Abstract
The marching-on-in-degree (MOD) time-domain integral equation (TDIE) solver for the transient electromagnetic scattering of the graphene is presented in this paper. Graphene’s dispersive surface impedance is approximated using rational function expressions of complex conjugate pole-residue pairs with the vector fitting (VF) method. Enforcing the surface impedance boundary condition, TDIE is established and solved in the MOD scheme, where the temporal surface impedance is carefully convoluted with the current. Unconditionally stable transient solution in time domain can be ensured. Wide frequency band information is obtained after the Fourier transform of the time domain solution. Numerical results validate the proposed method.
Highlights
A single layer of graphite, i.e., the monolayer graphene sheet, has many ideal properties and considerable potential in terahertz communications [1], stealth technologies [2], solar cells [3], etc.The transfer matrix method (TMM) [2] and rigorous coupled wave analysis (RCWA) [4] are very efficient for some particular graphene structures
The marching-on-in-degree (MOD) scheme [19,20,21,22,23,24,25] uses weighted Laguerre polynomials (WLPs) as the temporal basis functions, and involves no late-time instability, which may be encountered in the marching-on-in-time (MOT) scheme [26,27,28]
The frequency domain methods are recommended, but they may suffer from the ill-conditioned impedance matrix as well
Summary
A single layer of graphite, i.e., the monolayer graphene sheet, has many ideal properties and considerable potential in terahertz communications [1], stealth technologies [2], solar cells [3], etc. The transfer matrix method (TMM) [2] and rigorous coupled wave analysis (RCWA) [4] are very efficient for some particular graphene structures. The TDIE method has been more and more popular in solving transient electromagnetic problems. When handling resonant structures with a long tail current, many more degrees of WLPs are required. In this case, the frequency domain methods are recommended, but they may suffer from the ill-conditioned impedance matrix as well. When handling the potential internal resonance problems, the MOD scheme [19] and augmented electric field integral equation [22] might be the remedy. The MOD TDIE solver for the transient electromagnetic scattering of the graphene sheet is developed.
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