In this article we investigate the Fresnel diffraction characteristics of the hybrid optical element which is a combination of a spiral phase plate (SPP) with topological charge p and a thin lens with focal length f, named the helical lens (HL). As incident a Gaussian laser beam is treated, having its waist a distance from the HL plane and its axis passing through the centre of the HL. It is shown that the SPP introduces a phase singularity of p-th order to the incident beam, while the lens transforms the beam characteristic parameters. The output light beam is analyzed in detail: its characteristic parameters and focusing properties, amplitude and intensity distributions and the vortex rings profiles and radii, at any z distance behind the HL plane, as well as in the near and far field.
A generalized family of scalar structured Gaussian modes including helical-Ince--Gaussian (HIG) and Hermite--Laguerre--Gaussian (HLG) beams is presented with physical insight upon a hybrid topological evolution nature of multi-singularity vortex beams carrying orbital angular momentum (OAM). Considering the physical origins of intrinsic coordinates aberration and the Gouy phase shift, a closed-form expression is derived to characterize the general modes in astigmatic optical systems. Moreover, a graphical representation, Singularities Hybrid Evolution Nature (SHEN) sphere, is proposed to visua…
We find a solution of the wave equation in the paraxial approximation that describes the attosecond pulses with spatiotemporal helical structure in the phase and in the intensity recently generated by means of highly nonlinear optical processes driven by visible or infrared femtosecond vortex pulses. Having a simple analytical model for these helical pulses will greatly facilitate the study of their predicted applications, particularly their interaction with matter after their generation. It also follows from our analysis that the topological charge dispersion inherent to helical pulses allows…
The orbital angular momentum of an optical vortex field is found to twist high viscosity donor material to form a micron-scale 'spin jet'. This unique phenomenon manifests the helical trajectory of the optical vortex. Going beyond both the conventional ink jet and laser induced forward mass transfer (LIFT) patterning technologies, it also offers the formation and ejection of a micron-scale 'spin jet' of the donor material even with an ultrahigh viscosity of 4 Pas. This optical vortex laser induced forward mass transfer (OV-LIFT) patterning technique will enable the development of next generati…
Discretized vortex-producing lenses programmed on low performance spatial light modulators have been used for the generation of optical vortices. However, the description of these vortices has been supported only by numerical simulations. In this work, a general analytical treatment (any topological charge - any discretization levels) for the propagation of a Gaussian beam through a discretized vortex-producing lens is presented. The resulting field could be expressed as a sum of Kummer beams with different amplitudes and topological charges focalized at different planes, whose characteristics…
We present an analytical means of quantifying the fractional accumulation of geometric phase for an optical vortex transiting a cylindrical lens. The standard fiber bundle of a Sphere of Modes is endowed with a Supplementary Product Space at each point so that the beam waists and their positions can be explicitly tracked as functions of lens transit fraction. The method is applied to quantify the accumulation of geometric phase across a single lens as a function of initial state and lens position within the beam. It can be readily applied to a series of lenses as well.
The analytical solution for the propagation of the laser beam with optical vortex through the system of lenses is presented. The optical vortex is introduced into the laser beam (described as Gaussian beam) by spiral phase plate. The solution is general as it holds for the optical vortex of any integer topological charge, the off-axis position of the spiral phase plate and any number of lenses. Some intriguing conclusions are discussed. The higher order vortices are unstable and split under small phase or amplitude disturbance. Nevertheless, we have shown that off-axis higher order vortices ar…
University of Electronic Science and Technology of China（电子科技大学）；Yangtze Delta Region Institute (Huzhou), University of Electronic Science and Technology of China（电子科技大学长三角研究院（湖州））；Nanyang Technological University（南洋理工大学）；Universidad Politécnica de Madrid（马德里理工大学）；Hiroshima University（广岛大学）
In this paper, we present a tailored lens and a tailored reflector in order to reduce the large beam divergence inherent to Orbital Angular Momentum waves (OAM waves-Vortex waves) that are generated by an Uniform Circular Patch Antenna Array (UCA) at 10 GHz. The tailored lens and the tailored reflector are designed by the shape function (5) and (9) around the antenna s center axis, respectively. The tailored lens is compared to UCA without and with conventional lens. The simulated and measured results show a significant improvement when using the tailored lens. Following, a tailored reflector …
As one fundamental property of light, the orbital angular momentum (OAM) of photon has elicited widespread interest. Here, we theoretically demonstrate that the OAM conversion of light without spin state can occur in homogeneous and isotropic medium when a line-variant locally linearly polarized (LVLLP) beam is strongly focused by a high numerical aperture (NA) objective lens. The high-NA objective lens here acts as a modulator that enables the spin-to-orbital OAM conversion of the two components of left and right circular vibrations of the input SDLLP beam spatially separated. Hence, partial …
In the past few years, orbital angular momentum beams have contributed significantly to many applications in the optical-related fields due to their unique phase characteristics. Here, a novel approach about phase-helices structure for Laguerre-Gaussian beams carrying orbital angular momentum is presented. This proposal is based on numerical simulations to track the rotation of each helix in the phase and shows an impact on the rotational speed of the Laguerre-Gaussian phase distribution by using the characteristic of distinguishability of each helix. If the helices in the phase of a vortex ca…
