Interference of conoscopic pictures of optical crystals

Nonconventional conoscopic pictures in poorly passing bunches of light, localized in a plane of uni-axial optical crystal are received. At usage of two crystal slabs with the optical axes oriented at angle to the plane of slab the interference conoscopic pictures are observed. The model explaining interference of conoscopic pictures is presented.     

The new matrix and the polarization state of the transmitted light through the cholesteric liquid crystal

The cholesteric liquid crystal can be regarded as a multilayer that consists of many layer uniaxial thin films that exhibit optical rotation. For the convenient discussion of the polarization states of the transmitted wave through a cholesteric liquid crystal, a new 2×2 matrix is given, in which the matrix element is changed into the complex exponential. Here we discuss the treatment process of this method in detail and its role in the investigation of the polarization states. Using this method we easily study the polarization states of the transmitted wave. The calculated results show that the polarization states of wave will be changed when it propagates along the cholesteric liquid crystal.     

Bandwidth tuning of hybrid liquid-crystal Šolc filters based on an optical cancelling technique

We demonstrate that in addition to their role in tuning the wavelength of an N-stage hybrid liquid-crystal Šolc filter, liquid-crystal cells can also be used to vary the transmission bandwidth of such filter around any of the tuned wavelength. This bandwidth tuning is based on the variation of the number of stages by what we call here an “optical cancelling technique”. This is achieved by varying the birefringence of the liquid-crystal cells whose optical path difference switches between two particular values. We show that for a 10-stage filter and at λ_i = 1.532 μm, the calculated 3-dB bandwidth varies from 2.6 to 11.8 nm when the number of “optically-cancelled” hybrid plates increases from 0 to 8. During the tuning process, the contrast ratio remains equal to that of the equivalent classical Šolc filter.     

Identification of optical nonlinearities of dye-doped nematic and polymer-dispersed liquid crystals using Z-scan technique

This study investigates the nonlinear optical properties of azo-dye-doped nematic and polymer-dispersed liquid crystal (ADDPDLC) films with nano-sized LC droplets using the Z-scan technique, which is a simple but powerful technique for measuring the optical Kerr constants of materials. The results indicate that the optical Kerr constant (n₂) of the azo-dye-doped nematic LC (ADDLC) film is large because of the photoisomerization effect and the thermal effect. Therefore, the optical Kerr constant of this material can be modulated by varying the temperature of the sample and the direction of polarization of incident laser. The range of n₂ modulated is from −5.26 × 10⁻³ to 1.62 × 10⁻³ cm²/W. The optical Kerr constants of ADDPDLC films at various temperatures are also measured. The experimental results reveal that liquid crystals in the ADDPDLC film strengthen the nonlinearity. The n₂ of the ADDPDLC film is maximal at ∼35 °C, because of the decrease in the clearing temperature of the ADDPDLC films. The clearing temperatures of the liquid crystals (E7), and the ADDPDLC film used in this work were found to be 61 °C and 43 °C, respectively.     

Creation of tunable absolute bandgaps in a two-dimensional anisotropic photonic crystal modulated by a nematic liquid crystal

Photonic crystals (PCs) have many potential applications because of their ability to control light-wave propagation. We have investigated the tunable absolute bandgap in a two-dimensional anisotropic photonic crystal structures modulated by a nematic liquid crystal. The PC structure composed of an anisotropic-dielectric cylinder in the liquid crystal medium is studied by solving Maxwell's equations using the plane wave expansion method. The photonic band structures are found to exhibit absolute bandgaps for the square and triangular lattices. Numerical simulations show that the absolute bandgaps can be continuously tuned in the square and triangular lattices consisting of anisotropic-dielectric cylinders by infiltrating nematic liquid crystals. Such a mechanism of bandgap adjustment should open up a new application for designing components in photonic integrated circuits.     

Biphotonic effect of azo-dye-doped liquid crystals using the sequential Z-scan technique

This study investigates the biphotonic effect of azo-dye-doped liquid crystals (ADDLCs) using the sequential Z-scan technique. A spot on the sample is illuminated by a green light for 6 s, and then the same spot is illuminated simultaneously with a red light and a green light for 6 s. Measurements are made by scanning the sample near the beam waist of the green laser. The results show that the biphotonic effect is important to the nonlinear coefficient of the sample. The variations of the optical Kerr constant with intensity of red light are measured. Measurement results demonstrate that the molecular reorientation of liquid crystals induced by the photoisomerization of the azo dyes dominates at low red-light intensity, but the thermal effect compensates for the molecular reorientational nonlinearity of the sample at high red-light intensity.     

Color dispersion in two-dimensional phase array based on polymer-dispersed liquid crystal film

This work proposes a feasible method for fabricating a two-dimensional periodic structure with a sub-micrometer periodicity using a single laser beam, based on polymer-dispersed liquid crystal (PDLC) films. The resulting nano-PDLC morphology is highly symmetrical, and similar to that written using multi-beam interference. The increase in the electric-tunability of the optical behavior, including spatial diffraction and color dispersion, is examined. The color dispersion provides optical evidence of the periodic structure of the PDLC film.     

