Topological and morphological transformations of developing singular paraxial vector light fields

The paper is devoted to establishment of the real-time topological and morphological dynamics of generic developing paraxial elliptic speckle fields generated and driven by the system ‘laser beam + photorefractive crystal LiNbO₃:Fe’. Generic space-time development of full gamut of polarization ellipse parameters (ellipticity, azimuth, morphology of C points, optical diabolos and handedness) and their combination in fixed beam cross-section was measured in details by the elaborated quick-action real-time Stokes-polarimetry. Whole field irreversible evolution is fulfilled through totality of random space/time C point pair nucleation/annihilation. The ‘life-story’ of C point and optical diabolo pairs is realized through ‘local topological/morphological transition’ with fully reversible scenario. It starts from smooth fragment of speckle field by formation of pre-nucleation local structure and finishes by after-annihilation local structure which decays to another smooth structure. Scenarios of star-monstar pair nucleation/annihilation and monstar  ↔  lemon transformation were established. Measured statistics of C point and diabolo morphological forms was in excellent agreement with theory predictions. All allowed scenarios of diabolo pair ‘life-story’ started/finished as star-hyperbolic monstar-hyperbolic pair were measured. Evolution of polarization ellipses handedness is implemented through L contours movement and reconnection with a saddle as the catalyst. Reconnection of L contour peninsula leads to birth of closed L contour delimiting island of fixed handedness ellipses with/without C points. Elaborated approach and presented results start the dynamic singular optics of time-dependent vector light fields.     

Binary polarization pupil filter: Theoretical analysis and experimental realization with a liquid crystal display

The Jones matrix formalism has been applied to evaluate the response of an optical system when a non-uniform polarizing pupil is introduced. With this formalism we analyze and experimentally demonstrate the properties of a binary polarization pupil filter having two regions with two orthogonal linear polarization orientations. We first study the case when no analyzer is placed behind the pupil filter, and both, the transversal and the axial behavior are described in terms of the intensity and the local state of polarization. Then it is shown how the response of the optical system can be easily changed through the orientation of an analyzer placed behind the pupil. We experimentally verified the theory using a twisted nematic liquid crystal display, which produces two orthogonal linear polarization states for two different addressed voltages.     

Control of extraordinary light transmission through perforated metal films using liquid crystals

We calculate the effective dielectric tensor of a metal film penetrated by cylindrical holes filled with a nematic liquid crystal (NLC). We assume that the director of the NLC is parallel to the film, and that its direction within the plane can be controlled by a static magnetic field, via the Freedericksz effect. To calculate the effective dielectric tensor, we consider both randomly distributed holes (using a Maxwell-Garnett approximation) and a square lattice of holes (using a Fourier technique). Both the holes and the lattice constant of the square lattice are assumed small compared to the wavelength. The films are found to exhibit extraordinary light transmission at special frequencies related to the surface plasmon resonances of the composite film. Furthermore, the frequencies of peak transmission are found to be substantially split when the dielectric in the holes is anisotropic. For typical NLC parameters, the splitting is of order 5–10% of the metal plasma frequency. Thus, the extraordinary transmission can be controlled by a static magnetic or electric field whose direction can be rotated to orient the director of the NLC. Finally, as a practical means of producing the NLC-filled holes, we consider the case where the entire perforated metal film is dipped into a pool of NLC, so that all the holes are filled with the NLC, and there are also homogeneous slabs of NLC on both sides of the film. The transmission in this geometry is shown to have similar characteristics to that in which the NLC-filled screen is placed in air.     

Polarization Changes of Partially Coherent Electromagnetic Vortex Beams Propagating in Turbulent Atmosphere

We investigate the polarization change of partially coherent electromagnetic vortex beams propagating in turbulent atmosphere. It is shown that the polarization of the beams will experience changes, and the changes of the polarization are dependent on the spatial coherence, topological charges of the beams, and the degree of polarization of the source plane and the atmospheric turbulence. The results obtained may have applications in space optical communication.     

