Abstract: A transducer apparatus and method for generating sonic sound waves having a far field wavefront amplitude pattern in a Bessel or Gaussian distribution is disclosed. The transducer includes a piezoelectric element having uniformly poled dipoles formed therein. An unpoled backing body having the same dielecctric constant as the piezoelectric element contacts and is attached to the piezoelectric element. An indentation shaped to produce a beam amplitude distribution of a predetermined function is formed on the backing body.