Laguerre–Gaussian modal q-plates

Abstract

We propose space-variant uniaxial flat optical elements designed to generate pure Laguerre-Gaussian modes with arbitrary azimuthal and radial indices l and p from an incident Gaussian beam. This is done via the combined use of the dynamic and the geometric phases. Optimal design protocol for the mode conversion efficiency is derived, and the corresponding characteristics are given for -6≤l≤6 and 0≤p≤5. The obtained "modal q-plates" may find many applications whenever the radial degree of freedom of a light field is at play.

Laguerre-Gaussian quasi-modal q-plates from nanostructured glasses

“…Moreover, as noticed in Ref. 4, the latter design breaks the right/left symmetry and prevents the polarization-controlled transformation LG l;p ! LG l,p by flipping the helicity (r ¼ 61 !…”

“…From a practical point of view, the realization of optical components enabling the controlled generation of LG l,p modes is a long-standing issue and we refer to Ref. 4 for a concise overview. Here, we address the experimental implementation of a recent theoretical proposal based on the use of inhomogeneous and anisotropic optical elements.…”

“…Here, we address the experimental implementation of a recent theoretical proposal based on the use of inhomogeneous and anisotropic optical elements. 4 In Ref. 4, it has been shown that a structural upgrade of a so-called q-plate (QP, that is a slab of uniaxial optical material with uniform birefringent phase retardation D ¼ p and azimuthally varying optical axis orientation w ¼ q/ with q half-integer) may lead to the generation of circularly polarized LG l,p optical modes from circularly polarized Gaussian beams with opposite handedness.…”

“…4 In Ref. 4, it has been shown that a structural upgrade of a so-called q-plate (QP, that is a slab of uniaxial optical material with uniform birefringent phase retardation D ¼ p and azimuthally varying optical axis orientation w ¼ q/ with q half-integer) may lead to the generation of circularly polarized LG l,p optical modes from circularly polarized Gaussian beams with opposite handedness. This differs from the original QP design that corresponds to a polarizationcontrolled helical pure phase mask 5,6 whose applied and fundamental interests in classical and quantum optics are broad.…”

“…7 More specifically, the required analytical expressions D l;p ðrÞ and w l;p ðr; /Þ for the radially modulated anisotropic properties of a QP have been derived, assuming that its extraordinary refractive index can be modulated at a fixed ordinary refractive index. 4 However, obtained theoretical profiles having p þ 1 cusps along the radial coordinate are associated with discontinuous derivative functions @D l;p ðrÞ= @r and @w l;p ðr; /Þ=@r, which do not ease the fabrication of modal QPs. Moreover, as noticed in Ref.…”