24 th International Physics Congress of Turkish Physical Society, 28-31 August 2007, Malatya-TURKEY Balkan Physics Letters, 2008 Special Issue, Boğaziçi University Press, ISSN 1301-8329. Edited by B. Tanatar and M. E. Yakıncı Nonlinear Acoustic Pressure Field Structure in Two and Three Dimensions O. A. Kaya 1 , A. Şahin 2 and D. Kaleci 2 1 The İnönü University, Faculty of Education, Department of Computer Education and Instructional Technology, 44280, Malatya, Turkey. 2 The Inönü University, Faculty of Science and Art, Physics Department, 44280, Malatya, Turkey. Abstract. Nonlinear acoustics is widely used in many areas such as industry and medical applications. Recent developments in nonlinear acoustics motivate new studies for better understanding and detailed analysis of nonlinear wave propagation and nonlinear pressure fields. The purpose of this study was to simulate the nonlinear wave propagation in two and three dimensions in water, generated by a circular type flat transducer which was driven at 2.25 MHz. A numerical approach developed by Aanonsen, Baker and Sahin to the Kuznetsov, Zabolotskaya and Khokhlov, shortly known as KZK wave equation was used in this study to represent the nonlinear acoustic fields in two and three dimensions. The relations between sub harmonic components and side lobe reduction were discussed. Keywords: Ultrasound, circular source, nonlinear propagation. INTRODUCTION Many ultrasound systems increasingly use various transducer geometries for creating acoustic fields suitable for medical or industrial applications. Different types of one dimensional (1-D) and two dimensional (2-D) array acoustic sources are also used to create the acoustic field [1–4]. The characterization of such transducers and their optimization is generally based on computer simulation of the acoustic fields [5–7]. Several researchers analyzed the acoustic wave propagation in nonlinear media, using numerical methods in frequency domain [1, 6, 8] and also time domain [9, 10]. Recently, an increase in the computational power available has led to a renewed interest in the numerical solutions of nonlinear KZK wave equation [6, 11] as it has no full analytical solution. Aanonsen [1] explored a numerical solution to the KZK equation and results presented by Baker et al [6] showed good agreement with experimental data. Sahin and Baker [12] and Baker et al [8] extended this study to rectangular type apertures showing good agreement with their theoretical approach on the acoustic axis. A previous study by Ward et al [13] discussed the nonlinear wave propagation for the improvement of resolution in diagnostic medical ultrasound. A new technique for improved contrast detection developed by Ayache et al [14]. They suggested a new method based on selective imaging of the combined higher harmonics. This imaging method is known as “super harmonic imaging” and made possible the design and use of a new phased array transducer which operates over a wide frequency band. The studies by Humphrey [15] and Averkiou [4] have also generated considerable interest in tissue harmonic ultrasonic imaging. Most recently the developments in clinical use of nonlinear acoustics including tissue harmonic imaging were reviewed by Duck [16]. All these developments bring the need to better understanding of the nonlinear wave propagation and the structure of the pressure field in two and three dimensions. However many of the above mentioned works concentrated on computer based numerical solutions on the acoustic axis or across the acoustic axis. To the authors knowledge not much work appeared in the literature about 2-D and 3-D acoustic pressure field structure. So, main aim of this study is to present the two and three dimensional numerical simulation of nonlinear acoustic wave propagation in water. In order to simulate the 2-D and 3-D nonlinear acoustic wave propagation the governing KZK equation was solved numerically. Numerical data were organized by a computer to plot 2-D and 3-D acoustic pressure field graphs. The ratio of the acoustic pressure field amplitudes was also obtained to see the possible changes in 2-D and 3- D acoustic fields. 186