Mathematical Physics

    

Linear and Non-Linear Refractive Indices in Riemannian and Topological Spaces

Authors: Miftachul Hadi

The refractive index and curved space relation is formulated using the Riemann-Christoffel curvature tensor. As a consequence of the fourth rank tensor of the Riemann-Christoffel curvature tensor, the refractive index should be a second rank tensor. The second rank tensor of the refractive index describes a linear optics. In case of a non-linear optics, if susceptibility is a fourth rank tensor, then the refractive index is a sixth rank tensor. In a topological space, the linear and non-linear refractive indices are related to the Euler-Poincare characteristic. Because the Euler-Poincare characteristic is a topological invariant then the linear and non-linear refractive indices are also topological invariants.

Comments: 6 Pages. Written in English, 1 Figure.

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[v1] 2021-05-27 01:56:07

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