Features of light absorption in chiral photonic crystals with a strong local anisotropy

The interaction of light with a layer of a chiral photonic crystal is considered. Features of the Borrmann effect at a strong anisotropy are studied. The natural polarizations are considered, and it is shown that in the limit δ << 1 (δ = (?₁ ? ?₂)/(?₁ + ?₂), where ?₁ and ?₂ are the principal values of the dielectric permittivity tensor in the plane perpendicular to the medium axis) these polarizations are orthogonal and quasi-circular, while in the limit δ >> 1 they are orthogonal but linearly polarized. It is established that in the general case the chiral photonic crystals show a complete selectivity not to the circular polarizations (as at δ << 1), but to the natural polarizations.     

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.     

Optical edge modes in photonic liquid crystals

An analytic theory of localized edge modes in chiral liquid crystals (CLCs) is developed. Equations determining the edge-mode frequencies are found and analytically solved in the case of low decaying modes and are solved numerically for the problem parameter values typical for the experiment. The discrete edge-mode frequencies specified by the integer numbers n are located close to the stop-band edge frequencies outside the band. The expressions for the spatial distribution of the n’s mode field in a CLC layer and for its temporal decay are presented. The possibilities of a reduction of the lasing threshold due to the anomalously strong absorption effect are theoretically investigated for a distributed feedback lasing in CLCs. It is shown that a minimum of the threshold pumping wave intensity may be reached, generally, for the pumping wave propagating at an angle to the helical axis. However, for lucky values of the related parameters, it may be reached for the pumping wave propagating along the helical axis. The lowest threshold pumping wave intensity occurs for the lasing at the first low-frequency band-edge lasing mode and the pumping wave propagating at an angle to the spiral axis corresponding to the first angular absorption maximum of the anomalously strong absorption effect at the high-frequency edge of the stop band. The study is performed in the case of the average dielectric constant of the liquid crystal coinciding with the dielectric constant of the ambient material. Numerical calculations of the distributed feedback lasing threshold at the edge-mode frequencies are performed for typical values of the relevant parameters.     

Near-field optics with photonic crystals

Finite-difference time-domain (FDTD) analysis of light propagation in a defect mode of a two-dimensional photonic band-gap (PBG) structure demonstrates that the light field is localized in such a structure within areas with subwavelength (λ/10) sizes. FDTD simulations reveal efficient formation of an evanescent wave at the output of such a PBG structure, permitting the subwavelength resolution to be achieved in the near field. A probe object with a size less than the wavelength of incident light is shown to perturb the near-field distribution behind the PBG structure and to change the signal detected in the far-field zone. The field intensity distribution inside a PBG structure is also sensitive to the presence of a probe object, offering a way to control the light field localized in defect modes of PBG structures. Received: 9 August 1999 / Accepted: 18 October 1999 / Published online: 10 November 1999     

Localized photonic modes in photonic crystal heterostructures

In this work, interface modes of two-dimensional photonic crystal heterostructures have been investigated by usage of the supercell method. The photonic crystal heterostructure is made of two photonic crystals with square symmetry in which one of them is composed of circular dielectric rods in air background and the other one is constructed by drilled square holes in dielectric. It is shown that using of a proper supercell plays an important role in obtaining the correct interface modes. We have also showed that the guided interface modes and single mode which is different from those reported in some published works are nearly dispersionless.     

