Abstract

A generalized approach to the solution of paraxial four-wave-mixing problems is identified in this paper. It is shown that a Lie group symmetry SU(2, 2) exists for the multiple-grating four-wave-mixing problem. The cases of a reflection or a transmission grating are examined and shown to be irreducible subgroups of the full case. It is shown that a transmission or a reflection grating can be reduced to previous formalisms within this new framework and that a twofold degeneracy exists for these cases. These solutions provide the basis for attempting more complex problems within this framework. Results are also presented for the transmission and reflection gratings, which show stark contrasts between the solution manifolds. An approach to the solution of the mixed-transmission–reflection-grating problem is identified by use of the group formalism.

© 1997 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Solutions to vector four-wave mixing in cubic photorefractive materials

D. A. Fish and A. K. Powell
J. Opt. Soc. Am. B 14(10) 2628-2640 (1997)

Four-wave mixing with partially coherent waves in photorefractive media. I. Transmission grating approximation

Jianhua Zhao, Xianmin Yi, Xiaonong Shen, Ruibo Wang, and Pochi Yeh
J. Opt. Soc. Am. B 16(7) 1104-1111 (1999)

Time-dependent behavior of photorefractive two- and four-wave mixing

Moshe Horowitz, Daniel Kligler, and Baruch Fischer
J. Opt. Soc. Am. B 8(10) 2204-2217 (1991)

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 (11)

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 (195)

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