Off-Bragg analysis of the diffraction efficiency of transmission photorefractive holograms

Formulas for calculating the diffraction efficiency of gratings recorded in a photorefractive medium are given. The analysis uses coupled-wave theory for photorefractive hologram gratings and takes into account the photorefractive phase shift and fringe-bending effect. General solutions for diffracted (signal) and undiffracted (reference) waves are derived in a closed-form expression. By use of the derived formulas the diffraction efficiency for angle mismatch from the Bragg condition can easily be evaluated as compared with numerical-analysis methods. The diffraction efficiency is also quantified in terms of medium parameters and recording and reconstruction conditions.     

General solution of the coupled-wave equations of acousto-optics

The basic problem of the diffraction of an optical plane wave by an acoustic plane wave in an anisotropic homogeneous medium is considered. The acousto-optical interaction is considered indifferently of the isotropic or of the birefringent type. Coupled-wave equations are obtained rigorously and cast into an eigenvalue value problem. A general solution is obtained for the diffraction efficiency of diffracted orders, for any interaction length and diffraction regime. The theory includes the Bragg regime, the Raman-Nath regime, and all intermediate situations in the same formulation. The method of solution is both exact and computationally efficient. It is similar in character to the rigorous coupled-wave analysis of Moharam and Gaylord but differs by the choice of basis functions adapted to propagating rather than static gratings. Examples are given for acousto-optical interaction in paratellurite, TeO2.     

Influence of recording conditions on crossed-beam photorefractive gratings in doubly doped LiNbO3 crystals

The influence of the recording conditions, including the widths of the recording beams, the width ratio of the recording beams, and the recording angles, on the properties of crossed-beam photorefractive gratings in doubly doped LiNbO3 crystals is studied. A theoretical model that combines the band transport model with two-dimensional coupled-wave theory is proposed. The numerical calculations of the space-charge field, the intensity profiles of the diffracted beam, and the diffraction efficiency are presented.     

Diffraction properties of transmission photorefractive volume gratings in a cerium-doped potassium sodium strontium barium niobate crystal

The diffraction efficiency of volume gratings written by two-wave mixing in a cerium-doped potassium sodium strontium barium niobate (Ce:KNSBN) photorefractive crystal is studied. It is found that the diffraction efficiency strongly depends on the polarization of writing beams and exhibits loop behavior with respect to the fringe modulation. The fringe modulations before and behind the crystal are compared. Modified coupled-wave theory is used to fit the experimental data. This research presents data that are relevant to the application of Ce:KNSBN crystals to holographic recording and optical information processing.     

Thermal fixing of holographic gratings in BaTiO(3)

Fixing of a holographic grating in a single BaTiO(3) crystal is studied in detail by means of a thermal process. Above T = 78 °C, oscillations of the diffracted intensity of the sample appear, which are related to the fixing process. Different methods to perform and optimize the fixing process are described. A fixed diffraction efficiency of ~25% was obtained. Self-enhanced as well as self-depleted diffraction from the fixed photorefractive gratings was observed.     

Spatioangular-multiplexing scheme for dense holographic storage

A novel multiplexing scheme for dense holographic storage in photorefractive crystals, spatioangular multiplexing, is described in detail. Compared with spatial multiplexing, spatioangular multiplexing increases the storage capacity by fully utilizing the volume of the storage medium. On the other hand, spatioangular multiplexing reduces the number of holograms overlapping any one hologram in a given volume and so increases the diffraction efficiency achievable as compared with angular multiplexing. Using this scheme, we succeeded in storing 756 high-resolution patterns in an Fe:LiNbO(3) crystal of volume 1 cm(3), with an average diffraction efficiency of 0.5%. This large database is designed for practical use in a novel associative-memory system, called a high-order feedback neural network.     

Volume Amplitude Holograms in Photodichroic Materials

A theoretical analysis is made of the process of writing volume holograms on photodichroic materials. The real form of the recorded diffraction gratings at large exposures is found. Expressions are derived for the diffraction efficiency of transmission and reflection gratings for the case of pure amplitude recording and the results of some numerical calculations are presented. Maximum diffraction efficiencies for different parameters of the recording medium are determined.     

New noise-suppression technique in photorefractive crystals

On the basis of the idea that signal gratings have a faster formation rate than noise gratings and signal gratings have a slower erasure rate than noise gratings under the same erasing beam, we report a new technique to suppress or eliminate the noise in image processing in photorefractive crystals. A general theoretical analysis and experimental results in LiNbO(3):Fe crystals are given.     

