Experimental study of the fractional Fourier transform for a hollow Gaussian beam

• Experimental observation the Fractional Fourier transform(FRT) and truncated FRT of a hollow Gaussian beam.
• We examine the effect of the fractional order and truncated parameters on the beam profile in FRT plane.
• FRT optical system provides an efficient way for beam shaping of a hollow Gaussian beam.

Hollow Gaussian beam (HGB) was introduced in [Cai et al., Optics Letters 2003;28:1084–1086 [12]] and the fractional Fourier transform (FRT) for a HGB was studied theoretically in [Zheng, Physics Letters A 2006;355:156–161 [53]] . In this paper, we derive the analytical formula for the truncated FRT for a HGB, and we report experimental observation of the FRT and the truncated FRT for a HGB. The influences of the fractional order and the truncation parameter on the intensity distribution of the HGB in the FRT plane have been studied in detail both theoretically and experimentally. It is found that the FRT optical system provides an efficient way for modulating the beam profile of a HGB. Our experimental results agree well with the theoretical predictions.