Dynamic evolution of transverse energy flow in focused asymmetric optical vector-vortex beams

Abstract

We present here controlled generation of asymmetric optical vector-vortex beams using a two-mode optical fiber and study the dynamic evolution of the transverse energy flow (TEF) when focused through a spherical lens. The dependence of the TEF on various factors such as the vortex charge, vortex anisotropy and polarization structure around the vortex core is explored. It is found that the TEF is directly proportional to the phase gradient and its direction is governed by the vortex charge. The presence of C-point polarization singularity in the beam and the polarization structure around it results in vibrational phase gradient which is the major factor deciding the TEF in vector-vortex beams.

Introduction

Singularities exist in almost every field of physics, from quantum to cosmic level and are very curious objects of study due to a variety of interesting effects it imparts on its surroundings [1], [2], [3], [4], [5], [6], [7]. Singular optics specifically is one of the emerging branches of optics dealing with singularities in optical fields and physical phenomena associated with them [2]. Since Allen et al. [3], [4] associated orbital angular momentum (OAM) with the optical vortex beams, this field has become a very exciting and fast growing field of research due to its immense potential in a variety of applications including optical tweezers [5], [6], [7].

There are various methods of generation of scalar vortex beams such as computer generated hologram (CGH) [8], spatial light modulator (SLM) [7], spiral phase plate (SPP) [9], cylindrical lenses (CL) [10], [11] etc. For more details on the generation methods refer to [7]. In parallel, cylindrical vector beams (CVBs) wherein the optical beam has an additional spatial polarization modulation have also gained interest in a variety of applications [12]. The CVBs are generated using a variety of techniques including laser intracavity devices, axial dichroism created by a conical Brewster prism, a spatially variant λ/2 retarder (to convert the input linear polarized beam into cylindrical polarization) [12]. Interestingly, the output beam from two-/ few-mode optical fibers, excited appropriately, combines the vortex and vector beam characters mentioned above making it a simple and flexible method for the generation of optical vector-vortex beams (OVVBs) [13], [14], [15], [16]. The theory of two-mode optical fiber is summarized in the appendix. Optical fibers are also a convenient system with easily controllable degrees of freedom for the generation of OVVBs with switchable vortex charge and inhomogeneous polarization [16], tunable anisotropic phase profile and symmetric or asymmetric intensity in the beam cross section including embedded polarization singularity [15], [16], [17]. Such beams, in general can be classified as asymmetric optical vector-vortex beams (AOVVBs). The main advantage of using optical fiber is that the AOVVBs are generated with all the said features in a controllable way as compared to any of the other methods mentioned. The ability to tune the asymmetry of the AOVVBs will enable tuning of the total angular momentum of the beam. In addition, the beams provide additional degree of freedom in applications involving both phase and polarization gradients to trap and tweeze asymmetric and birefringent particles, hitherto to be explored. Also, these beams can be useful in applications where different amount (or even different direction) of rotation are required at different locations in a beam which is not possible with isotropic vortex beams.

To study and understand the dynamics of vortex beams with angular momentum, optical traps are extensively and exclusively used [5], [6], [7]. However, instead of using an optical trap, one can also assess the OAM of AOVVBs by means of the transverse energy flow (TEF) since the TEF is due to the transverse component of the Poynting vector and beams with transverse component of Poynting vector posses OAM [4], [18], [19]. This leads to the fact that the measurement of the TEF is a useful physical manifestation of the OAM. Also, TEF is a more practical and useful approach to understand the complex nature of wave fields which includes intensity, phase and polarization anisotropy in the beam cross section. The aim of the paper is to controllably generate certain topological defects in the beam using a two-mode optical fiber and study how they affect the transverse energy flow. We have experimentally explored various factors governing the TEF in AOVVBs including the vortex charge, the vortex core anisotropy and the polarization structure around the vortex core to better understand the dynamic evolution of AOVVBs. This is done by tracking the TEF trajectories using the asymmetry in intensity in the beam cross section as the beam focused by a spherical lens passes through the Rayleigh range (RR).