Towards implementation of a SPASER and an optical nanolens: Increasing the chances for success

The theory of scattering eigenstates or resonances of a monochromatic electromagnetic (EM) field is briefly reviewed, and is then used to expand the physical field which is present in a two-constituent composite medium when an external or incident field is applied to the system. Special attention is devoted to the case of a composite which has the form of a finite volume of p-constituent (usually metallic, with electric permittivity that has a large negative real part and a small imaginary part, both of them frequency dependent) embedded in an infinite volume of h-constituent (usually a conventional dielectric, with electric permittivity that is nearly real, positive, and frequency independent). Focusing on the case where the frequency is such that the system is close to one of those resonances, we develop a calculation of the shape of the physical field in the composite medium, as well as of the energy content and rate of dissipation of the physical field, and of its lifetime. Consequences for the shape of the physical field are that it is very similar in shape to the eigenfield, and its magnitude is very much amplified when that eigenstate is very localized in space. The size of this localization region is unrelated to the wavelength or any other EM length such as skin depth. It is determined only by the microstructure, whenever the micro-geometric features of the p-constituent are much smaller than any of the EM lengths. This is important in any attempt to use such a resonance in order to implement a nanolens, i.e., to focus an incident EM plane wave or other information-carrying field into a sub-wavelength-sized region.^1,2 Consequences for the lifetime of the physical field are discussed-those are important for any attempt to implement a SPASER^3-5 (Surface Plasmon Amplification by Stimulated Emission of Radiation) device.