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Symmetry-based analytical solutions to the χ^{(2)} nonlinear directional coupler
David Barral1, Kamel Bencheikh1, Peter J Olver2
1Centre de Nanosciences et de Nanotechnologies C2N, CNRS, Université Paris-Saclay, 10 Boulevard Thomas Gobert, 91120 Palaiseau, France.
Abstract:
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.
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