D'Aguanno, G.Centini, M.Scalora, M.Sibilia, C.Bertolotti, M.Bowden, Ch.M.Bloemer, M.J.2020-05-182020-05-182003D'Aguanno, G.; et al.; Quadratic Interactions in Finite, One-Dimensional, Photonic Band Gap Structures with Deep Gratings: beyond the Undepleted Pump Regime; Proceedings of the International Workshop NOA'02, Lukecin 2002; http://przyrbwn.icm.edu.pl/APP/ABSTR/103/a103-23-249.htmlhttps://doi.org/10.12693/APhysPolA.103.249http://hdl.handle.net/11603/18665Proceedings of the International Workshop NOA'02, Lukecin 2002;We theoretically study quadratic interactions in finite, one-dimensional, photonic band gap structures with deep gratings, under strong pumping and global phase matching conditions. For second harmonic generation, we find that above a certain input intensity a dynamics reminiscent of a competitive, multi-wave mixing process takes hold: the pump field is mostly reflected, revealing a novel type of optical limiting behavior, while forward and backward generation is generally balanced. We also study the case of parametric down-conversion, where an intense second harmonic signal is injected in order to control a much weaker fundamental beam. Our results reveal the onset of a new process that has no counterpart in bulk materials: both transmission and reflection display an unexpected, unusual, resonance-like effect as functions of input second harmonic power.14 pagesen-USThis item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author.Public Domain Mark 1.0This work was written as part of one of the author's official duties as an Employee of the United States Government and is therefore a work of the United States Government. In accordance with 17 U.S.C. 105, no copyright protection is available for such works under U.S. Law.Text