Abstract

The merits of various types of directed radiation beam have recently been the subject of consider able discussion. One specific area of controversy concerns the comparison of a truncated Bessel beam with a Gaussian beam, with different authors reaching different conclusions about the relative efficacy of the two beams.¹ The fact that the discussion centers around the distinction between two types of beam appears to us to be inappropriate. What one really wishes to deter mine is the optimum beam field, given that there are constraints imposed by the finite aperture and by the finite amount of available energy. For this reason we reformulate the problem as one of finding the field distribution in an aperture plane that gives the best match to a desired intensity distribution in a given plane, located some chosen distance behind the aperture, given the aperture size and the available energy. We solve the problem by variational techniques. We obtain the solution in the form of an integral equation with an Hermitian kernel which, in a number of cases of interest, can be solved analytically. The extension of this method to optimizing the energy distribution in a given volume, or optimizing both the intensity distribution and the depth of focus is also presented. It results in integral equations with Hermitian kernels that depend on the quantities to be optimized. This technique makes it possible to design an optimum physically realizable beam.

© 1991 Optical Society of America