Inverse problem in transformation optics

The straightforward method of transformation optics implies that one starts from the coordinate transformation and determines the Jacobian matrix, the fields and material parameters of the cloak. However, the coordinate transformation appears as an optional function: it is not necessary to know it. We offer the solution of some sort of inverse problem: starting from the fields in the invisibility cloak we directly derive the permittivity and permeability tensors of the cloaking shell. This approach can be useful for finding material parameters for the specified electromagnetic fields in the cloaking shell without knowing the coordinate transformation.