The study of Quality Factor calculation of Fano resonance in plasmonic nanostructures

Fano resonance in plasmonic nanostructures has been attracted more and more attentions because of its special optical properties and application potential. Quality factor(Q factor)is very important to evaluate the ability of electromagnetic energy storage of a resonator. In this paper, we firstly get the fitting formula in time domain from the original definition of the Q factor; based on this formula and combining with FDTD method, we calculate the Q factors of typical resonance in several plasmonic nanostructures(including metallic nanorod，nano-antenna and one sample showing evident Fano resonance). Besides, we also calculate the Q factor using the common frequency method (the FWHM formula). By comparing calculation results from the two method above, we find that the FWHM formula is not suitable when dealing with the Q factor of Fano resonance (sometimes incorrect results), although it could be accuracy enough and fast when treating simple plasmonic resonance with single peak; while the Q factor fitting formula from FDTD method could be used for all type of plasmonic resonance (including Fano resonance) because of its origin from the definition of Q factor.