1Department of Physics, Southeast University, Nanjing 210096 2School of Electronic Science and Engineering, Southeast University, Nanjing 210096 3Laboratory of Modern Acoustics of MOE, Nanjing University, Nanjing 210093
Further Notes on the Gaussian Beam Expansion
DAI Yu-Rong1, DING De-Sheng2,3**
1Department of Physics, Southeast University, Nanjing 210096 2School of Electronic Science and Engineering, Southeast University, Nanjing 210096 3Laboratory of Modern Acoustics of MOE, Nanjing University, Nanjing 210093
摘要We provide alternatively a simple way of computing the Fresnel field integral, a further extension to the Gaussian-beam expansion. With a known result that the circ function is approximately decomposed into a sum of Gaussian functions, the zero-order Bessel function of the first kind is similarly expanded by the Bessel–Fourior transform. Two expansions are together inserted in this integral, which is then expressible in terms of the simple algebraic functions. The approach is useful in treatment of the field radiation problem for a large and important group of piston sources in acoustics. As examples, the calculation results for the uniform and the simply supported piston sources are presented, in a good agreement with those evaluated by numerical integration.
Abstract：We provide alternatively a simple way of computing the Fresnel field integral, a further extension to the Gaussian-beam expansion. With a known result that the circ function is approximately decomposed into a sum of Gaussian functions, the zero-order Bessel function of the first kind is similarly expanded by the Bessel–Fourior transform. Two expansions are together inserted in this integral, which is then expressible in terms of the simple algebraic functions. The approach is useful in treatment of the field radiation problem for a large and important group of piston sources in acoustics. As examples, the calculation results for the uniform and the simply supported piston sources are presented, in a good agreement with those evaluated by numerical integration.
DAI Yu-Rong1, DING De-Sheng2,3**. Further Notes on the Gaussian Beam Expansion[J]. 中国物理快报, 2012, 29(2): 24301-024301.
DAI Yu-Rong, DING De-Sheng. Further Notes on the Gaussian Beam Expansion. Chin. Phys. Lett., 2012, 29(2): 24301-024301.
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2012, Vol. 29 
