Generation of isolated asymmetric umbilics in light's polarization

Abstract

Polarization-singularity C-points, a form of line singularities, are the vectorial counterparts of the optical vortices of spatial modes and fundamental optical features of polarization-spatial modes. Their generation in tailored beams has been limited to lemon and star C-points that contain symmetric dislocations in state-of-polarization patterns. In this article we present the theory and laboratory measurements of two complementary methods to generate isolated asymmetric C-points in tailored beams, of which symmetric lemons and stars are limiting cases; and we report on the generation of monstars, an asymmetric C-point with characteristics of both lemons and stars. So far, the study of line singularities relies on the diagnosis of natural occurrences. Non-separable superpositions of polarization and spatial mode of light can provide a vehicle for deliberately creating line-singularity patterns for their study. This polarization-spatial-mode hybridization also adds a new dimension to imaging, where polarization provides additional sensing information [10,11]. Different species exploit polarization-spatial combinations for their survival [12], and line singularities may provide the means to characterize them. At the quantum level, these hybrid modes provide larger Hilbert spaces for encoding information [13]. An investigation of polarization-spatial light modes is also essential for understanding this type of imaging at a deeper level [14].C-points are the umbilical points of the line singularities in the polarization of light because they connect the apex of two opposite cones (a diabolo): of semi-major and semi-minor axis lengths [2,15]. They consist of a state of circular polarization surrounded by a field of polarization ellipses in the optical field, with orientations that rotate about the C-point [16]. C-points are singular points of ellipse orientation. They are intimately linked to the optical vortices of scalar fields, but encode the optical dislocations in the state of polarization instead of the phase [17]. The production of the full spectrum of C-points is of interest in its own right, as it reveals a new domain of complex light not investigated before. The production and analysis of C-points are the basis for new techniques to produce and diagnose optical vortices, which are of interest in metrology due to their high sensitivity to perturbations [18].The two symmetric types of C-point singularities, known as lemons and stars, correspond to dislocations where the ellipse orientation varies linearly with and counter to the angle about the singularity, respectively. Yet, the generation of beams bearing isolated C-points (i.e., alone in a light beam) has been limited to these two cases [19][20][21]. The larger class of asymmetric C-points containing orientations evolving nonlinearly have been produced only in speckle patterns [6][7][8][9], or as C-point pairs (dipoles) in tailored beams [22].The two symmetric cases are the ends of a spectrum of C-points where the pattern of orientations in the ellipse f...

Roadmap on structured light

“…There is an analogy between atomic pseudo-spin (described on the Bloch sphere) and optical polarization (described on the Poincaré sphere) that can be exploited. This analogy enables the realization of the atom optical versions of birefringent optical components such as waveplates and q-plates [123]. In turn these atom optical elements enable the creation of atomic analogues of the optical C-point singularities in the atomic spin texture.…”

Preparation of Poincaré beams with a same-path polarization/spatial-mode interferometer

“…7 However, the cases with l 1 ¼ −l 3 ≠ 1 give rise to a larger variety of asymmetric C-points and hyper C-points that have not been studied previously, which are accessible with the apparatus presented here.…”

“…Since a vortex in one polarization is combined with a nonuniform phase with the other polarization, the result is that most, if not all, C-points are asymmetric, and with a subset of positive index C-points being monstars. 7 The first row of panels in Fig. 3 shows simulations with phases γ and δ set to match the experimental results, which are shown in the second row.…”

“…1,7,28 Here we focus on a general case that encompasses both. It involves beams in a general superposition mode given by…”

“…Poincare beams have been generated by direct superposition in either free space 1 or in optical fibers; 2 or by passage through either a subwavelength diffractive optical element, 3 a liquid-crystal birefringent optical element (socalled q-plate), 4 or a stress-birefringent optical element. 5 The use of these beams has enabled fundamental studies of polarization singularities, 6,7 and in the encoding of quantum information onto single photons. [8][9][10][11] The advantage of superposition methods stems from the freedom to encode any desired mode via electronic diffractive elements, such as spatial light modulators (SLM).…”