Transformation of double-half inverse Gaussian hollow beams into superposition of finite Airy beams using an optical Airy transform

In the present work, we investigate theoretically the transformation of a double-half inverse Gaussian hollow (DHIGH) beam into a superposition of finite Airy beams by using an optical Airy transform system. The analytical expression of the generated finite Airy beam is derived by means of the generalized Huygens-Fresnel integral diffraction. Numerical calculations show that the optical Airy transform system converts the central dark spot of the hollow incident beam into peak intensity. It is demonstrated that the characteristics of the transverse intensity distribution of the output finite Airy beam are determined by the phase pattern's constants of the Airy transform system and the radius size of the incident DHIGH beam. Moreover, it is shown that the profile of the central peak intensity of the generated beam can be controlled by means of the radius size of the incident hollow DHIGH beam.