Quasi-discrete Hankel transform of integer order for wave propagation

Manuel Guizar-Sicairos; Julio Cesar Gutierrez-Vega

doi:10.1117/12.555950

4 November 2004 Quasi-discrete Hankel transform of integer order for wave propagation

Manuel Guizar-Sicairos, Julio Cesar Gutierrez-Vega

Proceedings Volume 5556, Photonic Devices and Algorithms for Computing VI; (2004) https://doi.org/10.1117/12.555950
Event: Optical Science and Technology, the SPIE 49th Annual Meeting, 2004, Denver, Colorado, United States

Abstract

A numerical method for computing integer order Hankel transforms using a Fourier-Bessel expansion is presented. The method satisfies the discrete form of the Parseval theorem assuring energy conservation, this makes the formulation particularly useful for field propagation. Some relevant properties of the transformation matrix are discussed. Additionally, a numerical comparison with other typical methods is performed, the advantages and disadvantages of the method are discussed. To verify its accuracy to propagate an optical field, the method is used to obtain higher azimuthal order modes in an optical resonator using the iterative Fox & Li approach, resulting in a reduction of memory requirements and processing time, the results are compared to the traditional two-dimensional Fourier transform approach.

Citation Download Citation

Manuel Guizar-Sicairos and Julio Cesar Gutierrez-Vega "Quasi-discrete Hankel transform of integer order for wave propagation", Proc. SPIE 5556, Photonic Devices and Algorithms for Computing VI, (4 November 2004); https://doi.org/10.1117/12.555950

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