Photorefractive Bi12SiO20 Research Articles

Nonlinear Optical Characteristics of BSO and BGO Photorefractive Crystals in Visible and Infrared Ranges

Nonlinear refraction, nonlinear absorption and optical limiting in photorefractive crystals Bi12SiO20(BSO) and Bi12GeO20(BGO) at the wavelengths of 1064 and 532 nm were investigated. It was shown that both BSO and BGO crystals possess by positive nonlinear refraction in two investigated spectral ranges (n2BSO=(2.5 ± 0.5)× 10−12 esu, n2BGO=(6.3 ± 1.3)× 10−12 esu at λ equals 1064 nm; n2BSO=(4.4 plusmn; 0.9)× 10−12 esu, n2BGO=(7.4 ± 1.5)× 10−12 esu at λ= 532 nm). The nonlinear absorption was due to three-photon absorption at the wavelength of 1064 nm (β(3ω)BSO=(2.5 ± 0.8)× 10−20cm3W−2, β(3ω)BSO=(4.4 ± 1.3)× 10−20cm3W−2) and two-photon absorption at the wavelength of 532 nm (β(2ω)BSO=(2 ± 0.4)× 10−9cm W−1, β(2ω)BGO=(3.7 ± 0.7)× 10−9cm W−1).

Optical correlation of spatial-frequency-shifted images in a photorefractive BSO correlator.

The optical cross correlation of an image with another image that was spatial-frequency shifted in one dimension was demonstrated in a photorefractive VanderLugt correlator. The first image was stored as a Fourier-transform hologram in a photorefractive Bi12SiO20 crystal (BSO) and was successively correlated with different spatial-frequency-shifted versions of a second image. We implemented the spatial-frequency shift by rotating a galvanometer mirror in an image plane, causing the Fourier transform to be shifted laterally in the BSO. We verified that the resulting operation in the BSO was an accurate complex multiplication of the shifted and the stored Fourier transforms. As many as 20 successive readouts were conducted without measurable erasure of the stored hologram. The dynamic range, saturation behavior, and other performance parameters were measured and are discussed.

Three-Photon Absorption in Photorefractive BSO and BGO Crystals

The possibility of optical limitation of picosecond laser radiation in photorefractive Bi12SiO20 (BSO) and Bi12GeO20 (BGO) crystals at a wavelength of 1064 nm has been demonstrated. It is shown that the mechanism determining the process of optical limitation is three-photon absorption. The coefficients of three-photon absorption have been determined by the Z-scanning method.

Study of nonlinear-optical characteristics of photorefractive BSO and BGO crystals

Nonlinear refraction, nonlinear absorption, and optical limitation are studied in Bi12SiO20 (BSO) and Bi12GeO20(BGO) crystals at the 532-nm emission wavelength of a picosecond Nd : YAG laser.

Slowdown of group velocity of light by means of phase coupling in photorefractive two-wave mixing.

We show theoretically that the group velocity of light can be slowed down by means of phase coupling in the photorefractive two-wave mixing process. It is shown that the group velocity of light propagating in a photorefractive material could be significantly reduced because of a steep variation of the phase-coupling coefficient with respect to the angular frequency difference between two coupling beams in a two-wave mixing process. The results for the case of a photorefractive Bi12SiO20 crystal are presented and discussed in detail.

(2+1)-dimensional soliton formation in photorefractive Bi12SiO20 crystals.

(2+1)-dimensional spatial solitons in Bi12SiO20 (BSO) photorefractive crystals with large optical activity are experimentally demonstrated. The soliton formation when a Gaussian beam is injected at the input has been previously analyzed numerically and then experimentally investigated. We demonstrate analytically, numerically, and experimentally that by applying static electric biases of high values, the polarization rotation accelerates: this acceleration prevents the beam from broadening if the polarization rotation period becomes shorter than the diffraction length. Contemporary to this nonlinear optical activity, an induced birefringence affects the beam polarization state. Analysis of the polarization dynamics shows that the polarization changes nonuniformly across the beam (with a field dependent speed) until about 30-35 kV/cm; above this limit, the whole beam has just one polarization state. Representation on the Poincaré sphere of the polarization dynamics reveals the existence of a stable polarization trajectory closed around a polarization attractor that depends on the linear optical activity and on the photorefractive nonlinearity. The experimental soliton is well described by the analytical solutions already obtained [Fazio et al., Phys. Rev. E 66, 016605 (2002)].

Manifestation of long-lived photosensitivity gratings in two-wave mixing experiments with sillenite crystals

Transient recording dynamics and hologram fixing and retrieval were observed in photorefractive Bi12SiO20 crystal in two-wave mixing experiments under an ac electric field. These effects were explained by the light- and space-charge-induced spatial modulation of sample photoconductivity originating from the nonequilibrium initial population of relevant photoactive levels. Such a photosensitivity grating exhibits a relaxation time of several hours even when the crystal is illuminated by a spatially uniform light beam. Thus we have shown for what is the first time to our knowledge that optical information can be stored in a photoconductive crystal as a spatially modulated photosensitivity rather than in the form of a space charge.

