Hybrid simulation of Maxwell-Schrödinger equations for electromagnetic fields interacted with electrons confined in electrostatic potentials

The progresses of nano-technology in last some decades have enabled us to develop many attractive devices effectively utilizing cooperative effects between light and electrons. One of typical examples is plasmonic devices in which an enormous amount of electrons in matter simultaneously oscillates by incident fields and locally generates enhanced fields. In order to numerically design and analyze the plasmonic devices, some theoretical models based on the classical physics, namely Newton´s equation of motion for the electrons, have been often employed such as Drude or Lorentz-Drude models. Recent experimental works, however, have revealed that those conventional models cannot coincide with actual phenomena particularly for very small objects in sub-nano meter scale because of lack of consideration for quantum-mechanical effects. Therefore, very recently, some new ways taking into account the quantum-mechanical effects have been actively studied and proposed, for example hydrodynamic Drude model and combination of electromagnetic analysis and time-dependent density functional method.