Coupling of optical lumped nanocircuit elements and effects of substrates

We present here an analytical quasi-static circuit model for the coupling among small nanoparticles excited by an optical electric field in the framework of the optical lumped nanocircuit theory [N. Engheta, A. Salandrino, and A. Alù, Phys. Rev. Lett. 95, 095504 (2005)]. We derive how coupling effects may affect the corresponding nanocircuit model by adding lumped controlled sources that depend on the optical voltages applied on the coupled particles as coupled lumped elements. With the same technique, we may model the presence of a substrate located underneath the nanocircuit elements, relating its presence to the coupling with a properly modeled image nanoparticle. These results are of importance in the understanding and the design of complex optical nanocircuits at infrared and optical frequencies.