beside this, we have also calculated the transmittance of the superconducting photonic structure (PC1), metallic photonic structure (PC2) and heterostructure of metallic photonic and superconductor photonic crystals (PC1/PC2) for TE and TM-mode at the different angles of incidence.     

Investigation of Transmission Properties in One-Dimensional Quasi-periodic Superconducting Photonic Crystal

This paper explores the transmission characteristics of superconducting quasi-periodic photonic crystal structure arranged in Thue-Morse and double-period sequences. We mainly focused on the cutoff frequency of transmittance spectra. The study shows that the cutoff frequency can be appreciably tuned by generation number of sequence, thicknesses of constituent layers and operating temperature. Shifting behaviour of cutoff frequency is in contrast with periodic structure on varying superconductor thickness and temperature whereas it shows opposite trend on changing the dielectric layer thickness. It is also observed that different quasi-periodic structures show distinct values of cutoff frequency and different transmission properties. This features allow to tune the cutoff frequency or band gap in the whole infrared frequency region.     

Investigation of Absolute Photonic Band Gaps in Two-dimensional Dielectric Structures

Abstract

We examine the photonic band structure of two-dimensional (2D) arrays of dielectric holes using the coherent microwave transient spectroscopy (COMITS) technique. Such 2D hole arrays are constructed by embedding low-index rods (air) in a dielectric background of higher-index Stycast material (n = 3·60). The dispersion relation for electromagnetic wave propagation in these photonic crystals is directly determined using the phase sensitivity of COMITS. We find that both the square and triangular lattice structures exhibit photonic band gaps that are common to both polarizations for all wave-vectors along major symmetry axes. In addition, the connectivity of the high-index dielectric and the opening of a large gap for propagation with E field perpendicular to the hole cylinders are found to be important criteria for generating a large absolute photonic band gap.     

Analysis of Photonic Band Gaps in a Two-Dimensional Triangular Lattice with Superconducting Hollow Rods

In this work, we use the plane wave expansion method to calculate photonic band structures in two-dimensional photonic crystals which consist of high-temperature superconducting hollow rods arranged in a triangular lattice. The variation of the photonic band structure with respect to both, the inner radius and the system temperature, is studied, taking into account temperatures below the critical temperature of the superconductor in the low frequencies regime and assuming E polarization of the incident light. Permittivity contrast and nontrivial geometry of the hollow rods lead to the appearance of new band gaps as compared with the case of solid cylinders. Such band gaps can be modulated by means of the inner radius and system temperature.     

Investigating the Omnidirectional Photonic Band Gap in One-Dimensional Superconductor–Dielectric Photonic Crystals with a Modified Ternary Fibonacci Quasiperiodic Structure

In this paper, an omnidirectional photonic band gap (OBG) of one-dimensional (1D) superconductor–dielectric photonic crystals (SDPCs) with a modified ternary Fibonacci quasiperiodic structure which originates from Bragg gap is theoretically investigated by the transfer matrix method (TMM) in detail. The SDPCs are composed of superconductor and two kinds of homogeneous, isotropic dielectric. Such OBG is independent of the incidence angle and the polarization of electromagnetic wave (EM wave). From the numerical results, the OBG can be notably enlarged by tuning the thickness of superconductor and dielectric layers but cease to change with increasing the Fibonacci order. The OBG also can be manipulated by the ambient temperature of system. Especially, the ambient temperature of system is close to the critical temperature. However, the damping coefficient of superconductor has no effects on the OBG. The gap/midgap ratio of OBG also is studied by those parameters. It is shown that 1D SDPCs with a modified ternary Fibonacci quasiperiodic structure have a superior feature in the enhancement of OBG compared with the conventional 1D ternary and conventional ternary Fibonacci quasiperiodic SDPCs.     

Investigation of TE-polarized photonic band gap properties in matallodielectric photonic crystals composed of metal coated dielectric cylinders

Using the Dirichlet-to-Neumann map method and generalization of this method, we have been able to calculate the photonic band structure of two-dimensional (2D) metallodielectric photonic crystals composed of metal-coated circular dielectric rods. The rods are embedded in an air background with a square array. We are interested in considering transverse electric (TE) mode of electromagnetic waves. The resulting band structures show the existence of photonic band gaps as well as some flat band regions. We theoretically study the effect of the dielectric constant and radius of the dielectric core on the photonic band structures. There are some interesting results compared to the case of solid metallic rods (without dielectric core) such as appearing the new photonic band gaps and a flat band region with the characteristic of cavity modes.     

