 
Summary: Three wave mixing of airy beams in a quadratic nonlinear photonic crystals
Ido Doleva
and Ady Arie
Department of Physical Electronics, Fleischman Faculty of Engineering, TelAviv University,
TelAviv 69978, Israel
Received 6 September 2010; accepted 25 September 2010; published online 25 October 2010
We study three wave mixing processes of accelerating Airy beams in quadratic nonlinear crystals.
In order to frequency convert these beams, the nonlinear process should be performed with the
Fourier transform of the beam, rather than with the beam itself. This was confirmed experimentally
by frequency doubling of onedimensional and twodimensional Airy beams in a periodically poled
crystal. Sumfrequency or difference frequency process between two accelerating beam enable to set
the acceleration rate and direction of the generated beam. © 2010 American Institute of Physics.
doi:10.1063/1.3504247
In recent years there has been an increasing interest in
Airy beams, i.e., beams whose transverse amplitude depen
dence at origin is defined by the Airy function. These beams
have several unusual features, they are termed "nondiffract
ing" since the infinite Airy wavepacket does not spread as it
propagates and "freely accelerating," since this wavepacket
is centered on a parabolic trajectory in free space.13
