Fractional Fourier transform of super Lorentz-Gauss SLG₁₁ mode

An orthogonal family of super Lorentz-Gauss(SLG) beam has been introduced to describe the highly divergent higher-order modes, e.g. the far-field distributions of the highly divergent higher-order mode generated by diode lasers. The fractional Fourier transform(FRFT) is applied to treat the propagation of SLG11 mode. By means of the convolution theorem of Fourier transform, an analytical expression for the field of SLG11 mode passing through an FRFT system has been derived. According to the derived analytical formula, the properties of SLG11 mode in the FRFT plane are graphically illustrated with numerical examples. The influences of the fractional order and three beam parameters on the normalized intensity of SLG11 mode in the FRFT plane are sys