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Vector discrete nonlinear surface waves

Jared Hudock, Sergiy Suntsov, Demetrios N. Christodoulides, and George I. Stegeman

Open Access Open Access

Abstract

It is theoretically shown that multi-component discrete vector surface waves can exist in arrays of coupled waveguides. These mutually trapped surface states primarily reside in the first waveguide of a semi-infinite array. The existence and stability of such surface waves are systematically investigated.

©2005 Optical Society of America

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Figures (4)
Fig. 1.
Fig. 1. P - Δ diagrams for the linearly polarized (solid line) and elliptically polarized (dash line) discrete vector surface waves as well as for the scalar TE (dotted line) and TM (dotted-dash line) surface waves.

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Fig. 2.
Fig. 2. P-Δ for the TE (solid line) and TM (dashed line) components of the stable linearly polarized family of vector discrete surface waves

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Fig. 3.
Fig. 3. Stable propagation of the (a) TE component and (b) TM component of a linearly polarized discrete vector surface wave. (c) The eigenvalues of the perturbed problem.

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Fig. 4.
Fig. 4. Unstable propagation of the (a) TE component and (b) TM component of an elliptically polarized discrete vector surface wave. (c) The eigenvalues of the perturbed problem.

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Equations (4)

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i d a n dξ + a n + γ ( a n + 1 + a n − 1 ) + [ ∣ a n ∣ 2 + A ∣ b n ∣ 2 ] a n + B b n 2 a n * = 0 ,
i d b n dξ − b n + γ ( b n + 1 + b n − 1 ) + [ ∣ b n ∣ 2 + A ∣ a n ∣ 2 ] b n + B a n 2 b n * = 0 .
A 0 2 = γ [ ( A ± B ) exp ⁡ ( μ ) − exp ⁡ ( ν ) ] ( A ± B ) 2 − 1 ,
B 0 2 = γ [ ( A ± B ) exp ⁡ ( ν ) − exp ⁡ ( μ ) ] ( A ± B ) 2 − 1 ,
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