Topological Properties of Spatial Coherence Function

The topological properties of the spatial coherence function are investigated rigorously. The phase singular structures （coherence vortices） of coherence function can be naturally deduced from the topological current, which is an abstract mathematical object studied previously. We find that coherence vortices are characterized by the Hopf index and Brouwer degree in topology. The coherence flux quantization and the linking of the closed coherence vortices are also studied from the topological properties of the spatial coherence function.     

Polarization-selective grating mirrors used in the generation of radial polarization

Two novel methods to control the polarization of laser radiation are presented. The discrimination between different polarization distributions isperformed with a corrugation grating in the top high-index layer of a multilayer mirror, which couples the undesired polarization into a lossy waveguidemode of the multilayer. The generation of radially polarized radiation in a laser resonator is presented as a practical verification of the principle.This revised version was published online in May 2005. The Article Category was removed.This revised version was published online in August 2005 with a corrected cover date.     

Photoinduced linear and/or circular birefringences from light propagation through amorphous or smectic azopolymer films

The self-induced rotation of the azimuth of elliptically polarized light passing through birefringent azopolymer thin films is investigated. The experiments were carried out on thin films of the amorphous p(DR1M-co-MMA) and p(DR1M) azopolymer samples and of the p(6MAN) derivative in its glassy and liquid-crystalline phases. In fact, using various controlled input light ellipticities, linear birefringence (LB) and/or circular birefringence (CB) measurements were performed separately and in conjunction with polarization analyses of the transmitted pump beam. According to a general theoretical analysis based on Jones’ matrix formalism, it is thus shown that the induced rotation angle through the films depends mainly on the ellipticity of the input light, on the generated LB level and, to a lesser extent, on the CB photoinduced in the liquid-crystalline phase. In the latter case, it is concluded that irradiation with circularly polarized light does induce a chiral arrangement in the polymer film, although the photosensitive chromophores do not contain any optically active group. Received: 22 April 2002 / Revised version: 28 May 2002 / Published online: 25 September 2002 RID="*" ID="*"Corresponding author. Fax: +33-5/5684-8402; E-mail: csouri@morgane.lsmc.u-bordeaux.fr     

Polarization-resolved analysis of the characteristics of a Raman laser made with a polarization maintaining fiber

We derive a simple model describing steady characteristics of Raman fiber lasers made with polarization maintaining fibers. We show both theoretically and experimentally that this kind of laser simply consists of two independent Raman lasers linearly polarized along the fiber birefringence axes. The output power characteristics of the laser are shown not to be influenced by optical Kerr effect. Finally, we use our model to propose answers to questions recently raised about efficiency of Raman lasers made with polarization maintaining fibers.     

Analysis of Fabry-Perot interference effects on the modulation properties of liquid crystal displays

In this paper, we present the analysis of Fabry-Perot interferences in a twisted nematic liquid crystal display (LCD), and its influence on the modulation properties of the device. We develop a theoretical analysis based on the Jones matrix formalism and compare the results with the experimental response of a commercial display. The developed theory considers multiple reflections to derive a new Jones matrix for the display, which accounts for both polarization and Fabry-Perot interference effects. The validity of this treatment is limited to normal incidence illumination, but it is much simpler than other 4 × 4 matrix treatments developed for a general oblique incidence. It is shown that the existence of multiple reflections can be added to previously existing simplified models for the display, resulting in a modified Jones matrix with two new parameters: the Fresnel reflection coefficient r and the voltage independent phase Φ. In addition, a calibration procedure is proposed where the calculation of these two new parameters related with the multiple reflections, can be uncoupled from the calculation of the rest of the parameters, related with the modulation properties. We remark the good agreement between the theoretical results and the experimental measurements.     

Resolution improvement of surface plasmon-enhanced, liquid crystal spatial light modulator: Simulation studies

Spatial resolution is an important performance characteristic of spatial light modulators (SLM). One of the key factors affecting the spatial resolution of liquid crystal (LC)-based SLM is the fringing field effect. This effect can be reduced in thin LC cells with corresponding reduction in the electro-optical response. A strong electro-optic response in thin LC layer can be attained using the surface plasmon resonance (SPR) phenomenon. While SPR-based LC SLMs were already demonstrated about 15 years ago, their development has been hampered in part by low resolution, due to the finite propagation length of the surface plasmons (SPs). A fine patterning of the metal layer supporting the propagation of SPs is studied as a possible solution for reducing the spatial blurring associated with the long propagation length of SPs. The results of detailed computer simulations showing improved resolution SPR-LC-SLM are presented.     

Birefringent filter with amplitude beats

In this work, we show a very simple birefringent filter useful to modulate a broadband light spectrum. We first show the generation of various oscillating spectra using two identical multiple-order waveplates. In particular a sinusoidal broadband spectrum with a rapid oscillation is obtained. This spectrum is amplitude modulated by adding another waveplate to the system. This waveplate has a small phase shift, and with the proper orientation generates amplitude beats on the broadband spectrum. Finally, we show how this system can be voltage controlled by means of a ferroelectric liquid crystal modulator. We experimentally demonstrate this behavior with the aid of a portable spectrophotometer, and we provide a theoretical explanation on the basis of the Jones matrix formalism.     

