Tricomi beams and nondiffracting sheet beams

•We introduce a new non-diffracting beam family whose complex amplitude is mainly described by the Tricomi functions and characterized by four parameters.•The proposed beam is a general model which includes the on-axial, off-axial, and asymmetrical Bessel beams as its special cases.•We show that modulating the angular spectra in the frequency space greatly affects the intensity and phase distributions, enabling the transverse intensity pattern to be varied from a concentric ring profile to a controllable single sheet pattern.•We demonstrate that the physical mechanism of the modulation is based on the non-uniform distribution of the angular spectrum in which the proposed beam can be interpreted as a superposition of plane waves with unequal weighted amplitude.•Our work designs a route for generating non-diffracting beams by providing a means to control their transverse profile and to realize an adjustable laser sheet beam. 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.