Different types of quadratic, radially symmetric, nonlinear photonic crystals are presented. The modulation of the nonlinear coefficient may be a periodic or an aperiodic function of the radial coordinate, whereas the azimuthal symmetry of the crystal may be either continuous or discrete. Nonlinear interactions within these structures are studied in two orientations, transverse and longitudinal, for which the interacting beams propagate either perpendicularly or in the plane of modulation. We show that radially symmetric structures can phase match multiple arbitrary processes in any direction. We study multiple wavelength three-wave mixing interactions and multiple direction interactions and analyze spatially dependent polarization states of the generated harmonics.
© 2008 Optical Society of America
Original Manuscript: July 23, 2008
Manuscript Accepted: September 23, 2008
Published: December 15, 2008
Noa Voloch, Tal Ellenbogen, and Ady Arie, "Radially symmetric nonlinear photonic crystals," J. Opt. Soc. Am. B 26, 42-49 (2009)