Optical Lattice Model Toward Nonreciprocal Invisibility Cloaking

We propose the design theory of nonreciprocal invisibility cloaking for an optical camouflage device with unidirectional transparency in which a person in the cloak can see the outside but cannot be seen from the outside. Existing theories of designing invisibility cloaks cannot be used for this purpose, because they are based on the transformation optics that uses the Riemannian metric tensor independent of direction. To realize nonreciprocal cloaking, we propose the theory of effective electromagnetic field for photons, which is an extended version of the theory of effective magnetic field for photons. The effective electromagnetic field can be generated using a photonic resonator lattice. The Hamiltonian for a photon in this field has a similar form to that of the Hamiltonian for a charged particle in an electromagnetic field. Incident photons, therefore, experience a Lorentz-like force and a Coulomb-like force and show nonreciprocal movement depending on their traveling direction. We design an actual invisibility cloaking system on the basis of this theory and, with the aid of computer simulation, confirm the nonreciprocal propagation of light needed for nonreciprocal cloaking.