Analytic steady-state solutions to dynamic grating envelope

Abstract

The photorefractive holographic recording is a dynamic grating formulation process, where the grating is induced by the interference modulation of two beams, and the energies of the beams are exchanged with each other owing to their interaction in the induced grating. The grating modulation envelope is a comprehensive analysis for holographic dynamic recording and non-destructive readout, but analytic solutions can only be obtained by simultaneously solving the materials equations and the coupled wave equations. In this paper, based on Kukhtarev's model and Moharam's field function exact steady-state analytic expressions for dynamic grating envelopes are deduced for any constant values of light modulation depth and light excitation efficiency. Thus their approximations for straight formulation instead of parametric formulation are then obtained. These steady-state analytic solutions to envelopes describe the dynamic holographic recording and readout more clearly and exactly.     

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.     

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.     

A photorefractive effect accompanying the acoustooptical interaction in gyrotropic cubic crystals in the presence of an alternating electric field

A photorefractive effect in gyrotropic cubic crystals is considered. The effect accompanies the Bragg diffraction of light by an ultrasound in the presence of an alternating electric field. The possibility of recording holographic gratings with the help of the light waves diffracted by traveling ultrasonic waves is demonstrated. The amplitude of the index phase grating is studied as a function of the intensity of the recording ultrasound, the length of the region of acoustooptical interaction, and the specific rotation of the crystal.     

Talbot effect by a photorefractive volume phase grating

In our proposal a light intensity distribution generated by an incoherently illuminated planar amplitude grating is projected into a photorefractive crystal. This 3D distribution is mapped as an index refractive perturbation via the photorefractive effect thereby generating a volume phase grating. The self-imaging phenomenon in the Fresnel field of this volume phase grating coherently illuminated is theoretically and experimentally analyzed. A model to simulate this volume grating that considers the 3D light intensity distribution formed in the crystal combined with the photorefractive grating formation theory is proposed. A path-integral approach to calculate the self-image patterns which account for the inhomogeneous propagation through the photorefractive grating is employed. The experimental and theoretical results show that the self-images location coincides with that of the self-images generated by planar phase grating of the same period. Moreover, the self-images visibility depends on three parameters: the exit pupil diameter of the incoherent recording optical system, the external electric field applied on the crystal, and the crystal thickness. To study the visibility behavior, a phase parameter which includes the three mentioned parameters is proposed. The self-images visibility shows the typical sinusoidal dependence found in planar phase grating. A good agreement between theoretical and experimental results is observed.     

Tracking novelty filter at 780 nm based on a photorefractive polymer in a two-beam coupling geometry

We have constructed an all-optical tracking novelty filter based on the dynamic holographic properties of an efficient and fast infrared-sensitive photorefractive polymer. The photorefractive polymer was used in a two-beam coupling geometry. The polymer had a gain coefficient of 175 cm(-1) at a wavelength of 780 nm and an applied field of 72 V/mum. In contrast to what has been observed in photorefractive crystals, the gain coefficient and the filter contrast are largely independent of the writing beam's intensity ratio. We show images of a swinging pendulum observed through the novelty filter.     

Photorefractive trapping and the correlation between recording and erasure dynamics in a polymer composite

Abstract

The fast time constants of holographic contrast growth and erasure for various photorefractive polymer composites were measured under a wide range of experimental conditions. Either of two sensitizers, 2,4,7-trinitro-9-fluorenone (TNF) or (2,4,7-trinitro-9-fluorenylidene)malonodinitrile (TNFDM), were used in a degenerate four-wave mixing experiment under varying conditions of field, wavelength and intensity. Collected together, the fast growth and erasure time constants were found to be correlated with a coefficient of 0.96. From this correlation we conclude that the charge generation process during holographic recording and the optical de-trapping process during hologram erasure are indistinguishable. Hence in accordance with the photorefractive crystal model, hole recombination with the sensitizer anions forms the primary charge trapping mechanism in the majority of photorefractive polymer composites.     

Dynamic evolution of dissipative holographic solitons in photorefractive materials via two-wave mixing with a moving grating

The dynamic evolution and stability of bright dissipative holographic solitons supported by photorefractive materials via two-wave mixing with a moving grating are investigated numerically. Results show that these solitons are stable relative to small perturbations. The state of such solitons can be easily controlled by adjusting some system parameters, such as the linear loss of the crystal and the frequency detuning between the pump beam and the self-trapping beam. Potential amplification in optical switches, repeaters or splitters is discussed.     

