Self-collimation in photonic crystals with anisotropic constituents

In a photonic crystal composed of anisotropic constituents we quantify the range of input angles and the degree of collimation of the beam inside the crystal. The optical properties of a photobleached 4-dimethylamino-N-methyl-4-stilbazolium-tosylate (DAST) crystal are used in our model to demonstrate the efficacy of the self-collimation features.     

可调光子晶体研究进展

可调光子晶体是光子晶体研究中的一个新领域，文章简单介绍了当前可调光子晶体的发展状况，阐述了其调制机理及存在的问题，同时论述了可调光子晶体的发展趋势。     

Tunable photonic Bloch oscillations in electrically modulated photonic crystals

We exploit theoretically the occurrence and tunability of photonic Bloch oscillations (PBOs) in one-dimensional photonic crystals (PCs) containing nonlinear composites. Because of the enhanced third-order nonlinearity (Kerr-type nonlinearity) of composites, photons undergo oscillations inside tilted photonic bands, which are achieved by the application of graded external-pump electric fields on such PCs, varying along the direction perpendicular to the surface of layers. The tunability of PBOs (including amplitude and period) is readily achieved by changing the field gradient. With an appropriate graded pump ac or dc electric field, terahertz PBOs can appear and cover a terahertz band in an electromagnetic spectrum.     

Tunable full band gap in two-dimensional anisotropic photonic crystals infiltrated with liquid crystals

We analyze the tunability of full band gap in two-dimensional photonic crystals created by square and triangular lattices of anisotropic tellurium rods in air background, considering that the rods are infiltrated with liquid crystal. Using the plane-wave expansion method, we study the variation of full band gap by changing the optical axis orientation of liquid crystal.     

Tunable out-of-plane band gap of two-dimensional anisotropic photonic crystals infiltrated with liquid crystals

We analyze the tunability of out-of-plane band gap in two-dimensional photonic crystals created by square and triangular lattices of air holes in anisotropic tellurium background, considering that the rods are infiltrated with liquid crystal. Using the plane wave expansion method, we study the variation of out-of-plane band gap by changing the optical axis orientation of liquid crystal.     

Tunable band gaps in electro-optical photonic bi-oriented crystals

Electrically induced birefringence is studied in photonic bi-oriented crystals in terms of molding lightflow in optical devices. In photonic bi-oriented crystals, misorientation of dielectric anisotropic grains results in a dielectric contrast at the grain boundaries. The translational periodicity of the optical constants depends upon a regular network of twisted dielectrics. Due to the anisotropy of the bicrystalline structure the direction of light propagation determines the dielectric contrast at the grain boundaries. In a specific crystallographic arrangement the optical properties of the bi-oriented crystal can be tuned by the electro-optical effect: the periodic dielectric contrast is electrically induced and photonic bandgaps are generated by applying external electric fields. The geometrical requirements for tunable photonic bicrystals are evaluated based on materials employed for electro-optical applications. Tunable photonic bi-oriented crystals may be candidates for fast optical switches, modulators and multiplexers in the optical communication network. Received: 5 July 2001 / Revised version: 3 August 2001 / Published online: 15 October 2001     

反常色散材料光子晶体中光输运的光学控制

研究了光抽运对由铯原子蒸气构成的光子晶体的影响.研究发现,利用较弱光强的线抽运光即可显著地改变这种反常色散光子晶体的透射率.而利用圆偏振光抽运可以进一步降低抽运光的阈值,并在反常色散光子晶体中获得极大的法拉第旋转.反常色散光子晶体的这些特性为光控光开关的研究和制作提供了一条新途径.     

Tunable negative-index photonic crystals using colloidal magnetic fluids

The model of using colloidal magnetic fluid to build tunable negative-index photonic crystal is established. The effective permittivity εe and permeability μe of the two-dimensional photonic crystal are investigated in detail. For transverse magnetic polarization, both εe and μe exhibit a Lorentz-type anomalous dispersion, leading to a region where εe and μe are simultaneously negative. Then, considering a practical case, in which the thickness of photonic crystal is finite, the band structures for odd modes are calculated by the plane wave expansion method and the finite-difference time-domain method. The results suggest that reducing the external magnetic field strength or slab thickness will weaken the periodic modulation strength of the photonic crystal. Simulation results prove that the negative-index can be tuned by varying the external magnetic field strength or the slab thickness. The work presented in this paper gives a guideline for realizing the flat photonic crystal lens with tunable properties at optical frequencies, which may have potential applications in tunable near-field imaging systems.     

Tunable phase compensator based on one-dimensional photonic crystals with single-negative materials

The reflection phase difference between TE and TM waves in one-dimensional photonic crystals composed of single-negative (SNG) (permittivity- or permeability-negative) materials is investigated by transfer matrix method. Within two omni-directional gaps the reflection phase difference changes smoothly and increases with the increasing of the incident angle. In the center of the second omni-directional gap the reflection phase difference remains almost unchanged in a broad frequency band. Especially, at both the edges of the second omni-directional gap the reflection phase difference keeps zero in spite of the change of incident angle. Based on these properties, a continuously tunable phase compensators and an omni-directionally synchronous reflector for TE and TM waves can be designed. The working frequencies for the phase compensators and synchronous reflector are tunable.     

