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.
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