Optical Vortices, Faraday Rotation, Optical Activity.

Characteristic solutions to Maxwell's equations, constrained to equivalence classes by constitutive equations that have certain crystal symmetries, are represented by phase 1-forms, k, such that both 3-forms vanish: k^F=0 and k^G=0. Simple examples demonstrate that the differences between Faraday rotation where the 3-form of Topological Torsion, A^F, is not zero, and Optical Activity where the 3-form of Topological Spin, A^G, is not zero.

The 1-form, k, whose line integral generates the phase function, Theta, is not necessarily equal to the system 1-form of Action per unit charge, A, whose components form the vector and scalar potentials. The characteristic solutions demonstrate that linearly polarized solutions are to be associated with topological spin, and that circularly polarized solutions are to be associated topological torsion.

This result is counter to the popular view that ''spin'' is related to circular polarization.

When the 3-forms A^F and A^G are closed in a exterior differential sense, then their integrals over closed domains form deformable (topological) invariants with values whose ratios are rational (quantized). There are two types of optical phase defects. The first type of defect is related to Faraday rotation, circular polarization, and topological torsion, with A^F not equal to zero. The second type of defect is related to Optical Activity, linear polarization, and topological spin, with A^G not equal to zero.

It would appear appropriate to describe the first type of defect as Optical Vortices with defects of rotational shears. The second type of phase defect is related to dislocations which involve translational shears.


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Last update 08/27/2001
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