| Summary: | We introduce a non-diffracting beam family as a new beam solution of the scalar Helmholtz equation in Cartesian coordinates whose complex amplitude is mainly described by the Tricomi functions and characterized by four parameters. Based on the proposed beam model, the on-axial, off-axial, and asymmetrical Bessel beams can be obtained as special cases through appropriate selection of the complex parameters. We show that both the intensity and phase distributions can be tailored in a controlled manner through modulation of the angular spectra in the frequency space, enabling the transverse intensity pattern to be varied from a concentric ring structure, through a concentric arc configuration, to a single sheet pattern with different orientations and central positions.
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