Optical implementation of a wavelet transform by the use of dynamic holographic recording in a photorefractive material

An optical system that employs holographic recording in a photorefractive material is proposed and experimentally demonstrated for the implementation of a wavelet transform of two-dimensional mages. A scaling operation, to derive the family of wavelet filters from a mother wavelet filter, is performed by the use of an optical feedback loop. The selection of a desired wavelet filter from the family and the correlation for a wavelet transformation are made by the use of a holographic recording in a photorefractive material. The principle of operation of the system relies on the frequency detuning introduced inside the loop and the subsequent variation in the holographic grating diffraction. Experimental results on wavelet-filter selection and wavelet transformation are presented. This nonlinear optical wavelet-transform system is advantageous for pattern recognition applications.     

Optical gain by a simple photoisomerization process

Organic holographic materials are pursued as versatile and cheap data-storage materials. It is generally assumed that under steady-state conditions, only photorefractive holographic media exhibit a non-local response to a light-intensity pattern, which results in an asymmetric two-beam coupling or 'gain', where intensity is transferred from one beam to the other as a measure of writing efficiency. Here, we demonstrate non-local holographic recording in a non-photorefractive material. We demonstrate that reversible photoisomerization gratings recorded in a non-photorefractive azo-based material exhibit large optical gain coefficients beyond 1,000 cm(-1), even for polarization gratings. The grating characteristics differ markedly from classical photorefractive features, but can be modelled by considering the influence of the Poynting vector on the photoisomerization. The external control of the Poynting vector enables manipulation of the gain coefficient, including its sign (the direction of energy exchange), a novel phenomenon we refer to as 'gain steering'. A very high sensitivity of about 100 cm(2) J(-1) was achieved. This high sensitivity, combined with a high spatial resolution, suggests a great technical advantage for applications in image processing and phase conjugation.     

A holographic method for studying absorptivity modulation in transparent media

A dual-beam holographic method is described that can be used for measuring small induced absorptivity modulation in a transparent medium. The proposed method is based on a diffraction-interference scheme in which the interference field inducing an amplitude grating is shifted by a quarter of period relative to a reference volume phase grating. The induced amplitude grating introduces a nonequivalent energy exchange between the transmitted beams, which is proportional to changes in the absorption coefficient of the medium. The new dual-beam holographic method of measuring small absorptivity modulation is compared to the well-known single-beam diffraction technique.     

Spatio-temporal operator formalism for holographic recording and diffraction in a photorefractive-based true-time-delay phased-array processor

We present a spatio-temporal operator formalism and beam propagation simulations that describe the broadband efficient adaptive method for a true-time-delay array processing (BEAMTAP) algorithm for an optical beamformer by use of a photorefractive crystal. The optical system consists of a tapped-delay line implemented with an acoustooptic Bragg cell, an accumulating scrolling time-delay detector achieved with a traveling-fringes detector, and a photorefractive crystal to store the adaptive spatio-temporal weights as volume holographic gratings. In this analysis, linear shift-invariant integral operators are used to describe the propagation, interference, grating accumulation, and volume holographic diffraction of the spatio-temporally modulated optical fields in the system to compute the adaptive array processing operation. In addition, it is shown that the random fluctuation in time and phase delays of the optically modulated and transmitted array signals produced by fiber perturbations (temperature fluctuations, vibrations, or bending) are dynamically compensated for through the process of holographic wavefront reconstruction as a byproduct of the adaptive beam-forming and jammer-excision operation. The complexity of the cascaded spatial-temporal integrals describing the holographic formation, and subsequent readout processes, is shown to collapse to a simple imaging condition through standard operator manipulation. We also present spatio-temporal beam propagation simulation results as an illustrative demonstration of our analysis and the operation of a BEAMTAP beamformer.     

Self-stabilized recording of fixed gratings at high temperature in LiNbO3:Fe

A high quality fixed holographic grating was recorded in a photorefractive LiNbO(3):Fe crystal at about 100 degrees C in a homemade temperature-controlled vacuum chamber. The recording was carried out using self-stabilization techniques with lambda=532 nm beams guided onto the crystal by polarization maintaining fibers. The diffraction efficiency of the fixed grating was eta=0.44 when measured in the recording setup using the same lambda=532 nm recording beams. A compatible eta was measured with lambda=633 nm in an auxiliary setup, and a 1 mrad angular Bragg selectivity at FWMH was estimated, thus demonstrating the uniformity and good quality of the fixed grating.     

