We theoretically propose a new form of laser beam, named the finite-energy Airy–Lorentz–Gaussian (ALG) beam, which can be decomposed into an exponentially modified Airy function in the $x$ direction and a Lorentz–Gaussian function in the $y$ direction. Based on the Huygens diffraction integral formula, an analytical propagation expression for the finite-energy ALG beam passing through a paraxial ABCD optical system has been derived. For special cases, the propagation properties of the finite-energy ALG beam through the free space, a thin lens, and a fractional Fourier transformation (FrFT) system are studied numerically and graphically. Our results provide an effective and alternative way to describe the finite-energy non-diffracting light beams.
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