| FUNDAMENTAL AREAS OF PHENOMENOLOGY(INCLUDING APPLICATIONS) |
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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 |
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| Cite this article: |
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DING De-Sheng, DAI Yu-Rong 2012 Chin. Phys. Lett. 29 024301 |
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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.
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| Keywords:
43.20.Rz
43.20.Bi
43.20.E1
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Received: 21 October 2011
Published: 11 March 2012
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| PACS: |
43.20.Rz
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(Steady-state radiation from sources, impedance, radiation patterns, boundary element methods)
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43.20.Bi
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(Mathematical theory of wave propagation)
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43.20.E1
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