Elementary long-range plasmon modes are described assuming an exponential dependence of the refractive index in the neighbourhood of the interface dielectric-metal thin film. The study is performed using coupling mode theory. The interference between two longrange plasmon modes generated that way allows the synthesis of surface sinusoidal plasmon modes, which can be considered as completely coherent generalized plasmon modes. These sinusoidal plasmon modes are used for the synthesis of new partially coherent surface plasmon modes, which are obtained by means of an incoherent superposition of sinusoidal plasmon modes where the period of each one is considered as a random variable. The kinds of surface modes generated have an easily tuneable profile controlled by means of the probability density function associated to the period. We show that partially coherent plasmon modes have the remarkable property to control the length of propagation which is a notable feature respect to the completely coherent surface plasmon mode. The numerical simulation for sinusoidal, Bessel, Gaussian and Dark Hollow plasmon modes are presented.

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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.