Variable two-crystal cascade for conical refraction

Abstract

The cascade conical refraction occurs when a collimated light beam is passed consequently along the optic axes of several biaxial crystals arranged in a series. For commonly used optical arrangements, the general structure of light emerging from such a cascade is rigorously determined by the used crystals, leaving few possibilities for the variations of the established light pattern. A simple modification of a two-crystal arrangement where one of the two crystals is placed beyond the imaging lens is reported. This modification adds an extreme versatility to the effect and allows one to tune continuously the actual cascade parameters. As a result, practically any pattern of two-crystal cascade conical refraction can be obtained for any pair of biaxial crystals.

Conical refraction: fundamentals and applications

“…The same authors have further developed this trapping scheme by using an additional BC of the same length as the first one under conditions of cascaded CR. In this case the transverse intensity pattern obtained for circularly polarized illumination forms a central spot and an outer bright ring . As in the previous case, for LP illumination, the outer ring has an azimuthal intensity gradient.…”

“…The transformation of a light beam consecutively passing through a series of BCs with aligned optical axes, i.e., cascaded CR, has been theoretically and experimentally investigated for a cascade of two , three , and up to four BCs, with interesting applications in lasing , particle trapping , vortex generation , and free‐space optical communications . The diffractive theory of CR has been extended by Berry to the case of cylindrically symmetric beams propagating through a cascade of up to N BCs , providing an accurate description of the phenomenon in terms of Bessel functions.…”

“…For instance, for an optical system formed by N BCs in cascade with aligned optical axes, it has been shown that the output beam is formed by up to concentric light rings each one with its Poggendorff splitting . For two identical BCs with opposite orientations, the output beam after the second crystal preserves the properties of the beam impinging the first crystal . CR has also been studied in the non‐linear optics domain, showing that second harmonic generation processes in non‐linear c ‐cut BCs are possible , although the most efficient configuration is found when separating the CR and non‐linear processes in two different crystals .…”

Cascade conical refraction for annular pumping of a vortex Nd:YAG laser and selective excitation of low- and high-order Laguerre–Gaussian modes

“…To show our idea clearly, herein we revisit cascade CR by taking the example of two-crystal cascade CR where N = 2 [24], assuming that two BCs are the same material with individual lengths of d 1 and d 2 . In conventional arrangement of cascade CR, as shown in figure 1(a), both crystals are placed behind a focusing lens (FL), the incident light beam forms two concentric rings in the FIP, and the radii of the outer and inner rings are proportional to the sum of crystal lengths d 1 + d 2 and the difference between crystal lengths |d 1 − d 2 |.…”

Complex beam shaping by cascaded conical diffraction with intercalated polarization transforming elements

“…The general paraxial theory of cascaded conical diffraction was developed by Berry in 2010 [26]. An alternative approach based on the splitting and propagation of a bunch of classical rays was given by Turpin et al [27,28] and several experimental and application oriented investigations of cascaded configurations were recently performed [8,14,23,24,[29][30][31][32][33]. In general the cascade of N crystals leads to 2 N −1 conical diffraction rings [26,28], for a circularly polarized or unpolarized input beam the intensity is azimuthally homogeneous on each of the rings.…”