Time-Domain Formulation of Electromagnetic Scattering Based on a Polarization Mode Expansion and the Principle of Least Action

Abstract

A fresh approach to the full wave analysis of time evolution of the polarization induced in the electromagnetic scattering from dispersive non magnetic particles is presented. It is grounded on the combination of the Hopfield model for the polarization field, the expansion of the polarization field in terms of static longitudinal and transverse modes of the particle, the expansion of the radiation field in terms of transverse wave modes of free space, and the principle of least action. The polarization field is linearly coupled to the electromagnetic field. The losses of the matter are provided through a linear coupling of the polarization field to a bath of harmonic oscillators with a continuous range of natural frequencies. The set of linear ordinary differential integral equations of convolution type of the overall system is reduced by eliminating both the radiation degrees of freedoms and the bath degrees of freedom, and the reduced system of equations is studied. The role played by the radiation field in the coupling between the longitudinal and transverse mode amplitudes of the polarization is described. The principal characteristics of the temporal evolution of the mode amplitudes are found as the particle size varies, including the impulse response. Results are presented for the analytically solvable spherical particle. The proposed approach leads to a general method for the analysis of the temporal evolution of the polarization field induced in dispersive particles of any shape, as well as for the computation of transients and steady states.

References in corpus (11)

• Light interaction with photonic and plasmonic resonances
• Rigorous modal analysis of plasmonic nanoresonators
• From Lorenz to Coulomb and other explicit gauge transformations
• Brillouin-Wigner perturbation theory in open electromagnetic systems
• Field quantization in inhomogeneous absorptive dielectrics
• Electromagnetic modes and resonances of two-dimensional bodies
• Time-dependent Debye-Mie Series Solutions for Electromagnetic Scattering
• Magnetoquasistatic Resonances of Small Dielectric Objects
• Resonance frequency and radiative Q-factor of plasmonic and dielectric modes of small objects
• Quantum Theory of Radiative Decay Rate and Frequency Shift of Surface Plasmon Modes
• Modal Expansion of the Impulse Response Function for Predicting the Time Dynamics of Open Optical Cavities

Cited by in corpus (4)

• Operative Approach to Quantum Electrodynamics in Dispersive Dielectric Objects Based on a Polarization Modal Expansion
• Integral Formulation of Macroscopic Quantum Electrodynamics in Dispersive Dielectric Objects
• Static surface mode expansion for the full-wave scattering from penetrable objects
• Lower Bounds to the Q factor of Electrically Small Resonators through Quasistatic Modal Expansion