Abstract

We find an analytic expression for second-harmonic conversion efficiency (both forward and backward) in generic, 1D, finite, multilayered structures, where the respective roles of effective phase-matching conditions and field overlap are clearly identified. Our approach places the notions of effective index and effective phase-matching conditions on a more solid theoretical ground and clarifies the meaning and the limits of applicability of these concepts. We also define a coherence length for the process in an unambiguous way and point out similarities and differences with the coherence length that is usually defined for bulk materials. Finally, we address the role played by absorption and provide numerical examples that confirm the analytical results found.

© 2007 Optical Society of America

Non-phase-matched enhancement of second-harmonic generation in multilayer nonlinear structures with internal reflections

Marco Centini, Giuseppe D’Aguanno, Letizia Sciscione, Concita Sibilia, Mario Bertolotti, Michael Scalora, and Mark J. Bloemer
Opt. Lett. 29(16) 1924-1926 (2004)

Generalized coupled-mode theory for χ⁽²⁾ interactions in finite multilayered structures

Giuseppe D’Aguanno, Marco Centini, Michael Scalora, Concita Sibilia, Mario Bertolotti, Mark J. Bloemer, and Charles M. Bowden
J. Opt. Soc. Am. B 19(9) 2111-2121 (2002)

Application of transfer matrix method to second-harmonic generation in nonlinear photonic bandgap structures: oblique incidence

Han Li, Joseph W. Haus, and Partha P. Banerjee
J. Opt. Soc. Am. B 32(7) 1456-1462 (2015)

Enhanced Čerenkov second-harmonic generation in a planar nonlinear waveguide that reproduces a one-dimensional photonic bandgap structure

D. Pezzetta, C. Sibilia, M. Bertolotti, R. Ramponi, R. Osellame, M. Marangoni, J. W. Haus, M. Scalora, M. J. Bloemer, and C. M. Bowden
J. Opt. Soc. Am. B 19(9) 2102-2110 (2002)

Multiple-scale coupled-mode theory for second-harmonic generation in one-dimensional periodic structures

Costantino De Angelis, Gianfranco Nalesso, Daniele Modotto, Michele Midrio, Andrea Locatelli, and J. Stewart Aitchison
J. Opt. Soc. Am. B 20(9) 1853-1865 (2003)