Choice of optimal conditions for light diffraction and two-wave interaction in a cubic photorefractive piezoelectric Bi12SiO20 crystal

The maximum and minimum diffraction efficiencies and the effective amplification of a hologram are studied experimentally in a 2.1 mm thick, (1̄1̄0) cut Bi12SiO20 crystal as functions of the orientation angle formed by the vector of a holographic grating with the crystallographic direction [001]. A comparison is made between the orientation dependences of the polarisation azimuths at which the extrema of the diffraction efficiency and of the effective amplification are achieved. It is shown that the polarisation azimuths of the reading light corresponding to the maximum diffraction efficiency and the maximum effective amplification coincide within the orientation angles 0 — 90° and 270 — 360° and differ by 90° in the range 90 — 270°.

Vectorial wave interaction in cubic photorefractive crystals

An analytical theory of the polarization-degenerate interaction of light waves in cubic photorefractive crystals of the 23 and \(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) space symmetry groups is proposed. The theory, based on a systematic use of the spatial symmetry properties and the σ-matrix apparatus, provides for a unified description of the polarization and orientation properties of the wave interactions, including the AC and DC methods for enhancement of the nonlinear response and the influence of optical activity, elastooptical effect, and spatial inhomogeneity. The application of the theory to the description of the properties of photorefractive crystals Bi12TiO20 and Bi12SiO20 shows a good agreement with experimental data.

Temperature dependence of the relaxation time of photoconductivity and non-steady-state photocurrents in photorefractive Bi12SiO20 grown in an oxygen-free atmosphere

We present temperature measurements of the non-steady-state photocurrent and photoconductivity relaxation time in photorefractive sillenite crystal Bi12SiO20 grown in an oxygen-free atmosphere. The obtained dependencies are explained using a conventional model of semiconductor crystal with shallow energy level. The activation energy of shallow level obtained from photocurrent measurements was found to be ET=(0.45±0.11) eV. Independent measurements of the temperature dependence of the relaxation time of photoconductivity are in reasonable agreement with this estimation and give the value for ET equal to (0.56±0.01) eV.

Photorefractive effects in long, narrow BSO crystals with applied electric field

In a photorefractive Bi12SiO20 crystal with high applied electric ac field of square-wave shape a fast two-wave coupling response (less than 1 s) and a slow hologram readout decay (minutes) was found for a wavelength of 633 nm. This can be explained by electron–hole transport with two trap levels. An intensity dependence of the slower complementary grating was found. Illuminating with the readout wave without applied electric field leads to a very slow grating decay (many hours).

Optimum orientation of volume phase gratings in sillenite crystals: is it always [111

We study the simultaneous influence of optical activity, piezoelectric effect, and elasto-optic effect on two-wave mixing (TWM) under diffusion recording in photorefractive Bi12TiO20 and Bi12SiO20 crystals and find numerically the maximum of the TWM gain as a function of the orientation of the grating vector. Contrary to widespread belief, the grating orientation K∥[111] is the optimum orientation only if optical activity is negligibly small. Nonzero optical activity results in a strong dependence of the optimum grating orientation on the crystal thickness. The strongest deviation of the optimum from the [111] direction is achieved for ϱd=180°, where ϱ is the rotatory power and d is the crystal thickness. Our theory explains well prior results for crystals of moderate thickness and predicts new effects for thick (e.g., fiberlike) crystals.

Direct observation of charge distributions on photorefractive crystals with the force microscope

Images of the charge distribution at the surface of a photorefractive Bi12SiO20 crystal were obtained by electrostatic force detection with an atomic force microscope. The images show charge gratings with periods of 1.6 and 0.23 μm written by two intersecting laser beams at 514 nm. In addition, they reveal a microstructure in the charge distribution that is caused by surface inhomogeneities. Grating profiles obtained at different writing fluences permit the study of saturation processes. The polarity of the charge carriers was determined by measurement of the phase shift between the light grating and the charge grating.

Parallel interconnection through a multimode optical fiber with a tandem arrangement of two photorefractive crystals

We propose a new method for one-way multipixel image transmission through a multimode optical fiber (MOF). The method is based on the two-pass method, in which a light field bearing an image makes a round trip through a MOF. One-way multipixel image transmission can be realized even through a long and/or winding MOF in which the fiber modes are strongly scrambled with a tandem arrangement of two photorefractive crystals to generate a precise phase-conjugated wave. In this study, images of two pixels (2-bit data) are transmitted through a 100-m MOF more than 20 times for one recording of holograms onto a photorefractive Bi12SiO20 crystal. We also show that a reference beam with a distorted wave front can be utilized, which is transmitted by another MOF instead of a single-mode optical fiber.

