Abstract. The transfer of a Gaussian laser beam trough gratings, realized as chemically bleached transparencies of the photoreduced computer-generated Archimedean spiral patterns, is studied theoretically. It is shown that the gratings create nonhomogeneous waves with Bessel transverse profile and Gaussian longitudinal shape. The order of the Bessel profile, as well as the width of the dark axial region of the beam, depends upon the number of Archimedean spirals in the grating and the diffraction order.
The Bessel Gaussian beams, created by the grating, are diverging beams if the waist of the incident Gaussian beam is at arbitrary finite distance from the grating.
They become nondiverging (or nondiffracting) beams if the waist is in the plane of the grating.

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