A theoretical result on dispersion in a photonic crystal

A theoretical result on the type of dispersion of a photonic crystal is derived by using the fact that the refractive index of the crystal is a periodic function of wavelength whose period is the atomic lattice spacing of the crystal as well as by using Rolle's theorem of differential calculus.     

Phase response of omnidirectional reflection one-dimensional photonic crystals and defect modes

In this paper, we investigate the phase properties of light reflected from one-dimensional omnidirectional reflection photonic crystal. We observe that the phase changes drastically at large incident angles. This asymmetrical phase change should be considered at oblique incidence, and various phase compensators and retarders can be designed by this nonlinear curved surface of phase shift. Furthermore, for the coupled defect 1D PC, the phase change depends mainly on the top of the sharp peak of the weak undulation within the rectangular defect band, because the top of the peak of the undulation is very sharp, i.e. large phase change look like within almost a single frequency. This drastic phase change can be used to design phase controllers.     

Complete photonic band gaps in one-dimensional ternary photonic crystals containing single negative materials

Complete photonic band gaps (PBGs) are found in one-dimensional ternary photonic crystals (1D TPCs) composed of an ordinary dielectric and single negative metamaterials. The proposed TPC gives omni directional PBG completely independent of polarizations dependent weekly on angle of incidence. Here the choice of different parameters of TPC is done in such a way so that it eliminates the Brewster's-angle transmission resonance, thus allowing a complete 3D PBG. It exhibits a photonic band or gap near frequencies where either the magnetic permeability or the electric permittivity of the metamaterial changes sign, whose width increases with the increasing angle of incidence. These result from the dispersive properties of the metamaterials and disappear for the particular case of propagation along the stratification direction. The results are discussed in terms of incident angle, layer thickness, dielectric constant of the dielectric material for TE and TM polarizations.     

Properties, applications and fabrication of photonic crystals with ring-shaped holes in silicon-on-insulator

We show that photonic crystals with ring-shaped holes (RPhCs) exhibit superior properties compared to conventional photonic crystals (PhCs). At low air-fill factors RPhCs can have a larger bandgap than conventional PhCs. Moreover, RPhC waveguides with both high group index and small group velocity dispersion can be designed. RPhC waveguides are also more sensitive to external refractive index changes, which is attractive for sensor applications. Finally we set up a procedure to pattern RPhCs in silicon-on-insulator.     

Plasma photonic crystals numerical and filter characteristics analysis based on symplectic algorithm

From the Maxwell equation, the method of symplectic finite-difference time-domain is applied in analyzing one-dimensional plasma photonic crystal. The propagation process of electromagnetic pulse in one-dimensional vacuum plasma photonic crystal structure is simulated by symplectic algorithm discrete in 2nd order time 2nd order space (T2S2), and 2nd order time 4th order space (T2S4) respectively. Then, from the perspective of frequency domain, the reflection coefficient of the plasma–vacuum photonic crystals is analyzed. The results show that the symplectic finite-difference time-domain method is accuracy and correctness. In the end, the filter characteristics of the plasma photonic crystals (PPCs) are analyzed in different thickness of plasma.     

Modal propagation characteristics of EM waves in ternary one-dimensional plasma photonic crystals

We have theoretically studied the modal dispersion characteristics, group velocity, and effective group as well as phase index of refraction of ternary one-dimensional (1D) plasma photonic band gap (PBG) structure having periodic multilayers of three different materials in one unit cell. The dispersion characteristics related for such structure is derived by solving Maxwell wave equation based on principle of Kronig-Penny model. From the computed results we observe that the dispersion characteristics of such structure also show the frequency gap and cutoffs as found in (binary) one-dimensional plasma photonic crystal. The frequency gap is shown to become larger with the increase of plasma frequency as well as plasma width. It is seen that such structure provide additional degree of freedom to control dispersion characteristic, group velocity and effective index of refraction compared to conventional one-dimensional plasma photonic crystal.     

Wideband and low dispersion slow light in slotted photonic crystal waveguide

We present a procedure to generate wideband and low dispersion slow light in slotted photonic crystal waveguide. By shifting the first and second rows of air holes of slotted photonic crystal waveguide, the bandwidth of slow light can be increased, with small group velocity dispersion. Using 2D plane wave expansion method, we numerically demonstrate slow light with the nearly constant group indices of 23, 42, and 54 over 17.6 nm, 6.7 nm and 3.3 nm bandwidth, respectively. The maximal normalized delay-bandwidth product is 0.26. From the fabrication's point of review, shifting the position of holes is easier to be controlled technically than changing the diameters of air holes. In addition, our simulations suggest this design is tolerant to deviation for positions of the first two rows of air holes. Therefore, the proposed approach decreases the dependence on the fabrication accuracy.     