Photorefractive devices

In this paper we review four photorefractive devices which have been investigated and further developed in our laboratories. We discuss the fundamental behavior of a photorefractive Bi12SiO20 autocorrelator optimized for particle image velocimetry. The all optical correlator determines the velocities of particles in a cross section of a flow. We show that the autocorrelator is perfect for investigating both laminar and turbulent flows. Photorefractive materials can also be used for vibration analysis of diffusely scattering structures. We discuss recent work from a four-wave mixing interferometric setup with Bi12SiO20 and show that introducing a proper sinusoidal phase shift in one of the pump beams leads to a complete mapping of the vibrational phase and amplitude everywhere on the vibrating structure. Photorefractive materials are also promising candidates for optical storage devices. We discuss holographic storage in LiNbO3 and describe a detailed procedure to obtain a high signal to noise ratio in this device. Finally, we discuss the photorefractive interference filter which consists of alternating quarter-wave layers of high and low index. It has a unique high wavelength selectivity, and the reflectivity and center wavelength can be controlled dynamically by two external laser beams.

Nonlinear combinations of gratings in Bi_12SiO_20: theory and experiments

Multiple optical interference patterns generate phase gratings in Bi12SiO20 as a result of the photorefractive effect. Because of the nonlinear response of the space-charge field to the optical interference pattern, these primary gratings interact and cause the formation of additional gratings at frequencies that are combinations of the primary grating frequencies. Only the diffusion regime is considered in the present investigation. In our setup, two primary gratings are induced as the result of interference among one reference and two closely situated object beams. The interference between the two object beams leads to a negligible photorefractive grating, because the photorefractive Bi12SiO20 crystal cannot respond to the corresponding large fringe spacing. We show theoretically that nonlinear combinations of gratings are introduced through this third interference pattern even though the corresponding grating itself is absent. We obtain analytical expressions for the fundamental frequency components of the space-charge field in the special case of a weak reference beam. In the general case, the frequency components of the space-charge field are calculated numerically by the use of Fourier transforms and are incorporated into the coupled-wave equations. The optical beam propagation method is then used for solving these equations numerically. The effect is probed in a three-wave mixing experiment that uses a sinusoidal phase modulation on one of the object beams to control the grating strength. With this technique one of the gratings is specifically canceled out, and the relative change of the diffraction efficiency in the remaining grating is measured. It is shown that nonlinear combinations of gratings may cause relative changes of more than 35% in the diffraction efficiency. The theoretical predictions are in excellent agreement with our experimental results and the cross talk observed in dynamic optical interconnects.

Nonlinear grating interaction in photorefractive Bi12SiO20

Recently significant crosstalk has been observed in a multibeam experiment in which gratings were previously thought to be independent. In this letter, it is shown that the crosstalk is due to a coherent nonlinear combination of the primary gratings, which causes additional peaks to occur in the diffraction pattern and changes the diffraction efficiency of the primary gratings explaining the apparent crosstalk. It is shown that the effect can be derived from the band transport model when all the terms in the expression for the generation of charge carriers are retained. Results are presented for a configuration consisting of a reference beam and two object beams and show experimental results that confirm the model.

Parametric Instability Boundaries for Spatial Subharmonics in Photorefractive Moving Gratings: Theory and Experiments

We have derived a nonlinear spatiotemporal differential equation for spacecharge fields from Kukhtarev's material equations in a moving coordinate system and obtained the spatial subharmonic instability boundaries by using linear stability analysis. It is also found that there is an analogy between the temporal subharmonic and the spatial subharmonc instabilities in the sense that the governing differential equations describing the instability boundaries are formally identical. The experiments for generating spatial subharmonic waves are performed in a photorefractive Bi12SiO20 crystal by using conventional moving grating technique. The threshold detunings are experimentally determined and the results are compared with the theory.

Crosstalk in dynamic optical interconnects in photorefractive crystals

We have investigated the crosstalk between two neighboring gratings in photorefractive Bi12SiO20 optical interconnects. The gratings are induced by the interference between one reference beam and two object beams. By applying a suitable phase shift in one of the object beams, we can selectively switch off one of the gratings. The crosstalk between the two gratings is experimentally determined from the diffraction efficiency in the remaining grating before and after applying the phase shift. The magnitude of the crosstalk is determined by the intensity ratio between the reference beam intensity and the object beam intensity. Crosstalk can be avoided by choosing a certain intensity ratio between the reference and the object beams.

Quantitative measurement of the vibrational amplitude and phase in photorefractive time-average interferometry: A comparison with electronic speckle pattern interferometry

Time-average interferometry is dealt with using four-wave mixing in photorefractive Bi12SiO20. By introducing a proper sinusoidal phase shift in the forward pump beam it is possible to measure the amplitude and phase everywhere on a vibrating object. Quantitative measurements of the phase and amplitude of the vibrating structure are demonstrated in photorefractive time average interferometry. The photorefractive interferometer is compared with the performance of a commercial electronic speckle pattern interferometer (ESPI). It is shown that the dynamic photorefractive holographic interferometer improves the image quality considerably and is able to extend the measurable range for the acoustic vibration amplitude and frequency compared to what is obtainable with the ESPI equipment.