Two types of radially symmetric three-dimensional nonlinear photonic crystals with the cylindrical structure and the egglike structure are proposed, from which the conical and the spherical quadratic harmonic waves can be produced, respectively, by three-dimensional quasi-phase matching. First, the cylindrical structures with periodic and aperiodic modulations of the nonlinear coefficient are both studied, showing their significant advantages compared to the corresponding two-dimensional structures. The dependencies of the transverse and the longitudinal phase-matching periods on harmonic propagating directions are also calculated and analyzed. Then, the egglike structure is designed by programming and the distribution of reciprocal vectors is presented, indicating its ability to generate the spherical harmonic as a point light source. The investigation of the intensity distribution on the spherical wavefront is also performed, showing its strong dependence on the harmonic polarization and the quadratic nonlinear coefficients.
© 2011 Optical Society of America
Original Manuscript: September 7, 2010
Revised Manuscript: November 12, 2010
Manuscript Accepted: November 16, 2010
Published: January 10, 2011
Junjie Chen and Xianfeng Chen, "Generation of conical and spherical second harmonics in three-dimensional nonlinear photonic crystals with radial symmetry," J. Opt. Soc. Am. B 28, 241-246 (2011)