Physical optics of photonic crystals

A one-dimensional harmonic model of a photonic crystal is considered using the methods of physical optics. The theoretical formalism is based on the notion of the Fresnel volume reflection and the system of two first-order differential equations, which are equivalent to the wave equation. Using the Rayleigh layer as an example, it is shown that the volume reflection plays a role of the friction, similar to the friction in oscillations of a pendulum, and, in a strongly inhomogeneous medium, can suppress field oscillations and turn the group velocity to zero. In the approximation of small modulation factor, the models of two, four, and six waves are considered. In the two-wave model, the dispersion relation contains a zone of inhomogeneous waves, whose width is determined by the Fresnel reflection coefficient from one period. The refinement in terms of the four-wave or six-wave model yields only a small correction to the position of the zone, retaining its width unchanged. The wavenumber as a function of frequency is described by a circle inside the zone of inhomogeneous waves and by a hyperbola outside this zone. Mathematically, the method used is significantly simpler than those based on the application of the Floquet theorem to the wave equation. It is shown that the notion of forbidden zones is inconsistent with respect to photonic crystals, and the term zones of inhomogeneous waves is proposed instead.     

Electromagnetic modes in semi-infinite photonic crystals

In a real photonic crystal, there exist three modes: propagation mode, evanescence mode and surface mode. Using ideal modal, semi-infinite photonic crystals, we study their effects on the transmission spectrum of photonic crystals, respectively. Because there exists only one air–crystal interface in a semi-infinite photonic crystal, no multiple reflection occurs and no evanescent modes and backward-propagating modes exist in this structure. The effects of the evanescence modes are studied by comparing the transmission spectrum of a finite-thickness photonic crystal slab and that of a semi-infinite photonic crystal. In addition, the effects of the backward-propagating modes are investigated using a coated semi-infinite photonic crystal structure. Finally, we study the effects of the surface modes, and find that the transmission spectrum of a semi-infinite photonic crystal is strongly dependent on its termination.     

Near-field optics and control of photonic crystals

We discuss recent progress and the exciting potential of scanning probe microscopy methods for the characterization and control of photonic crystals. We demonstrate that scanning near-field optical microscopy can be used to characterize the performance of photonic crystal device components on the sub-wavelength scale. In addition, we propose scanning probe techniques for realizing local, low-loss tuning of photonic crystal resonances, based on the frequency shifts that high-index nanoscopic probes can induce. Finally, we discuss prospects for on-demand spontaneous emission control. We demonstrate theoretically that photonic crystal membranes induce large variations in spontaneous emission rate over length scales of 50 nm that can be probed by single light sources, or nanoscopic ensembles of light sources attached to the end of a scanning probe.     

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.     

Electrical tuning of photonic crystals infilled with liquid crystals

In this paper we perform a complete study of electrical tuning in liquid crystal-infilled two-dimensional (2D) photonic crystals (PCs). The nematic liquid crystal (NLC) is characterized by a full range of bulk and surface elastic parameters. An essentially DC tuning field is applied in the axial direction. By minimizing the total (elastic plus electromagnetic) free energy, the configuration of the NLC directors, as a function of radial distance, is obtained. Three possible configurations are considered: escaped radial, planar radial, and axial. It is found that, in general, the escaped radial configuration is the preferred one. However, for sufficiently large applied fields, a phase transition occurs to the axial configuration. For example, in the case of the NLC 5CB, this transition is realized at about 14 V/μm provided that the cylinder radius is greater than about 50 nm. The configuration of the NLC directors determines the dielectric tensor as function of radial distance and this, in turn, leads to the eigenvalue equation for the PC. We present two such equations: one exact and the other approximate. The exact eigenvalue equation is based on the full anisotropy of the dielectric tensor and does not result in the usual separation of normal modes in a 2D PC. The approximate eigenvalue equation is derived from the average (over the cylinder cross-section) dielectric tensor and leads to modes that are polarized in the directions either parallel (E-mode) or perpendicular (H-mode) to the cylinders. Our calculations of the photonic band structure, by both methods, show that the approximate calculation works very well for the 5CB NLC cylinders in a silicon oxide (silica) host. This allows us to introduce the terminology quasi-E and quasi-H polarizations. We show how the partial photonic band gap in the [1 0 0] direction for these polarizations can be tuned and even completely closed. This behavior could be applied to the design of versatile, tunable polarization filters.     

