Peculiarities of radiation of a stack of cholesteric liquid crystal and isotropic medium layers

Peculiarities of radiation of a stack of cholesteric liquid crystal and isotropic medium layers are considered. The problem is solved by Ambartsumian’s layer addition modified method. Peculiarities of the reflection spectra and the spectra of photonic density of states are studied. It is shown that the system can be used in laser technique for constructing low-threshold lasers, which are tunable in a wide band of the radiation wavelength.     

Chiral photonic crystals with an anisotropic defect layer: Oblique incidence

In the present paper we consider some properties of defect modes in chiral photonic crystals with an anisotropic defect layer at oblique light incidence. The problem is solved by Ambartsumian’s layer addition method. We investigated some peculiarities of the discussed system’s reflection spectra of the oblique light incidence for both the minimum and essential influences of the dielectric boundaries. Then we investigated some particulars of the density of photonic states spectra. We also discussed some peculiarities of the light energy distribution in the system. We found out that at large incidence angles two defect modes arise in the two regions of the selective reflection, each in one respectively, meanwhile, none arises in the central region of the complete reflection. Our investigations show that it is possible to rather widely change the emission peak wavelength in the subject system doped with some laser dye, by changing the incidence angle.     

Specific features of the emission of chiral photonic crystals with an anisotropic defect: I. Thickness effects

The specific features of defect modes of chiral photonic crystals with an anisotropic defect have been investigated. Peculiarities of the spectra of polarization observables of the system under consideration are analyzed at different thicknesses of the defect layer. It is shown that single refraction occurs in a defect mode, even though the system is anisotropic and inhomogeneous. We also investigated the specific features of the spectra of the photon density of states, light intensity at the defect center, and the Q factor of defect modes at different thicknesses of the defect layer and chiral photonic crystals. It is shown that the lasing wavelength of chiral photonic crystals with an anisotropic defect enriched in laser dyes (resonant atoms) can be controlled in a different way: by varying the defect layer thickness. It is shown that this system can operate as a narrow-band filter (mirror) with a controlled frequency width and location of the total transmission (reflection) range on the frequency scale.     

Zone structure and polarization properties of the stack of a metamaterial-based cholesteric liquid crystal and isotropic medium layers

The optical properties of a stack of metamaterial-based cholesteric liquid crystal (CLC) layers and isotropic medium layers are investigated. The problem is solved by a modification of Ambartsumian’s layer addition method. CLCs with two types of chiral nihility are defined. The peculiarities of the reflection spectra of this system are investigated and it is shown that the reflection spectra of the stacks of CLC layers of these two types differ from each other. Besides, in contrast to the single CLC layer case, these systems have multiple photonic band gaps. There are two types of such gaps: those selective with respect to polarization of the incident light and nonselective ones. It is shown that the system eigenpolarizations mainly coincide with the quasi-orthogonal, quasi-circular polarizations for normally incident light, except the regions of diffraction reflection selective with respect to the polarization of incident light. The influence of the CLC sublayer thick-nesses, the incidence angle, the local dielectric (magnetic) anisotropy of the CLC layers, and the refractive indices and thicknesses of the isotropic media layers on the reflection spectra and other optical characteristics of the system is investigated.     

Transmission and reflection spectra of a photonic crystal with a Raman defects

Features of Raman gain of probe radiation in three-level atoms placed in a defect of a one-dimensional photonic crystal in the presence of laser radiation (pump) at an adjacent high-frequency transition have been theoretically investigated. It has been shown that there is a pump intensity range where narrow peaks (resonances) simultaneously appear in the transmission and reflection spectra of the probe field. Beyond this region, the peak in the transmission spectrum is transformed to a narrow dip. The spectral position of these peaks is determined by the Raman resonance and the transmittance and reflectance can be larger than unity at pump intensities from several microwatts per square centimeter to several tens of milliwatts per square centimeter. The nature of narrow peaks is due to a sharp dispersion of a nonlinear refractive index near the Raman resonance; this dispersion is responsible for a strong decrease in the group velocity of probe radiation. The proposed scheme makes it possible to obtain controlled ultranarrow resonances in the transmission and reflection spectra of the photonic crystal.     

