Abstract

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 [M. V. Berry and C. Upstill, in Progress in Optics, E. Wolf, 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

Full Article  |  PDF Article
OSA Recommended Articles
Interference between two diffraction fields with a common caustic region

Gabriel Martı́nez-Niconoff, Javier Muñoz-Lopez, and Alejandro Cornejo-Rodriguez
J. Opt. Soc. Am. A 16(8) 1970-1973 (1999)

Generalization of the theory of far-field caustics by the catastrophe theory

P. S. Theocaris and J. G. Michopoulos
Appl. Opt. 21(6) 1080-1091 (1982)

Self-focusing transmittances

Gabriel Martinez-Niconoff, Javier Munoz-Lopez, Javier Silva-Barranco, Adrian Carbajal-Domínguez, and Patricia Martínez-Vara
Opt. Lett. 37(11) 2121-2123 (2012)

References

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Figures (4)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Equations (39)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Metrics

You do not have subscription access to this journal. Article level metrics are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription