Propagation-invariant vectorial Bessel beams obtained by use of quantized Pancharatnam-Berry phase optical elements

Propagation-invariant vectorial Bessel beams with linearly polarized axial symmetry based on quantized Pancharatnam-Berry phase optical elements are described. The geometric phase is formed through the use of discrete computer-generated space-variant subwavelength dielectric gratings. We have verified the polarization properties of our elements for laser radiation at 10.6-microm wavelength and also demonstrated propagation-invariant, controlled rotation of a propeller-shaped intensity pattern through the simple rotation of a polarizer.     

Recording of geometric phase elements based on liquid crystal polymers

A technique is developed for recording the centrally-symmetric liquid crystal phase plates with the anisotropic orientation of molecules providing a smooth change of the optical axis in a thin film of liquid crystal polymer. The technique enables one to record the elements with the cylindrically-symmetric and planar-symmetric distributions. Such structures can be used to develop the optical elements with the new functional possibilities. Using the developed techniques, the polarization-sensitive Fresnel lens is realized which is functioning either as a collecting or as a scattering lens for the light beams with the orthogonal circular polarizations.     

Optical properties of polarization-dependent geometric phase elements with partially polarized light

The behavior of geometric phase elements illuminated with partially polarized monochromatic beams is investigated both theoretically and experimentally. The element discussed in this paper is composed of wave plates with π-retardation and a space-variant orientation angle. We found that a beam emerging from such an element comprises two polarization orders; right-and left-handed circularly polarized states with conjugate geometric phase modification. This phase equals twice the orientation angle of the space-variant wave plate comprising the element. Apart from the two polarization orders, the emerging beam coherence polarization matrix includes a “vectorial interference matrix” which contains information concerning the correlation between the two orthogonal, circularly polarized portions of the incident beam. In this paper we measure this correlation by a simple interference experiment. In addition, we found that the equivalent mutual intensity of the emerging beam is modulated according to the geometric phase induced by the element. Other interesting phenomena concerning propagation will be discussed theoretically and demonstrated experimentally. The experiment made use of a spherical geometric phase element that was realized by use of a space-variant subwavelength grating illuminated with CO₂ laser radiation of 10.6 μm wavelength.     

Two-dimensional vectorial photonic crystals formed in azo-dye-doped liquid crystals

A 2D, square lattice, vectorial photonic crystal is formed by vectorial holography using an azo-dye-doped liquid-crystal material. Four coherent beams are interfered to generate a highly stable, switchable polarization holography structure. The formation of the vectorial lattice by the liquid-crystal molecular orientation is confirmed by diffraction pattern and polarization microscopy analysis. Simulations of the alignment and diffraction pattern are in good agreement with the experimental results. Polarization sensitive diffraction behavior is also consistent with the Kakichashvili model.     

Modeling and computation of two phase geometric biomembranes using surface finite elements

Biomembranes consisting of multiple lipids may involve phase separation phenomena leading to coexisting domains of different lipid compositions. The modeling of such biomembranes involves an elastic or bending energy together with a line energy associated with the phase interfaces. This leads to a free boundary problem for the phase interface on the unknown equilibrium surface which minimizes an energy functional subject to volume and area constraints. In this paper we propose a new computational tool for computing equilibria based on an L² relaxation flow for the total energy in which the line energy is approximated by a surface Ginzburg–Landau phase field functional. The relaxation dynamics couple a nonlinear fourth order geometric evolution equation of Willmore flow type for the membrane with a surface Allen–Cahn equation describing the lateral decomposition. A novel system is derived involving second order elliptic operators where the field variables are the positions of material points of the surface, the mean curvature vector and the surface phase field function. The resulting variational formulation uses H¹ spaces, and we employ triangulated surfaces and H¹ conforming quadratic surface finite elements for approximating solutions. Together with a semi-implicit time discretization of the evolution equations an iterative scheme is obtained essentially requiring linear solvers only. Numerical experiments are presented which exhibit convergence and the power of this new method for two component geometric biomembranes by computing equilibria such as dumbbells, discocytes and starfishes with lateral phase separation.     

