Metallic and Superconducting Photonic Crystal

We have investigated the transmittance for two kinds of photonic crystals; (i) One-dimensional metallic photonic crystals (1DMPCs) and (ii) One-dimensional superconducting photonic crystals (1DScPCs). The variance of the intensity and the bandwidth of the transmittance are strongly dependent on the thicknesses and frequencies. We have compared the transmittance spectra in 1DScPCs and 1DMPCs at low frequencies, and we present some details about the transmittance spectra by using Transfer Matrix Method (TMM) at the same conditions.      

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.     

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.     

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.     

Filtering Properties of Photonic Crystal Dual-Channel Tunable Filter Containing Superconducting Defects

In this work, we analyze filtering properties in a photonic crystal (PC) dual-channel tunable filter. The filter structure containing twin superconducting thin films is denoted as (1/2) ^M S₁(2/1) ^N S₂(1/2) ^M . Here, 1 and 2 are dielectrics of SrTiO₃ and Al₂O₃, respectively. S₁ and S₂ are two high-temperature superconducting thin films taken to be the typical system, YBa₂Cu₃O_7?x . The two channel frequencies can be designed to locate within the photonic band gap (PBG) of the original PC (1/2) ^M . Channel frequencies can be significantly changed by changing N, the stack number of the center PC. With the use of superconducting defects, channel frequencies are temperature-dependent, that is, the filter is thermally tunable. The proposed filter structure is of technical use in superconducting photonic applications at terahertz frequency.     

Analysis of Temperature-Dependent Optical Properties in 1D Ternary Superconducting Photonic Crystal with Mirror Symmetry

The temperature dependence of the defect mode in a 1D ternary superconducting photonic crystal (PC) with mirror symmetry was theoretically investigated by simultaneously considering thermal expansion effect and thermal-optical effect. Three different materials H (high-refractive index dielectric), L (low-refractive index dielectric), and S (superconducting material) are used to construct the ternary superconducting PC structure. For comparison, six structures are discussed. It is found that the structure (HLS) ^N (SLH) ^N has the highest temperature sensitivity. Here, N is the number of periods. The average change in the central wavelength of the defect mode is 31.18 nm/K as the thickness of superconducting layer is 50 nm. Thus, based on the structure (HLS) ^N (SLH) ^N , a low temperature sensor with higher sensitivity can be designed to realize the low temperature sensor.     

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.     

Maximization of Photonic Bandgaps in Two-Dimensional Superconductor Photonic Crystals

In this paper, we investigate the properties of photonic band structures in two-dimensional superconductor photonic crystals (2D-SCPCs) using the frequency dependent plane wave expansion method. We consider two types of 2D-SCPCs, which are composed of superconductor (dielectric) rods embedded into a dielectric (superconductor) background, named type I (type II) SCPCs. We target maximization of the gap-to-mid-gap ratio by varying many parameters, namely, shape of the rods, the operating temperature, the permittivity of the dielectric material, and the threshold frequency of the superconductor. We show that the type II SCPCs have a higher gap-to-mid-gap ratio than the type I SCPCs. In addition, the PBGs can be tuned efficiently by the operating temperature. Moreover, the photonic band structures can be tailored by changing the dielectric constant of the background (rods) in the type I (type II) SCPCs.     

Broadening of Photonic Band Gap in a One—Dimensional Superconductor Star Waveguide Structure

The present paper describes the theoretical investigation of enlarged reflection bands (photonic band gaps) in a 1D star waveguide (SWG) structure consists of superconductor and dielectric as its constituent materials. For the present study, we take the different combinations of superconductor and dielectric materials as a backbone and side branches of the SWG structure. In order to obtain the dispersion relation, Interface Response Theory (IRT) has been employed. Photonic band gaps of SWG structure having superconductor?Csuperconductor, superconductor?Cdielectric, and dielectric?Csuperconductor materials are compared with the band gaps of the conventional photonic crystal (PC) structure having superconductor?Csuperconductor and dielectric?Csuperconductor materials. Analysis of the dispersion characteristics shows that there exists no band gaps for conventional PC when both layers are made of the same superconducting materials (as the usual case) while the SWG structure shows forbidden bands of finite width even the backbone and side branches are made of same materials. Also, the SWG structure having superconductor?Cdielectric shows the wider reflection bands in comparison with the structure having dielectric?Csuperconductor as its constituent materials, while for the conventional PC structure it is same in both the cases. Further, the effect of temperature and the effect of variation of number of grafted branches on the photonic bands of SWG structure have been studied.     

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.     

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.     

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.     