Dielectric and Superconducting Photonic Crystals

We present the transmittance of two types of one-dimensional periodic structures. The first type of structure consists of alternating layers of a dielectric material. The second type of structure consists of alternating layers of a dielectric material and a superconductor whose dielectric properties are described by the two-fluid model. The variance of the intensity and the bandwidth of the transmittance are strongly dependent on the thicknesses, temperature, and frequencies. We have compared the transmittance spectra and present some details about the two types of structure. In the first type, we will make a comparison between the optical properties of the high temperature superconducting photonic crystal (HTScPC) by using the YBa₂Cu₃O₇ as a superconductor layer with SrTiO₃ as a dielectric layer. The second type consists of the dielectric photonic crystals (DPCs) and Al₂O₃ or MgO with SrTiO₃ within the ultra-violet region. The comparison obtained according to the difference of the thickness of SrTiO₃ and the variance of the number of periods. The common result is changed in the number of PBGs within the UV range.     

Ultra-wide Low-Frequency Band Gap of One-Dimensional Superconducting Photonic Crystals Containing Metamaterials

In this paper, the low-frequency band gap properties of one-dimensional superconducting photonic crystal which is composed of superconductor and metamaterials have been theoretically investigated by the Bloch theorem together with the transfer matrix method. Numerical results show that the width of the low-frequency band gap increases first and then decreases with the increase of thickness ratio, which is defined as the ratio of the thickness of the metamaterials layer to that of the superconductor layer. A critical thickness ratio is found at which the ultra-wide low-frequency band gap appears. The influence of the metamaterials layer’s relative permittivity, the superconductor layer thicknesses and the operating temperature on the ultra-wide low-frequency band gap are also investigated in this paper.     

Analysis of Reflectance Properties in 1D Photonic Crystal Containing Metamaterial and High-Temperature Superconductor

In the present work, reflectance properties of one-dimensional photonic crystal (1D PC) containing a metamaterial and high-temperature superconductor have been investigated theoretically and analyzed. The reflectance/transmittance spectrum of the proposed structure is obtained by using the characteristic or transfer-matrix method (TMM). The results show that by increasing the thickness of the metamaterial layer, the width of the second reflection band decreases while the width of the first reflection band remains almost the same though it shifts towards the higher frequency side. In addition to this, a new band gap arises in the lower side of frequency. But, when the thickness of the superconductor layer is increased, the width of both the bands increases and no additional band arises in this case. Moreover, the reflection band is also affected by varying the operating temperature of the superconducting layer and the results show that bands get narrower by increasing the operating temperature. Finally, the effect of incident angle on the reflection band has been discussed for both transverse electric (TE) and transverse magnetic (TM) polarizations.     

Properties of Photonic Band Gaps in Superconductor Multilayer Structure with Periodically Varying Ambient Temperature

The properties of the reflectance for a superconductor multilayer structure with periodically varying ambient temperature have been theoretically investigated by the transfer matrix method (TMM). From the numerical results, it has been shown that such system has the photonic band gap (PBG) properties of photonic crystals (PCs), so it can also be called superconductor photonic crystals (SPCs). It is found that the locations and bandwidths of PBGs can be modulated by the incident angle. The frequency ranges and central frequencies of PBGs can be tuned by the temperature and thickness of superconductor layer A (higher temperature superconductor layer), respectively. The bandwidths of PBGs can be notably enlarged with increasing the temperature of superconductor layer A. The frequency ranges of PBGs can be controlled by increasing the thickness of superconductor layer A, and the more PBGs appear. The damping coefficient of superconductor and the number of periods have little effect on the bandwidths of PBGs under low-temperature conditions. It is shown that this kind of SPCs has potential applications in filters, microcavities, and fibers, etc.     

光子晶体应用于浓度检测的模拟研究

采用平面波展开法数值计算二维光子晶体在TE和TM偏振态下的带隙,给出了光子晶体中的禁带存在的理论依据,选择二维三角晶格光子晶体（GaAs）作为基底,在气孔内填充浓度为一定的待测溶液硫酸铜材料,计算温度为298K情况下介电常数在71．917～62．530变化时,光子晶体在不同偏振模式下的光子禁带结构,结果表明,以硫酸铜的水溶液作为空气圆孔中的介质材料,当溶液质量百分浓度不同时光子带隙（PBG）发生显著变化。     

Enhancement of Omnidirectional Photonic Bandgaps in One-Dimensional Superconductor–Dielectric Photonic Crystals with a Staggered Structure

In this paper, the properties of the omnidirectional photonic bandgap (OBG) realized by one-dimensional (1D) photonic crystals with a staggered structure which is composed of superconductor and isotropic dielectric have been theoretically investigated by the transfer matrix method (TMM). From the numerical results, it has been shown that such OBG is insensitive to the incident angle and the polarization of electromagnetic wave (EM wave), and the frequency range and central frequency of OBG can be tuned by the ambient temperature of system, the average thickness of superconductor layer, the average thickness of dielectric layer, and staggered parameters, respectively. The bandwidth of OBG can be notably enlarged with increasing average thickness and staggered parameter of superconductor layer. Moreover, the frequency range of OBG can be narrowed with increasing the average thickness, staggered parameter of dielectric layer, and ambient temperature, respectively. The damping coefficient of superconductor layer has no effect on the bandwidth of OBG under low-temperature conditions. It is shown that 1D superconductor–dielectric photonic crystals (SDPCs) have a superior feature in the enhancement of frequency range of OBG. This kind of OBG has potential applications in filters, microcavities, and fibers, etc.     

