Peculiarities of the intrinsic symmetry of linear and nonlinear optical susceptibility tensors in nonabsorbing inhomogeneous media with nonlocality of optical response

We show that using the Landau–Lifshitz form of the constitutive equations to construct electrodynamics of inhomogeneous nonabsorbing media with nonlocality of optical response leads to previously unknown intrinsic symmetry relations of the spatially dependent tensors of local and nonlocal optical susceptibilities guaranteeing that the energy conservation law is fulfilled. The discovered relations drastically differ from the analogous relations for homogeneous spatially dispersive media and make it possible to correctly write down the balance equation for the energy conservation law in inhomogeneous media with nonlocality of optical response without the previously accepted artificial addition of any new terms to the classical constitutive equations suggested by Landau and Lifshitz.