Bandres Miguel A, Gutiérrez-Vega Julio C, Chávez-Cerda Sabino
Photonics and Mathematical Optics Group, Tecnológico de Monterrey, Monterrey, N.L. 64849, Mexico.
Opt Lett. 2004 Jan 1;29(1):44-6. doi: 10.1364/ol.29.000044.
We demonstrate the existence of parabolic beams that constitute the last member of the family of fundamental nondiffracting wave fields and determine their associated angular spectrum. Their transverse structure is described by parabolic cylinder functions, and contrary to Bessel or Mathieu beams their eigenvalue spectrum is continuous. Any nondiffracting beam can be constructed as a superposition of parabolic beams, since they form a complete orthogonal set of solutions of the Helmholtz equation. A novel class of traveling parabolic waves is also introduced for the first time.
我们证明了抛物光束的存在，它构成了基本无衍射波场家族的最后一个成员，并确定了其相关的角谱。它们的横向结构由抛物柱面函数描述，与贝塞尔光束或马蒂厄光束不同，它们的本征值谱是连续的。任何无衍射光束都可以构造为抛物光束的叠加，因为它们形成了亥姆霍兹方程解的一个完备正交集。还首次引入了一类新型的行波抛物波。
