Analytical expressions for real and complex Fano parameters in a simple classical harmonic oscillator system

We analytically studied the Fano resonance in a simple coupled oscillator system. We demonstrate directly from the equation of motion that the resonance profile observed in this system is generally described by the Fano formula with a complex Fano parameter. The analytical expressions are derived for resonance frequency, resonance width, and Fano parameter, moreover conditions under which the Fano parameter becomes a real number are also examined. These expressions, derived for the simple system, are expected to be helpful for considering various other physical systems because the Fano resonance is a general wave phenomenon.