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Irreducible forms of the SU(2, 2) group in four-wave mixing

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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

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