# Nonlocal multicomponent metamaterials

The slides of the talk *Nonlocal multicomponent metamaterials* I gave
at the MexSIAM Annual Meeting 2021 on June 23, 2021 can be found
here. Using a spinor-like
representation, I can extend the calculation of the macroscopic
response of a metamaterial to multicomponent systems with and without
retardation. The trick is to use an *Euclidean* instead of a
*Hermitian* inner product to define matrix elements, and to use a
spinor like representation of the fields, with two *components* `+k`

and `-k`

, corresponding to Bloch waves moving in opposite
directions. This way, all relevant operators become symmetric, even
when there is dissipation, and I can use some of the usual *linear
algebra* theorems about orthogonality to build a Haydock
representation that allows an efficient calculation of the macroscopic
response and the microscopic fields. Some tests are shown to verify
that the formalism works. The ideas were published here. They have
been implemented in the `Photonic`

package (link1 and link2).