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.     

Optical properties of a stack of right- and left-handed layers of a cholesteric liquid crystal

We have studied the optical properties of a stack that consists of right- and left-handed layers of a cholesteric liquid crystal (CLC). The problem has been solved using the modified Ambartsumyan layer-summation method. We have examined particular features of the reflection spectra of this system and have shown that, as distinct from a single CLC layer, this system has multiple photonic band gaps. Particular features of the spectra of the photonic density of states have been considered. We have shown that this system has unique polarization characteristics; thus, in particular, if the number of sublayers is even, the eigenpolarizations of the system are degenerate (both eigenpolarizations coincide) and, as distinct from ordinary gyrotropic media, the rotation of the plane of polarization can decrease with increasing thickness of the system, the sign of the rotation depends on the sign of the chirality of the first sublayer of the system, the system is very sensitive to the variation in the number of sublayers, etc. We have investigated how the sublayer thickness, the angle of incidence, the local dielectric anisotropy, and the pitch of helix of sublayers affect the reflection spectra and other optical characteristics of the system.     

Optical properties of a stack of cholesteric liquid crystal and isotropic medium layers

Some new optical properties of a stack consisting of cholesteric liquid crystal (CLC) and isotropic medium layers are studied. The problem is solved by the modified Ambartsumyan method for the summation of layers. Bragg conditions for the photonic band gaps of the proposed system are presented. It is shown that the choice of proper sublayer parameters can be used to control the band structure of the system. In the general case, the effect of full suppression of absorption, which is observed in a finite homogeneous CLC layer, is not detected in the presence of anisotropic absorption in CLC sublayers. It is shown that this effect can be generated in the system under study if certain conditions are imposed on the isotropic sublayer thickness. Under these conditions, the maximum photonic density of states (PDS) increases significantly at the boundaries of the corresponding band. The influence of a change in the CLC sublayer thickness and the system thickness on PDS is investigated.     

Light transmission through a stack of right- and left-hand cholesteric liquid crystal layers with indefinite dielectric and magnetic permittivities. I. Reflection peculiarities

Optical properties of a stack of layers of right- and left-hand cholesteric liquid crystal (CLC) with locally indefinite dielectric and magnetic permittivities are investigated. The problem is solved by the modified Ambartsumian??s layer addition method. The peculiarities of reflection spectra of this system are studied and it is shown that, in contrast to a single layer of CLC, this system has multiple photonic band gaps (PBG). It is shown that the indefinite character of the dielectric and magnetic permittivities essentially affects the PBG map of the system. These multiple PBG can find wide application, in particular, in technologies of production of displays.     

Anisotropy of light propagation in thin opal films

Thin opal films are prepared by crystallization in a moving meniscus, and their optical transmission spectra are recorded in polarized light and studied. It is shown that the anisotropy of light propagation in the films is unambiguously related to the photonic band structure of opal and depends on the angle of incidence, the orientation of the incidence plane with respect to the opal lattice, and the wavelength and polarization of the incident light. Azimuthal diagrams of transmitted polarized light are constructed in the range of photonic band gaps of three orders for oblique incidence of a light beam. The anisotropy is found to vary with the light wave-length independently in perpendicular polarizations. A model of the band structure of opal wherein opal is represented as an fcc lattice of close-packed spheres adequately describes the optical transmission of opal films only in the range of the first-order photonic band gap.     

Li-impurity effect in optical spectra of KTaO<Subscript>3</Subscript>:Er<Superscript>3+</Superscript> crystals

The optical properties of one-dimensional photonic crystals based on porous anodic aluminum oxide films have been studied by measuring transmittance and specular reflectance spectra in the visible and UV spectral regions. Angular dependences of the spectral positions of optical stop bands are obtained. It is shown that the reflectance within the first stop band varies from point to point on the sample surface, reaching a level of 98–99% at some points. The dispersion relation for electromagnetic waves in the model of infinite periodic structure is calculated for the samples under study. The possibility of using models with an infinite or finite number of layers to calculate reflectance spectra near the first optical stop band is discussed.     

Specific features of light propagation in a periodic structure with regular arrangement of defect layers

Specific features of light propagation in a periodic structure with a large number of identical regularly arranged defect layers are considered. Rigorous analytical formulas for the transmittance and reflectance of the structures are derived. It is shown that the presence of periodically arranged inclusions may give rise to new photonic band gaps, with their positions controlled by the dielectric properties and thickness of the defect layers.     

