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

Abstract

Abstract We analytically study 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 the resonance frequency, resonance width, and Fano parameter, and the conditions under which the Fano parameter becomes a real number are examined. These expressions for the simple system are also expected to be helpful for considering various other physical systems because the Fano resonance is a general wave phenomenon.