Propagation of random electromagnetic beams through axially nonsymmetrical optical systems

When random electromagnetic beams passing through axially nonsymmetrical ABCD optical systems, the analytical formula for the transformation of the elements of 2 × 2 cross-spectral density matrix is obtained with the help of vector integration. We derive analytical expressions of the spectral degree of polarization, the spectral degree of coherence, and the spectral density in any output plane z > 0. Some numerical calculations are illustrated relating to the electromagnetic Gaussian Schell-model beams propagating through such optical systems.     

The Imbert-Fedorov shift of paraxial light beams

We present a solution to the problem of reflection and transmission of a polarized paraxial light beam at an interface between two homogeneous media by using a two-form amplitude and an extension matrix to represent the vectorial angular spectrum of a three-dimensional (3D) light beam. We derive general formulas for the Imbert-Fedorov (IF) shift of the reflected and transmitted beams of a polarized paraxial light beam. The IF shift of two different types of polarized beams is calculated, and the influence of the polarization state and the polarization feature of the vectorial angular spectrum on the IF shift is discussed.     

Coherent and incoherent polarization encoding of electromagnetic fields

We study a method generating certain distributions of the degree and state of polarization of a light field across a transverse beam cross-section. We use the introduced polarization encoding scheme to study the distribution of polarization ellipses in a cross-section of a beam generated by superposing two encoded beams, the effects of coherence relation between the input beams on this distribution were theoretically analyzed and illustrated by contour plots of the parameters representing polarization ellipses.     

Transverse energy flows in vectorial fields of paraxial beams with singularities

A general study of transverse energy flows (TEF) as physically meaningful and informative characteristics of paraxial light beams’ spatial structure is presented. The total TEF can be decomposed into the spin and orbital contributions giving rise to the spin and orbital angular momentums, correspondingly. Definitions and properties of these constituents are discussed in relation with the optical field representation through linear and circular orthogonal polarization bases. With the help of model examples, the results are applied to investigation of TEF singularities in connection with the usual polarization morphology characteristics of paraxial optical fields. An analysis of TEFs near singular points has been carried out; in particular, the behavior of TEF and its partial contributions near polarization singularities (C-points) has demonstrated the special role of a boundary flow in the origin of the spin angular momentum. The analytical and experimental applicability of the introduced concepts are discussed.     

Depolarization of multiply scattered light in transmission through a turbid medium with large particles

An approximate analytical method for solving the vector radiative transfer equation is proposed. The method is based on the assumption that single scattering of light by large-scale inhomogeneities occurs predominantly through small angles. The method is applied to calculate the polarization state of multiply scattered light. The results obtained are discussed for various turbid media.     

Coherence, polarization, and entanglement for classical light fields

We examine a classical version of entanglement between spatial and polarization degrees of freedom for classical light. We examine the relation between classical entanglement, polarization, and several recently introduced measures of coherence for vectorial waves. We show that there is no definite relation between quantum and classical entanglement.     

Quantum phase-space description of light polarization

We present a method to characterize the polarization state of a light field in the continuous-variable regime. Instead of using the abstract formalism of SU(2) quasidistributions, we model polarization as the superposition of two harmonic oscillators of the same angular frequency along two orthogonal axes, much in the classical way of dealing with this variable. By describing each oscillator by an s-parametrized quasidistribution, we derive in a consistent way the final function for the polarization. We compare with previous approaches and show how this formalism works in some relevant examples.     

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     

Surface reorientation dynamics of nematic liquid crystals

In this paper we report an experimental investigation on the dynamics of the azimuthal director reorientation at a nematic-solid interface. Three qualitatively different kinds of substrates have been investigated: I) intrinsically anisotropic SiO-substrates (-evaporation), II) isotropic SiO-substrates (-evaporation) and III) rubbed PVA-substrates. In the case II), an in-plane anisotropy was induced cooling slowly the thermotropic nematic liquid crystal (NLC) from the isotropic phase in the presence of a 0.75 T magnetic field. The reorientation dynamic of the surface azimuthal director angle at the switching-on and off of a magnetic (or electric) field has been investigated. All the substrates show comparable azimuthal anchoring energies and two dynamic regimes: a fast dynamic response, driven by the bulk director reorientation and an extremely slow reorientation. The slow dynamics is explained in terms of anisotropic adsorption of NLC molecules on the solid substrate and is well represented by a stretched exponential. Received 7 December 1998     

Topological response of inhomogeneous,elliptically polarized,light fields to controlled anisotropic perturbations

The effect of controlled anisotropic losses on the topological structure of complex, elliptically polarized, light fields has been investigated. It has been shown that they can either initiate topological reactions with the appearance/disappearance of C points, saddle points, etc., or induce only their slight shift. Both strong and slight topological responses can be realized in the same field at sections with different inhomogeneity degrees of the polarization parameters of the field.     

