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<sub>c</sub>, the on-axis flat-top length <i>L</i>, and the on-axis central position z<sub>c</sub>. When LS<sub>c</sub>≫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 J<sub>0</sub> beam when L→∞. It is revealed that the superposition of multiple AFTB fields can give multiple on-axis flattop intensity regions when some appropriate conditions are satisfied.
© 2000 Optical Society of America
Qing Cao and Sien Chi, "Axially symmetric on-axis flat-top beam," J. Opt. Soc. Am. A 17, 447-455 (2000)