Angular tuning of defect modes spectrum in the one-dimensional photonic crystal with liquid-crystal layer

A one-dimensional ZrO₂/SiO₂ photonic crystal with a 4-n -pentyl-4' -cyanobiphenyl (5CB) nematic defect layer was used to investigate the transmission spectra of light polarized parallel and perpendicular to the liquid-crystal director at different angles of incidence. The spectra of the photonic crystal were shown to split into four polarized components T_ij at oblique incidence. When the incident angle increased, the bandgap edges and the defect modes shifted towards short wavelengths, while the amplitudes of the defect modes increased for the transverse magnetic polarization and decreased for the transverse electric polarization. The observed discrepancy between the defect mode amplitudes in the center and near the edges of the photonic bandgap was found to be related to the radiation losses inside the defect layer of a non-ideal photonic crystal. The simulated transmission spectra obtained using recurrence relations and taking into account the decay of defect modes are in good agreement with the experimental data.     

Optical defect modes at an active defect layer in photonic liquid crystals

An analytic approach to the theory of the optical defect modes in photonic liquid crystals in the case of an active defect layer is developed. The analytic study is facilitated by the choice of the problem parameters related to the dielectric properties of the studied structures. The chosen models allow eliminating polarization mixing at the external surfaces of the studied structures. The dispersion equations determining the relation of the defect mode (DM) frequency to the dielectric characteristics of an isotropic, birefringent and absorbing (amplifying) defect layer and its thickness are obtained. Analytic expressions for the transmission and reflection coefficients of the defect mode structure (DMS) (photonic liquid crystal-active defect layer-photonic liquid crystal) are presented and analyzed. The effect of anomalously strong light absorption at the defect mode frequency for an absorbing defect layer is discussed. It is shown that in a distributed feed-back lasing at the DMS with an amplifying defect layer, adjusting the lasing frequency to the DM frequency results in a significant decrease in the lasing threshold and the threshold gain decreases as the defect layer thickness increases. It is found that, generally speaking, the layer birefringence and dielectric jumps at the interfaces of the defect layer and photonic liquid crystal reduce the DM lifetime in comparison with the DMS with an isotropic defect layer without dielectric jumps at the interfaces. Correspondingly, generally speaking, the effect of anomalously strong light absorption at the defect mode frequency and the decrease in the lasing threshold are not so pronounced as in the case of the DMS with an isotropic defect layer without dielectric jumps at the interfaces. The case of a DMS with a low defect layer birefringence and sufficiently large dielectric jumps are studied in detail. The options of effectively influencing the DM parameters by changing the defect layer dielectric properties, and the birefringence in particular, are discussed.     

Polariton local states in periodic Bragg multiple-quantum-well structures

We study analytically the optical properties of several types of defect in Bragg multiple-quantum-well structures. We show that a single defect leads to two local polariton modes in the photonic bandgap. These modes lead to peculiarities in reflection and transmission spectra. Detailed recommendations for experimental observation of the effects studied here are given.     

Photonic density and nonreciprocal optical properties in chiral liquid crystals

Nonreciprocal optical properties of anisotropic (nano-film) heterostructures made of a cholesteric and nematic liquid crystal (CLC-NLC) layers are studied. Namely, a NLC-CLC (and CLC-NLC) structures are considered in which the NLC layer is a quarter-wave plate. The problem is exactly solvable by Ambartsumians’ modified layer addition and Mullers’ transfer-matrix methods. The peculiarities of the polarization dependent properties, such as the photonic density of states, reflection spectra, the polarization plane rotation and ellipticity spectra are investigated. It is shown that such a system canwork as a light modulator, an element for obtaining linearly polarized light with an electrically tunable polarization plane rotation, or a transformer of non-polarized source into linearly polarized light. The analysis of the optical properties in investigated structures can be used for design of perspective optical diodes, microlasers and multifunctional elements on chiral liquid crystals with electrically tunable polarization plane rotation and field controlled light polarization.     