We present a set of paraxial light beams with cylindrical symmetry, smooth and localized transversal profile carrying finite power, that develop intensity singularities when they are focused in a linear medium, such as vacuum. They include beams with orbital angular momentum and with radial polarization, in which case they develop punctual phase and polarization singularities surrounded by infinitely bright rings, along with singular longitudinal fields. In practice, these effects are manifested in focal intensities and spot sizes, vortex bright ring intensities and radii, and strengths of the…
Optical vortices, which have been extensively studied over the last decades, offer an additional degree of freedom useful in many applications, such as optical tweezers and quantum control. Stimulated Brillouin scattering, providing a narrow linewidth and a strong nonlinear response, has been used to realise quasi-continuous wave (CW) lasers. Here, we report stable oscillation of optical vortices and acoustic modes in a Brillouin laser based on chiral photonic crystal fibre, which robustly supports helical Bloch modes (HBMs) that carry circularly-polarized optical vortex and display circular b…
In optics, mode conversion is an elegant way to switch between Hermite Gaussian and Laguerre Gaussian beam profiles and thereby impart orbital angular momentum onto the beam and to create vortices. In optics such vortex beams can be produced in a setup consisting of two identical cylinder lenses. In electron optics, quadrupole lenses can be used for the same purpose. Here we investigate generalized asymmetric designs of a quadrupole mode converter that may be realized within the constraints of existing electron microscopes and can steer the development of dedicated vortex generators for high b…
The applications of vortex beam in biomedical field are always hindered by light scattering of biological tissues. Recently wavefront shaping technology has shown the potential in focusing a structured light field through scattering media. Herein we have proposed a novel theory to describe the field transformation property of the opaque lens. This theory makes it possible to generate foci with specified amplitude and phase profiles by well-designing the incident field. We verify the validity of this theory by experimentally generating doughnut-shaped foci with various topological charges, and …
In this work, an analytic expression is derived for the optical field generated by an off-axis Gaussian beam diffracted by a Discrete Vortex-Producing Lens. With this system, a multifocal arrangement of asymmetric optical vortices is obtained whose topological charge values change with the position along the optical axis. This scheme allows obtaining a principal asymmetric vortex corresponding with the topological charge value of the phase mask and secondary ones with different charges. With the analytical expression, the effects induced by the discretization and misalignment on the irradiance…
Experimental studies of the optical properties of compressible, viscous and rapidly-rotating gas flows (vortices) are presented. Gas vortices can function as optical elements such as lenses or waveguides. The optical properties are determined from direct interferometric phase measurements and beam propagation analysis. Output beams are analyzed in terms of Zernike polynomials for a range of gas flow parameters, including choked flow. The absolute radial gas density distribution is measured and a technique for adjusting it is demonstrated.
We demonstrate, both analytically and experimentally, free-space pin-like optical vortex beams (POVBs).Such angular-momentum-carrying beams feature tunable peak intensity and undergo robust anti-diffracting propagation, realized by judiciously modulating both the amplitude and the phase profile of a standard laser beam. Specifically, they are generated by superimposing a radially-symmetric power-law phase on a helical phase structure, which allows the inclusion of an orbital angular momentum term to the POVBs. During propagation in free-space, these POVBs initially exhibit autofocusing dynamic…
We propose a twisted plasma accelerator capable of generating relativistic electron vortex beams with helical current profiles. The angular momentum of these vortex bunches is quantized, dominates their transverse motion, and results in spiraling particle trajectories around the twisted wakefield. We focus on a laser wakefield acceleration scenario, driven by a laser beam with a helical spatiotemporal intensity profile, also known as a light spring. We find that these light springs can rotate as they excite the twisted plasma wakefield, providing a new mechanism to control the twisted wakefiel…
Pancharatnam-Berry phase optical elements for wavefront shaping in the visible domain: switchable helical modes generation
本文报道了Pancharatnam-Berry位相光学元件的研制[Z.博姆宗湾Biener，V. Kleiner，and E. Hasman，Opt. Lett. \textbf{27}，1141（2002）]，用于基于图案化液晶技术在可见光谱域中工作的波前整形。该器件产生可见光的螺旋模式，通过控制输入圆偏振的旋向性，可以在相反的螺旋度之间进行电光切换。通过级联这种方法，可以实现多个波前螺旋度之间的快速切换，具有潜在的应用于多态光学信息编码。本文所提出的方法可以推广到其他偏振控制的波前整形器件，如可切换透镜、分束器和全息元件。
In light optics, beams with orbital angular momentum (OAM) can be produced by employing a properly-tuned two-cylinder-lens arrangement, also called $π$/2 mode converter. It is not possible to convey this concept directly to the beam in an electron microscope due to the non-existence of cylinder lenses in commercial transmission electron microscope (TEM). A viable work-around are readily-available electron optical elements in the form of quadrupole lenses. In a proof-of-principle experiment in 2012, it has been shown that a single quadrupole in combination with a Hilbert phase plate produces a …
The twin beam vortex interferometer with phase-conjugating mirror is analyzed in rotating reference frame.Circular motion of the interference pattern occurs due to exchange of the angular momenta between photons and interferometer. Using the concept of the $ideal$ phase-conjugating mirror it is shown that motion of the helical interference pattern of the interacting vortex photons with topological charge $\ell$ may be used for the detection of the slow rotations. The higher density of interference fringes may improve the sensitivity by factor containing $2 \ell$ compared to the conventional Mi…
