Abstract
Analytical expressions of the electric field, the centriod, the beam half width, and the linear momentum of the fractional Fourier transform (FrFT) of an Airyprime beam are derived, respectively. The relation between the centriods or the beam half widths of an Airyprime beam in the exit and the input planes of a FrFT system is also presented. The effect of the fractional order p on the FrFT of an Airyprime beam is investigated in detail and graphically presented. The cycle of the light intensity, the centriod, and the linear momentum of an Airyprime beam in the exit plane of a FrFT system versus p is 4, while the cycle of the beam half width versus p is 2. This research in the FrFT of an Airyprime beam has potential applications. First, special laser beams with different shapes can be generated by controlling p. Then, the FrFT of an Airyprime beam can be used as an optical switch due to the reversal of the positive and the negative signs of the linear momentum in the first and the last half cycle. Finally, the mirror transformation of the spatial orientation of the beam spot for the FrFT of an Airyprime can be used in optical micro-manipulation.
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