We describe the focusing region associated with transmittances, analyzing its associated phase function. We show that generic features can be studied from the differential equation for focusing geometry, which is obtained through angular representation for diffraction fields. With the treatment, we recover the results for circular zone plates, and by introducing a linear transformation into the transmittance function we generate structures that keep the ability to generate focusing. According to the choice of the parameters involved, the diffraction field presents new focusing regions, whose three-dimensional geometry and spatial evolution can be described in a selective fashion with analysis of only the phase singularities associated with the diffraction field and avoidance of the integral representation. The treatment is also applied to a simple lens. We recover the theoretical predictions obtained by Berry and Upstill [BerryM. V.UpstillC., in Progress in Optics, WolfE., ed. (North–Holland, Amsterdam, 1980), Vol. XVIII, p. 259], and these predictions are corroborated experimentally. The results obtained are shown.
© 2001 Optical Society of America
Original Manuscript: September 15, 2000
Revised Manuscript: February 20, 2001
Manuscript Accepted: February 20, 2001
Published: September 1, 2001
Gabriel Martı́nez-Niconoff, Javier Muñoz-Lopez, and Edgar Méndez-Martı́nez, "Description of phase singularities and their application to focusing design," J. Opt. Soc. Am. A 18, 2089-2094 (2001)