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.
© 2004 Optical Society of America
(050.1960) Diffraction and gratings : Diffraction theory
(140.3300) Lasers and laser optics : Laser beam shaping
(260.1960) Physical optics : Diffraction theory
(350.5500) Other areas of optics : Propagation
Miguel A. Bandres, Julio C. Gutiérrez-Vega, and Sabino Chávez-Cerda, "Parabolic nondiffracting optical wave fields," Opt. Lett. 29, 44-46 (2004)