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We present our computationally efficient approach to modeling tunable graphene-based active metadevices, where the integral multivariate surface conductivity is reformulated in the time and frequency domains with physically interpretable and fast-to-compute integration-free terms. The derivation is built on an expansion to power series of $ {z}= -\text {exp}(-\mu /k_{B}T)$ that converges very fast for non-zero chemical potential values. The model reveals interesting decomposition of graphene response into a universal constant term plus a damped oscillator (digamma functions in the frequency domain) plus non-oscillating correction terms for near-zero potentials. The number of terms in that series is analyzed theoretically for a given accuracy. In practice, only a few series terms are required, making our approach very efficient for simulation of active metasurfaces compared with direct integration of Kubo’s formulas. A simple performance test comparing run times with our code versus the numerical integration of the original Kubo’s formulas demonstrates a speedup exceeding 103. The proposed models can be critical for the initial ellipsometric characterization of graphene and advanced global optimization of graphene-controlled metadevices. [ABSTRACT FROM AUTHOR]

We analyze the electrostatic interaction between two equal-sized charged conducting spheres. We obtain exact closed-form expressions for the capacitance coefficients and the electrostatic force in terms of the special q -digamma function. Additionally, we provide simpler-to-use approximate expressions for the capacitance coefficients and the force between the spheres, and then compare the approximations with the exact results. [ABSTRACT FROM PUBLISHER]