Using the multiple-scale approach, we derive an analytical expression for the conversion efficiency of second-harmonic generation (SHG) in a one-dimensional photonic crystal. The results, obtained in the undepleted pump limit for the continuous-wave case, allow us to describe the role played by the feedback and the dispersion introduced by the periodic structure and hence to optimize the SHG process. Numerical simulations are then used to explore the pulsed pump case, proving that the obtained results retain their validity up to a pump field bandwidth of less than approximately 12% of the stack transmission bandwidth. Shorter pulses experience both a reduced conversion efficiency and shape distortions.
© 2003 Optical Society of America
(190.0190) Nonlinear optics : Nonlinear optics
(190.2620) Nonlinear optics : Harmonic generation and mixing
(190.4360) Nonlinear optics : Nonlinear optics, devices
(230.4170) Optical devices : Multilayers
Costantino De Angelis, Gianfranco Nalesso, Daniele Modotto, Michele Midrio, Andrea Locatelli, and J. Stewart Aitchison, "Multiple-scale coupled-mode theory for second-harmonic generation in one-dimensional periodic structures," J. Opt. Soc. Am. B 20, 1853-1865 (2003)