5. Conclusions

The statistical properties of the distribution of random holes or equivalently the speckle pattern were transferred to a metal surface to stablish the conditions to generate long-range curved plasmonic modes. In the case of hole distribution, this

can be implemented by masking a thin metal film with two screens that allows controlling the correlation trajectory whose geometry corresponds to a curved longrange surface plasmonic mode. Another possibility was illuminating the metal thin film with two correlated speckle patterns. An important consequence of these configurations is that the set of curved surface plasmonic modes presents a vortex structure that allows to induce magnetic properties [17]. Using the evanescent character of the plasmon modes, the electric field was transferred to the propagation in a tandem array of thin metal films offering applications to design photonic crystals with tunable and localized magnetic properties.

The theoretical point of view presented in this study allows incorporating other effects such as percolation effects which consist in propagating the electric field through random structures. The main characteristic is that the plasmon field presents fractal properties which are the origin of interesting magnetic properties implicit in the curved trajectory of the set of plasmonic modes; more details can be found in [18]. The model presented can be extended by implementing different hole distribution geometries which modify the plasmonic resonance effects. Notably, the curved trajectories have associated focusing regions, and, subsequently, the corresponding magnetic singularity offers the possibility of implementation in the generation of plasmonic magnetic mirrors.

Finally, we remark that the analysis presented offers applications to photonic crystal as a metamaterial design [19–23] since breaking the periodicity or incorporating another type of metal on a selected region is similar to doping the structure and then is possible to induce localization effects. The excitation of plasmon fields using a speckle patterns offers the possibility to incorporate the tunable behavior of the correlation trajectory offering interesting applications in the development of plasmonic antennas and synthesis of accelerating plasmon modes [21], extending the plasmonic optical models.
