Abstract
We discuss the nonparaxial focusing of laser light into a three-dimensional (3D) spiral distribution. For calculating the tangential and normal components of the electromagnetic field on a preset curved surface we propose an asymptotic method, using which we derive equations for calculating stationary points and asymptotic relations for the electromagnetic field components in the form of one-dimensional (1D) integrals over a radial component. The results obtained through the asymptotic approach and the direct calculation of the Kirchhoff integral are identical. For a particular case of focusing into a ring, an analytical relation for stationary points is derived. Based on the electromagnetic theory, we design and numerically model the performance of diffractive optical elements (DOEs) to generate field distributions shaped as two-dimensional (2D) and 3D light spirals with the variable angular momentum. We reveal that under certain conditions, there is an effect of splitting the longitudinal electromagnetic field component. Experimental results obtained with the use of a spatial light modulator are in good agreement with the modeling results.
Highlights
In the classical geometric optics light is assumed to propagate along light rays, which are straight lines in a uniform medium
For calculating the tangential and normal components of the electromagnetic field on a preset curved surface we propose an asymptotic method, using which we derive equations for calculating stationary points and asymptotic relations for the electromagnetic field components in the form of one-dimensional (1D) integrals over a radial component
Based on the electromagnetic theory, we design and numerically model the performance of diffractive optical elements (DOEs) to generate field distributions shaped as two-dimensional (2D) and 3D light spirals with the variable angular momentum
Summary
In the classical geometric optics light is assumed to propagate along light rays, which are straight lines in a uniform medium. The diffraction integral not always can be calculated with the stationary phase method as in some cases, its use leads to the appearance of irremovable singularities, with the electromagnetic field intensity at the point tending to infinity. This is what happens in the neighborhood of geometric caustics. The method is analogous to reducing the Helmholtz equation to the solution of an eikonalequation and a transfer equation. it has some advantages, this approach only allows one to find the field in the neighborhood of non-singular caustics. [11], where classical vortex beams that form axisymmetric caustics were studying, in this work, we look into light fields with a spiral caustic. The considered approach expands the family of beams with optical vortices, which have found their applications in various fields including optical manipulation and laser structuring [25,26,27,28,29,30,31,32]
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