Defect modes supported by optical lattices in photovoltaic-photorefractive crystals

We study defect modes in optically induced one-dimensional lattices in photovoltaic-photorefractive crystals. These defect modes exist in different bandgaps due to the change of defect intensity. For a positive defect, defect mode branches exist not only in the semi-infinite bandgap, but also in the first and second bandgaps. When the defect mode branch is fixed, the confinement of defect modes increases with the defect strength parameter. For a negative defect, defect mode branches exist only in the first and second bandgaps. For a given defect mode branch, the strongest confinement of the defect modes appears when the lattice intensity at the defect site is not the smallest in its branch. On the other hand, when the defect strength parameter is fixed, the most localized defect modes arise in the semi-infinite bandgap for the positive defect and in the first bandgap for the negative defect.     

Analytical investigation of one-dimensional photonic crystals with a dielectric-superconducting pair defect

We have studied the dielectric-superconducting pair defect embedded into one-dimensional photonic crystals by an analytical method based on the Kronig-Penny model. The superconducting defect has been considered by using of two-fluid model whose permittivity depends on the frequency and superconductor parameters. We have showed that in contrast to the usual defect modes, superconducting defect modes are nearly invariant upon the change of defect size and with increasing defect sizes, the enhancement behavior is observed in the peak of electric field profiles. In addition, the physical parameters have less effect on the defect modes, which is placed under cutoff frequency of superconductor.     

Nonlinear localized modes at phase-slip defects in waveguide arrays

We study light localization at a phase-slip defect created by two semi-infinite mismatched identical arrays of coupled optical waveguides. We demonstrate that the nonlinear defect modes possess the specific properties of both nonlinear surface modes and discrete solitons. We analyze the stability of the localized modes and their generation in both linear and nonlinear regimes.     

Band-gap guidance in optically induced photonic lattices with a negative defect

We report the first experimental demonstration of band-gap guidance of light in an optically induced two-dimensional photonic lattice with a single-site negative defect (akin to a low-index core in photonic-crystal fibers). We discuss the difference between spatial guidance at a regular and a defect site, and show that the guided beam through the defect displays fine structures such as vortex cells that arise from defect modes excited at higher band gaps. Defect modes at different wavelengths are also observed.     

Localized defect modes in finite magnetic two-dimensional photonic crystals

We present a detailed study of localized defect modes in finite two-dimensional magnetic photonic crystal consisting of cylindrical ferrite material in air background by using the scattering matrix method. It is shown that due to having positive and negative value of the effective magnetic permeability in interested photonic band gap, the defect modes present different behavior. Our results show that the modes appeared in positive permeability region have features similar to the modes supported by the dielectric photonic crystal while those created in the negative permeability region are strongly localized at the interface of defect ferrite rod with air background. Moreover, results indicate that defect modes occurred in the negative region are sharper than those appeared in the positive one which means the quality factor of former case is extremely high.     

Surface defect linear modes in one-dimensional photonic lattices

We report on the existence of surface defect linear modes at an interface between the defect of one-dimensional photonic lattices and the uniform media. The interface defect can significantly affect the properties of linear modes. Such new type of modes exists in the first bandgap for positive defects; while they exist in the second bandgap for negative defects. Particularly, when a Gaussian beam, which is similar to the linear mode, is launched at the defect site, we find that the Gaussian beam can be strongly confined at defect site and robustness along longitudinal direction for a long distance. When launched at a small angle into the defect site, the Gaussian beam exhibits stable snake propagation.     

Demonstration of defect modes in coupled microresonator arrays fabricated in silicon-on-insulator technology

We show experimentally the existence of defect modes in mutually coupled microring resonator arrays fabricated in silicon-on-insulator technology. The movements of donor-like and acceptor-like modes are demonstrated for various defect lengths, in good agreement with earlier theoretical prediction.     

Driving defect modes of Bose-Einstein condensates in optical lattices

We present an approximate analytical theory and direct numerical computation of defect modes of a Bose-Einstein condensate loaded in an optical lattice and subject to an additional localized (defect) potential. Some of the modes are found to be remarkably stable and can be driven along the lattice by means of a defect moving following a steplike function defined by the period of Josephson oscillations and the macroscopic stability of the atoms.     