可见光波段SiO2/CdSe一维光子晶体及缺陷模的研究究

采用SiO2/CdSe构建了可见光波段一维光子晶体结构,并在其中引入LiTaO3缺陷层。利用传输矩阵法,分析了电磁波在无缺陷与含LiTaO3缺陷层两种光子晶体中的带隙结构,系统地研究了缺陷层参数对光子晶体可见光波段带隙结构的影响规律。计算结果表明：LiTaO3的引入,有利于带隙宽度的增加,调整缺陷层结构参数,缺陷模的位置可在不同颜色区域出现,如红光、黄光等缺陷模。该结构有望用于制作可见光波段的滤波器。     

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.     

Use of photonic quantum well as tunable defect in multilayer narrowband reflection-and-transmission filter

By using a photonic quantum well (PQW) as a tunable defect layer, a theoretical analysis on the optical properties in a multilayer narrowband reflection-and-transmission filter can be given. It is found that the resonant peaks in the reflection and transmission spectra are shifted to shorter wavelengths as the number of periods in the PQW increases. The shifting feature is more salient if the QW is deeper, that is, the refractive index contrast in the constituents of the PQW is increased. This novel design provides an alternative for achieving a tunable filter instead of using the usual electrooptical defect.     

Optical properties of chiral photonic crystals with an anisotropic defect layer

Properties of defect modes in chiral photonic crystals with an anisotropic defect are considered. The influence of the defect layer thickness, its location in the crystal and orientation of its optical axis, as well as of the chiral photonic crystal thickness on the properties of defect modes is studied. It is shown that at certain values of the defect layer thickness the medium loses its main property, namely, the polarization dependence of the diffraction reflection. At certain thicknesses of the defect layer this system transforms from the source of the right circular polarization into the source of the left circular polarization, if the layer position in the chiral photonic crystal changes.     

Defect modes of chiral photonic crystals with an isotropic defect

Specific features of the defect modes of cholesteric liquid crystals (CLCs) with an isotropic defect, as well as their photonic density of states, Q factor, and emission, have been investigated. The effect of the thicknesses of the defect layer and the system as a whole, the position of the defect layer, and the dielectric boundaries on the features of the defect modes have been analyzed. It is shown that when the CLC layer is thin the density of states and emission intensity are maximum for the defect mode, whereas when the CLC layer is thick, these peaks are observed at the edges of the photonic band gap. Similarly, when the gain is low, the density of states and emission intensity are maximum for the defect mode, whereas at high gains these peaks are also observed at the edges of the photonic band gap. The possibilities of low-threshold lasing and obtaining high-Q microcavities have been investigated.     

One-dimensional photonic crystals with a planar oriented nematic layer: Temperature and angular dependence of the spectra of defect modes

Transmission spectra of a one-dimensional photonic crystal (PC) formed by two multilayer dielectric mirrors and a planar oriented layer of 5CB nematic liquid crystal (LC) that is sandwiched between these mirrors and serves as a structure defect are investigated experimentally. Specific features of the behavior of the spectrum of defect modes as a function of the angle of incidence of light on the crystal are studied for two polarizations: parallel and perpendicular to the director of the LC; the director either lies in the plane of incidence or is perpendicular to it. It is shown that, for the configurations considered, the maxima of the defect modes shift toward the short-wavelength region as the tilt angle of incidence radiation increases; this tendency is more manifest for the parallel-polarized component, when the director lies in the plane of incidence. In the latter case, the width of the photonic band gap (PBG) appreciably decreases. The temperature dependence of the polarization components of the transmission spectra of a PC is investigated in the case of normal incidence of light. The spectral shift of defect modes due to the variation of the refractive index of the LC at the nematic-isotropic liquid phase transition point is measured. It is shown that, in real PCs, the amplitude of defect modes decreases when approaching the center of the band gap, as well as when the number of layers in the dielectric mirrors increases. Theoretical transmission spectra of the PCs calculated by the method of recurrence relations with regard to the decay of defect modes are in good agreement with experimental data.     

