IRREDUCIBLE FORMS OF THE SU(2,2) GROUP IN 4-WAVE-MIXING

A generalized approach to the solution of paraxial four-wave-mixing pr oblems is identified in this paper. shown that a Lie group symmetry SU (2, 2) exists for the multiple-grating four-wave-mixing problem. cases of a reflection or a transmission grating are examined and shown to b e irreducible subgroups of the full case. It is shown that a transmiss ion or a reflection grating can be reduced to previous formalisms with in this new framework and that a twofold degeneracy exists for these c ases. These solutions provide the basis for attempting more complex pr oblems within this framework. Results are also presented for the trans mission and reflection gratings, which show sl;ark contrasts between t he solution manifolds. An approach to the solution of the mixed-transm ission-refection-grating problem is identified by use of the group for malism. (C) 1997 Optical Society of America.