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. Details of the growth of a Fano profile under the harmonic excitation are shown. For an incident ultra-wideband pulse, the reaction of the system becomes universal and coincides with the time-dependent response function. The results of numerical calculations clarify two alternative ways for the experimental measurement of complete characteristics of the system: via direct observation of the system response to a monochromatic force by frequency scanning or recording the time-dependent response to a d-pulse. As a specific example, the time-dependent excitation in a system consisting of a quantum dot and a metal nanoparticle is calculated. Then, we show the use of an extended model of damped oscillators with radiative correction to describe the plasmon Fano resonance build-up when a femtosecond laser pulse is scattered by a nanoantenna.