Diffraction of light in intermediate regime of acoustooptical interaction at oblique incidence

The diffraction of light by ultrasound in an isotropic medium at arbitrarily small angles of incidence onto the acoustic layer is calculated. The intermediate regime of diffraction is considered, for which the conditions of observation of the Raman-Nath and Bragg diffraction are not satisfied in terms of the wave parameter. The effect of the acoustooptical interaction length and angle between the incident light beam and the acoustic wave on the light intensity distribution over the diffraction peaks is studied as a function of the acoustic power. Specific features of the transition from the Raman-Nath to the Bragg diffraction regime through the intermediate regime of diffraction are analyzed.     

Effect of the spatial structure of an acoustic field on Bragg’s acoustooptic diffraction under strong acoustic anisotropy conditions

Bragg’s acoustooptic diffraction in an acoustically anisotropic medium is considered taking into account the two-dimensional spatial diffraction structure of the acoustic beam. The conditions are determined under which reverse transfer of optical power from the diffracted to the transmitted beam in the regime of 100% efficiency of diffraction is considerably suppressed. It is shown that this effect is due to diffraction bending of wave fronts of the acoustic beam in the acoustooptic diffraction plane. The problem of optimization of the piezoelectric transducer size and the spatial position of the input light beam is solved using the criterion of the minimal required power of the acoustic field. The results of simulation in a wide range of the acoustooptic interaction parameters for a Gaussian light beam are reported. The correctness of the model is confirmed experimentally. Recommendations for designers of acoustooptic devices are formulated.     

Acoustooptic multiplication of the frequency shift of optical radiation on the basis of bragg polarization splitting

A technique for the acoustooptic multiplication of the frequency shift of an optical beam is proposed. The technique is based on the cascade diffraction of the beam by a single acoustic wave with the use of Bragg polarization splitting in a uniaxial crystal. The fundamental possibility of the practical realization of the technique is confirmed experimentally by using anisotropic acoustooptic diffraction in LiNbO₃.     

Anisotropic acoustooptic modulator of nonpolarized light based on diffraction by a slow acoustic wave in a paratellurite crystal

The problem of anisotropic Bragg diffraction of nonpolarized light by a slow acoustic wave in a TeO₂ crystal is solved. Two independent acoustic waves are excited in the crystal. Nonpolarized light splits in the crystal into two orthogonally polarized eigenmodes, either diffracting by its associated acoustic beam. Conditions under which the angles of incidence and diffraction are the same for both diffraction processes are found. Depending on the acoustic frequency, the diffracted light at the exit from the crystal may be represented either by a single nonpolarized beam or by two orthogonally polarized beams with different directions and orthogonal polarizations. This may provide a high diffraction efficiency (up to 100%) for nonpolarized light in a TeO₂ crystal. Theoretical calculations are supported by experiments. Modulators capable of controlling a high-power laser operating at a wavelength of 1.06 μm are fabricated.     

Acousto-optic interaction in crystals with large acoustic anisotropy

The Bragg diffraction of light from a sinusoidal phase grating induced in an anisotropic medium by an acoustic wave has been studied theoretically for the case of a large acoustic energy walk-off. Based on the modified coupled-wave equations, the frequency and angular characteristics of an anisotropic diffraction in a paratellurite crystal have been calculated. It is shown that the acoustic beam walk-off significantly changes the angular and frequency ranges of acousto-optic interactions.     

Acousto-optic interaction of diverging Gaussian beams in anisotropic media

A strong acousto-optic interaction of bounded light and sound beams of a Gaussian shape is considered for different geometries permitting long-term interaction. The anisotropic spreading of an acoustic beam in the course of its propagation is taken into account. The spectra of light beams are described by a Gaussian-polynomial expression, and a set of differential equations is derived which allows one to describe various geometries of acousto-optic diffraction. It is demonstrated that the transmission function of an acousto-optic cell essentially depends on the ratio between the dimensions of the light and sound beams and on the angle between the propagation direction of the diffracted beam and that of the incident beam. The degree of spreading of the acoustic beam noticeably affects the suppression of the transmission side lobes.     

Anisotropic light diffraction in crystals with a large acoustic-energy walk-off

The influence of energy walk-off in an acoustic beam on the characteristic of anisotropic Bragg diffraction of light has been investigated by the example of paratellurite crystal. The angular and frequency characteristics of acousto-optic diffraction have been calculated in wide ranges of ultrasound frequencies and Bragg angles using the modified Raman-Nath equations. It is shown that the walk-off of an acoustic beam may change (either widen or narrow) significantly the frequency and angular ranges. The calculation results have been experimentally checked on an acousto-optic cell made of 10.5°-cut paratellurite crystal.     