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.     

Common electronic band gaps and similar optical properties of ZnO nanotubes

Electronic and optical properties of single-walled zinc oxide （ZnO） nanotubes are investigated from the firstprinciples calculations. Electronic structure calculations show that ZnO nanotubes are all direct band gap semiconducting nanotubes and the band gaps are relatively insensitive to the diameter and chirality of tubes. The origin of the common electronic band gaps of ZnO nanotubes is explained in terms of band-folding from the two-dimensional band structure of graphite-like sheet. Moreover, the optical properties such as dielectric function and energy loss function spectra of different ZnO nanotubes are very similar, relatively independent of diameter and chirality of tubes. The calculated dielectric function and loss function spectra show a moderate optical anisotropy with respect to light polarization.     

Low-dimensional waveguide microwave photonic crystals

Structures containing periodically alternating elements, which are a source of high-order waves, are investigated as low-dimensional waveguide microwave photonic crystals. The band character of the transmittance and the reflectance of a photonic crystal, which consists of sequentially alternating dielectric layers and thin metallic plates partially overlapping the waveguide section, is revealed by the numerical modeling and the experimental investigation of amplitude-frequency characteristics. It has been shown that the application of metallic plates with gaps in the structure of the photonic crystal made it possible to decrease its longitudinal size substantially compared with photonic crystals fabricated based on elements made of alternating dielectric layers with various permittivities.     

NLC-CLC-NLC cell as an electrically tunable polarization plane rotator

A liquid crystal optical device made of an optically anisotropic heterostructure is considered. The device consists of a cholesteric liquid crystal (CLC) layer sandwiched by two phase-shifting anisotropic layers of a nematic liquid crystal (NLC). In this structure each of the NLC layers is a quarterwave plate. The problem is solved both by Ambartsumian’s method of layer addition and Muller’s matrix method. The peculiarities of reflection spectra, eigen polarizations, rotation of polarization plane and polarization ellipticity are studied. It is shown that this device can work as a light modulator or a system for obtaining linearly polarized light with electrically tunable rotation of the polarization plane (which is especially important for optical communication), as well as a device for obtaining the linearly polarized light from a non-polarized one.     

Influence of the polarization and optical axis on the transmission behavior in a one dimensional photonic crystal containing uniaxial metamaterial

In this letter, we introduce a one-dimensional photonic crystal (1DPC) structure with a uniaxial metamaterial defect layer. It is proposed to control the transmitted wave of the defect mode by adjusting the orientation of the optical axis and incidence angle for both polarization states. The 4 × 4 transfer matrix method was employed to calculate the transmittance spectrum of the proposed structure. It is shown that the photonic band gaps, the intensity and the peak wavelength of the defect mode depends on the polarization, the orientation of the optical axis and the incidence angle of the wave, due to the strong anisotropy of the metamaterial. The transmittance spectrum curves at different optical axes of the uniaxial metamaterial and the distinct incidence angles are illustrated graphically. It is shown that the defect mode appears as a peak in the transmission spectrum. Pronounced contrasts in the intensity, wavelength positions of the defect mode and photonic band gap were demonstrated depending on the incidence angle and the orientation of the optical axis of the uniaxial metamaterial defect layer for both polarizations. Our structure offers a great variety of possibilities for designing and controlling the transmitted intensity of the defect mode.     

Optical properties of magnetic photonic crystals with an arbitrary magnetization orientation

We have studied the peculiarities of diffraction of light in magnetic photonic crystals at large values of magnetooptical activity parameter and modulation depth. We have considered the case of an arbitrary angle between the directions of the external static magnetic field and the normal to the layer. The problem has been solved by the modified Ambartsumyan layer summation method. It has been shown that the given system is nonreciprocal with respect to not only circular, but linear polarizations also. In this case, a new type of nonreciprocity is observed (namely, the relation R(α) ≠ R(–α) holds, where R is the reflection coefficient and α is the angle of incidence). It has been demonstrated that in the case of oblique incidence, there appears a new photonic forbidden band that is not selective relative to the polarization of incident light. We have detected strong dependences of reflectance, absorbance, transmittance nonreciprocity, and other characteristics on the angle between the direction of the external static magnetic field and the normal to the layer boundary. Such a system can be used as a controllable polarization filter and a mirror, as well as a source of circular (elliptic) polarization, a controllable optical diode, and so on.     

