Study of extended focal segment formation by conic axicons and layered lenses

Abstract

It is known that the axicon forms focal segment with a large depth of focus, which is useful in many applications. One advantage is due to the weak requirements for alignment of optical components in systems. However in some cases, such as fibers couplers for optical telecommunication, axicon shape is inconvenient. Therefore, we consider the possibility of replacing the conical axicon by gradient lens with a linear variation of the refractive index. We write analytical expressions, allowing to agree the parameters of the conical axicons and gradient lenses. We also study numerically diffraction of Gaussian beam by conical micro-axicons and gradient microlenses consisting of layers with sub-wavelength thickness using finite-difference time-domain method (FDTD). We estimate characteristics of focal segments generated by both types of considered elements and compare by the depth of focus (DOF) and by transverse dimension (full width at half maximum, FWHM). Studies have shown that a layered lens with linear variation of the refractive index has advantages over the conical axicon with the same numerical aperture, as it allows to form more long and more narrow focal segments.