Fixed holograms in iron-doped lithium niobate: simultaneous self-stabilized recording and compensation

We analyze the mechanisms leading to a highly diffractive fixed hologram in photorefractive Fe-doped lithium niobate crystals by simultaneous self-stabilized holographic recording and compensation at moderately high temperatures. We show that a partially compensated running hologram is produced during recording under this condition and discuss the performance of the process in terms of the operating temperature, the degree of oxidation ([Fe(3+)]/[Fe(2+)] ratio) of the sample, and the effect of the absorption grating arising from the spatial modulation of the Fe(2+) concentration produced during photorefractive recording. We experimentally measure the evolution of the uncompensated remaining hologram during recording and the evolution of the diffraction efficiency of the fixed hologram during white-light development and show that the maximum fixed grating modulation to be achieved is roughly limited by Fe-dopant saturation. A reproducible eta approximately 66% efficiency fixed grating was obtained on a sample exhibiting an otherwise maximum fixed eta approximately 3% when using the classical three-step (recording at room temperature--compensating at high temperature--developing at room temperature) process.     

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.     

Dynamic holographic interferometry by photorefractive crystals for quantitative deformation measurements

A holographic interferometer that uses two-wave mixing in a photorefractive (Bi12SiO20) crystal under an applied ac field is described. The interferometer uses a repetitive sequence of separate record and readout times to obtain quasi real-time holographic interferograms of vibrating objects. It is shown that a good signal-to-noise ratio of the interferometer is obtained by turning off the object illumination and the applied ac field during readout of the hologram. The good signal-to-noise ratio of the resulting holographic interferograms enables phase measurement, which allows for quantitative deformation analysis.     

Fabrication of holographic blazed grating with Fourier synthesis exposure

A simple, direct, and universal fabrication method for holographic blazed gratings is proposed and a 79 lines/mm holographic echelle grating with 4 μm depth quasi-triangular grooves experimentally demonstrated as an example of a blazed grating fabricated directly by Fourier synthesis exposure. With the method, we converted a periodic grating groove profile into the exposure energy spatial distribution on the surface of a photoresist with the response characteristics of the particular photoresist. Then the exposure energy could be decomposed into a series of sinusoidal functions using Fourier series, and realized by superposing a series of two-beam interference patterns. In contrast with mechanically ruled gratings, the fabrication process of holographic gratings is quite quick and low cost, and especially no Rowland ghosts appear in their dispersion spectrum. The reported work will offer a new approach for blazed grating fabrication with a holographic process.     

Organic Photorefractive Materials and Applications

This review describes recent advances and applications in the field of organic photorefractive materials, an interesting area in the field of organic electronics and promising candidate for various aspects of photonic applications. We describe the current state of knowledge about the processes involved in the formation of photorefractive gratings in organic materials and focus on the chemical and photo‐physical aspects of the material structures employed in low glass‐transition temperature amorphous composites and organic photorefractive glasses. State‐of‐the art materials are highlighted and recent demonstrations of photonic applications relying on the reversible holographic nature of the photorefractive materials are discussed.     

Observation of high gain in a liquid-crystal panel with photoconducting polymeric layers

A novel, to our knowledge, liquid-crystal panel suitable for real-time holographic purposes has been prepared. A nematic liquid-crystal layer sandwiched between photoconducting polymeric layers, when exposed to a sinusoidal light-intensity pattern, shows efficient formation of refractive-index gratings. The unique feature of the presented panel is its ability to switch energy from beam to beam in a manner similar to the charge-diffusion-controlled photorefractive effect. In a two-wave-mixing experiment multiple orders of diffraction are present, and a very high two-beam coupling-gain ratio (2.5) and a net exponential gain coefficient of ? = 931 cm(-1) have been measured. This gain was achieved in samples biased by a dc external electric field and tilted with respect to the beam-incidence bisector at 45 degrees . The time constants for grating formation and erasure in the studied system are functions of the applied voltage and can be made as short as a few milliseconds under favorable conditions. The mechanism of beam coupling is linked with an electric-field-driven reorientation of the nematic director as a result of a spatially modulated space-charge field created by light in a photoconducting poly(3-octyl)thiophene polymeric layer.     

Flat field concave holographic grating with broad spectral region and moderately high resolution

In order to deal with the conflicts between broad spectral region and high resolution in compact spectrometers based on a flat field concave holographic grating and line array CCD, we present a simple and practical method to design a flat field concave holographic grating that is capable of imaging a broad spectral region at a moderately high resolution. First, we discuss the principle of realizing a broad spectral region and moderately high resolution. Second, we provide the practical method to realize our ideas, in which Namioka grating theory, a genetic algorithm, and ZEMAX are used to reach this purpose. Finally, a near-normal-incidence example modeled in ZEMAX is shown to verify our ideas. The results show that our work probably has a general applicability in compact spectrometers with a broad spectral region and moderately high resolution.