Photonic band gaps in 12-fold symmetric quasicrystals

The 12-fold symmetric quasicrystal shows great potential as a novel photonic band gap (PBG) structure exhibiting a band gap for relatively low filling fractions and dielectric contrasts. The band gaps are highly homogeneous with respect to the angle of incidence of the incoming light due to the crystal's high degree of rotational symmetry. These crystals have been analyzed using a finite element method developed specifically for modelling PBG structures. We present and discuss quasicrystal structures and their optical properties.     

Photonic band gaps in quasicrystal-related approximant structures

Abstract

We propose a method for a systematic investigation of quasicrystal-related approximant structures in view of photonic bandgap applications. A detailed study is presented in the case of approximants formed by dielectric cylinders and constructed from a two-dimensional quasiperiodic lattice with octagonal symmetry. We show that isotropic photonic bandgaps are obtained even for the lowest order approximants generated by successive hyperspace shear. The main Fourier components of the dielectric function, responsible for the first photonic bandgap opening, are derived from the main component set of the quasiperiodic lattice. The magnitudes of the corresponding Brillouin zone vectors are shown to be directly related to the average distance between the planes passing by the dielectric cylinders. In other words, the approximant gap position is rather determined by the fundamental lattice parameters common to the quasiperiodic and approximant structures than by the approximant period. We also show that structure point symmetry is not indispensable for the band gap opening.     

Study of Defect Modes in 1d Photonic Crystal Structure Containing High and Low T c Superconductor as a Defect Layer

The present paper describes the study of defect modes in a one-dimensional photonic crystal (1d-PC) containing a high and low temperature superconductor as a defect layer at different temperatures below the superconducting transition temperature (T _c ). Since the refractive index of the superconducting material is dependent on the penetration depth, which depends on the temperature of the superconducting material, hence by changing the temperature of the superconducting material its refractive index can also be changed. Analysis of the transmission spectra of defect modes in the reflection band of 1d-PC structure shows a shift in the wavelength peak of the defect mode. The shift in peak is different for different superconducting materials and it increases with the increase in temperature whether the defect layer is high T _c or low T _c superconductors. We also study the presence two defect layers in a 1d-PC structure, one with high T _c and other with a low T _c superconductor. Further, the effect of variation in the thickness of the defect layer on the defect modes of the PC structure has also been studied In order to obtain the transmission (reflection) spectra of a 1d-PC structure with a defect, we employ the transfer matrix method (TMM). This property of the defective PC structure can be exploited in designing the temperature sensor and narrow optical filters. Further, this tunable feature of superconductor photonic crystal has technical use in the superconducting electronics and photonics.     

Photonic bandgaps of different unit cells in the basic structural unit of germanium-based two-dimensional decagonal photonic quasi-crystals

Based on the infrared optical material germanium, in the basic structural unit of a two-dimensional decagonal photonic quasi-crystal, photonic bandgaps of four square unit cells with a scattering radius in the range of [0,0.3a] have been calculated within two cases of construction (i.e., air cylinders arranged in germanium and germanium cylinders arranged in air) by using the plane wave expansion method. In considering the Bragg-like scattering effect in two-dimensional photonic quasi-crystals as the elastic collision in physics, we put forward the photonic bandgap impact function F=q(1)q(2)q(3)επr(2) for the first time, to the best of our knowledge. A certain unit cell structure shares some similar photonic bandgap properties with a periodic structure. For a certain structure of the unit cell, the center frequency change trends of the photonic bandgap and the type of photonic bandgap generated are not related with the period of the photonic crystal, but with the relative dielectric constant and the construction, respectively. Different unit cell structures own different photonic bandgap structures. This occurs because the high degree of rotational symmetry of the quasi-periodic structure and weak long-range order of the basic structural unit lead to different Bragg-like scattering effects within the unit cell structures.     

Fano Resonance by Means of the One-Dimensional Superconductor Photonic Crystals

In the present work, we introduce a study about the reflectance properties of a one-dimensional superconductor photonic crystal in a different manner. Our structure is designed from alternately layers of high-temperature superconducting material (BSCCO) and a conventional superconducting material (Nb) terminated by the dielectric cap layer. The investigated numerical results are essentially based on the basics of the transfer matrix method and the two-fluid model. The numerical results showed the appearance of two sharp peaks, which are referred to Fano and electromagnetic-induced reflectance resonances. Also, we demonstrate the effects of many parameters on the reflectance properties of Fano resonance and the electromagnetic-induced reflectance. The effects of the constituent layer thicknesses, the number of periods, the operating temperature, the angle of incidence, and the refractive index of the dielectric cap layer are all considered. Finally, the effects of hydrostatic pressure on the Fano and EIR resonances are studied and calculated. This structure can play an important role in optical switching devices.     

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。     

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.     

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.