  The transformation optics uses geometrized Maxwell's constitutive equations
to solve the inverse problem of optics, namely to solve the problem of finding
the parameters of the medium along the paths of the electromagnetic field
propagation. The quadratic Riemannian geometry is usually used for the
geometrization of Maxwell's constitutive equations, because of the usage of the
general relativity approaches. However, the problem of the insufficiency of the
Riemannian structure for describing the constitutive tensor of the Maxwell's
equations arises. The authors analyze the structure of the constitutive tensor
and correlate it with the structure of the metric tensor of Riemannian
geometry. It was concluded that the use of the quadratic metric for the
geometrization of Maxwell's equations is insufficient, since the number of
components of the metric tensor is less than the number of components of the
constitutive tensor. The possible solution to this problem may be a transition
to Finslerian geometry, in particular, the use of the Berwald-Moor metric to
establish the structural correspondence between the field tensors of the
electromagnetic field.