Control of light polarization by acousto-optic diffraction from leaky acoustic wave in LiNbO₃

The acousto-optic control of light polarization due to diffraction by leaky acoustic waves in ZX-LiNbO? has been demonstrated. The randomly polarized light of 633 nm wavelength is converted by the anisotropic diffraction into two beams with mutually orthogonal polarizations, the relative intensities of which depend on the light incidence angle and acoustic frequency. Variation in acoustic frequency from 108 to 112 MHz rotates the polarization of the output optical beam by 90°. The acousto-optic control is accomplished entirely by electronic means and can be applied for implementation of fast polarization converters.     

Conditions for the suppression of spatial harmonics at a two-frequency acoustooptic interaction in the Raman-Nath mode

It is demonstrated that the diffraction of a plane light wave by an acoustic wave of fundamental frequency in the Raman-Nath mode with admixture of the second acoustic harmonic may be accompanied by a considerable change in the higher diffraction orders with numbers ±2, ±3, etc. Conditions for the selective suppression of the orders are obtained in the weak and strong interaction modes. Results of a numerical simulation are presented.     

Implementation of the Laser Diffraction Technique for Acoustic Cavitation Bubble Investigations

Knowledge of the acoustic cavitation cloud would be useful for improving ultrasound reactor design. Among the characterisation techniques, few are adapted to bubble investigations in an intense ultrasound field. Some problems raised by these measurements result from interactions between the acoustic pressure wave and the measuring light wave. This paper reports the implementation of the laser diffraction technique to determine the size and volume concentration of bubbles generated by a dipping horn operating at 20 kHz. Measurements were performed with a Malvern 2600 instrument. The size distribution, deduced from the diffraction pattern scattered by the bubble cloud crossed by a laser beam, is disturbed by the acoustic pressure wave involving deviation of a light beam at low diffusion angles (acousto‐optic effect). A bubble size correction procedure based on the subtraction of the light energy due to the ultrasound wave is described. The size measurements, and thus the correction procedure, were validated by a second laser technique based on a different measuring principle: phase Doppler interferometry. The measurement reliability was further confirmed by an original application of laser diffraction based on measurements performed just after sonication. These three methods lead to a mean bubble size (Sauter mean diameter) of about 10 μm at a high ultrasound power input. Concerning the void fraction, only measurements achieved after sonication and by laser diffraction predict a correct estimation of this parameter.     

Acoustooptic Bragg diffraction without overemodulation with a phased-array transducer

Acoustooptic Bragg diffraction without overemodulation (i.e., with the extended high-efficiency region on the diffraction efficiency dependence vs. sound amplitude) is studied theoretically and experimentally. It is found that this effect appears in the case of a symmetrically nonuniform acoustic field and is due to the equality of additional opposite phase shifts of light beams passing through symmetric regions of the acoustic field. The situation is considered when an acoustic field is excited by a three-section phased-array transducer. The conditions are determined, in which reverse optical power transfer from the diffracted beam to transmitted beam (overemodulation) in the case of a high (close to 100%) diffraction efficiency is considerably suppressed. In the case of a phased array, the effect weakly depends on the frequency of sound and the size of transducer sections, which makes it possible to observe it in a wide range of acoustooptic interaction parameters.     

Collinear diffraction of a divergent light beam by ultrasound in a paratellurite crystal

The collinear acousto-optical interaction of a divergent light beam with ultrasound along the approximate [110] direction in a TeO₂ paratellurite crystal is investigated theoretically and experimentally. The collinear diffraction is studied at an ultrasonic frequency f ≈ 149 MHz under exposure of the crystal to an uncollimated laser light beam at a wavelength λ = 633 nm and at an angle of divergence as large as 4°. It is shown that the collinear diffraction along the direction forbidden for acousto-optical interactions of plane waves occurs only under conditions where the light beam is uncollimated and the diffraction efficiency increases with an increase in the divergence of the light beam. It is proved that the attenuation of an acoustic wave brings about a decrease in the diffraction efficiency and an increase in the transmission bandwidth of the device used. A model of the collinear acousto-optical filter based on a paratellurite crystal with an interaction length l = 2.7 cm is analyzed. The collinear acousto-optical filter is characterized by a high resolving power (～3000), a high diffraction efficiency (I₁/I₀ ≈ 0.8), and a large angular aperture (Δ? ≈ 4°). This makes collinear diffraction promising for use in acousto-optical filters based on paratellurite crystals.     

