Displacements and deformations of a vortex light beam produced by the diffraction grating with embedded phase singularity

Properties of vortex light beams produced by a diffraction grating with groove bifurcation (“fork” structure) are studied in the case of small diffraction angles. Analytical expressions are derived for the amplitude distribution of a diffracted beam generated from an incident Gaussian beam with arbitrary radius and wavefront curvature, transversely shifted and inclined with respect to the nominal axis (normal to the grating crossing it at the bifurcation point). In such situations, the output beam becomes asymmetric; the optical vortex core and the intensity maximum displace orthogonally to the incident beam shift direction. The nearest vicinity of the vortex core preserves its circular symmetry and the optical vortex remains locally isotropic. The effects of misalignment depend on the incident beam characteristics, the diffraction order and the propagation distance behind the grating. Experimental measurements support the results of calculations.     

Total internal reflection diffraction grating in conical mounting

The main conditions and parameters for obtaining surface relief total internal reflection diffraction gratings in conical mounting are presented. Calculated and experimental investigations reveal that there are ranges of grating periods, incidence angles, diffraction angles and gratings depths for which such gratings could be obtained, both for TE and TM polarizations. With optimized grating parameters the diffraction efficiency of the total internal reflection diffraction gratings can be greater than 90%.     

Tunable grating-assisted surface plasmon resonance by use of nano-polymer dispersed liquid crystal electro-optical material

This paper reports on the experimental observation of the displacement of a surface plasmon resonance (SPR) excited by a metallic diffraction grating. This effect is achieved by the use of an electro-optical material composed of nano-sized droplets of liquid crystals dispersed in a host polymer. The average refractive index of this material in the form of a thin film on the undulated metal surface can be modified with the application of an external electric field and to tune the wavelength at which the SPR excitation leads to a reflection minimum. The theoretical design and experimental demonstration of the principle of this component are described.     

Extremely asymmetrical scattering in gratings with weak dissipation: some physical analogies

A detailed analysis of new effects related to extremely asymmetrical scattering (EAS) of bulk and guided weakly dissipating electromagnetic waves in oblique periodic gratings is presented. A very important role of the previously determined critical grating width is demonstrated for EAS in dissipative gratings. Incident and scattered wave amplitudes inside and outside the grating are analysed as functions of dissipation coefficient, grating width, grating amplitude, etc. Strong differences in the patterns of scattering in gratings that are narrower and wider than the critical width are demonstrated and discussed. Deep analogies between EAS and other resonant optical effects, such as attenuated total reflection, Fabry–Pérot interferometry, etc. are revealed and discussed. A physical interpretation of the obtained results is presented. Received: 19 February 2002 / Revised version: 28 June 2002 / Published online: 22 November 2002 RID="*" ID="*"Corresponding author. Fax: +61-7/3864-9079, E-mail: d.gramotnev@qut.edu.au     

Influence of auxiliary violet light on holographic kinetics at low and high recording intensities in bacteriorhodopsin film

The photochromic bacteriorhodopsin (BR) film can be used as a rewritable holographic recording medium. Due to the saturation absorption and the scattering and reflecting lights from the BR film, the grating contrast-ratio of the hologram is diminished during the hologram recording. When the intensity of the recording light is low, the influence of the saturation absorption and the scatter and reflection of BR film on the grating contrast-ratio is weak. But for the case of intense recording light, this influence is more serious. It is found that the influence of the auxiliary violet light on the holographic kinetics of diffraction efficiency is distinct under different recording intensities. At the low recording light intensity, the steady diffraction efficiency is increased and the peak diffraction efficiency is suppressed by the auxiliary violet light. But for intense recording light, the steady diffraction efficiency and the peak diffraction efficiency are both increased by the auxiliary violet light. Based on the two-state model of BR photochromism, we give a good theoretical explanation to the above phenomena.     

Denisiuk-type reflection holography display with sillenite crystals for imaging and interferometry of small objects

A novel setup for imaging and interferometry through reflection holography with Bi₁₂TiO₂₀(BTO) sillenite photorefractive crystals is proposed. A variation of the lensless Denisiuk arrangement was developed resulting in a compact, robust and simple interferometer. A red He-Ne laser was used as light source and the holographic recording occurred by diffusion with the grating vector parallel to the crystal [0 0 1]-axis. In order to enhance the holographic image quality and reduce noise a polarizing beam splitter (PBS) was positioned at the BTO input and the crystal was tilted around the [0 0 1]-axis. This enabled the orthogonally polarized transmission and diffracted beams to be separated by the PBS, providing the holographic image only. The possibility of performing deformation and strain analysis as well as vibration measurement of small objects was demonstrated.     

