{"title":"Four-Wave Mixing Steady-State Solutions Utilising the Underlying SU(2) Group Symmetry","authors":"D. Fish, A. K. Powell, T. J. Hall","doi":"10.1364/pmed.1991.mc11","DOIUrl":null,"url":null,"abstract":"A method of solution for the scalar four wave mixing equations has been known for many years [1]. We show that these equations have an underlying symmetry in the form of the SU(2) group. This formulation identifies the conserved quantities of four wave mixing in an obvious sense rather than in the ad-hoc fashion used previously. The method also solves the equations in terms of beam amplitudes rather than beam ratios.","PeriodicalId":355924,"journal":{"name":"Photorefractive Materials, Effects, and Devices","volume":"68 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Photorefractive Materials, Effects, and Devices","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1364/pmed.1991.mc11","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
A method of solution for the scalar four wave mixing equations has been known for many years [1]. We show that these equations have an underlying symmetry in the form of the SU(2) group. This formulation identifies the conserved quantities of four wave mixing in an obvious sense rather than in the ad-hoc fashion used previously. The method also solves the equations in terms of beam amplitudes rather than beam ratios.
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