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应用时域有限差分（FDTD）方法分析目标电磁特性时，需要对目标进行空间离散．当宏观电磁目标包含“无限薄”石墨烯界面时，该界面不能进行纵向剖分，同时界面上存在面电流，使界面上的切向电场不能用常规方法计算．对于含不可纵向剖分石墨烯界面的电磁目标，提出一种等效源电流（Equivalent Source Current，ESC）-时域有限差分方法。将石墨烯界面上的面电流等效为源体电流，从而采用有源Maxwell方程，然后通过中间变量并结合处理色散介质问题的移位算子方法，得到石墨烯界面上切向电场的迭代计算式，最终实现含“无限薄”石墨烯界面目标的FDTD计算．多个算例的计算结果都和解析结果有很高的吻合度，表明该方法是正确有效的．本文方法可以推广应用于含“无限薄”导电色散界面目标电磁特性的数值分析．The finite - difference time - domain (FDTD) modeling of targets with infinitely thin graphene sheets poses a challenge due to the existence of surface current and the inability of longitudinal discretization. When analyzing the electromagnetic properties of targets via FDTD method, spatial discretization of the target is essential. In the case of macroscopic electromagnetic targets that incorporate ‘infinitely thin’ graphene interfaces, this interface cannot be longitudinally partitioned. Moreover, a surface current exists on the interface, rendering the conventional calculation methods for the tangential electric field on the interface inapplicable. To address this issue, we put forward a novel Equivalent Source Current (ESC) approach. The proposed method enables the graphene sheet to retain a two - dimensional structure and be positioned on the surface of the Yee cell during the spatial discretization of the FDTD method(Fig.2). Subsequently, the surface current on the graphene sheet is approximated as a source volume current. Then, the active Maxwell's equations are discretized at the tangential electric - field nodes on the graphene surface(Fig.2, Fig.3), thereby obtaining a modified formula for the electric - field. By introducing intermediate variables and integrating the Shift Operator (SO) method, which is employed to handle issues related to dispersive media, to process the correction formula, an FDTD iterative formula for calculating the tangential electric field at the graphene interface is deduced. This ultimately enables the FDTD calculations for targets with ‘infinitely thin’ graphene sheets. Excellent agreement between our FDTD results and analytical solutions in several numerical examples validates the proposed method. The methodological framework proposed in this study can be generalized and applied to the ‘zero-thickness’ dispersive interfaces with surface current distributions (such as metallic films and two-dimensional transition metal sulfides). This allows for a convenient numerical analysis of the electromagnetic properties of structures incorporating conductive dispersive interfaces.
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