Vectorial vortex mode transformation for a hollow waveguide using Pancharatnam-Berry phase optical elements

Transformation and inverse transformation between a free-space linearly polarized beam and the vectorial vortex mode of a circular hollow waveguide by use of Pancharatnam-Berry phase optical elements is proposed. Demonstration was achieved by fabricating GaAs subwavelength gratings and utilizing a 300 microm diameter hollow metallic waveguide for 10.6 microm wavelength CO(2) laser radiation. The mode transformations and the excitation of a single vectorial mode inside the hollow waveguide were verified by full polarization measurements. In addition, the inverse mode transformation of the single vectorial mode excitation in the waveguide enabled us to experimentally obtain a linearly polarized bright spot with a high central lobe.     

Generation of the determined vectorial vortex beams by use of an achromatic axially symmetric waveplate

Optical Review - We review the generation of the determined vectorial vortex beams in the terahertz (THz) beams at frequencies of 0.16 and 0.36 THz, and intense middle infrared pulsed beam at...     

Nulling interferometry by use of geometric phase

Nulling interferometry is a method of detecting a faint source near a bright one, in which destructive interference is realized for the light from the bright source. A nulling interferometer that makes use of geometric phase (Pancharatnam phase) is proposed. An experimental setup is constructed to simulate a stellar interferometer with geometric-phase modulation. We attained extinction of 6 x 10(-5) in white light.     

Polychromatic optical parametric generation by simultaneous phase matching over a large spectral bandwidth

The parametric generation of broad spectral bandwidths by the use of suitable phase-matching geometries is reported. Greater than 100-nm simultaneous bandwidth in the visible is generated in a collimated signal beam from a novel, noncollinear phase-matching geometry in a beta-barium borate optical parametric oscillator, which is pumped by the collimated output of a Q -switched and frequency-tripled Nd:YAG laser. Dispersive cavity tuning of the optical parametric oscillator by use of a rotatable Littrow-mounted grating, with a static crystal and pump configuration, is also described. A tunable bandwidth of >100 nm is also demonstrated.     

Electrically tunable generation of vectorial vortex beams with micro-patterned liquid crystal structures

We develop a new method for smooth and continuous space-variant alignment of the liquid crystal medium in micro-patterned structures, which is based on a radial micro-structured pattern of polymeric ribbons exhibiting out-of-plane orientation with respect to the ITO-coated glass plates. Thanks to the broad range of electrical tunability of the optical retardation for the micro-patterned liquid crystal structures, transformation of the fundamental Gaussian beam into different types of specific beams, including generalized cylindrical vector beams, vortex beams, and vectorial vortex beams, is efficiently demonstrated.     

共轴双涡旋声束形成离轴多涡旋的定位

涡旋声束具有螺旋的相位波前,中轴线上形成声强为零的相位奇点,其所携带的轨道角动量在粒子操控领域有着广阔的应用前景。传统声涡旋只在传播轴线上形成一个拓扑荷可控的涡旋波束,这限制了声涡旋的应用灵活性。基于环形点声源阵列和相位编码技术,利用奇偶声源分别产生共轴双涡旋声束的声场叠加,在传播截面上形成了具有中心涡旋和子涡旋的离轴多涡旋声场;研究了双涡旋拓扑参数对离轴涡旋的个数、位置及拓扑荷的影响,基于声涡旋的径向声压和相位分布,确定了离轴涡旋的离轴半径,并结合声源位置推导子涡旋中心方位角的计算公式,实现离轴涡旋的精确定位。本研究突破了沿轴分布的涡旋声场只能形成单点涡旋势阱的操控局限,为利用离轴多涡旋实现多点粒子捕获提供了理论依据,促进涡旋声场在精确粒子操控和传输方面的高效应用。     

共轴双涡旋声束形成离轴多涡旋的定位

涡旋声束具有螺旋的相位波前,中轴线上形成声强为零的相位奇点,其所携带的轨道角动量在粒子操控领域有着广阔的应用前景。传统声涡旋只在传播轴线上形成一个拓扑荷可控的涡旋波束,这限制了声涡旋的应用灵活性。基于环形点声源阵列和相位编码技术,利用奇偶声源分别产生共轴双涡旋声束的声场叠加,在传播截面上形成了具有中心涡旋和子涡旋的离轴多涡旋声场;研究了双涡旋拓扑参数对离轴涡旋的个数、位置及拓扑荷的影响,基于声涡旋的径向声压和相位分布,确定了离轴涡旋的离轴半径,并结合声源位置推导子涡旋中心方位角的计算公式,实现离轴涡旋的精确定位。本研究突破了沿轴分布的涡旋声场只能形成单点涡旋势阱的操控局限,为利用离轴多涡旋实现多点粒子捕获提供了理论依据,促进涡旋声场在精确粒子操控和传输方面的高效应用。     

