3.1 Graphical description and experimental implementation of the correlation trajectory

A fundamental part of the chapter consists of describing a method to generate surface plasmon fields propagating along predetermined trajectories. This can be obtained analyzing the correlation function between two screens where each one has a random hole distribution following a predetermined probability density function. This method has the characteristic that the correlation trajectory geometry presents a tunable curvature which allows the possibility to generate long-range surface plasmon.

An alternative model to generate the curved correlation trajectories is performed using a speckle pattern as it is shown in Figure 4.

The optical system that rotates the image can be a prism-type Dove. Modifying the illumination configuration using a convergent beam and changing the relative distance between the two speckle patterns obtained by shifting one mirror a scale factor are introduced. The irradiance superposition between the two speckle patterns generates the desired correlation trajectories. The speckle pattern is shown in Figure 3.

It is known that the irradiance function for the speckle pattern has associated a probability density function-type exponential decreasing function. The decreasing

Figure 3. Speckle pattern generated with a rough surface illuminated with a plane wave.

term can be matched with the decaying ratio of the plasmon mode. This configuration allows improving the generation of plasmon field avoiding the masking of the metal surface which must be made with lithography techniques. These comments represent novel applications of the speckle pattern.

The correlation trajectories generated will be implemented in the following section to describe the surface plasmon. By the fact that the correlation occurs in a curved trajectory, we expect the surface plasmon to present a magnetic behavior.
