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Curved long-range surface plasmon-polariton waveguides

Pierre Berini and Junjie Lu

Open Access Open Access

Abstract

The propagation of the long-range surface plasmon-polariton mode in waveguides comprised of a curved thin metal film of finite width embedded in a homogeneous background dielectric is described. The curve and its mode are modelled in cylindrical coordinates using a rigorous vectorial numerical method and an absorbing boundary condition is applied on the radiating side of the bend. From the results obtained, it is confirmed that long-range structures are not incompatible with bending and that reasonably small radii of curvature can be used.

©2006 Optical Society of America

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Figures (3)
Fig. 1.
Fig. 1. Curved waveguide in (a) cross-sectional and (b) top views.

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Fig. 2.
Fig. 2. (a) Insertion loss, (b) radiation loss and (c) Re{neff } of the ssb0 mode versus radius of curvature for w = 1 μm and t = 15 nm. (d) Summary of r0,opt and ILmin for all (w, t) cases considered.

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Fig. 3.
Fig. 3. Normalised contours of Re{Ez } of the ssb0 mode for w = 1 μm, t = 15 nm, (a) r0 = 1 m and (b) r0 = r0,opt . (c) Normalized distributions of Re{Ez } along a horizontal cut immediately above the metal for w = 1 μm, t = 15 nm and r0 = 1 m, 100 μm and 50 μm. (d) Summary of the transition loss at r0 = r0,opt for all (w, t) cases considered.

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Equations (8)

Equations on this page are rendered with MathJax. Learn more.

∇ × H = jω ε 0 ε r E
∇ × E = − jω μ 0 H
∇ ∙ H = 0
∇ ∙ ( ε y E ) = 0
H = jω ε 0 ∇ × Π e
∇ 2 Π e − ε r − 1 ( ∇ ε r ) ∇ · Π e + ε r β 0 2 Π e = 0
E = ε r − 1 ∇ × ∇ × Π e
α = 20 ( log 10 e ) ∙ θ ∙ Im ( β ϕ ) = 20 ( log 10 e ) ∙ θ ∙ r 0 ∙ β 0 Im ( n eff )
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