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Covariant description of transformation optics in nonlinear media

: Paul, Oliver; Rahm, Marco

Postprint (1 MByte; PDF; )

Optics Express 20 (2012), Nr.8, S.8982-8997
ISSN: 1094-4087
Zeitschriftenaufsatz, Elektronische Publikation
Fraunhofer IPM ()
nonlinear optic; optical engineering; metamaterial

The technique of transformation optics (TO) is an elegant method for the design of electromagnetic media with tailored optical properties. In this paper, we focus on the formal structure of TO theory. By using a complete covariant formalism, we present a general transformation law that holds for arbitrary materials including bianisotropic, magneto-optical, nonlinear and moving media. Due to the principle of general covariance, the formalism is applicable to arbitrary space-time coordinate transformations and automatically accounts for magneto-electric coupling terms. The formalism is demonstrated for the calculation of the second harmonic wave generation in a twisted TO concentrator.