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.
© 2008 Optical Society of America
Original Manuscript: May 23, 2008
Manuscript Accepted: June 6, 2008
Published: July 22, 2008
Miguel A. Bandres, "Accelerating parabolic beams," Opt. Lett. 33, 1678-1680 (2008)