Development of theory and experiments to retrieve Green's functions from cross correlations of recorded wave fields between two receivers has grown rapidly in the last seven years. The theory includes situations with flow, mechanical and electromagnetic disturbances and their mutual coupling. Here an electromagnetic theory is presented for Green's function retrieval from cross correlations that incorporates general bianisotropic media, which is the most general class of linear media. In the presence of dispersive non-reciprocal media, the Green's function is obtained by cross correlating the recordings at two locations of fields generated by sources on a boundary. The only condition for this relation to be valid is that the medium is non-dissipative. The principle of bianisotropic Green's function retrieval by cross correlation is illustrated with a numerical example.
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