DB boundary conditions at the inner surface of an arbitrarily shaped cloak

Sufficient boundary conditions for cloaking on the constitutive parameters of an arbitrarily shaped shell are derived by formulating the cloaking problem in terms of nonradiating cancelling equivalent volumetric currents. Transformation optics (TO) cloaks are retrieved as special cases of the general formulation and it is found that the DB boundary conditions at the inner surfaces of cloaks are sufficient conditions to not scatter the incident fields outside the cloaks and to produce zero fields within the cavities of the cloaks.