Modelling and design of complete photonic band gaps in two-dimensional photonic crystals

In this paper, we investigate the existence and variation of complete photonic band gap size with the introduction of asymmetry in the constituent dielectric rods with honeycomb lattices in two-dimensional photonic crystals (PhC) using the plane-wave expansion (PWE) method. Two examples, one consisting of elliptical rods and the other comprising of rectangular rods in honeycomb lattices are considered with a view to estimate the design parameters for maximizing the complete photonic band gap. Further, it has been shown that complete photonic band gap size changes with the variation in the orientation angle of the constituent dielectric rods.      

A detailed derivation of eigenvalue equation in two dimensional and three dimensional photonic crystals

A detailed derivation of eigenvalue equation in two dimensional and three dimensional photonic crystals is given by the plane-wave expansion method. Some mathematical formulas such as the rotation of vector, the gradient of scalar, the divergence of the vector, the vector triple product and the conversion between scalar and vector are employed. The eigenvalue equation in photonic crystals has become the important base for obtaining the band structure and the distribution of eigenmode.     

Decay lifetime and evolution of semiconductor quantum dots in photonic crystals

Spontaneous emission from GaAs/AlGaAs quantum dots (QDs) embedded in photonic crystals with a narrow photonic band gap is studied theoretically. The results show that the decay lifetime is very sensitive to the sizes of QDs, and both inhibited and accelerated emission can occur, which had been indicated in a previous experiment. The Weisskopf–Wigner approximation, good for atoms and molecules, may be incorrect for QDs. A damped Rabi oscillation of the excited state with the transition frequency outside the photonic band gap may appear, which is impossible for atoms and molecules.     

Omnidirectional photonic band gaps in one-dimensional gradient refractive index photonic crystals considering linear and quadratic profiles

By using the transfer matrix formalism, in this work it is presented the study of the optical properties of 1D photonic structures constructed with M periods of bilayers of dielectric material and slabs with gradient refractive index (GRIN) profile of two types: linear and quadratic. By varying the profile parameters, preserving the average value of the refractive index for the GRIN slab, the results show the formation of new photonic band gaps whose bandwidths depends on the slope and the curvature of the linear and quadratic profile respectively. Also, it can be observed the formation of omnidirectional photonic bandgaps for the TE and TM polarizations, one for the linear profile and three for the quadratic one, for which their bandwidths depend linearly on the slope and the curvature of the GRIN profiles. It is expected that the presented results could be useful in the construction of optical devices based in their optical response under oblique incidence.     

Tamm states and nonlinear surface modes in photonic crystals

We predict the existence of surface gap modes, known as Tamm states for electronic systems, in truncated photonic crystals formed by two types of dielectric rods. We investigate the energy threshold, dispersion, and modal symmetries of the surface modes, and also demonstrate the existence and tunability of nonlinear Tamm states in binary photonic crystals with nonlinear response.     

On transmittance and localization of the electromagnetic wave in two-dimensional graphene-based photonic crystals

Two-dimensional graphene-based photonic crystal (GPC) formed by a periodic array of the homogeneous dielectric cylinders etched in the alternating graphene and dielectric layers and its inverse counterpart are considered. The transmittance of the photonic crystal is obtained. The waveguide due to the localization of the electromagnetic wave on the lattice defect that breaks the translational symmetry of the GPC of two different topologies is studied. The different topologies of GPC are characterized by different photonic band structures with different widths of photonic band gaps (PBG) and provide different frequencies for the localized electromagnetic wave due to the defect. The frequencies of the localized mode for both type of the GPC, located inside the lowest PBG, are in the range of THz or tens of THz depending on the topology of the GPC. It is shown that the photonic band gap always can be tuned by changing the chemical potential of graphene to provide formation of the localized photonic mode due to the defect. The technological advantages of the GPC, as well as the opportunity to tune the PBG and the frequency of the localized electromagnetic wave in the terahertz region of spectrum for the GPC are discussed.     

The influence of shape and orientation of scatterers on the photonic band gap in 2D metallic photonic crystals

Using the revised plane wave method, we have calculated the photonic band structures of 2D metallic photonic crystals composed of parallel metallic rods in air background and air holes drilled in metal background. We discuss the maximization of gap-to-midgap ratio as a function of scatterer parameters with different shapes and orientations in three types of lattices.     

Topological photonic states in gyromagnetic photonic crystals: Physics,properties, and applications

Topological photonic states (TPSs) as a new type of waveguide state with one-way transport property can resist backscattering and are impervious to defects, disorders and metallic obstacles. Gyromagnetic photonic crystal (GPC) is the first artificial microstructure to implement TPSs, and it is also one of the most important platforms for generating truly one-way TPSs and exploring their novel physical properties, transport phenomena, and advanced applications. Herein, we present a brief review of the fundamental physics, novel properties, and practical applications of TPSs based on GPCs. We first examine chiral one-way edge states existing in uniformly magnetized GPCs of ordered and disordered lattices, antichiral one-way edge states in cross magnetized GPCs, and robust one-way bulk states in heterogeneously magnetized GPCs. Then, we discuss the strongly coupling effect between two co-propagating (or counter-propagating) TPSs and the resulting physical phenomena and device applications. Finally, we analyze the key issues and prospect the future development trends for TPSs in GPCs. The purpose of this brief review is to provide an overview of the main features of TPSs in GPC systems and offer a useful guidance and motivation for interested scientists and engineers working in related scientific and technological areas.     

