Acousto-optic interaction in a non-homogeneous acoustic field excited by a wedge-shaped transducer Vladimir I. Balakshy a, * , Bogumil B.J. Linde b , Anna N. Vostrikova a a Moscow State University, Department of Physics, Vorobyevy Gory 1, 119991 Moscow, Russia b University of Gdan ´ sk, Institute of Physics, 80-952 Gdan ´ sk, Poland Received 3 January 2008; accepted 8 January 2008 Available online 16 January 2008 Abstract The article is devoted to theoretical analysis of light diffraction in a non-homogeneous acoustic field created by a wedge-shaped piezoelectric transducer. Relationships describing electrical, acoustic and acousto-optic properties of the acousto-optic cell are derived in the approximation of a small thickness of the piezoelectric plate. Principal characteristics of acousto-optic interaction are examined such as dependences of the light diffraction efficiency on the phase mismatch and the acoustic wave amplitude. It is shown that the acous- tic field has a complicated amplitude-phase structure changing with the acoustic frequency. It is demonstrated that the diffraction efficiency in the Bragg regime can approach 100% in spite of a noticeable phase mismatch. The appropriate optimal values of ultrasound power and incidence angles of light are found. Ó 2008 Elsevier B.V. All rights reserved. Keywords: Acousto-optic interaction; Bragg regime; Piezoelectric transducer; Acousto-optic cell 1. Introduction At one time, measuring characteristics of acousto-optic (AO) cells made in our laboratory, we unexpectedly revealed that some cells demonstrated a perfectly strange frequency dependence of the Bragg angle [1]. Instead of a straight line inherent to the AO isotropic diffraction, we obtained in some frequency range the curves like shown in Fig. 1. It is seen that the discrepancy between theoretical ðh theor B Þ and experimental ðh exp B Þ values of the Bragg angle was not negligibly small; it exceeded three times. If the AO cell was turned through 180°, the difference h exp B  h theor B changed only in sign. Analysing these results, we proposed that the emerged effect was caused by an acoustic wave front rotation with frequency that resulted, in its turn, from a wedge-like form of the transducers. To verify this proposition, we made a few small outer electrodes instead of a big solitary one. Measuring resonant frequencies of these small transducers, we convinced ourselves that the thickness of the piezoelec- tric plates really changed from one edge to the other. Formerly, the revealed effect could be considered only as a hindering one, which had to be eliminated. At the present time, the situation has changed. The technology of trans- ducer making has become so perfect that transducers of almost either form can be fabricated. This circumstance opens up new possibilities for applied acousto-optics. It is known that the Bragg angle frequency dependence plays a very important role in AO devices. It is not overstated to say that all advantages of anisotropic diffraction in com- parison with isotropic one result from quite another and very diverse form of this dependence [2–4]. The implemen- tation of transducers with varying thickness enables us to get one more possibility for regulation of the Bragg angle or, in other words, for apodization of AO cells to specific problems to be solved. It should be noticed that in acoustics the transducers of this kind have already been studied in the context of 0041-624X/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.ultras.2008.01.001 * Corresponding author. Tel.: +7 495 939 4697. E-mail address: balakshy@phys.msu.ru (V.I. Balakshy). www.elsevier.com/locate/ultras Available online at www.sciencedirect.com Ultrasonics 48 (2008) 351–356