Diffraction characteristics of Hermite-Cosh-Gaussian beams through an Airy Transform Optical System

In the present paper, we elaborate analytical field expressions of diffracted Hermite-Cosh-Gaussian (HChG) beams through an Airy Transform Optical System (ATOS). It is demonstrated that the resulting beams consist of a superposition of modes whose amplitudes are expressed as Airy function and derivative Airy function multiply polynomials. It is shown through numerical calculations that the outgoing fields possess the Airy-like profile with a central peak less powerful than the outer lobes. Furthermore, a complex structure of oscillations is observed for the third-order HChG beam. The effects of the beam order, the decentred parameter the ATOS parameters on the generated fields are illustrated in detail with numerical examples. This investigation constitutes a generalization of the previous studies dealing with the conversion of the fundamental Gaussian and cosh-Gaussian beams by an ATOS.