Far-field intensity of Lorentz related beams

•We introduce a sufficient condition under which the Lorentz beam convolution with other beams constitutes valid cross-spectral densities.•The far-field intensity patterns in the Cartesian symmetries by the convolution operation of the Lorentz beams with multi-sinc beams, and the Lorentz beams with multi-sinc Gaussian beams, are shown respectively.•We find that different beam order can result distinct far field intensity changes.

We introduce a sufficient condition under which the Lorentz beam convolution with other beams constitutes valid cross-spectral densities. Two examples are given to show how the Lorentz related beam can be used for generation of a far field being a modulated version of another one. The far-field intensity patterns in the Cartesian symmetries by the convolution operation of the Lorentz beams with multi-sinc beams, and the convolution operation of the Lorentz beams with multi-sinc Gaussian beams, are shown respectively. We find that different beam order can result distinct far field changes.