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.     

Effect of acoustooptic Bragg diffraction on the degree of spatial coherence of a light beam

The effect of acoustooptic (AO) Bragg diffraction on the degree of spatial coherence of an optical beam formed as the result of transmission of a Gaussian beam through a diffuser is studied. Experiments performed on the basis of the AO Bragg interaction in a single crystal of TeO₂ confirmed that the optical beam areas characterized by a higher spatial coherence diffract with a considerably higher efficiency than the low-coherence areas. In addition, the character of the speckle-structure distribution of the optical field of the diffracted beam is practically isotropic.     

Efficient multiple-beam Bragg acoustooptic diffraction with phase optimization of a multifrequency acoustic wave

The subject of investigation is the formation of a highly efficient multiple-beam diffraction field resulting from acoustooptic diffraction by a periodically modulated acoustic wave and acoustic signal composed of a set of independently generated equidistant frequency components. Conditions for minimization of optical losses associated with higher diffraction orders are analyzed. A highly efficient multiple-beam diffraction field is formed by optimizing the phases and amplitudes of signal independent components. A technique of acoustooptic measurements at a high laser radiation intensity is developed, and the basics of the theory are verified experimentally. An attempt to split the power of a laser beam propagating through an optical fiber into seven channels of equal intensities is realized with a net efficiency of 80%.     

An acoustooptic method of measuring the noise equivalent power of optical heterodyne systems

The noise equivalent power of optical heterodyne detection at 10.6 m has been measured with a method based on Raman-Nath diffraction of a CO₂ laser beam. One of the frequency shifted first order diffracted beams is used as the signal radiation. The local oscillator radiation is obtained by splitting off a part of the laser beam incident upon the device used for the acoustooptic diffraction. The signal power can be varied over a large dynamic range by changing the acoustic input power. A study of the probable errors shows that the total error in the NEP measurement is less than 30%.     

Optical-gyroscope application of efficient crossed-channel acoustooptic devices

An acoustooptic (AO) deflector/modulator using a single-mode crossed-channel waveguide of 2n type and an interdigital transducer is fabricated in aY-Z LiNbO₃ substrate. This module has shown a high diffraction efficiency. A 50% diffraction efficiency and a bandwidth of 13.4 MHz were obtained with 0.13 W of surface-acoustic wave power centered at 320MHz. Since the cross section of the channel waveguide and that of the optical fiber are comparable, the interfacting of the resultant acoustooptic devices with fiber optical systems would greatly simplified. In addition, the frequency-shifted optical beam can be conveniently used as a reference signal or local oscillator in heterodyne detection. Consequently, this cross-channel acoustooptic device should find a variety of applications in realizing an integrated-optics module with a 50–50% power slit, optical communication, and an optical fiber system. One of those applications, optical gyroscopes, is proposed by using this kind of crossed-channel AO device.     

声光效应实验研究

介绍声光效应的最新理论进展。采用光栅假设，对各向同性介质中的声光效应作了简要讨论，导出了第m级衍射光的衍射效率公式。研究和介绍一种新的声光效应实验装置。在实验中，应用线阵CCD光强分布测量仪等，通过改变超声波的频率和功率，分别实现了对激光束方向的控制和强度的调制；定量给出了声光偏转量的关系曲线和声光调制测量的关系曲线。实验表明，在布喇格衍射下，通过固定超声波功率，测量衍射光相对于零级衍射光的相对光强与超声波频率的关系曲线，不仅可以计算声速，还可以确定声光器件的带宽和中心频率。     

Isotropic diffraction of a light beam by acoustic waves of fundamental frequency and harmonics

A set of equations describing acoustooptic diffraction of a light beam by acoustic waves of a fundamental frequency and its harmonics in an isotropic medium is obtained. The possibility of suppressing higher diffraction orders by adding the second or third harmonic to the fundamental monochromatic acoustic signal is theoretically justified. It is demonstrated that the maximum degree of suppression decreases with an increase in the light beam divergence. Results of simulation are presented for some particular cases of diffraction.     

