Propagation characteristics of elegant Laguerre-Gaussian beams in the fractional Hankel transform plane |
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Authors: | Zhangrong Mei Juguan Gu |
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Institution: | a Department of Physics, Huzhou Teachers College, Huzhou 313000, PR China b Department of Physics, Zhejiang University, Hangzhou 310027, PR China |
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Abstract: | The fractional Hankel transform (FRHT) system is applied to study the transformation properties of elegant Laguerre-Gaussian beams (ELGBs). An analytical formula is derived for the FRHT of ELGBs based on the definition of the FRHB. By using the derived formula and the definition of the kurtosis parameter, the analytical propagation expression for the kurtosis parameter of ELGBs in the FRHT plane is derived. Some detailed numerical examples are given to illustrate the analytical results. The results show that the intensity distribution and the kurtosis parameter of elegant Laguerre-Gaussian beams in the fractional Hankel transform plane not only depend on order p and index m of Laguerre polynomial, but also evolve periodically with fractional order p of fractional system. |
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Keywords: | Fractional Hankel transform Elegant Laguerre-Gaussian beams Propagation equation Kurtosis parameter |
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