Localized electromagnetic modes and the transmission spectrum of a one-dimensional photonic crystal with lattice defects

The properties of localized electromagnetic modes in a one-dimensional photonic crystal with a structural defect layer were studied. The role of the defect was played by an anisotropic nematic liquid crystal layer. The frequency and the damping factor of defect modes were shown to substantially depend on the defect layer thickness and the orientation of the optical axis of the nematic. The transmission spectra of photonic crystals with one and two lattice defects were studied. Taking into account the special feature of nematic liquid crystals distinguishing them from usual crystals, namely, large permittivity anisotropy, it was shown that the transmission spectrum of the photonic crystal could be controlled by varying the orientation of the optical axis of the nematic, for instance, under the action of an external electric field.     

一维光子晶体缺陷模激光器的放大特性

光子晶体中引入缺陷后将形成缺陷模,这些缺陷模在增益介质中将被放大形成激光。基于麦克斯韦方程和速率方程相结合的模型,用时域有限差分法(FDTD)计算和分析了一维单缺陷光子晶体激光器中缺陷模的空间分布和频谱特性,以及这些缺陷模的放大特性,主要研究了缺陷层的厚度、晶体层数对缺陷模放大特性的影响。模拟结果显示,类似于传统激光腔的腔模,这些缺陷模能够被放大,形成激光。调整缺陷层的厚度、晶体层数等结构参量,将改变缺陷模的谐振,激射频率以及空间分布,这将直接影响激射阈值和饱和特性。增加晶体的层数,激光器的阈值将降低,饱和值将增加,但晶体层数增加到一定限度时,这种增减趋势变弱。模拟结果证明了有效层数的存在。     

表层厚度渐变一维耦合腔光子晶体的反射相位特性及其应用

利用传输矩阵法研究了表层厚度渐变的一维非对称耦合腔光子晶体的反射相位特性. 研究表明, 光子禁带内(包括缺陷模附近)的反射率在98%以上, 且基本不受表层厚度影响, 特别是, 在非正入射情况下, 简并的缺陷模随着表层厚度的变化会发生分裂; 进一步研究发现, 在缺陷模分裂处附近, TE, TM偏振的反射相位以及它们之间的相位差均敏感地依赖于表层厚度的变化, 从而使得反射光的偏振态也随表层厚度的变化而敏感变化, 其物理机理在于缺陷模分裂所造成的剧烈相位变化. 基于上述特性, 设计了一种表层厚度呈二维周期变化的一维光子晶体结构, 从该结构反射的激光经透镜聚焦后, 在聚焦区域同时存在各种偏振态(包括沿不同方向的线偏振、左旋或右旋圆偏振、椭圆偏振等)的子光束, 它们叠加后在聚焦区域将产生具有无规相位和无规偏振态的光场. 以上结果能有效降低激光的相干性, 在激光核聚变等领域有潜在的应用价值.     

Properties of defect modes in one-dimensional photonic crystals containing a graded defect layer

The properties of defect modes in one-dimensional photonic crystals (PCs) containing a graded defect layer are studied theoretically. The relative permittivity and magnetic permeability of the graded defect layer vary continuously along the direction perpendicular to the surface of the layer. The effect of the linear gradation profiles of the relative permittivity and permeability are studied in detail. It is shown that the defect modes appear inside the forbidden band gaps in its transmission spectra and the gradation profiles of the relative permittivity and permeability affect the defect modes significantly. By changing the gradation parameters, the intensity and position of the defect modes can be tuned. Therefore, introducing a graded defect layer in one-dimensional PCs provides possible mechanism for tuning the defect modes. This may be useful in the design of channeled filters.     

一维掺杂光子晶体嵌入负介电常数材料和负磁导率材料的性质

对一维掺杂光子晶体嵌入负介电常数材料和负磁导率材料中缺陷模的透射性质进行了研究.利用转移矩阵方法,分别计算了负介电常数材料和负磁导率材料的反射相位谱和一维掺杂光子晶体的透射相位谱.研究发现,在特定条件下,负介电常数材料和负磁导率材料的反射相位以及一维掺杂光子晶体的往返透射相位之和是0或者2π的整数倍.这样的研究结果表明,在满足一定的条件下,一维掺杂的光子晶体嵌入负介电常数材料和负磁导率材料中后,无论杂质的厚度多大,在光子带隙中仅出现一个缺陷模.而且,由于负介电常数材料和负磁导率材料性质的限制,单个缺陷模的品质因子会大大提高.