Abstract

Six parameterizations of the wave functions and the phase fields of anisotropic optical vortices (phase singularities) are described and compared. These parameterizations include seventeen different parameters that involve four partial derivatives of the real and the imaginary parts of the wave function, two Hilbert space rotational invariants, four gauge invariants, three geometric parameters, and four phase function parameters. Probability-density functions for all 17 parameters are presented for a Gaussian random wave field. It is shown quite generally that, within any given parameterization, four independent parameters are required to describe the wave function, three independent parameters are needed for the phase function, and two independent parameters suffice for the differential phase morphology. Vortex product wave functions with especially interesting transformation properties are also discussed.

© 1997 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Optical vortices in Gaussian random wave fields: statistical probability densities

Isaac Freund
J. Opt. Soc. Am. A 11(5) 1644-1652 (1994)

Parameterization and orbital angular momentum of anisotropic dislocations

Yoav Y. Schechner and Joseph Shamir
J. Opt. Soc. Am. A 13(5) 967-973 (1996)

Propagation dynamics of optical vortices with anisotropic phase profiles

Guang-Hoon Kim, Hae June Lee, Jong-Uk Kim, and Hyyong Suk
J. Opt. Soc. Am. B 20(2) 351-359 (2003)

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 (6)

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 (49)

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