多个子玻色-爱因斯坦凝聚气体膨胀叠加形成的量子涡旋现象研究

基于二维模型,研究了多个子玻色-爱因斯坦凝聚气体在谐振势阱内膨胀叠加形成的量子涡旋现象.运用传播子方法,分析了对称分布的三个子玻色-爱因斯坦凝聚气体膨胀叠加形成宏观量子涡旋的物理过程,得到量子涡旋随时间演化的规律;发现涡旋核分布在谐振势阱内出现振荡;涡旋与反涡旋随时间演化而相互转变,并对这些现象进行了物理分析.     

用四台阶相位板产生涡旋光束

涡旋光束的产生与应用是当前光学领域的研究热点. 利用傅里叶级数展开法分析了四台阶相位板的相位结构, 发现四台阶相位板可看作是由一系列不同拓扑荷数的螺旋相位板所组成, 用线偏振光直接照射相位板时, 将产生多级衍射光波, 各级衍射光均为不同拓扑荷数的涡旋光波, 由于多级衍射光波间的干涉导致光强分布偏离轴对称分布, 因而与涡旋光波有一定差距. 在此基础上, 提出了用四台阶相位板产生涡旋光束的新方案, 借助于Mach-Zehnder 干涉仪光路, 两块四台阶相位板产生的衍射光干涉叠加, 通过调节干涉仪光路的相位差, 使一部分衍射级干涉相消, 另一部分衍射级干涉相长, 相互加强, 从而把线偏振光转换为涡旋光束. 数值模拟计算了几种周期数不同的四台阶相位板衍射光强和角动量分布, 并与螺旋相位板进行比较, 证明用简单的四台阶相位板不仅能够获得与用螺旋相位板相同的涡旋光束, 而且可以用周期数较小的四台阶相位板产生具有大拓扑荷数的涡旋光束, 降低了制作相位板的难度.     

Distortion correction by phase conjugation of nonparaxial vectorial beams: a general proof

We present a general proof of the distortion-correction theorem, that is, of the possibility of correcting wave distortion by the technique of optical phase conjugation. The proof is valid for fully vectorial nonparaxial propagation in the presence of a tensorial refractive-index perturbation and backscattering of the incident field.     

Fractional vortex dipole phase filter

In spatial filtering experiments, the use of vortex phase filters plays an important role in realizing isotropic edge enhancement. In this paper, we report the use of a vortex dipole phase filter in spatial filtering. A dipole made of fractional vortices is used, and its filtering characteristics are studied. It is observed that the filter performance can be tuned by varying the distance of separation between the vortices of the dipole to achieve better contrast and output noise suppression, and when this distance tends to infinity, the filter performs like a 1-D Hilbert mask. Experimental and simulation results are presented.     

A millimeter-wave geometric phase interferometer

A millimeter-wave interferometer operating purely on the geometric phase is presented. Like its optical counterpart described by Hariharan and Roy, this system uses two circular polarizers with a half-wave section in between. The geometric phase of each signal is determined by the orientation of the half-wave section.     

Flow field measurements of leading-edge separation vortex formed on a delta wing with vortex flaps

Wind tunnel tests are carried out using a 70 delta wing model with leading-edge vortex flaps. The structure of the leading-edge separation vortex over the leading-edge vortex flap is measured by use of a 5 holes pitot probe, surface pressure measurement technique and oil flow visualization technique. Separation vortices formed on a plain delta wing, on a vortex flap and inboard the vortex flap hinge line are clearly visualized. Results indicate that the flow around the vortex flaps is classified into several different cross flow patterns. The streamwise flap deflection angle is defined to discuss the vortex flap performance. The optimum lift to drag ratio is attained when the amount of the wing angle of attack is not far different from that of the streamwise flap deflection angle, as long as the vortex flap is deflected modestly.