Tunable photonic band-gaps in one-dimensional photonic crystals containing linear graded index material

We have demonstrated control of the photonic band gaps (PBGs) in 1-D photonic crystals using linear graded index material. The analysis of PBG has been done in THz region by considering photonic crystals in the form of ten periods of second, third and fourth generation of the Fibonacci sequence as unit cell. The unit cells are constituted of two kinds of layers; one is taken of linear graded index material and other of normal dielectric material. For this investigation, we used a theoretical model based on transfer matrix method. We have obtained a large number of PBGs and their bandwidths can be tuned by changing the grading profile and thicknesses of linear graded index layers. The number of PBGs increases with increase in the thicknesses of layers and their bandwidths can be controlled by the contrast of initial and final refractive index of the graded layers. In this way, we provide more design freedom for photonic devices such as reflectors, filters, optical sensors, couplers, etc.     

Tunable double-channel filter based on two-dimensional ferroelectric photonic crystals

A tunable double-channel filter is presented, which is based on a two-dimensional nonlinear ferroelectric photonic crystal made of cerium doped barium titanate. The filtering properties of the photonic crystal filter can be tuned by adjusting the defect structure or by a pump light. The influences of the structure disorders caused by the perturbations in the radius or the position of air holes on the filtering properties are also analyzed.     

Tunable lightwave propagation in two-dimensional hole-type photonic crystals infiltrated with nematic liquid crystal

Photonic crystals have many potential applications because of their ability to control lightwave propagation. We have investigated the tunability of lightwave propagation in two-dimensional hole-type photonic crystal structures. The linear waveguides can be obtained by the infiltration of liquid crystals into air holes in hole-type photonic crystal with square lattices. The refractive indices of liquid crystals can be changed by rotating the directors of liquid crystals. Therefore, we can control the lightwave propagation in two-dimensional hole-type photonic crystal structures. Such a mechanism of lightwave adjustment should open up a new application for designing components in photonic integrated circuits.     

Tunable face-centered-cubic photonic crystal formed in holographic polymer dispersed liquid crystals

We report on the fabrication and electro-optic measurements of face-centered-cubic (fcc) lattices in holographic polymer dispersed liquid-crystal materials. Four linearly polarized coherent plane waves were interfered to generate a fcc optical lattice that was subsequently and indefinitely recorded as an arrayed pattern of nanometer-sized liquid-crystal droplets (approximately 50 nm) at lattice nodes within a polymer matrix. Observed transmission spectra and Kossel diffraction curves are consistent with fcc crystal structure. A completely reversible 2% wavelength shift of the (+/- 111) stop band was observed on application of an electric field.     

Tunable Fabry-Pérot filter based on one-dimensional photonic crystals with liquid crystal components

A theoretical study of a tunable Fabry-Pérot multilayer structure composed of alternating layers of silicon and liquid crystal is presented and analyzed. The structure possesses two resonant frequencies within the stop band with tunable wavelengths and transmission properties. Tuning is achieved by allowing different orientations of the liquid crystal optical axes within the cavity and within the mirrors, while keeping the optical axes parallel to the layers. Applying the transfer matrix method for thin layers of anisotropic materials we demonstrate that the resonant wavelengths depend on the difference between the liquid crystal optical axis orientations. Besides, we are able to obtain a complete characterization of the structure in the form of its Jones matrix. From this, we propose an optical two-channel equalizer for applications around 1.55 μm that allows tuning the two resonant wavelengths and their relative amplitude levels.     

Thermo-optical sensitivity analysis in photonic crystal circuits based on semiconducting or metallic metamaterial constituents

We introduce a novel analysis technique for predicting thermo-optical sensitivities in photonic crystal (PC) circuits composed of either dielectric-semiconducting or metallic constituents. The proposed numerical analysis is based on a hybrid formalism of the scattering matrix technique combined with the adjoint network method. The proposed computational scheme can, with modest computational resources, predict with high accuracy, the effect of the temperature fluctuations to the light-wave propagation in PCs. Numerical simulations show that PC circuits based on metallic metamaterial platforms are significantly less sensitive to temperature variations than the usual dielectricor semiconducting PCs.     

Tunable Goos-Hänchen shift for self-collimated beams in two-dimensional photonic crystals

We present finite-difference time-domain studies of the Goos-Hänchen effect observed at the reflection of a self-collimated beam from the surface of a two-dimensional photonic crystal. We describe a method of tuning the shift of the reflected beam in photonic crystals through the modification of the surface, first structurally, as a change in the radius of the surface rods, and then all-optically, with the addition of nonlinear material to the surface layer. We demonstrate all-optical tunability and intensity-dependent control of the beam shift.     

Tunable photonic crystals based on ferroelectric and ferromagnetic materials by focused ion beam

By making photonic crystals in ferroelectric and ferromagnetic materials, field-provoked tunability of photonic crystals is broadening the interest in new applications of on-chip photonic devices. We report a nano-precise fabrication of various designs of photonic crystals in these non-conventional materials using the focused ion beam milling technique. Standard methods are developed and parameters for different materials are calibrated. Optical responses such as bandgaps and polarization status changing from planar film waveguide system with these patterns have been examined on ferromagnetic materials.     

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     

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.     

Two-dimensional photonic crystals with pure germanium-on-insulator

We have investigated pure germanium two-dimensional photonic crystals. The photonic crystals which exhibit resonances in the near infrared spectral range were fabricated on germanium-on-insulator substrates using standard silicon-based processing. The germanium-on-insulator substrate consists of a thin layer of pure germanium-on-oxide deposited on a silicon substrate. The optical properties are probed by the direct band gap optical recombination of pure germanium at room temperature. Resonant optical modes are evidenced between 1.68 and 1.53 μm in different type of hexagonal cavities (H1-H5). The spectral position of the modes is controlled by the lattice periodicity and air filling factor of the photonic crystals. Close to the Ge band edge, the quality factors are limited by the bulk material absorption.