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In my recent study of dyadic products I found out that physical quantities expressend as 2nd rank tensors can also be expressed as a dyadic product of two vectors. Similarly 2nd rank tensor fields can be expressed as pointwise dyadic products of two vector fields.

One such quantity seems to be the index of refraction. I am used to solving geometrical optics problems, say in 2 dimensions, using calculus of variations and a (Riemannian) metric tensor with elements n^2 on the diameter and 0's elsewhere. But I've been at a loss for a while now regarding how to understand that metric tensor in terms of a dyadic product.

I'll be grateful if someone explains this to me or points me to some works (preferably online) wherein this is explained. Please note that I'm primarily concerned with real indices of refraction and transparent media.

Thanks in advance.

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# Dyadic Product and Index of Refraction

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