Quantum electrodynamics and plasmonic resonance of metallic nanostructures

Plasmonic resonance of a metallic nanostructure results from coherent motion of its conduction electrons driven by incident light. At the resonance, the induced dipole in the nanostructure is proportional to the number of the conduction electrons, hence 107 times larger than that in an atom. The interaction energy between the induced dipole and fluctuating virtual field of the incident light can reach a few tenths of an eV. Therefore, the classical electromagnetism dominating the field may become inadequate. We propose that quantum electrodynamics (QED) may be used as a fundamental theory to describe the interaction between the virtual field and the oscillating electrons. Based on QED, we derive analytic expressions for the plasmon resonant frequency, which depends on three easily accessible material parameters. The analytic theory reproduces very well the experimental data, and can be used in rational design of materials for plasmonic applications.