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arXiv · 1506.01336

Analytical solution of the fundamental waveguide mode of one-dimensional transmission grating for TM polarization

A. T. M. Anishur Rahman·Krasimir Vasilev·Peter Majewski
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Abstract

This article presents an analytical solution of the effective index of the fundamental waveguide mode of $1$D metallo-dielectric grating for Transverse Magnetic (TM) polarization. In contrast to the existing numerical solution involving transcendental equation, it is shown that the square of the effective index ($n_{Eff}$) of the fundamental waveguide mode of $1$D grating is inversely proportional to the slit width ($w$) and the refractive index ($n_m$) of the ridge material and varies linearly with the incident wavelength ($\lambda$). Further, it has also been demonstrated that the dependence of $n_{Eff}$ on the grating period ($P$) and the incidence angle ($\theta$) is minimal. Agreement between the results obtained using the solution presented in this article and published data is excellent.

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A. T. M. Anishur Rahman, Krasimir Vasilev, Peter Majewski. 2015-06-03. Analytical solution of the fundamental waveguide mode of one-dimensional transmission grating for TM polarization. https://arxiv.org/abs/1506.01336

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