Pseudo-Resonance and Energy Band Gap in Plasmonic Crystals

Abstract

In this paper, using the generalized coupled pseudoforce model with driving elements, we develop a method to study the plasmon excitations and energy band structure in a plasmonic crystal. It is shown that the presence of the periodic ion core potential leads to pseudo-resonance condition in the plasmon wavefunction and electrostatic potential profiles, quite analogous to the frequency resonance, leading to the gap formation in the energy dispersion profiles. It is found that the dual length scale character of plasmon excitations lead to occurrence of a critical value of $a_c=2πλ_p$ for the lattice constant ($λ_p$ being the plasmon wavelength) above and below which the energy band structure of plasmonic crystals becomes substantially different. It is also found that energy band gap positions of parabolic free electron energy dispersion relation are slightly higher compared to that of the plasmon excitations. Here based on the plasmon definition and due to the dual length scale character of plasmons compared to that of single electrons, we provide a simplified interpretation of the wave-particle duality in quantum physics and provide the length scale regime in which both wave and particle properties can be simultaneously examined in a single experiment, where, the complementarity principle breaks down. However, the dual characteristics of electron-plasmon coupled excitations, quite analogous to starling murmuration phenomenon, strongly suggests that the long south de Broglie-Bohm pilot wave of electron is nothing but the plasmon itself. The wavefunction and electrostatic potential solution for a one dimensional plasmonic lattice with a generalized periodic potential is also derived in this research.