New acoustooptic effect: Constant high diffraction efficiency in wide range of acoustic power

A new effect, viz., acoustooptic Bragg diffraction without the overmodulation mode, in which the efficiency of the Bragg order attains its maximal value (close to 100%) upon an increase in the intensity of an acoustic wave and then remains practically unchanged, is predicted theoretically and observed experimentally. The effect takes place in the case of considerable bending of phase fronts of the acoustic field in the acoustooptic diffraction plane and attains its maximal value at a relatively low frequency of sound, a small width of a piezoelectric transducer, strong acoustic anisotropy of the medium, and a large distance between the light beam and the piezoelectric transducer.     

Visualization of a sound beam with a single order of Raman-Nath diffraction of light

This letter reports a novel way of imaging the acoustic power carried in a sound beam by using either +1 or −1 order of Raman-Nath diffraction of light.     

Gaussian laser beam tailoring using acoustooptic cell

Profile shaping of a Gaussian laser beam by an acoustic wave is well described using Collins integral and ABCD matrix formalism. It is shown by a numerical simulation that the relative width of the laser beam to the ultrasonic wavelength and the acoustic pressure inside the acoustooptic cell act on the light intensity diffraction pattern.Obtained results show that the output intensity profile differs from the incident Gaussian beam shape, and it is more broadened with an increase in the acoustic pressure. The intensity of a focused laser beam is transformed in a flat form in the central region if the acoustic pressure is proprely controlled.On the other hand the intensity longitudinal range (ILR) of the flat shape is discussed along the propagation axes, we have found the ILR is about 2 mm for a focal length distance f=100 mm.     

X-ray diffraction in AT-cut quartz single crystal at acoustic excitation at the fundamental frequency

X-ray diffraction on different atomic planes of an AT-cut quartz crystal is studied experimentally in the Laue geometry in case of excitation by acoustic waves at the first resonant (fundamental) frequency. Acoustic waves lead to an increase in the integral intensity of the reflection-diffracted beam. The amplification coefficients in reflection are measured in dependence on the amplitude of a.c. voltage applied to the crystal at the resonant frequency. The frontal distributions of the intensity of the beam diffracted in the reflection direction are obtained for different atomic planes.     

Infrared probing of a gaseous diffraction grating

The use of an infrared beam to optically probe an acoustic diffraction grating propagating in air is discussed. With the use of acoustic diffraction gratings for providing beam splitting action for intense infrared radiation, the need for determining the homogeneity of gaseous diffraction gratings has arisen. The study was performed at the Bragg reflection angle using a 10.6 μm wavelength CO₂ laser probe and an acoustic diffraction grating of 0.33 mm spacing.     

Acousto-optic diffraction at liquid-solid interface with light incident at critical angle

A new acousto-optic diffraction configuration is described. At a liquid-solid interface, a light beam is incident from the solid side of higher refractive index. The maximum acousto-optic diffraction of the Raman-Nath type occurs in the liquid with light incident at the critical angle. The angular dependence of the diffraction efficiency indicates accurate optical alignment requirement. Application to acoustic imaging is briefly discussed.     

Angular splitting of the Bragg diffraction order in an acoustooptical modulator due to a frequency-modulated acoustic wave

Effects of angular splitting of the Bragg diffraction order arising in light acoustooptical diffraction by a frequency-modulated acoustic wave are considered. These effects occur when the size of the light spot in the acoustooptical interaction zone exceeds the characteristic spatial period of the modulating function. The Bragg diffraction order is found to be split into several beams. The directions of the additional beams, their number, and intensities are determined by the modulation parameters. In particular, there occurs a situation where the diffracted field consists of three beams of equal intensity spaced at a distance approximately equal to the diffraction divergence of the incident beam and the diffraction total efficiency is of the order of 100%. Therein lies the difference between this diffraction regime and the case where several independent acoustic waves are generated in the interaction domain and the diffraction total efficiency is limited to the intermodulation arisen. The effect is used in design of modulators for systems of image plotting with the help of high-power lasers.     

Measurements of harmonic profiles of a bounded ultrasonic beam in a liquid medium

The acoustic field of a bounded finite-amplitude beam is governed by competing mechanisms such as medium non-linearity, interference, and attenuation. An analytic determination of the distribution of sonic energy in the individual harmonic components is often not reliable; consequently an experimental mapping of those harmonic components may be more appropriate. An experimental method is presented here which involves a miniature hydrophone probe which has been frequency calibrated for each harmonic component using a light diffraction technique. Measurements (made across the sound field) of the acoustic amplitude of the first three harmonic components are presented.