Circular grating coupler for creating focused azimuthally and radially polarized beams

We show a planar optical circuit design that takes light from an input waveguide and creates a focused azimuthally or radially polarized beam emanating from the surface of the substrate. It is implemented in silicon-on-insulator waveguides and does not require any external components to focus the beam. The focal spot size can be subwavelength and is potentially useful for lithography, imaging, optical data storage, optical trapping, optical excitation of molecules, or coupling to optical fibers.     

多艾里光束合成自聚焦光束的实验实现

多光束合成和单光束聚焦一直是提高激光束功率和功率密度的两个重要方法. 结合艾里光束在自由空间中沿弯曲路径传播的特性, 从数值模拟和实验两个方面, 研究了利用多个一维艾里光束合成自由空间自聚焦光束的方法, 并对所得到的模拟和实验结果进行了对比. 采用分步束传播法, 分别模拟了由四个和八个一维艾里光束合成的自聚焦光束在自由空间中的传播过程, 给出了自聚焦光束在传播过程中横向和纵向的光强分布和变化趋势. 采用计算全息和空间光调制器技术实验, 实现了多个一维艾里光束合成的自聚焦光束. 实验中分别测量了四个和八个一维艾里光束合成的自聚焦光束的横向光强分布. 实验结果和理论结果符合得较好. 另外, 为了进一步增大自聚焦光束的功率, 可以增加参与合成的一维艾里光束的数量. 同时, 自聚焦光束的焦距可以通过调整各个一维艾里光束的相对位置进行调节.     

Relation between Airy beams and triple-cusp beams

Airy beams and triple-cusp beams are two kinds of accelerating beams. The propagation characteristics and internal topological structures of accelerating Airy beams are well understood because of the developed mathematical theory about Airy function. However, limited information is available about the optical characteristics of accelerating triple-cusp beams. In this work, the relationship between Airy beams and triple-cusp beams is examined theoretically and experimentally. Results reveal some important optical characteristics of triple-cusp beams based on the optical characteristics of Airy beams. These findings are expected to provide a foundation for future applications of triple-cusp beams.     

Cartesian beams

A new and very general beam solution of the paraxial wave equation in Cartesian coordinates is presented. We call such a field a Cartesian beam. The complex amplitude of the Cartesian beams is described by either the parabolic cylinder functions or the confluent hypergeometric functions, and the beams are characterized by three parameters that are complex in the most general situation. The propagation through complex ABCD optical systems and the conditions for square integration are studied in detail. Applying the general expression of the Cartesian beams, we also derive two new and meaningful beam structures that, to our knowledge, have not yet been reported in the literature. Special cases of the Cartesian beams are the standard, elegant, and generalized Hermite-Gauss beams, the cosine-Gauss beams, the Lorentz beams, and the fractional order beams.     

Ince-Gaussian beams

We demonstrate the existence of the Ince-Gaussian beams that constitute the third complete family of exact and orthogonal solutions of the paraxial wave equation. Their transverse structure is described by the Ince polynomials and has an inherent elliptical symmetry. Ince-Gaussian beams constitute the exact and continuous transition modes between Laguerre and Hermite-Gaussian beams. The propagating characteristics are discussed as well.     

平顶高斯光束和超高斯光束传输特性的相似性

在直角坐标系下对平顶高斯光束和超高斯光束的传输特性的相似性问题作了讨论。研究表明,当有相同的M2因子但束宽不同的平顶高斯光束和超高斯光束通过光阑效应可忽略ABCD光学系统传输时,在广义菲涅尔数F相等处有相似的光强分布。对于有光阑和用球差透镜聚焦的情况,若平顶高斯光束和超高斯光束具有相同的M2因子和束腰宽度,则在相同传输距离处仍可得到相似的光强分布。     

Fourier-space generation of abruptly autofocusing beams and optical bottle beams

We demonstrate analytically and experimentally that a circular abruptly autofocusing (AAF) Airy beam can be generated by Fourier-transforming an appropriately apodized Bessel beam whose radial oscillations are chirped by a cubic phase term. Depending on the relation between the chirp rate and the focal distance of the Fourier-transforming lens, it is possible to generate AAF beams with one or two foci, the latter case leading to the formation of an elegant paraboloid optical bottle.     