Second-order grazing-angle scattering in uniform wide holographic gratings

Grazing-angle scattering (GAS) is a type of Bragg scattering in slanted wide periodic gratings. It occurs when the diffracted order satisfying the Bragg condition (scattered wave) propagates at a grazing angle to the grating boundaries. Previous research has been concerned only with first-order GAS, which has been shown to be a highly unusual type of scattering characterised by a strong resonant increase of amplitudes of the scattered and incident waves in the grating. In this paper, a rigorous numerical study of second-order GAS is presented for the case of bulk TE electromagnetic waves in planar holographic gratings. A highly unusual pattern of strong resonances in the grating, which is strongly different from that for first-order GAS, is predicted, described, and discussed. Physical interpretations of the predicted results are presented. In particular, a special new type of eigenmodes in a slanted wide periodic grating with large amplitude is predicted. These eigenmodes are shown to be guided by the grating alone without any conventional guiding effect in the structure. The typical field structure in such eigenmodes is investigated and discussed. Received: 16 September 2002 / Revised version: 4 November 2002 / Published online: 22 January 2003 RID="*" ID="*"Corresponding author. Fax: +61-7/3864-9079, E-mail: d.pile@osa.org     

Phase Controlled Laser Interference for Tunable Phase Gratings in Dye-Doped Nematic Liquid Crystals

A phase controlled multi-beam interference is applied to excite the doped liquid crystals. Control of the phase difference between the exciting beams allows the external control of the interference pattern inside the liquid crystal. The dynamic variation of the grating is made possible with a time-dependent phase change to derive the nonlinear refractive index as well as the responding speed of the material. The induced grating structure is numerically modelled with reorientational phase gratings in the liquid crystal, and the diffraction dynamics is found to be in good agreement between theoretical and experimental results.     

Impact of the sublinear photoconductivity law on the interpretation of holographic results in BaTiO3

Thick holographic refractive index gratings are written in nominally pure and in iron doped BaTiO₃ crystals. The phase shift between refractive index grating and light pattern is studied as a function of an externally applied electric field by a direct phase shift measuring technique. The choice of the method is suggested by a theoretical analysis which allows for the effect of a nonlinear relation between photoconductivity and light intensity on the holographic writing process.     

Design of High-Efficiency Diffraction Gratings Based on Rigorous Coupled-Wave Analysis for 800nm Wavelength

We report on the design of a high diffraction efficiency multi-layer dielectric grating with wide incident angle and broad bandwidth for 80Ohm. The optimized grating can achieve 〉 95% diffraction efficiency in the first order at an incident angle of 5° from Littrow and a wavelength from 77Ohm to 83Ohm, with peak diffraction efieieney of 〉 99.5% at 80Ohm. The electric field distribution of the optimized multi-layer dielectric grating within the gratings ridge is 1.3 times enhancement of the incidence light, which presents potential high laser resistance ability. Because of its high-effieieney, wide incident, broad bandwidth and potential high resistance ability, the multi-layer dielectric grating should have practical application in Ti：sapphire laser systems.     

Inscription of holographic gratings using circularly polarized light: influence of the optical set-up on the birefringence and surface relief grating properties

The polarization properties of the optical set-up used for holographic recording of diffraction gratings on azopolymer thin films are analyzed. The state of polarization of circularly polarized light is fully analyzed after reflection on a mirror at various incidences (Lloyd-mirror set-up). The Stokes analysis is performed using a photopolarimeter and the phase shift, the ellipticity and the azimuth orientation are compared with those calculated from Fresnel formulae. At large angles of incidence, an initially right circularly polarized (RCP) beam becomes elliptically polarized with an azimuth of nearly +45°. From these results, holographic diffraction gratings are recorded on an azobenzene-containing polymer thin film using (i) co- and contra-circularly polarized beams and (ii) a right circularly polarized beam interfering with a +45° linearly polarized light beam. Using Jones-matrix formalism, the polarization states of the diffracted orders from the birefringence (Δn) and the surface-relief (2Δd) gratings are derived and compared with experimental measurements. Finally, the induced local birefringences and surface-relief amplitudes are discussed in connection with atomic force microscopy measurements. The diffraction efficiencies obtained under the (+45°+RCP) and (LCP + RCP) (where LCP = left circularly polarized) configurations are thus compared and discussed. Received: 5 October 2001 / Revised version: 26 November 2001 / Published online: 17 January 2002     

Space charge field limitations in photorefractive LiNbO3:Fe crystals

We use holographic techniques for the investigation of strongly oxidized LiNbO₃:Fe crystals with small Fe²⁺ concentrations and compare the results with theoretical predictions. Experimental evidence is presented for enhanced phase shifts between light intensity pattern and refractive index grating and for limitations of optically induced space charge fields in photovoltaic crystals due to the low concentration of filled traps. Our findings do not support the model of a nonlocal photovoltaic effect in LiNbO₃.     

