Generalized propagation-invariant wave fields

Necessary and sufficient conditions are presented that determine a generalized class of propagation-invariant wave fields. The existence of wave fields with transverse distributions that are periodically reproduced with different azimuthal orientations is demonstrated. These fields are conveniently described in the longitudinal-azimuthal frequency representation. An interesting subclass is characterized by aperiodic rotated self-images, in the sense that they never return to their original orientation along the propagation. Other subclasses include the conventional self-imaging wave fields, the so-called nondiffracting beams, and the rotating wave fields.