Axially symmetric on-axis flat-top beam.

A synthesis method for arbitrary on-axis intensity distributions from axially symmetric fields is developed in the paraxial approximation. As an important consequence, a new pseudo-nondiffracting beam, the axially symmetric on-axis flat-top beam (AFTB), is given by an integral transform form. This AFTB is completely determined by three simple parameters: the central spatial frequency S(c), the on-axis flat-top length L, and the on-axis central position z(c). When LS(c) >> 1, this AFTB can give a nearly flat-top intensity distribution on the propagation axis. In particular, this AFTB approaches the nondiffracting zero-order Bessel J0 beam when L--> infinity. It is revealed that the superposition of multiple AFTB fields can give multiple on-axis flat-top intensity regions when some appropriate conditions are satisfied.