Single beam one-way imaging through a thick dynamic turbulent medium

A new method to record an image through a thick dynamic phase distorting medium by using a photorefractive LiNbO3 crystal is demonstrated. The method uses only one beam of light, the object light. By making use of the photorefractive fanning effect, gratings are formed in the LiNbO3 crystal through the interference between the object light and its own fanning light. Because the time scale of the distorting fluctuation is much shorter than the writing time of the LiNbO3 crystal, the fluctuated light does not induce any fanning. Therefore only the static portion of the image is recorded in the crystal, and the intensity distribution of the image can then be reconstructed at any later time.     

Polarization Holographic Gratings

Abstract

The photoinduced anisotropy (dichroism and birefringence) in AgCl emulsions is studied as well as the possibility for chemical fixing of this anistropy. A theoretical relation between the diffraction efficiency of amplitude—phase polarization holographic gratings and the photoanisotropy of the recording medium is derived. Based on this relationship an estimation of the properties of the gratings is presented. Polarization holographic gratings with spatial frequencies of 200 to 2000 mm^?1 and diffraction efficiency up to 1·8% are recorded. The gratings are stable, and do not change in time for more than a year.     

All-dielectric reflection gratings: a study of the physical mechanism for achieving high efficiency

The physical mechanism for the all-dielectric reflection gratings to achieve high efficiency in the -1st-order Littrow mounting is studied. The all-dielectric gratings consist of two parts, a surface-relief grating and a highly reflecting dielectric stack. The surface-relief grating sits on top of the reflecting stack. A simple analytical expression for diffraction efficiency is obtained in terms of the S-matrix elements of the two parts. By analyzing the expression we show that the diffraction can be interpreted as the interference of a symmetric wave and an antisymmetric wave. The conditions for achieving high diffraction efficiency are also identified. The analytical results are illustrated by numerical computations.     

Edge enhancement by use of moving gratings in a bismuth silicon oxide crystal and its application to optical correlation

The technique of moving gratings in a photorefractive crystal is applied to the edge enhancement of objects and edge-enhanced optical correlation. The nonlinear dependence of the optimum fringe velocity on the fringe modulation and the variation of the enhancement of the diffraction efficiency with fringe modulation at a fixed fringe velocity appropriate to high fringe modulations are experimentally investigated. It is shown that the diffraction at high fringe modulations, which corresponds to the high-spatial-frequency components of the Fourier spectrum, is enhanced by a factor of approximately 3.7, whereas the diffraction at low fringe modulations is suppressed by a factor of 0.6. The proposed technique has the advantages of real-time enhancement, arbitrary selection of the spatial frequency to be enhanced, and improved stability of the output. Experimental results of the edge enhancement of objects and edge-enhanced correlation are presented.     

光栅衍射特性的耦合波分析、计算与讨论

本文从麦克斯韦方程组及电磁场边界条件出发,推导了广泛应用于各类光栅衍射问题的矢量分析方法--严格的耦合波分析方法.针对光栅的衍射特性,编写了基于严格的耦合波分析方法的计算程序,并以TE模情形为例对光栅的衍射效率和收敛性作了数值计算.结果表明,当谐波数不断增加,即便对于厚光栅(d/λ>10)情形,光栅的衍射效率仍将收敛于某一确定值.     

Dichromated pullulan diffraction gratings: influence of environmental conditions and storage time on their properties

Investigations of the environmental stability of diffraction gratings, recorded in dichromated pullulan (DCP), are reported. Profile changes of DCP surface relief gratings, under high humidity conditions, were analyzed using an atomic force microscope. It was found that the profile was not altered, while the diffraction efficiency was preserved. The influence of storage life on the diffraction efficiency and surface profile of DCP gratings were also investigated. It was concluded that DCP gratings offer much better stability compared with the dichromated gelatin.     

Diffraction Efficiency and Angular Selectivity of Volume Phase Holograms Recorded in Photorefractive Materials

The recording and replay of volume phase gratings in photorefractive crystals is investigated for both transmission and reflection geometries. Differential equations are derived and solved for a range of parameters including the length of the crystal, the magnitude, spatial distribution and phase angle of the refractive index modulation, the beam ratio at recording, and the angular range at replay. The recording process is assumed to reach a steady-state limit before replay with a weak probe beam. Solution of the repaly equations is mainly by numerical integration, although analytic solutions are derived for special cases. It is found that in certain cases the diffraction efficiency can be greatly increased by replaying the hologram at an angle different from the recording angle.     

