Abstract: Based on Collins diffraction integral method, the propagation characteristics of controllable anomalous hollow beams in gradient refractive index medium are studied. The propagation expression of controllable anomalous hollow beams at any position in the gradient refractive index medium is derived, and the beam width and on-axis light intensity are calculated. Furthermore, the influence of gradient refractive index distribution coefficient and beam modulation parameters on beam transmission characteristics is analyzed through numerical simulation. The results show that by controlling the modulation parameters, the controllable anomalous hollow beam can exhibit a variety of different morphologies during evolution process, and during the propagation process of beam, with the increase of propagation distance, the propagation trajectory, beam width and on-axis light intensity distribution show periodic changes, with the period size determined by the gradient refractive index distribution coefficient. In addition, it is also shown that the larger the beam wavelength, the more obvious the focusing effect of the radially gradient refractive index medium on the controllable anomalous hollow beam.

Key words: physical optics, controllable anomalous hollow beam, gradient refractive index medium, transmission characteristic