Acoustooptic nonpolar light controlling devices and polarization modulators based on paratellurite crystals

A complex of investigations and projects aimed at solving problems of highly effective acoustooptic control of nonpolarized laser radiation is generalized on the basis of anisotropic Bragg’s diffraction in a TeO₂ crystal from a slow acoustic wave, which is characterized by extraordinarily high acoustooptic quality. Modulators of the zeroth diffraction order, modulators of the first Bragg’s order, and a polarization-insensitive deflector are considered. The developed systems ensure the control of the polarization state of optical radiation. These systems are employed in setups and devices based on high-power solid-state and fiber lasers with a wavelength of 1.06 μm.     

Efficiency of collinear acoustooptic interaction in an anisotropic medium

Collinear acoustooptic interaction in crystals with different values of birefringence is theoretically studied. The crystal medium is considered as a system of thin layers where the orientation of optical indicatrix varies from layer to layer due to the presence of an ultrasonic wave. For collinear diffraction in LiNbO₃, α-SiO₂, Te, CaMoO₄, and Tl₃AsSe₃ crystals, expressions for the transmitted and diffracted intensities are obtained by means of acoustooptic methods and a new method based on the Jones calculus.     

Acoustooptic cells with nonuniform length of light-sound interaction

Diffraction of light by acoustic waves that are generated in the acoustooptic cells of piezoelectric transducers with complex geometry is studied. The diffraction by acoustic beams with triangular, quadrangular (rhombic), hexagonal, etc., cross sections, when the lengths of light-sound interaction in the cross-sectional area of the light beam are different, is considered in the plane wave approximation. The difference in the length of interaction affects the instrument function of acoustooptic devices and provides the suppression of the side lobes in their transmission function. The advantages of using cells with complex-geometry transducers in tunable acoustooptic filters that are incorporated into fiber-optic communication lines with wavelength-division multiplexing (WDM) are discussed.     

Acoustooptic 2×2 switch for radiation with different wavelengths as an element of a fiber-optic gyroscope

Planar acoustooptic 2×2 directional couplers that switch optical rays with different wavelengths are considered. A method for calculating the angular and frequency characteristics of such switches is developed, and the parameters of a switch based on a planar Ti-LiNbO₃ structure are calculated. Experiments employing bulk acoustooptic diffraction in TeO₂ are performed, confirming the basic theoretical assumptions. It is shown experimentally that the best conditions for switching optical rays directed into optical fibers can be provided nearly always by varying the diffraction angles and the frequencies of the sound waves. The functional possibilities of the 2×2 directional coupler investigated in a fiber-optic gyroscope are described. Zh. Tekh. Fiz. 67, 57–62 (July 1997)     

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.     

Elastic and photoelastic properties of KGd(WO4)2 single crystals

The elastic and photoelastic properties of a potassium-gadolinium tungstate KGd(WO₄)₂ crystal are determined. A complete matrix of elastic constants for the material is obtained for the first time and the velocity diagrams in the five most practically important planes are constructed on its basis. The coefficients of acoustooptic quality M ₂ are measured for the first time for the crystal in the case of isotropic diffraction for all basic configurations of acoustooptic interaction, which makes it possible to reveal the directions of the most effective interaction.     

Improving the efficiency of an acoustooptic modulator with a two-lobe directivity pattern by correcting the two-frequency electric signal

The feasibility of forming an efficient two-lobe directivity pattern at Bragg acoustooptic diffraction is theoretically substantiated for the first time. It is shown that the efficiency of diffraction into main beams can be increased by mixing the two-frequency signal with additional spectral components that correspond to the closest combination frequencies. Mixing is accomplished using an original electronic circuit designed for polynomial nonlinear correction of the control signal. Bragg diffraction by the corrected signal is studied experimentally in a high-efficiency paratellurite (TeO₂) modulator. Satisfactory agreement with the theory is obtained, and results of applied interest are obtained. In particular, the maximal overall efficiency of diffraction into two main beams is increased from 68 to 79%.     