Improvement of sensitivity and refractive-index changes in LiNbO3:Ce:Cu crystals with UV light

A nonvolatile recording scheme is proposed using LiNbO₃:Ce:Cu crystals and modulated UV light to record gratings simultaneously in two centres and using red light to bleach the grating in the shallow centre to realize persistent photorefractive holographic storage. Compared with the normal UV-sensitized nonvolatile holographic system, the amplitude of refractive-index changes is greatly increased and the recording sensitivity is significantly enhanced by recording with UV light in the LiNbO₃:Ce:Cu crystals. Based on jointly solving the two-centre material equations and the coupled-wave equations, temporal evolutions of the photorefractive grating and the diffraction efficiency are effectively described and numerically analysed. Roles of doping levels and recording-beam intensity are discussed in detail. Theoretical results confirm and predict experimental results.     

The Properties of Holographic Overlap Gratings

The analysis of a holographic beam expander which can, under perfect lossless conditions, convert a plane input beam into a plane diffracted beam, with a specified diffraction efficiency and beam width expansion ratio, is presented. Using solutions of the coupled-wave differential equations of [2], the effects of average loss, and both constant and spatially dependent dephasing are studied. These solutions are also used to compare the properties of overlap gratings with Kogelnik's [1] results for infinite gratings, and to extend the analysis of [4] to lossy, dephased cases. The maximum possible diffraction efficiency of an absorption overlap grating is shown to depend on its shape and also to lie between the values for Kogelnik's reflection and transmission cases.     

Finite-number-of-periods holographic gratings with finite-width incident beams: analysis using the finite-difference frequency-domain method

The effects of finite number of periods (FNP) and finite incident beams on the diffraction efficiencies of holographic gratings are investigated by the finite-difference frequency-domain (FDFD) method. Gratings comprising 20, 15, 10, 5, and 3 periods illuminated by TE and TM incident light with various beam sizes are analyzed with the FDFD method and compared with the rigorous coupled-wave analysis (RCWA). Both unslanted and slanted gratings are treated in transmission as well as in reflection configurations. In general, the effect of the FNP is a decrease in the diffraction efficiency with a decrease in the number of periods of the grating. Similarly, a decrease in incident-beam width causes a decrease in the diffraction efficiency. Exceptions appear in off-Bragg incidence in which a smaller beam width could result in higher diffraction efficiency. For beam widths greater than 10 grating periods and for gratings with more than 20 periods in width, the diffraction efficiencies slowly converge to the values predicted by the RCWA (infinite incident beam and infinite-number-of-periods grating) for both TE and TM polarizations. Furthermore, the effects of FNP holographic gratings on their diffraction performance are found to be comparable to their counterparts of FNP surface-relief gratings.     

Wavelength demultiplexing with layered multiple Bragg gratings in LiNbO3:Fe crystal

Dense wavelength division multiplexing (DWDM) is an important technology for expanding the capacity of optical network. The optical component based on the superimposed Bragg gratings shows that it can be used as one of advantageous multichannel components because of its excellent angle and wavelength selectivities. An optimized method for recording multiple Bragg gratings for wavelength demultiplexing in optical telecommunication band is proposed to achieve gratings with equal diffraction efficiency. A structure of three layers with twenty four gratings is demonstrated in a LiNbO(3):Fe crystal by employing the optimized recording method. Then an initial wavelength demultiplexing experiment based on the formed gratings is carried out in optical telecommunication C-band. The results obtained by measuring and analyzing the transmitted spectra of the fabricated gratings show that the diffraction efficiencies of the gratings are uniform. It is suggested that this kind of multiple gratings can be used for increasing the number of the demultiplexed wavelengths in recording medium with unit volume for WDM.     

Production and evaluation of silicon immersion gratings for infrared astronomy

Immersion gratings, diffraction gratings where the incident radiation strikes the grooves while immersed in a dielectric medium, offer significant compactness and performance advantages over front-surface gratings. These advantages become particularly large for high-resolution spectroscopy in the near-IR. The production and evaluation of immersion gratings produced by fabricating grooves in silicon substrates using photolithographic patterning and anisotropic etching is described. The gratings produced under this program accommodate beams up to 25 mm in diameter (grating areas to 55 mm x 75 mm). Several devices are complete with appropriate reflective and antireflection coatings. All gratings were tested as front-surface devices as well as immersed gratings. The results of the testing show that the echelles behave according to the predictions of the scalar efficiency model and that tests done on front surfaces are in good agreement with tests done in immersion. The relative efficiencies range from 59% to 75% at 632.8 nm. Tests of fully completed devices in immersion show that the gratings have reached the level where they compete with and, in some cases, exceed the performance of commercially available conventional diffraction gratings (relative efficiencies up to 71%). Several diffraction gratings on silicon substrates up to 75 mm in diameter having been produced, the current state of the silicon grating technology is evaluated.