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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Grover Swartzlander
  • Vol. 30, Iss. 9 — Sep. 1, 2013
  • pp: 2507–2522

Variational theory of soliplasmon resonances

A. Ferrando, C. Milián, and D. V. Skryabin  »View Author Affiliations

JOSA B, Vol. 30, Issue 9, pp. 2507-2522 (2013)

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We present a first-principles derivation of the variational equations describing the dynamics of the interaction of a spatial soliton and a surface plasmon polariton (SPP) propagating along a metal/dielectric interface. The variational ansatz is based on the existence of solutions exhibiting differentiated and spatially resolvable localized soliton and SPP components. These solutions, referred to as soliplasmons, can be physically understood as bound states of a soliton and an SPP, which dispersion relations intersect, allowing resonant interaction between them [Phys. Rev. A 79, 041803 (2009)]. The existence of soliplasmon states and their interesting nonlinear resonant behavior has been validated already by full-vector simulations of the nonlinear Maxwell’s equations, as reported in [Opt. Lett. 37, 4221 (2012)]. Here, we provide the theoretical analysis of the nonlinear oscillator model introduced in our previous work and present its rigorous derivation. We also provide some extensions of the model to improve its applicability.

© 2013 Optical Society of America

OCIS Codes
(240.6680) Optics at surfaces : Surface plasmons
(190.6135) Nonlinear optics : Spatial solitons

ToC Category:
Optics at Surfaces

Original Manuscript: May 6, 2013
Revised Manuscript: July 27, 2013
Manuscript Accepted: July 30, 2013
Published: August 26, 2013

A. Ferrando, C. Milián, and D. V. Skryabin, "Variational theory of soliplasmon resonances," J. Opt. Soc. Am. B 30, 2507-2522 (2013)

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  18. Recall that Es=Cfs and H¯y=k0cβnp−1E¯npx, so that the plasmonic projection gives ∫ℝH¯y0|Es|2Enpx∼∫E¯npx(0)Enpxfs2∼O(e−2κsa), whereas the soliton one yields ∫ℝf¯s(0)Enpxfs2∼O(e−(2κs+κs0)a). Both are negligible in the weak coupling approximation. An analogous argument holds for the Es2Enpx* term.
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  21. This exchange of energy is visible in the figures presented in [2] showing the propagation of a perturbed soliplasmon field along the surface, in which the flux of the Poynting vector is represented. One should remark at this point that these simulations are the result of solving the full nonlinear vector Maxwell’s equations (1) numerically.
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  26. A. Marini, D. V. Skryabin, and B. Malomed, “Stable spatial plasmon solitons in a dielectric–metal–dielectric geometry with gain and loss,” Opt. Express 19, 6616–6622 (2011). [CrossRef]
  27. A. Marini and D. V. Skryabin, “Ginzburg–Landau equation bound to the metal–dielectric interface and transverse nonlinear optics with amplified plasmon polaritons,” Phys. Rev. A 81, 033850 (2010). [CrossRef]
  28. C. Milián and D. V. Skryabin, “Nonlinear switching in arrays of semiconductor on metal photonic wires,” Appl. Phys. Lett. 98, 111104 (2011). [CrossRef]

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Fig. 1. Fig. 2. Fig. 3.

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