Equivalent RLC Ladder Circuit for Scattering by Graphene-Coated Nanospheres

In this paper, an equivalent RLC ladder circuit is derived for a graphene-coated nanosphere. Using this model, it is feasible to tune the resonance frequency of graphene surface plasmons by means of closed-form formulas. To this end, the spherical Bessel and Hankel functions of the modified Mie-Lorenz coefficients are expanded in terms of polynomials and then they are expressed as simple continued fraction forms from which the parameters of the equivalent circuit are derived. It is observed that due to the presence of graphene complex surface conductivity, the impedance of each circuit element is complex, and the real part represents a positive- or negative-valued resistor and the imaginary part modeling an inductor or capacitor. The emergence of the negative resistor which results in the field enhancement is discussed in detail.