The temperature dependence of intensity and the function of the transition dipole moment for the induced optical absorption bands of oxygen in the region of the Herzberg photodissociation continuum (200–230 nm)

Application of coherent interaction of laser light with a focused ultrasonic wave to the technique of acoustooptic visualization in multiple-scattering media is discussed. By analyzing spatial distribution of the optical radiation modulated by ultrasound (the photocurrent at ultrasonic frequency), images of large-sized inhomogeneities embedded into the scattering medium have been obtained. A light-absorbing half-plane and a square with sides of 5 mm were used as the inhomogeneities. The visualization was performed under optimal conditions for measuring the alternating photocurrent calculated for the proposed model of coherent interaction between the laser and acoustic beams (the Raman-Nath diffraction). The alternating current at the ultrasonic frequency was obtained as a result of mixing the waves of the diffraction fields on the detector’s photocathode. All experimental values were obtained from a single measurement without averaging the alternating photocurrent at the ultrasonic frequency of 3 MHz, with the scattering parameter varying up to μL≤37.5, where μ is the extinction coefficient and L is the thickness of the scattering medium along the laser beam axis. The measured quantities varied in the course of the measurements by more than 10 orders of magnitude.     

Investigation into the acoustooptic properties of tellurium crystals by anisotropic diffraction of light

The optical, acoustic, and acoustooptic properties of tellurium crystals viewed as a candidate material for mid-and far-IR acoustooptic devices are considered. The phase velocities, polarization, and drift angles of the acoustic energy in different crystal planes are calculated. The acoustooptic figure of merit for tellurium under the anisotropic diffraction conditions is estimated, and light-sound interaction geometries promising for acoustooptic applications are discussed. Measuring data for the optical and acoustooptic parameters of tellurium crystals are given.     

Inverse acoustooptic problem: Coherent summing of optical beams into a single optical channel

A highly efficient summing of mutually coherent beams (channels) into a single beam with the same divergence and aperture (an inverse acoustooptic problem) is realized via diffraction in a Bragg cell. The multibeam field to be converged is formed as a result of the diffraction (splitting) of a single laser beam. Theoretical and experimental evidence is obtained for the fact that the repeated diffraction can provide a highly efficient (up to 100%) reconstruction of beam with initial parameters. The experiments are performed with a single-mode laser radiation at 0.63 μm and multimode radiation at 0.96 μm. The virtually attained summing efficiency is on the order of 70%. The factors that act to diminish the experimental efficiency below the predicted value, the ways to raise the efficiency, and possible applications of the results of this study are discussed.     

Diffraction of light beams by damped ultrasonic waves in gyrotropic cubic crystals

The diffraction of light beams by ultrasound with a two-dimensionally nonuniform, exponentially damped amplitude distribution in gyrotropic cubic crystals is investigated theoretically. An analytical model of strong acoustooptic interaction is constructed on the basis of self-consistent solutions of the vector-matrix partial differential equations for coupled waves written in the amplitudes of the light beam. The model can be used to determine the spatial profiles of the intensity and the polarization structure of the diffracted field for arbitrary diffraction efficiencies and geometries. Numerical simulation results are given.State Academy of Control Systems and Radio Electronics, Tomsk. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 8–19, February, 1995.     

Evaluation of the modulation index of the standing wave Raman-Nath mode-locking device

The performance of an acoustooptic standing wave Raman-Nath deflector as active mode-locking switch is evaluated and compared with theory. The time averaged intensities of the diffracted beam up to the eight order are calculated for acoustic phase shifts up to Δ? = 4. With fused quartz the highest attainable value of σ_m was 6.4 at 633 nm. In the theory describing the pulse width of homogeneously broadened AM mode-locked laser oscillators the modulation index σ_m is a parameter, given by δ_m = 2 Δ?.     

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.