Abstract
The fractional Fourier transform (FRT) is applied to study the transformation properties of flattened Gaussian beams (FGBs). An analytical formula is derived for the FRT of FGBs based on the definition of FRT. By using the derived formula, we study the intensity distribution properties of FGB in the FRT plane. The influences of the fractional order on the intensity distribution properties of FGB with different order in the fractional Fourier plane are studied in detail. The evolution of the kurtosis parameter of FGB in the FRT plane is also studied.
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