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This paper is concerned with electromagnetic wave scattering of an annular nanogap in the terahertz regime. We present an efficient vertical mode expansion method (VMEM) to solve the scattering problem, and study the extraordinary optical transmission and field enhancement for the nanostructure with various configurations. The VMEM expands the electromagnetic field in and outside the nanogap along the invariant direction by the one-dimensional modes, where the expansion coefficients satisfy scalar two-dimensional Helmholtz equations on the cross-sectional plane. The continuity conditions of electromagnetic fields on the vertical boundaries of neighboring regions are then employed to establish the linear system for the unknown coefficients. Based on the numerical simulations, we investigate the field enhancement in the nanogap. In particular, we investigate the nanostructure with a series of gap sizes and push the gap width limit to 1 nm in the numerical simulation. The normal and oblique incidence cases and the transverse electric (TE) and transverse magnetic (TM) polarization cases are considered.

Fast vertical mode expansion method for the simulation of extraordinary terahertz field enhancement in an annular nanogap