Volume integral method for investigation of plasmonic nanowaveguide structures and photonic crystals

A. M. Lerer; I. V. Donets; G. A. Kalinchenko; P. V. Makhno

doi:10.1364/PRJ.2.000031

Journals >Photonics Research >Volume 2 >Issue 1 >Page 31 > Article

Photonics Research
Vol. 2, Issue 1, 31 (2014)

Volume integral method for investigation of plasmonic nanowaveguide structures and photonic crystals

A. M. Lerer^*, I. V. Donets, G. A. Kalinchenko, and P. V. Makhno

Author Affiliations

Physics Department, Southern Federal University Rostov-na-Donu, Zorge St. 5, 344090 Rostov-na-Donu, Russia

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DOI: 10.1364/PRJ.2.000031 Cite this Article Set citation alerts

A. M. Lerer, I. V. Donets, G. A. Kalinchenko, P. V. Makhno. Volume integral method for investigation of plasmonic nanowaveguide structures and photonic crystals[J]. Photonics Research, 2014, 2(1): 31 Copy Citation Text

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Abstract

A vector integral–differential equation to describe electromagnetic wave propagation in nanowaveguides and photonic crystals containing thin metal layers is developed. Exact solution of the equation is obtained with the Galerkin method, taking into account the complex dielectric permittivity of metals in the optical range. A simple method for finding complex effective refractive indices for low-loss waveguide structures is developed and proved. Surface plasmon-polariton waves are simulated in the structures under consideration.

\frac{D_{r} (x, y, z)}{τ} = \sum_{p = - \infty}^{\infty} \sum_{q = - \infty}^{\infty} \sum_{s = 1}^{3} \int_{V} \exp [i (α_{p} \bar{x} + β_{q} \bar{y})] {\tilde{g}}_{r s} (z, z^{'}) D_{s} (z^{'}) d v^{'}, r = 1, 2, 3, x, y, z \in V,

(1)

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D_{r} (x, y, z) = \sum_{l = - N_{φ}}^{N_{φ}} \sum_{m = 1}^{N_{r}} X_{lmn}^{r} V_{lmn} (x, y, z),

(2)

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V_{lmn} (x, y, z) = \exp (i l φ) J_{l} (ζ_{m}^{(l)} r (z)) Z_{n} (z),

(3)

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x = a_{x} (z) r \sin φ, y = a_{y} (z) r \cos φ .

(4)

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β (ε^{'} - i ε^{''}) \approx β (ε^{'}) - i [β (ε^{'}) - β (ε^{'} - ε^{''})] - [β (ε^{'} + ε^{''}) + β (ε^{'} - ε^{''}) - 2 β (ε^{'})] .

(5)

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d n \cos φ / λ = 0.5,

(7)

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A. M. Lerer, I. V. Donets, G. A. Kalinchenko, P. V. Makhno. Volume integral method for investigation of plasmonic nanowaveguide structures and photonic crystals[J]. Photonics Research, 2014, 2(1): 31

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