一维光子晶体的带隙特性研究

一维光子晶体是指介质只在一个方向成周期性排列的材料。利用薄膜光学的特征矩阵法研究了一维光子晶体的禁带特性,分析了填充率变化、厚度的随机扰动对光子带隙的影响。结果表明,随着填充率的变化,各能级的带隙率变化,并且存在一个极大值;厚度的随机扰动对光子带隙也有一定的影响,随机度不同,对光子带隙的影响也不一样。本研究对一维光子晶体的设计与制备有一定的参考价值。     

Angle- and Thickness-Dependent Photonic Band Structure in?a?Superconducting Photonic Crystal

The angle- and thickness-dependent photonic band structures in a one-dimensional superconducting photonic crystal are theoretically investigated based on the transfer matrix method. The band structure is studied near and below the threshold frequency at which the superconducting material has a zero permittivity. The gap structure is analyzed as a function of the thicknesses of the two constituent superconducting and dielectric materials. In the angular dependence of the band structure, it is found that in the TM-polarization there exists a strongly localized superpolariton gap in the vicinity of the threshold frequency. This gap is shown to be enhanced as the angle increases.     

Photonic Crystals

Abstract

In this paper, we review the early motivation for photonic crystal research which was derived from the need for a photonic bandgap in quantum optics. This led to a series of experimental and theoretical searches for the elusive photonic bandgap structures: those three-dimensionally periodic dielectric structures which are to photon waves, as semiconductor crystals are to electron waves. We shall describe how the photonic semiconductor can be ‘doped’, producing tiny electromagnetic cavities. Finally, we shall summarize some of the anticipated implications of photonic band structure for quantum electronics and the prospects for the creation of photonic crystals in the optical domain.     

Optical Properties of New Type of Superconductor-Semiconductor Metamaterial Photonic Crystals

Based on the fundamentals of the characteristic matrix method, we theoretically investigate the optical properties of onedimensional superconductor metamaterial photonic crystals. The photonic crystals are composed of a superconductor layer and two semiconductor metamaterial layers of In_0.53Ga_0.47As with different doping densities. The numerical results show negative values in permittivity of the metamaterial layer along a broad band of the incident radiation. The negative values show a significant effect on the optical properties of the present structure. Moreover, the optical properties of our design can be controlled by different parameters such as thicknesses of the layers, the operating temperature and the doping density. Our results may be suitable for different applications in the optical community.     

光子晶体的能带结构、潜在应用和制备方法

光子晶体是指具有光子能带和能隙的一类新型材料,它具有奇特的调节光子传播状态的特性．本文将从光子晶体的能带结构、潜在应用和制备方法三方面对其进行综述性介绍．由于光子晶体有着非常广阔的应用前景,这一领域已成为当今世界范围内的研究热点．     

Thermal properties and two-dimensional photonic band gaps

The effect of temperature on a two-dimensional square lattice photonic crystal composed of Si rods arranged in an air background was investigated theoretically using the plane-wave expansion method. Both the thermal expansion effect and thermo-optical effect are considered simultaneously. We have discussed the role of temperature in creating the complete photonic band gap as a function of temperature. Two different shapes of rods, i.e. square and circular, are considered in the presence of the two polarization states, i.e. TE and TM waves. The numerical results show that the photonic band gap can be significantly enlarged compared to the photonic band gap at room temperature. The effect of temperature on the complete photonic band width in the cylindrical rods case is more significant. Cylindrical and square Si rods may work as a temperature sensor or filter, among many other potential applications.     

YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7−<Emphasis Type="Italic">x</Emphasis></Subscript>/BaTiO<Subscript>3</Subscript> 1D Superconducting Photonic Crystal with Tunable Broadband Response in the Visible Range

Based on the transfer matrix method, we studied theoretically the transmittance of a 1D photonic crystal (PC), consisting of alternating layers of a dielectric material (BaTiO₃) and a superconductor (YBa₂Cu₃O_7?x ). The dielectric properties of this system are described by the two fluid model. We have investigated the transmittance intensity and its bandwidth dependence on the superconductor thickness, incident angle, and temperature in the PC. It was found that the electromagnetic wave propagation can be controlled to be forbidden or allowed in certain wavelengths in the visible and ultraviolet range, and the photonic band gap (PBG) width can also be tuned varying these parameters. We showed that by increasing the thickness of the superconductor layer it is possible to control the number of PBGs in the structure. Also, we found that the frequency ranges of PBGs are sensitive to the incident angle and the polarization of the electromagnetic waves; the bandwidth of PBGs can be notably enlarged by increasing the angle in the TE polarization, but narrowed in the TM one. Additionally, we found that transmission is not markedly affected by temperature variation, but small shifts in the PBGs are presented. We hope these results can be of technical use for developing potential applications in optoelectronic devices.