Gradient-index axicon lenses: a quasi-geometrical study

Geometrical-light-propagation in non-normalized symmetric gradient-index media

Typically, as a means to obtain a less complicated ray tracing method on a gradient-index (GRIN) medium, a normalization is done. This normalization is based upon the fact that the values of the refractive index on the surface of the GRIN medium and the value of the refractive index medium where it is immersed are the same. In this paper, a Fermat's-ray-invariants-based ray tracing method in a non-normalized GRIN medium is presented. This method is so simple that it is no longer necessary to perform normalization to reduce ray tracing complications in GRIN media. In order to observe its operation, the method is implemented in different GRIN media with rectangular, cylindrical, and spherical symmetry. Also, the method is implemented in two different axicon GRIN lenses. MATLAB codes for the implementations are provided as supplementary files. Finally, it is possible to observe that the Fermat's ray invariant is still preserved even outside the lens. This implies that it is not necessary to apply Snell's law when the ray leaves the GRIN medium, because the conservation of the Fermat's ray invariant performs the refraction as if Snell's law had been applied.

MCVD-based GRIN-axicon for the generation of scalable Bessel-Gauss beams

In this Letter, we introduce a graded-index (GRIN)-lens combination named GRIN-axicon, which is a versatile component capable of generating high-quality scalable Bessel-Gauss beams. To the best of our knowledge, the GRIN-axicon is the only optical component that can be introduced in both larger-scale laboratory setups and miniaturized all-fiber optical setups, while having an easy control of the dimensioning of the generated focal line. We show that a GRIN lens with a hyperbolic secant refractive index profile with a sharp central dip and no ripples generates a Bessel-Gauss beam with a high-intensity central lobe when coupled to a simple lens. Such fabrication characteristics are very suitable for the modified chemical vapor deposition (MCVD) process and enable easy manufacturing of an adaptable component that can fit in any optical setup.

Design and manufacture of a gradient-index axicon

A gradient-index axicon with its initial focus offset from the back surface was designed with the thin-lens approximation. Two samples were fabricated by means of the time-varying boundary condition diffusion method, which is based on the modified quasi-chemical diffusion model. Intensity profile measurements were taken along the focal region of the axicons. The samples produced extended line foci. From the intensity measurements, the central spot widths and back focal lengths were determined. The peak widths matched theoretical predictions made with the diffraction theory for the samples and showed good agreement with the predicted widths for a pseudo-Bessel beam, showing that the axicon produced a pseudo-diffractionless beam.