Transverse Anderson localization of channel plasmon polaritons

Photonic lattices and coupled waveguide arrays represent convenient systems in which the evolution of the waves in complex structures can be studied. It has been shown that by engineering of the propagation constants of the... [ view full abstract ]

Photonic lattices and coupled waveguide arrays represent convenient systems in which the evolution of the waves in complex structures can be studied. It has been shown that by engineering of the propagation constants of the individual waveguides and their mutual couplings one can explore a rich variety of quantum-optical analogies. In this paper we investigate the transverse Anderson localization (TAL) of the surface plasmon polaritons induced by an off-diagonal disorder. Our system consists of a metallic (silver) surface perturbed by N parallel rectangular grooves with the same width w and depth d cut into the planar surface of a metal. The off-diagonal disorder is introduced by uniform random variation of the separation distance s between the neighboring grooves in the range [s₀-Δs, s₀+Δs]. Each groove supports bound surface electromagnetic wave - channel plasmon polariton (CPP). Solving the Maxwell equation for the array of grooves represents a full 3D problem, however, the spatial evolution of the CPP beam along the system (z) can be conveniently described by the coupled mode theory (CMT). The two key parameters of the structure, coupling coefficient C and the change in the CPP propagation constant Δβ, that enter the CMT model and their dependencies on s are rigorously evaluated (Comsol). The power distribution of the CPP beam for a periodic system (Δs=0) exhibits a diffractive spreading with increasing the transverse distance into the array of grooves. A transition from this ballistic regime to TAL is observed with increasing the disorder strength Δs (see Fig. 1, parameters: w=100 nm, d=350 nm, wavelength=600 nm, s₀=100 nm, N=300, the results are averaged over 200 realizations). Fig. 2 shows an effective longitudinal length L_eff (the shortest propagation distance at which the beam width becomes approximately constant) for various s₀ and Δs compared with the CPP propagation length L_p. Clearly, the Ohmic losses and the effect of relative disorder strength Δs/s₀ on the coupling between the grooves play a central role in realization of the TAL. We suggest two strategies which are beneficial for its observation and discuss a potential impact of randomness on beam steering in the plasmonic nanodevices.