Reciprocity in nonlocal nano-optics

The principle of optical reciprocity is examined in the long wavelength limit in the presence of an isotropic nonlocal medium, by generalizing a previous result established in the literature on the symmetry of the Green’s function. Our focus here is in its possible application to plasmonics, i.e. optics with metallic nanostructures. It is shown that reciprocity will still hold as long as the dielectric function is symmetric with ε( r , r ′) = ε( r ′, r ). Hence, under this symmetric condition, anisotropic dielectric response is necessary for the breakdown of reciprocity in the long wavelength limit. We further show in the appendix that this breakdown only occurs for an asymmetric dielectric tensor, in both the local and nonlocal response cases. An example is given to illustrate this symmetry in the problem of an emitting dipole interacting with a metallic nanoparticle whose response is described by certain dielectric functions which are both frequency and wavevector dependent.