Abstract

From group theory, it is known that the three-dimensional Helmholtz equation is separable in four orthogonal cylindrical coordinate systems: rectangular (i.e. Cartesian), circular, elliptic, and parabolic systems [1]. Invariant Optical Fields (often referred to as nondiffracting beams) have been demonstrated theoretical and experimentally for plane waves in Cartesian coordinates, for Bessel beams in circular cylindrical coordinates [2,3], and for Mathieu beams in elliptic coordinates [4,5]. We introduce in this work a new class of invariant optical fields which are exact solutions of the Helmholtz equation in parabolic coordinates. The spatial distribution of these PIOFs is described in terms of the even and odd Parabolic cylinder functions Pe and Po, namely

© 2003 Optical Society of America