Optical properties of structures composed of periodic,quasi-periodic,and aperiodic sequences of particulate monolayers

The spectra of the coherent transmission and reflection coefficients of multilayers consisting of the periodic, Fibonacci (quasi-periodic), and Thue–Morse (aperiodic) sequences of plane-parallel monolayers of monodisperse spherical alumina and silica particles are investigated using the quasi-crystalline approximation (QCA) and the transfer matrix method (TMM). The additional opportunities for the transmission and reflection spectra manipulation in comparison with the periodic sequence of monolayers are demonstrated. Photonic band gaps in the spectra of the particulate structures are shifted to the short-wavelength range in comparison with those for systems of homogeneous layers. The shift is larger for the Thue–Morse sequence. The widths of the photonic band gaps for particulate systems are narrower than the ones for multilayers consisting of homogeneous layers of an equivalent volume of matter. The results can be used to create optical, optoelectronics, and photonics devices—for example, multispectral filters, light emitting diodes, solar cells, displays.     

基于自发辐射相干效应的可调光子带隙反射率的提高方法

光子带隙是指某一频率范围的波不能在周期变化的空间介质中传播,即这种结构本身存在“禁带”,并已成功地应用于滤波器、放大器和混频器等器件的设计中.此前,许多专家都致力于提高带隙的反射率,但其只能逐渐接近1.本文在囚禁于一维光晶格中的冷原子介质中实现两个可调光子带隙,并通过选择两基态为精细结构的三能级∧型原子系统,考虑自发辐射相干效应来探究这两个带隙的反射率.适当调节参数,探测场出现增益,从而获得较高反射率的带隙结构,甚至可以超过1.此外,两个带隙反射率还可以通过调节偶极矩之间的夹角以及非相干驱动场强度等参数来操控.     

Large forbidden band in one-dimensional multi-layered structure containing exponentially graded materials

In the present communication, we have presented band spectra and reflectance properties of one-dimensional multi-layered structure containing dielectric exponentially graded and simple dielectric layers. This study has been performed theoretically by using transfer matrix method. In this paper we have taken the multi-layered structure where refractive index of odd layers is varying continuously along the direction perpendicular to the surface of the layer in exponential form. The effect of the graded profiles are studied and compared with the conventional multi-layered structure of suitable contrast of refractive indices in detail. In this study the materials are considered as non-magnetic and layers other than the graded are taken to be homogeneous and isotropic dielectric medium of constant refractive index. It has been found that the introduction of graded layers enhanced the forbidden band gaps and affects the reflectance of electromagnetic wave spectra significantly. By changing the grading profiles and the contrast, we obtained the forbidden band gaps and the reflectance of such structural change accordingly. Therefore, introducing a graded exponential layer of dielectric in the one-dimensional multi-layered structure provides possible mechanism for enhancing the reflectance as well as the forbidden gap in the optical region. Such multi-layered structure may be useful in the design of a broadband filter.     

Anisotropic photonic crystals and microcavities based on mesoporous silicon

A technique to prepare one-dimensional anisotropic photonic crystals and microcavities based on anisotropic porous silicon exhibiting optical birefringence has been developed. Reflectance spectra demonstrate the existence of a photonic band gap and of an allowed microcavity mode at the photonic band gap center. The spectral position of these bands changes under rotation of the sample about its normal and/or under rotation of the plane of polarization of the incident radiation. The dependence of the shift of the spectral position of the photonic band gap edges and of the microcavity mode on the orientation of the polarization vector of incident electromagnetic wave with respect to the optical axis of the photonic crystals and microcavities was studied.     

Fabrication of near infrared metallodielectric photonic crystal using metal-coated dielectric spheres

A metallodielectric photonic crystal with photonic band gaps in near infrared regime has been constructed using layer-by-layer stacking of two-dimensional micro-size metal-coated dielectric spheres array. In transmission spectra two photonic band gaps are observed at 1.38 μm and 2.46 μm, which are in agreement with theoretical calculations. Experimental results show that the photonic band gaps can be realized with about ten layers. The structure with metallic microspheres provides us a novel way for fabrication of near infrared metallic photonic crystals.     

Controlled optical properties of a five-level atom embedded in photonic crystals with defect modes

The optical spectra of a five-level atom embedded in a photonic crystal are studied by considering the double-band photonic band gap reservoir with defect modes in the band gap. It is shown that some interesting phenomena such as absorption, transparency, normal or anomalous dispersion, and large amplification of a weak probe field can be observed by modulating system parameters.     

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.