Optically induced Fréedericsz effect

Conclusion It is clear from the foregoing that the state of a nematic liquid crystal, characterized by the director field, is altered by the action of a light field.Just as in spatially homogeneous constant external fields, the director reorientation may obey the laws governing a second-order phase transition (the Frédericsz transition), in which case the very same laws are manifested.There is, however, also a specific feature. Particular interest attaches to the self-oscillations of the NLC director in the field of ordinary light waves — an effect that can be observed only in a light field.Also important is a second aspect of the light-induced Fréederivsz transition — the reaction of the light wave to the change it produces in the NLC state, namely, aberrational self-focusing accompanied by a Fréedericsz transition in narrow light beams. It is a new method of investigating the effect itself (reorientation and relaxation of the director field) as well as the properties of liquid crystals themselves (elasticity and viscosity).Translated from Preprint No. 38 of the Lebedev Physics Institute, Academy of Sciences of the USSR, Moscow, 1989.     

Reorientational optical nonlinearity of nematic liquid-crystal cells near the nematic-isotropic phase transition temperature

We address the reorientational optical nonlinearity of homogeneously aligned neamtic liquid-crystal (NLC) cells. The propagation of light in NLC cells depend strongly on temperature. At a temperature approaching the clearing point, an undulating beam and multifocal points are observed in the NLC cell by use of a polarizing optical microscope. Using a conoscopic technique, we observed novel consecutive concentric and parabolic patterns projected onto a screen. Optical energy is considered to compete with thermal energy to affect NLC's orientation and to generate singularities in the steady state. A model of the configuration of the liquid crystal's orientation is proposed.     

Stochastic electromagnetic vortex beam and its propagation

The recent theory formulated in terms of the 2×2 cross-spectral density matrix and the propagation law of cross-spectral density are employed to investigate the stochastic electromagnetic vortex beam and its propagation characterization. Based on these, we derived the general formulae for the intensity distribution, degree of coherence and degree of polarization for stochastic electromagnetic vortex beam while propagating in free space. It is shown that the intensity distribution and the degree of polarization of the stochastic electromagnetic vortex beam propagating in free space depend on the correlation length and the topological charge of the vortex beam.     

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.     

Focus shaping of cylindrically polarized vortex beams by a high numerical-aperture lens

The focus-shaping technique of a cylindrically polarized vortex beam by a high numerical-aperture lens is reported. Such a polarized vortex beam is decomposed into radial and azimuthal polarization. It is shown that the total intensity distribution in the focal region is dependent not only on the numerical-aperture maximal angle and the polarization rotation angle but also on the topological charge. By choosing the proper combination of parameters, the adjustably confined flat-topped focus and focal hole can be obtained. The focus-shaping technique may find wide applications, such as optical tweezers, laser printing and material processing.     

Phase control algorithms for focusing light through turbid media

Light propagation in materials with microscopic inhomogeneities is affected by scattering. In scattering materials, such as powders, disordered metamaterials or biological tissue, multiple scattering on sub-wavelength particles makes light diffuse. Recently, we showed that it is possible to construct a wavefront that focuses through a solid, strongly scattering object. The focusing wavefront uniquely matches a certain configuration of the particles in the medium. To focus light through a turbid liquid or living tissue, it is necessary to dynamically adjust the wavefront as the particles in the medium move. Here we present three algorithms for constructing a wavefront that focuses through a scattering medium. We analyze the dynamic behavior of these algorithms and compare their sensitivity to measurement noise. The algorithms are compared both experimentally and using numerical simulations. The results are in good agreement with an intuitive model, which may be used to develop dynamic diffusion compensators with applications in, for example, light delivery in human tissue.