Covariant Description of Transformation Optics in Linear and Nonlinear Media

Abstract

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 generation in a twisted TO concentrator.

19 pages, 2 figures

References in corpus (9)

• Design of Electromagnetic Cloaks and Concentrators Using Form-Invariant Coordinate Transformations of Maxwell's Equations
• Transformation media that rotate electromagnetic fields
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Cited by in corpus (4)

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• Covariant kinematics of light in media and a generalized Raychaudhuri equation
• Transformation Acoustics in Generic Elastic Media
• Transformation-Optics-Based Design of a Metamaterial Radome for Extending the Scanning Angle of a Phased Array Antenna