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

Formulas are given for the calculation of diffraction efficiency of reflection-type gratings recorded in a photorefractive medium. The analysis incorporates the coupled-wave theory that was developed for photorefractive hologram gratings. This analysis takes into account grating slant with respect to the medium surface, light absorption during reconstruction, any incident angle of the reference beam, and any photorefractive phase shift. General solutions for signal and reference wave functions are given in a closed-form expression by use of a hypergeometric function. The optimum media parameters and recording conditions for high diffraction efficiency are obtained by the derived formulas. The diffraction properties for off-Bragg conditions are also discussed.     

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.     

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.     

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.     

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.     

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.     

Pulse shaping properties of volume holographic gratings in anisotropic media

Based on a modified coupled wave theory, the pulse shaping properties of volume holographic gratings (VHGs) in anisotropic media VHGs are studied systematically. Taking photorefractive LiNbO(3) crystals as an example, the combined effect that the grating parameters, the dispersion and optical anisotropy of the crystal, the pulse width, and the polarization state of the input ultrashort pulsed beam (UPB) have on the pulse shaping properties are considered when the input UPB with arbitrary polarization state propagates through the VHG. Under the combined effect, the diffraction bandwidth, pulse profiles of the diffracted and transmitted pulsed beams, and the total diffraction efficiency are shown. The studies indicate that the properties of the shaping of the o and e components of the input UPB in the crystal are greatly different; this difference can be used for pulse shaping applications.     

Spatial resolutions for applying photorefractive polymers to diffractive elements

Spatial resolutions of diffracted beams by photorefractive polymers are investigated in detail for applying the polymers to diffractive optical elements. The coupled wave equations for the four-wave mixing in photorefractive polymers and their solutions by applying the two-beam coupling approximation are derived taking the orientational enhancement effect into consideration. Characteristics of the diffraction efficiency of the polymers for the applied electric field, the incident angles of beams, the incident radiation intensity and the polarization are clarified. Furthermore, resolutions of diffracted images with the polymers are discussed by a numerical analysis from the viewpoint of the Bragg diffraction in a spatial frequency domain. An experiment with the TPD (tetra-phenyl-diphenyldiamine) acrylate based photorefractive polymers and the USAF test target is also performed to measure the spatial resolution of two-dimensional images diffracted by the polymer and to verify the calculated results. It is revealed that high resolution over 50 lp mm^?1 can be obtained with sufficient diffraction efficiency in the case of the polymer thickness of several 10 µm.     

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.     

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.     

Photorefractive properties of nanostructured organic materials doped with fullerenes and carbon nanotubes

The phenomenon of a significant increase in the photoinduced changes in refractive index, non-linear refraction, and nonlinear third-order optical susceptibility in organic materials based on polyimides, pyridines, and prolinols upon the introduction of fullerenes and carbon nanotubes (CNTs) into the organic matrix is briefly considered (with emphasis on the dominating effect of CNTs). It is established that the values of these photorefractive parameters determined in said fullerene- and CNT-doped materials using a four-wave-mixing scheme are close to the analogous values in bulk silicon-based materials. The results can be useful in developing thin-film nonlinear filters, thin diffraction gratings for passive data recording, and optically-addressed light modulators, in medical applications, and in display technology (e.g., for creating a three-dimensional medium prototype).     

Dual-use chromophores for photorefractive and irreversible photochromic applications

Holographic experiments are performed on a series of dual-use chromophore molecules wherein both irreversible photochromic and erasable photorefractive holographic gratings can be written in the same storage volume. At 675 nm, the chromophore undergoes a photochemical reaction leading to the creation of irreversible holographic gratings. Alternatively, at longer wavelengths, application of an electric field during grating formation allows the storage of erasable photorefractive holograms in the same location as previously stored permanent photochemical holograms. Photochemical gratings (eta > 60%) can be written in less than 1 min, whereas photorefractive gratings (eta > 50%) can be written in less than 1 s. The photochemical gratings have a diffusion-limited dark half-life of as long as two weeks depending on the glass transition temperature of the composite.     

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.     

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.     

Diffraction characteristics with various polarizations of overlapping holographic gratings in a uniaxial crystal

By the Riemann method, a coupled wave model is derived for the ordinary-to-ordinary (OO) and extraordinary-to-extraordinary (EE) Bragg diffraction of a Gaussian beam by overlapping holographic gratings in a uniaxial crystal. The computer simulation is used to discuss the relations among the diffraction efficiency, the index modulation, the wavelength sensitivity, the angular sensitivity, and the the widths of the recording and reading beams. The characteristics of EE and OO diffraction in a uniaxial crystal are found to be remarkably different. The simulation shows that EE diffraction may exhibit far higher diffraction efficiency than does OO diffraction for very low index modulation with the same hologram size, for example, nearly 90% when the size is 8.2 x 10(-5).     

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.     

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.     

Diffraction properties of a reflection photorefractive hologram

Diffraction properties of a photorefractive hologram have been described previously in most cases with Kogelnik's uncoupled-recording-wave-theory, which was originally derived for nonphotorefractive holograms. Despite its simplicity and good approximation, the theory has shown its practical limitations and discrepancies when the refractive-index perturbation is large. We study the diffraction properties of a reflection photorefractive hologram using a coupled-recording-wave approach. A closed-form expression for the diffraction efficiency is obtained. The important aspect of the new formula is that it predicts a lower cross-talk noise (or, a higher wavelength sensitivity) than Kogelnik's formula. This offers an explanation for the apodization phenomenon (i.e., lower cross-talk noise from the experiment as compared with the analytical result) as found by Rakuljic et al. [Opt. Lett. 17, 1471-1473 (1992)].     

Maxwell equations in Fourier space: fast-converging formulation for diffraction by arbitrary shaped, periodic, anisotropic media.

We establish the most general differential equations that are satisfied by the Fourier components of the electromagnetic field diffracted by an arbitrary periodic anisotropic medium. The equations are derived by use of the recently published fast-Fourier-factorization (FFF) method, which ensures fast convergence of the Fourier series of the field. The diffraction by classic isotropic gratings arises as a particular case of the derived equations; the case of anisotropic classic gratings was published elsewhere. The equations can be resolved either through classic differential theory or through the modal method for particular groove profiles. The new equations improve both methods in the same way. Crossed gratings, among which are grids and two-dimensional arbitrarily shaped periodic surfaces, appear as particular cases of the theory, as do three-dimensional photonic crystals. The method can be extended to nonperiodic media through the use of a Fourier transform.