Optical transmission properties of an anisotropic defect cavity in one-dimensional photonic crystal

We investigate theoretically the possibility to control the optical transmission in the visible and infrared regions by a defective one dimensional photonic crystal formed by a combination of a finite isotropic superlattice and an anisotropic defect layer. The Green's function approach has been used to derive the reflection and the transmission coefficients, as well as the densities of states of the optical modes. We evaluate the delay times of the localized modes and we compare their behavior with the total densities of states. We show that the birefringence of an anisotropic defect layer has a significant impact on the behavior of the optical modes in the electromagnetic forbidden bands of the structure. The amplitudes of the defect modes in the transmission and the delay time spectrum, depend strongly on the position of the cavity layer within the photonic crystal. The anisotropic defect layer induces transmission zeros in one of the two components of the transmission as a consequence of a destructive interference of the two polarized waves within this layer, giving rise to negative delay times for some wavelengths in the visible and infrared light ranges. This property is a typical characteristic of the anisotropic photonic layer and is without analogue in their counterpart isotropic defect layers. This structure offers several possibilities for controlling the frequencies, transmitted intensities and the delay times of the optical modes in the visible and infrared regions. It can be a good candidate for realizing high-precision optical filters.     

Independently tunable multichannel terahertz filters

We numerically demonstrate terahertz multichannel filters with independently tunable defect modes based on fractal photonic crystals. Single defect and multiple defects models are proposed to fabricate the multichannel terahertz filters. The facts that the wave functions of the defect states do not overlap and their bases are orthogonal lead to the independency among the defect modes. The simulated results theoretically provide the principle for fabricating independently tunable multichannel terahertz filters by utilizing one-dimensional photonic crystals with defects.     

十二重准晶中的方向缺陷

采用多重散射的方法研究了十二重准晶中的缺陷模,发现在十二重准晶中存在方向缺陷,且当缺陷组合围绕对称中心旋转时,在保持原有缺陷模的基础上,出现了新的缺陷模. 关键词： 准晶 缺陷 带隙     

Donor and acceptor guided modes in photonic crystal fibers

We present a triangular photonic-crystal-fiber structure that exhibits guided modes simultaneously above and below the first conduction band. We achieve this configuration by decreasing the size of one of the airholes (the defect) in a specific triangular lattice. More generally, we analyze the behavior of guided modes that depends on the size of the defect. Defects generated by decreasing or increasing the size of one of the holes produce donor or acceptor guided modes, respectively, in analogy with impurity levels in solid-state crystals. We conclude that the guiding mechanism for both donor and acceptor modes is produced by a unique phenomenon of multiple interference by a periodic structure.     

Stability and instability of nonlinear defect states in the coupled mode equations—Analytical and numerical study

Coupled backward and forward wave amplitudes of an electromagnetic field propagating in a periodic and nonlinear medium at Bragg resonance are governed by the nonlinear coupled mode equations (NLCME). This system of PDEs, similar in structure to the Dirac equations, has gap soliton solutions that travel at any speed between 0 and the speed of light. A recently considered strategy for spatial trapping or capture of gap optical soliton light pulses is based on the appropriate design of localized defects in the periodic structure. Localized defects in the periodic structure give rise to defect modes, which persist as nonlinear defect modes as the amplitude is increased. Soliton trapping is the transfer of incoming soliton energy to nonlinear defect modes. To serve as targets for such energy transfer, nonlinear defect modes must be stable. We therefore investigate the stability of nonlinear defect modes. Resonance among discrete localized modes and radiation modes plays a role in the mechanism for stability and instability, in a manner analogous to the nonlinear Schrödinger/Gross-Pitaevskii (NLS/GP) equation. However, the nature of instabilities and how energy is exchanged among modes is considerably more complicated than for NLS/GP due, in part, to a continuous spectrum of radiation modes which is unbounded above and below. In this paper we (a) establish the instability of branches of nonlinear defect states which, for vanishing amplitude, have a linearization with eigenvalues embedded within the continuous spectrum, (b) numerically compute, using Evans function, the linearized spectrum of nonlinear defect states of an interesting multiparameter family of defects, and (c) perform direct time-dependent numerical simulations in which we observe the exchange of energy among discrete and continuum modes.     

Transverse mode competition in defect states of a waveguide with corrugated walls

We investigate the defect states arising in the Bragg and non-Bragg gaps by inserting a straight duct into a waveguide with periodically corrugated walls. In periodic waveguides, the Bragg gap is created by the interference of the same transverse modes whereas the different mode coupling leads to the non-Bragg one. Due to the involved high-order modes, there are two defect states observed in the non-Bragg gap while only one in the Bragg gap, indicating that transverse modes play a significant role in the creation of defect states. Furthermore, the frequency of each defect state highly relies on the defect geometries and their band widths can be optimized by the number of waveguide segments. The proposed transverse mode competition analysis reveals the mechanism of frequency shifting and provides an opportunity for guided wave control engineering, which would definitely benefit their applications in various functional devices, such as filters, sensors, and amplifiers.     