Tunneling modes in photonic crystals with anisotropic single-negative metamaterials

We study tunneling modes in a one-dimensional photonic crystal (1DPC) with multilayered periodic structures containing dispersive anisotropic single-negative (ASNG; permittivity- or permeability-negative) metamaterials. A defect layer is introduced into the proposed structure, and some unusual properties are found in contrast with that of a tunneling mode in PCs with isotropic single-negative (SNG) gaps.     

Nonlinear optics of extremely short pulses in photonic crystals with controlled dispersion

The propagation of optical pulses with few oscillations in quadratically nonlinear media with modulated dispersion has been studied. It is shown that a periodic change in the velocity mismatch and the third-order dispersion coefficient makes it possible to suppress the walk-off and decompression of pulses, as a result of which the efficiency of interaction of extremely short pulses significantly increases.     

Local-field anisotropy in cholesteric liquid crystals

The first experimental values of the Lorentz tensor components L _j for the cholesteric and smectic A phases of derivatives of cholesterol have been obtained using the dispersion of the refractive indices in the visible range. The temperature dependence of the components L _j has been determined; it is invariant with respect to the cholesteric-smectic A phase transition. The effect of the isotropization of the Lorentz and local field tensors with decreasing anisotropy of the molecular polarizability has been revealed.     

Bloch waves and non-propagating modes in photonic crystals

We investigate the propagation of electromagnetic waves in finite photonic band gap structures. We analyse the phenomenon of conduction and forbidden bands and we show that two regimes are to be distinguished with respect to the existence of a strong field near the interfaces. We precise the domain for which an effective medium theory is sounded.     

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.     

Two-dimensional vectorial photonic crystals formed in azo-dye-doped liquid crystals

A 2D, square lattice, vectorial photonic crystal is formed by vectorial holography using an azo-dye-doped liquid-crystal material. Four coherent beams are interfered to generate a highly stable, switchable polarization holography structure. The formation of the vectorial lattice by the liquid-crystal molecular orientation is confirmed by diffraction pattern and polarization microscopy analysis. Simulations of the alignment and diffraction pattern are in good agreement with the experimental results. Polarization sensitive diffraction behavior is also consistent with the Kakichashvili model.     

Transition of lasing modes in disordered active photonic crystals

The transition from a photonic band-edge laser to a random laser in two-dimensional active photonic crystals is described. The lasing modes in the active photonic crystals shift from the edge of the photonic bandgap to the bulk of the gap when a certain amount of position and size disorder is introduced. The shift of lasing modes is determined with various gain profiles. The results show that the modulation of lasing modes is significant when the lasing transition wavelength overlaps the photonic bandgap.     

双周期厚度调制的一维光子晶体的电磁模

计算了厚度调制的双周期一维光子晶体的能带. 当一维光子晶体的厚度被周期性地调制时， 原来的能带分裂为许多子能带，其中一些很窄的子能带进入了原来的单周期光子晶体的带隙 内. 这些窄带内的电磁模的场强具有双周期性分布的特点，并有较强的局域性. 在较宽的子 能带中的电磁模是扩展的. 关键词： 光子晶体 双周期 电磁模     

复合周期的介质-液晶光子晶体研究

本文研究了掺入各向同性周期性介质层缺陷的一维复合周期胆甾型液晶光子晶体的禁带特性.发现同一般的胆甾型液晶不同,复合介质-液晶周期结构对左旋偏振入射光和右旋入射光都会出现共同禁带.当各向同性介质层占一个周期的厚度比例越小,左旋偏振光的禁带效应逐渐消失,而右旋偏振光的禁带则逐渐合并变大;且各向同性介质的折射率越大,则两种偏振光的禁带效应越明显,更容易出现共同禁带;通过调整厚度比,可以在可见光范围内出现对应红、绿、蓝色波长的禁带,从而可以用于液晶显示的反射式彩色滤光片. 关键词： 胆甾型液晶 光子晶体 禁带 缺陷