Temperature effect on the diffraction efficiency of the liquid crystal spatial light modulator

Temperature effect on the diffraction efficiency of the liquid crystal spatial light modulator is investigated. The birefringence of the liquid crystal as functions of the temperature is measured with and without the power supply. It is shown that the birefringence reduces while the temperature increases. And the change magnitude of the birefringence has an exponential decay relation with the applied voltage for different temperature intervals. The scalar diffractive theory is used to analyze this effect on the diffraction efficiency. It indicates that the diffraction efficiency decreases from 98.7% to 27.2% while the temperature increases from 10 to 90 °C for 16 quantified levels. At last, temperature effect on its applications in optical testing and wavefront correction is discussed. It indicates that it has almost no effect on optical testing, but has an important effect on wavefront correction. And two solutions are given to eliminate this effect.     

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.     

Development of thermally fixed photorefractive holograms without light

Holographic gratings are recorded and thermally fixed in iron-doped photorefractive lithium-niobate crystals. A spatially modulated concentration of filled and empty electron traps (Fe²⁺ and Fe³⁺) yields a modulated dark conductivity. As a consequence, dark diffusion currents and dark drift currents arise. Space–charge fields and electro-optic refractive-index changes build up. An additional refractive-index grating, which may originate from a modulated proton concentration, as well as a pronounced absorption grating arising from the modulated Fe²⁺ concentration are also observed. The dark development has practical advantages: thermally fixed holograms can be used in devices without the need to develop them freshly from time to time by illumination. Although with dark development diffraction efficiencies up to 50% are demonstrated, in general the efficiencies are smaller compared to those achieved by development with light. Received: 28 June 2000 / Published online: 8 November 2000     

Reconstruction of parasitic holograms to characterize photorefractive materials

Photoinduced light scattering is a serious drawback that limits the applicability of thick holographic recording media but provides valuable information on the recording medium. As long as there is no correlation between the scattering centers in the crystal, photoinduced light scattering may be explained to result from the interference pattern of the incident beam and the field scattered from a single point-like scattering center. The hologram of this ellipsoidally scattered wave field will have practically the same structure in the reciprocal space modified by a response function which reflects the anisotropic properties of the recording medium. We studied photoinduced light scattering in LiNbO₃:Fe, a model system for photorefractive materials. The transmitted intensity in the stationary state of the scattering process is investigated as a function of the reconstruction angle at different wavelengths and polarizations of the reconstructing beam. The experimental results are analyzed by a simple phenomenological model based on the Ewald construction and can be used to choose suitable conditions at which holographic scattering can be minimized as well as to extract some physical parameters of the crystal. Received: 27 September 2000 / Revised version: 1 December 2000 / Published online: 21 February 2001     

Display method with compensation of the spatial frequency response of a liquid crystal spatial light modulator for holographic femtosecond laser processing

Liquid crystal spatial light modulators, which are widely used as display devices for computer-generated holograms, have modulation characteristics that depend on spatial frequency. We describe a method for displaying a computer-generated hologram on a liquid crystal spatial light modulator with compensation of its spatial frequency response. Using this method, we demonstrate a binary phase grating with smaller dependence on the spatial frequency. We also demonstrate application of the display method to holographic femtosecond laser processing.     

Absorption gratings in ferroelectric Bi4Ti3O12

4 Ti₃O₁₂. Basic properties of absorption gratings in this crystal are investigated with beam-coupling experiments. Depending on the grating spacing, wavelength, and intensity of the writing beams, an absorption grating in our sample can be either in phase or shifted by 180° with respect to the light pattern. The formation mechanism of absorption grating is discussed and proposed to originate from a shallow-trap effect. Received: 10 February 1997     

Gain optimization with respect to the thickness of a sillenite crystal

Simple analytical expressions for the dependence of the maximum gain on the polarization angle of the interacting light waves and the crystal thickness are obtained for two-wave mixing in a cubic optically active piezoelectric crystal. By applying the theory to Bi₁₂SiO₂₀ and Bi₁₂TiO₂₀ crystals, the optimum gain is found also with respect to the grating orientation. The r?le of the (inverse) piezoelectric effect is investigated. Received: 23 November 1998 / Revised version: 8 January 1999 / Published online: 7 April 1999