Two-Dimensional Photonic Band-Gap Defect Modes with Deformed Lattice

A numerical study of the defect modes in two-dimensional photonic crystals with deformed triangular lattice is presented by using the supercell method and the finite-difference time-domain method. We find the stretch or shrink of the lattice can bring the change not only on the frequencies of the defect modes but also on their magnetic field distributions. We obtain the separation of the doubly degenerate dipole modes with the change of the lattice and find that both the stretch and the shrink of the lattice can make the dipole modes separate large enough to realize the single-mode emission. These results may be advantageous to the manufacture of photonic crystal lasers and provide a new way to realize the single-mode operation in photonic crystal lasers.     

多个单负材料缺陷一维光子晶体的孪生缺陷模

分析了含有多个单负材料缺陷层的一维光子晶体中缺陷模的性质。在两种单负(负介电常量或负磁导率)材料交替堆叠形成的一维光子晶体中,掺入了多个周期排列的单负材料缺陷层,得到在该光子晶体的零有效相位(zero-effective phase)带隙内存在孪生缺陷模。通过改变缺陷的数目或缺陷层的厚度,可调节缺陷模的频率间隔,但缺陷模的数目总保持为两个。计算结果显示,该孪生缺陷模的频率对入射角度的依赖较弱;随着入射角度的改变,缺陷模频率的相对改变量总保持在0.03以下。此外,对应缺陷模频率的电场在该光子晶体中传播时,将被强烈地局域在缺陷层与周期结构的交界面上。     

Optomechanical coupling in a two-dimensional photonic crystal defect cavity

Periodically structured materials can sustain both optical and mechanical modes. Here we investigate and observe experimentally the optomechanical properties of a conventional two-dimensional suspended photonic crystal defect cavity with a mode volume of ~3(λ/n)3. Two families of mechanical modes are observed: flexural modes, associated to the motion of the whole suspended membrane, and localized modes with frequencies in the GHz regime corresponding to localized phonons in the optical defect cavity of diffraction-limited size. We demonstrate direct measurements of the optomechanical vacuum coupling rate using a frequency calibration technique. The highest measured values exceed 80 kHz, demonstrating high coupling of optical and mechanical modes in such structures.     

Finite-dimensional model for defect-trapped light in planar periodic nonlinear structures

We study the dynamics of 2D gap solitons (GSs) in Bragg resonant nonlinear (photonic) gratings in the presence of localized defects. Previous work [Stud. Appl. Math.115, 209 (2005)] explains the mechanism of trapping the GS-carried energy at a defect via a resonant energy transfer from the GS into defect modes. We derive a finite-dimensional model that describes the evolution of the defect-trapped state as an interaction of linear defect modes and show that this model approximates the full dynamics very well in the regime when moderate amounts of GS energy are trapped.     

一维光子晶体掺杂缺陷模研究

用特征矩阵法计算了光波在包含多种掺杂缺陷的一维光子晶体中的传播规律,与不包含缺陷的结构相比较,在禁带中形成缺陷模。缺陷模的位置、数目和强度不仅和缺陷的产生方式有关,还和缺陷位置处的光学厚度及折射率的变化有关。当掺杂缺陷的位置呈等间距时,相应缺陷模也呈等间距排列。随着掺杂缺陷光学厚度的变化,缺陷模的位置、数目也随之变化。保持掺杂缺陷光学厚度不变,掺杂缺陷折射率的变化将会引起缺陷模强度的变化,并存在一个最大值。缺陷模的出现一般使带隙加宽,尤其是掺杂介质的折射率与周期介质的折射率差别较大时更加明显。掺杂空气介质时可使缺陷模的透射率近似为1。     

A simple derivation of the overlap Dirac operator

We derive the vector-like four-dimensional overlap Dirac operator starting from a five-dimensional Dirac action in the presence of a delta-function space–time defect. The effective operator is obtained by first integrating out all the fermionic modes in the fixed gauge background, and then identifying the contribution from the localized modes as the determinant of an operator in one dimension less. We define physically relevant degrees of freedom on the defect by introducing an auxiliary defect-bound fermion field and integrating out the original five-dimensional bulk fields.