Self-focusing transmittances

Abstract

In this Letter, we describe the optical field associated with transmittances characterized by a slit-shaped curve. The influence of the curvature is that the diffraction field generates focusing regions. The focusing geometry corresponds to the geometry of the transmittance curve, except for scaling, rotations or translations. A relevant point is that the changes in the morphology of the diffraction field are bounded by the focusing regions. Our experimental and computational results are in good agreement with the theoretical predictions.

Topological Shaping of Light by Closed-Path Nanoslits

“…The concept basically relies on the introduction of cusped design. Interestingly, cusped slits with width-to-wavelength ratio $10 3 have been recently noticed for their intriguing scalar diffraction properties [16].…”

Diffraction by three-dimensional slit-shape curves: decomposition in terms of Airy and Pearcey functions

“…In addition, the walls of the cylinder present adiabatic features in the phase function, which physically means that caustic regions present no more wave behavior. Experimental evidence of this can be found in a previous work [5]. In this way, a very important topic to research is the establishment of the relation between the geometry of the different kinds of caustic regions with the transmittance function.…”

“…The diffraction fields associated with a transmittance containing a slit circular curve when it is illuminated with a plane wave at normal incidence generate nondiffracting fields whose geometry corresponds with a zero-order Bessel beam [9]. Modifying the illumination angle with a tilt in the transmittance, the diffraction field geometry changes dramatically, generating a cusped caustic region [5], as is shown in Fig. 1.…”

“…In this way, a very important topic to research is the establishment of the relation between the geometry of the different kinds of caustic regions with the transmittance function. The simplest case occurs when the optical field emerges from a planar transmittance containing a slit-shape curve, which has changes only in the curvature function [5][6][7]. In the present study, we go a step further and analyze the optical field when the boundary condition is a three-dimensional (3-D) slit-shape curve, i.e., the transmittance curve has curvature and torsion.…”

Kinematic of focusing regions

“…During the interaction period, part of the energy modifies the geometry of the focusing region while another may generate vortex-like effects, both these features being analyzed in the present study. The analysis is supported by the fact that focusing regions exhibit adiabatic features [8,9], which means that such optical fields have particle-like features and the interaction between focusing regions can be modeled as a kind of collision between particles, establishing a direct analogy with mechanical systems.…”