Light Propagation in Two Dimensional Plasmonic Arrays
We present results on the dynamics of light beams propagating in two dimensional dielectric/metallic waveguides. We show how different configurations provide a rich dynamics of localization, solitary wave formation and instabilities.
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Abstract We present results on the dynamics of light beams propagating in two dimensional dielectric/metallic waveguides. We show how different configurations provide a rich dynamics of localization, solitary wave formation and instabilities.
1 Introduction Light propagation in one dimensional coupled nonlinear waveguide arrays is a mature area of research with numerous experimental and theoretical discoveries on localization, discrete soliton formation and modulational instability dynamics to name some [11]. The pioneering experiment demonstrating light localization [5] triggered efforts by many groups which lead to a large body of work in a variety of arrays in different optical media (fibers, liquid crystals, etc.). This, together with the parallel theoretical studies on the discrete nonlinear Schrödinger equation (DNLSE) and the long-wavelength integrable NLSE approximations, has advanced our understanding of the dynamics and possible applications in this area. Amongst the advances that followed from one dimensional arrays in large measure due to the emergence of photonics crystals was that of two dimensional arrays, for which spatio-temporal localization and optical bullet formation first proposed in [2] and later experimentally demonstrated in [14]. For a long time, the models studied were uniform and only recently interesting scenarios that depart from uniformity in the array have been explored. Two examples are: disordered arrays where Anderson localization has been demonstrated [18] and binary arrays, where either the array consists of dielectric waveguides of different size and/or unequal spacing
D. Wang A.B. Aceves () Department of Mathematics, Southern Methodist University, Dallas, TX 75275, USA e-mail: [email protected]; [email protected] R. Carretero-González et al. (eds.), Localized Excitations in Nonlinear Complex Systems, Nonlinear Systems and Complexity 7, DOI 10.1007/978-3-319-02057-0__9, © Springer International Publishing Switzerland 2014
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[15, 19] or plasmonic arrays of alternating metallic/dielectric waveguides [3]. In both cases, where the coupled mode theory applies, the resulting system of equations break into two pairs which together with their long wavelength continuum approximations depart from NLSE turning into models such as the coupled mode equations (with gap soliton solutions) or the Dirac equations [1]. Distinct features that result from these models include the presence of gaps and singular (diabolical) points in the dispersion relation [1, 16]. These models also predict the existence (and co-existence) of bright and dark [10] solitary waves. By now the type of one dimensional binary arrays continues to be extensively studied [4, 6–9, 12, 13, 17]. In this work we report results on two dimensional binary (metallic/dielectric) nonlinear waveguides (see Fig. 1), which can be seen as a two dimensional tension of the work in [3]. We discuss dispersion properties both in the discrete and in the continuum approximation, modulational instabi
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