Nonreciprocal frequency doubling of electromagnetic waves through double resonance and Bragg reflection in photonic crystals

A computational study of the uni-directional second-harmonic generation in a one-dimensional dual photonic crystal structure made of GaAs, AlAs and SiO₂ with quadratic optical nonlinearity and material dispersion is presented. The computational approach uses a shooting method to solve nonlinear wave equations for coupled fundamental and second-harmonic fields and the invariant imbedding method to obtain the linear transmittance and group index spectra. The dual structure consists of two substructures, the conversion structure creating a strongly enhanced second-harmonic signal and the filter structure blocking the fundamental frequency field by Bragg reflection while permitting the passage of the second-harmonic field. The conversion structure is built with an elementary cell consisting of four sublayers whose thicknesses are systematically varied. Doubly resonant second-harmonic generation with very high conversion efficiency is achieved for light incident from the conversion structure side by choosing the geometrical parameters of the elementary cell optimally and controlling the band structure. A new mechanism to enhance second-harmonic generation by controlling the energy flow between the fundamental frequency and second-harmonic fields has also been found.     

Design and analysis of slow light regime in silicon carbide 2D photonic crystal waveguides

We theoretically demonstrate the slow light capabilities of 2D silicon carbide based photonic crystal W1 waveguides (SiC-PhC-W1Ws) with numerical simulations. The PhC is assumed to be created by devising air-holes with hexagonal lattice in a standard SiC substrate having oscillator type ordinary refractive index. Numerical simulations show that by means of selective optofluidic infiltration and varying the air-holes radii, SiC-PhC-W1Ws are capable of slowing light down by about 473 times while their group velocity dispersions are tailored to near zero values. Our numerical study also suggests the possibility of slow-light guiding with n_g × Δλ/λ_c values as high as 0.42 in SiC-PhC-W1Ws at optical telecommunications wavelengths.     

Coherent Raman and hyper-Raman spectroscopy of excited and autoionizing states of atoms and ions in laser-produced and electric-discharge plasma

Summary The experimental results on four-wave Raman and hyper-Raman scattering in a laser-produced and electric-discharge plasma are presented. It has been shown that in spectra of four-wave mixing processes resonances appear due to the Raman and hyper-Raman scattering on atomic and ionic excited states. The temporal behaviour of the scattered-signal intensity has been found to be connected with the population relaxation of atomic and ionic excited states. We have observed for the first time the resonance in the spectrum of coherent hyper-Raman scattering in electric-discharge plasma associated with the electron transition between the excited and autoionizing state of a copper atom. Paper presented at the ?XI European CARS Workshop?, Florence, Italy, 23–25 March, 1992.     

二维介电光子晶体中的赝自旋态与拓扑相变

基于背散射抑制且对缺陷免疫的传输性质,光子拓扑绝缘体为电磁传输调控提供了一种新颖的思路.类比电子体系中的量子自旋霍尔效应,本文设计出一种简单的二维介电光子晶体,以实现自旋依赖的光子拓扑边界态.该光子晶体是正三角环形硅柱子在空气中排列而成的蜂窝结构.将硅柱子绕各自中心旋转60°,可实现二重简并的偶极子态和四极子态之间的能带翻转.这两对二重简并态的平均能流密度围绕原胞中心的手性可充当赝自旋自由度,其点群对称性可用来构建赝时间反演对称.根据k·p微扰理论,给出了布里渊区中心附近的有效哈密顿量以及对应的自旋陈数,由此证实能带翻转的实质是拓扑相变.数值计算结果揭示,在拓扑非平庸和平庸的光子晶体分界面上可实现单向传输且对弯曲、空穴等缺陷免疫的拓扑边界态.本文中的光子晶体只由电介质材料组成并且晶格结构简单,实现拓扑相变时无需改变柱子的填充率或位置,只需转动一个角度.因此,这种结构在拓扑边界态的应用中更为有效.     

Nonlinearities in the reflection and transmission spectra of the photonic bandgap heterostructures with n–i–p–i crystals

Nonlinear optical properties of photonic crystal heterostructures with embedded n–i–p–i superlattices are investigated. Self-consistent calculations of the transmission and reflection spectra near the defect mode are performed using the transfer-matrix method and taking into account the gain saturation. Analysis of features and output characteristics is carried out for one-dimensional photonic crystal heterostructure amplifiers in the GaAs–GaInP system having at the central part an active “defect” from doubled GaAs n–i–p–i crystal layers. The gain saturation in the active layers in the vicinity of the defect changes the index contrast of the photonic structure and makes worse the emission at the defect mode. Spectral bistability effect, which can be exhibited in photonic crystal heterostructure amplifiers, is predicted and the hysteresis loop and other attending phenomena are described. The bistability behavior and modulation response efficiency demonstrate the potential possibilities of the photonic crystal heterostructures with n–i–p–i layers as high-speed optical amplifiers and switches.