Surface Plasmon Singularities

With the purpose to compare the physical features of the electromagnetic field, we describe the synthesis of optical singularities propagating in the free space and on a metal surface. In both cases the electromagnetic field has a slit-shaped curve as a boundary condition, and the singularities correspond to a shock wave that is a consequence of the curvature of the slit curve. As prototypes, we generate singularities that correspond to fold and cusped regions. We show that singularities in free space may generate bifurcation effects while plasmon fields do not generate these kinds of effects. Experimental results for free-space propagation are presented and for surface plasmon fields, computer simulations are shown. 1. Introduction The contemporary trends in plasmon optics consist of establishing a parallelism with the traditional optical models. The wave nature of the electromagnetic field in both cases implies that the mathematical analysis may present many similarities. However, the physical features may be completely different. An important common behavior is that the electromagnetic field is organized around the singular regions. The simplest singular region is kind fold, and the union of twofold focusing regions generates a cusped focusing region [1]. These are the only focusing regions that can be detected on a plane [1, 2], so that they are the expected singularities for surface plasmon fields. From this fact, some physical features can be analyzed. For optical fields in free space, the inverse process may occur, that is, when a cusped focusing region is split into two folds, vortex and bifurcation effects may occur [3]. For the case of plasmon fields, these features do not appear; however, the focusing region generates charge redistribution [4, 5]. This latter property offers many interesting applications; for example, it can be implemented to polarize particles, allowing the design of plasmonic tweezers. In the present study, we describe the synthesis of singular regions propagating in free space and they are compared with the singular regions for surface plasmon fields. In both cases, the singularities geometry can be obtained from the phase function [6, 7], and it satisfies the nonlinear partial differential equation [6] where L is the optical path length. When the boundary condition is a slit-shaped curve, (1) has a simple geometrical interpretation. The singularity is generated by means of the envelope region of a ray set, and each ray must satisfy the Fermat principle [8], and this construction is sketched in Figure 1. According to the