Beam propagation in a uniaxial crystal under small angle to the optical axis and arrays of bottle beams

Abstract

We show both, experimentally and analytically, generation of bottle beam by uniaxial crystal, in the case optical axis of a uniaxial crystal tilted with respect to axis of a beam. Intensity and polarization structure of a bottle beam experiences dramatic changes. At the angle of 3.5 deg. closed three dimensional structure, of initially circularly polarized beam, breaks. Both analytically and experimentally, we demonstrate that if the beam initially linearly polarized, it structure changes faster than in the case of circular polarization and two focuses of bottle beam "switch" positions. We experimentally, generate arrays of tilted bottle beams with a uniaxial crystal.

Focusing of Gaussian beam passed under small angle to optical axis of uniaxial crystal

“…At this point, the intensity distributions are presented in figure 4(b). It is important to stress that the foci do not move along the axis of beam z, as was stated in the conference proceedings [15], but gradually move out of plane y0z, while the projection of the distance between the foci δ on the z axis shortens. Therefore, strictly speaking, we track positions of the projections of the foci locations on the z axis.…”

“…For simplicity, we placed origin z = 0 at the front face of the crystal (figure 2). The crystal has a thickness of L. The distance between the crystal and the lens is given by d 0 + Δ(f) (rather than just d 0 , as in [15]), where d 0 is the distance between the lens and the crystal when f = 0, and…”

“…To unambiguously track the positions of the foci, as mentioned earlier, we passed a linearly polarized Gaussian beam through Figure 4 shows the measured (dots) and calculated (solid line) dependence of distance between the foci δ on the angle of the tilt of crystal f of initially linearly polarized beam and its experimental intensity distributions in locations of the foci points for different values of f. As can be seen from both the calculated and experimental curves, the maximum distance between the foci δ corresponds to the axial propagation, when f = 0°and is equal to δ = 2 cm. Considering a of change of distance d and substituting d → d 0 + Δ(f) into calculation (3) leads to significant improvement of the calculated results shown in the conference proceedings [15], where the calculated curve shows no physical result, specifically, the minimum distance between the foci in the case of the axial propagation. The intensity distribution at this point is presented in figure 4(a) and corresponds to the vertical bar in the focus area of the o-beam, and to the horizontal bar for the ebeam.…”

“…Since then, the search for ways of forming such light structures has been the focus of many research groups. Optical bottle beams were generated by using computer-generated holograms [2], by interference of beams [3,4], by axicon [5,6], by spatial light modulators (SLMs) [7,8], by superposition of Bessel [9] or of Airy beams [10], by conically refracted light (biaxial crystal) [11], with diffractive optical element [12] and by uniaxial crystal [13][14][15], to name just a few common techniques. The authors of this paper [14] have shown in detail the formation of an optical bottle beam, by focusing a Gaussian beam after passing it along the optical axis of a uniaxial crystal, with the focus on the control of the features of the bottle beam by polarization of the incident beam.…”

“…However, the important issue of the focusing of the Gaussian beam after passing it under a small angle to the axis of the uniaxial crystal has not been considered. In the recent conference proceedings [15] we touched on this question. However, the main emphasis was on the creation of arrays of bottle beams.…”