Nonlinear optical properties and photoinduced anisotropy of an azobenzene ionic liquid-crystalline polymer

The nonlinear optical properties and photoinduced anisotropy of an azobenzene ionic liquid-crystalline polymer were investigated. The single beam Z-scan measurement showed the polymer film possessed a value of nonlinear refractive index n₂ = −1.07 × 10⁻⁹ cm²/W under a picosecond 532 nm excitation. Photoinduced anisotropy in the polymer was studied through dichroism and photoinduced birefringence. A photoinduced birefringence value Δn ∼ 10⁻² was achieved in the polymer film. The mechanism for the nonlinear optical response and the physical process of photoinduced anisotropy in the polymer were discussed.     

Geometry of nematic liquid crystals under shearing flow

In this work, an extended version of the Hess-Baalss conformal approach is used to propose a relation connecting the viscosity coefficients of the nematic liquid crystals. Starting from the well-known fact that, in its usual form, the conformal transformation leads to results which are not observed experimentally, it is shown that, when the director field of an ordered nematic phase under sheared motion is taken as a three-dimensional surface with torsion, the resulting theory describes the observed experimental data efficiently. Moreover, this model predicts that the five viscosity coefficients of the Leslie ah hoc model are not independent, but connected. A comparison of the deduced relationship with experimental data is performed and an excellent agreement is obtained.     

Rotations of eigenvibration direction in anisotropic crystals

The electric field of incident light induces dipoles in anisotropic media, vibrating in two perpendicular directions of the principal axes. Because of the tensor property of the dielectric constant, an induced dipole is subject to a torque, tending to rotate it about the axis parallel to the propagation direction. The directions of eigenvibration of the ordinary (o-ray) and extraordinary (e-ray) waves are no longer perpendicular in this sense. We propose here the relationships to describe the rotation of the induced dipole in the perpendicular electric fields. The rotation angles are found to increase with increasing dielectric constants and electric field strength of the incident light, exhibiting large values near the resonance frequencies in the infrared range at the azimuth angle /4 of the polarized incident light. Piezoelectric and ferroelectric crystals have a large value of the dielectric constant in the infrared frequency range. Rotations of the vibration direction of the o-ray and the e-ray waves are shown in the infrared transmission spectra recorded by incidence of the polarized light and transmission through piezoelectric and ferroelectric crystals (-quartz, LiNbO₃, and LiTaO₃). Interference of the o-ray and the e-ray waves transmitted through the crystals confirms the rotations of the vibration directions, a self-modulation effect of light in piezoelectric and ferroelectric crystals induced by the electric field of the propagating light.     

Mode splitting in an optical slab waveguide filled with nematic liquid crystals

Mode splitting was observed when a He-Ne laser beam was reflected through a prism-coupled liquid-crystal slab waveguide under an applied electric field. The splitting manifests itself as the imposed voltage reaches a critical level, and diminishes when the voltage increases above a critical high value. If the applied voltage increases even further, mode splitting vanishes, attributing to the result that almost all the directors of the liquid crystal turn upright to the surface. The multi-layer matrix simulation can satisfactorily account for this phenomenon by exploiting the property of the anisotropic optical birefringence of a liquid crystal under applied voltages. Received: 2 December 2002 / Revised version: 24 January 2003 / Published online: 23 May 2003 RID="*" ID="*"Corresponding author. Fax: +886/3572-3052, E-mail: jtlue@phys.nthu.edu.tw     

Bloch oscillations for circularly polarized light

All previous investigations on the Bloch oscillations of waves focus on scalar waves. Here we demonstrate, for the first time, the existence of Bloch oscillations of vector fields for circularly polarized light (CPL) propagating through a designed liquid crystal structure. To obtain the Wannier-Stark ladder of the CPL, we have designed a cholesteric liquid crystal structure with spatially varying pitch. The Bloch oscillations of the CPL have been observed in such a structure by exact numerical simulations. We have also shown that such a phenomenon can be easily detected in time-resolved reflection experiments.     

Fluid dynamical enstrophy and the number of optical vortices in a paraxial beam

Vortex-bearing optical beams have a tendency to maintain the maximum number of vortices during propagation. This tendency is reminiscent of the concept of enstrophy, which is a conserved quantity in two-dimensional fluid dynamics, and which is given in terms of the vorticity in the fluid. We derive the optical equivalent for the fluid vorticity and show that it represents the optical topological charge density in paraxial beams. It then follows that the optical equivalent of the enstrophy represents the total number of optical vortices on a cross-section of the beam. We then argue that this concept forms an important part of the tendency of paraxial beams to maintain their maximum number of vortices. As part of the derivation we provide a summary of some of the pertinent topological properties of phase functions.