Optical Engineering • Open AccessFractional Fourier transform of hollow sinh-Gaussian beams
The analytical expression for hollow sinh-Gaussian (HsG) beams propagating through a paraxial ABCD optical system is derived and used to investigate its propagation properties in a fractional Fourier transform (FrFT) optical system. Several influence parameters of both the HsG beams and the FrFT optical system are discussed in detail. Results show that the FrFT optical system provides a convenient way for modulating HsG beams: HsG beams maintain their dark-centered distribution when the fractional order p is low, and low-ordered HsG beams lose their original dark-centered distribution more quickly than high-ordered ones when the value of p increases. Eventually all HsG beams’ intensities evolve into peak-centered distributions with some side lobes located sideways. Furthermore, our results also show that HsG beam intensity distribution versus the fractional order is periodical and the period is 2. The results obtained in this work are valuable for HsG beam shaping.