In general, the ubiquitous χ(2) nonlinear directional coupler, where nonlinearity and evanescent coupling are intertwined, is nonintegrable. We rigorously demonstrate that matching excitation to the even or odd fundamental supermodes yields dynamical analytical solutions for any phase matching in a symmetric coupler. We analyze second harmonic generation and optical parametric amplification regimes and study the influence of fundamental field parity and power on the operation of the device. These fundamental solutions are useful to develop applications in classical and quantum fields such as all-optical modulation of light and quantum-states engineering.
Bibliographical noteFunding Information:
We thank K. Belabas for useful discussions. This work was supported by the Agence Nationale de la Recherche through the INQCA project (Grant Agreement No. PN-II-ID-JRPRO-FR-2014-0013 and ANR-14-CE26-0038), the Paris Île-de-France region in the framework of DIM SIRTEQ through the project ENCORE, and the Investissements d'Avenir program (Labex NanoSaclay, Reference ANR-10-LABX-0035).
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