3.2 Generation of curved surface plasmon modes

The previous statistical description will be employed for the synthesis of surface plasmonic modes. The expression for the electric field of an elementary surface plasmonic mode propagating along the z-axis is given by

$$E(\mathbf{x}, z) = \left(\hat{i}a + \hat{k}b\right) \exp\left\{-a\mathbf{x}\right\} \exp\left\{i\beta\mathbf{z}\right\},\tag{18}$$

˜ °<sup>1</sup>=<sup>2</sup> where <sup>β</sup> <sup>¼</sup> <sup>w</sup> <sup>ε</sup>1ε<sup>2</sup> <sup>¼</sup> <sup>ξ</sup> <sup>þ</sup> <sup>i</sup><sup>η</sup> is the dispersion relation function and <sup>ε</sup>1, <sup>ε</sup><sup>2</sup> repre- <sup>c</sup> <sup>ε</sup>1þε<sup>2</sup> sent the permittivity of the dielectric and metal, respectively. Rotating the reference system along the x-axis, the elementary surface plasmon mode acquires the form

$$E(\mathbf{x}, \mathbf{z}) = \left(\hat{i}a + \hat{j}b\sin\theta + \hat{k}b\cos\theta\right) \times \exp\left\{-a\_1\mathbf{x}\right\} \exp\left\{i\beta(\mathbf{z}\cos\theta + y\sin\theta)\right\}.\tag{19}$$

Using the functional relation given by Eq. (17), the expression for the curved plasmonic mode is given by

$$E(\mathbf{x}, \mathbf{y}) = \left(\hat{i}a + \hat{j}b\sin\theta + \hat{k}b\cos\theta\right) \times \exp\left\{-a\mathbf{x}\right\} \exp\left\{i\theta(\mathbf{y}^a\cos\theta + y\sin\theta)\right\}.\tag{20}$$

By means of the Maxwell equations, we can obtain the expression for the magnetic field and the energy flux given by the Poynting vector.

Synthesis of Curved Surface Plasmon Fields through Thin Metal Films in a Tandem Array DOI: http://dx.doi.org/10.5772/intechopen.81931

For the experimental setup, we propose to illuminate a thin flat Au film (thickness �20–40 nm) with a correlated speckle pattern as shown in Figure 4. The illumination consists in two speckle patterns: each one is visualized as a set of circular motes randomly distributed following a Gaussian probability density function. The wavelength is λ ¼ 1550 nm. The geometrical parameters are agreeing with those reported in [8]. The correlation curve corresponds to the surface plasmonic mode given by Eq. (20). Notably, the statistical properties of the speckle pattern are transferred to the metal surface as the plasmonic mode propagating along the correlation trajectory. In order to allow the generation of a long-range curved plasmonic mode, the correlation length must be less than 2μ to guarantee resonance effects [9, 10]; this can be controlled with the roughness parameters of the surface implemented to generate the speckle pattern avoiding the power decay along the correlation trajectory. The experimental setup is sketched in Figure 5.

Figure 5. Masked metal surface: The typical wavelength is IR.

The analysis presented can be extended to other plasmonic configurations which are presented in the following section.
