We describe the generation of plasmonic modes that propagate in a curved trajectory. This is performed by masking a metal surface with two screens containing a randomly distributed set of holes that follow a Gaussian statistic. The diameter of the holes is less than the wavelength of the illuminating plane wave. By implementing scaling and rotations on each screen, we control the correlation trajectory and generate long-range curved plasmonic modes. The study is generalized for the transmission of a plasmonic mode propagating in a tandem array of thin metal films using the evanescent character of the electric field.
We analyze the diffraction field when changes in the curvature function of the boundary condition are implemented. The study is performed using differential geometry models with a curvature function displaying local behavior. Depending on the sign of curvature, we classify the diffraction field as elliptic, hyperbolic, or parabolic. In particular, it is shown that the optical field is organized around the parabolic regions, which correspond to focusing regions. The model is experimentally corroborated by applying a coordinate transformation to the transmittance of a zone plate. The reason to use this transmittance comes from the fact that its diffraction field displays multiple foci allowing identification, description, and control of bifurcations and morphogenesis effects, which are studied using the curvature function.
We describe the evolution of a linear transmittance when it is perturbed with multiplicative noise; the evolution is approximated through an ensemble of random transmittances that are used to generate diffraction fields. The randomness induces a competition mechanism between noise and transmittance, and it is identified through the self-correlation function. We show that the geometry of the self-correlation function is a single peak preserved in the diffraction field that can be matched with localization-like effects. To corroborate the theoretical predictions, we perform an experiment using a linear grating where the noise is approximated by a stochastic Markov chain. Experimental results are shown.
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