平顶高斯光束和超高斯光束传输特性的相似性

 在直角坐标系下对平顶高斯光束和超高斯光束的传输特性的相似性问题作了讨论。研究表明,当有相同的M²因子但束宽不同的平顶高斯光束和超高斯光束通过光阑效应可忽略ABCD光学系统传输时,在广义菲涅尔数F相等处有相似的光强分布。对于有光阑和用球差透镜聚焦的情况,若平顶高斯光束和超高斯光束具有相同的M²因子和束腰宽度,则在相同传输距离处仍可得到相似的光强分布。     

Flat electron beams

Electrons from a source in a solenoidal magnetic field emerge from that field with a characteristic angular momentum. This behavior can be used to produce a flat ribbon-like electron beam with zero thickness (to first order). We show that this can be done using a quadrupole triplet and provide analytical expressions for the focal length of each lens. Solutions can be found over a wide range of practical values of the parameters.     

Superoscillatory diffraction-free beams

It is theoretically shown that by superimposing diffraction-free solutions of the Helmholtz equation, one can construct localized diffraction-free beams that pass through predetermined points on subwavelength distances. These beams are based on the phenomenon of superoscillations and thus do not contain any evanescent waves. The effect of an aperture and noise is examined in specific examples where truncated beams with λ/3 subwavelength features can propagate into the far field.     

Elegant Ince-Gaussian beams

The existence of elegant Ince-Gaussian beams that constitute a third complete family of exact and biorthogonal elegant solutions of the paraxial wave equation is demonstrated. Their transverse structure is described by Ince polynomials with a complex argument. Elegant Ince-Gaussian beams constitute exact and continuous transition modes between elegant Laguerre-Gaussian and elegant Hermite-Gaussian beams. The expansion formulas among the three elegant families are derived.     

Accelerator neutrino beams

Neutrino beams at from high-energy proton accelerators have been instrumental discovery tools in particle physics. Neutrino beams are derived from the decays of charged π$\pi$ and K   mesons, which in turn are created from proton beams striking thick nuclear targets. The precise selection and manipulation of the π/K$\pi /K$ beam control the energy spectrum and type of neutrino beam. This article describes the physics of particle production in a target and manipulation of the particles to derive a neutrino beam, as well as numerous innovations achieved at past experimental facilities.     

Generalized Hermite-Laguerre-Gauss beams

Some classes of structurally stable paraxial light fields depending on a continuous parameter and generalizing standard Hermite-Gauss and Laguerre-Gauss beams are theoretically investigated.     

Accelerating parabolic beams

We demonstrate the existence of accelerating parabolic beams that constitute, together with the Airy beams, the only orthogonal and complete families of solutions of the two-dimensional paraxial wave equation that exhibit the unusual ability to remain diffraction-free and freely accelerate during propagation. Since the accelerating parabolic beams, like the Airy beams, carry infinite energy, we present exact finite-energy accelerating parabolic beams that still retain their unusual features over several diffraction lengths.     

Three-Airy autofocusing beams

We numerically and experimentally demonstrate that a three-Airy autofocusing beam can be generated by superposing three deformed two-dimensional(2 D) Airy beams with a triangle symmetry. When the initial angle between two wings of the deformed 2 D Airy beams increases, such a three-Airy autofocusing beam exhibits that the focusing length decreases and the intensity contrast at the focal point changes. Moreover, after introducing an optical vortex phase, this three-Airy autofocusing beam displays a transverse rotation in propagation. The rotation angle is determined by the topological charge of the vortex and the initial wing angle. Our results may have some potential applications in optical manipulation.