Application of the coupled classical oscillators model to the Fano resonance build-up in a plasmonic nanosystem

We study the excitation dynamics of Fano resonance within the classical model framework of two linear coupled oscillators. An exact solution for the model with a damped harmonic force is obtained. The details of growth a Fano profile under the harmonic excitation is shown. For incident ultra-wideband pulse, the reaction of a system becomes universal and coincides with the time-dependent response function. The results of numerical calculations clarify two alternative ways for experimental measurement of the complete characteristics of a system: direct observation of the system response to a monochromatic force by frequency scanning or recording of time-dependent response to the delta-pulse. As a specific example, time-dependent excitation in a system consisting of a quantum dot and a metal nanoparticle is calculated. Then it is shown the applicability of the extended model of damped oscillators with radiative correction to describe the build-up a plasmon Fano resonance in a scattering of a femtosecond laser pulse by nanoantenna.