Effective index analysis of bowtie aperture plasmonic waveguides via TM–TE mode decomposition
Date
2025
Authors
Nagi, Udhav
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Abstract
A Modified Effective Index Method (MEIM) is presented for determining the propagation constant of nanoscale bowtie aperture waveguides operating across the 𝟓𝟎𝟎 − 𝟏𝟎𝟎𝟎 𝒏𝒎 spectral range. The approach uses staircase discretization to approximate the tapered bowtie geometry and employs a geometry-driven formulation to maintain numerical stability for sub-𝟑𝟎 𝒏𝒎 features. The transverse-magnetic (TM) response is computed using the hyperbolic-tangent dispersion relation for a three-layer metal–insulator–metal (MIM) stack, while the transverse-electric (TE) contribution is incorporated using a multi-slab transfer-matrix method (TMM) that enforces field continuity across discretized slabs. By combining these formulations, the model reproduces the expected plasmonic behaviour, including a monotonic decrease in effective index with increasing wavelength and stronger confinement for smaller bowtie gaps. Using wavelength-dependent Silver permittivity data, the MEIM results agree well with the rectangular-slab reference problem, confirming the correctness of both the TM and TE formulations. The framework remains computationally efficient, physically interpretable, and easily extendable to other subwavelength apertures, offering a useful preliminary design tool for plasmonic waveguides and sensing structures.
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Keywords
Effective Index Method, propagation constant, bowtie aperture waveguide, geometry-driven, sub-30 nm features, metal-insulator-metal, transfer-matrix method