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On the Geometry and Topology of Transformation Optics
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We generalize the geometrical model of transformation optics to Rieman-Cartan space with torsion by introducing topological defects in physical space. By relaxing the integrable condition, we show explicitly that the generalized equivalent medium are bi-anisotropic where the magnetoelectric coupling parameters emergent as the dislocation density. We also show the generation of orbital angular momentum of light. Our theory may open intriguing venues for controlling the vectorial degree of freedom of light with metamaterials.
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Torsional selection rule for the spin--orbit conversion of light
Geometric torsion converts optical spin to OAM with selection rule Δℓ=q via rank-one contortion, conserving screw charge while exchanging (2-q)ℏ with the defect lattice.
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