  In this paper, the optimal solution of effective nonlinear coefficient of
quasi-phase-matching (QPM) crystals for coupled third harmonic generation
(CTHG) was numerically investigated. The effective nonlinear coefficient of
CTHG was converted to an Ising model for optimizing domain length distributions
of aperiodically poled lithium niobate (APPLN) crystals with lengths as 0.5 mm
and 1 mm, and fundamental wavelengths ranging from 1000 nm to 6000 nm. A method
for reconstructing crystal domain poling weight curve of coupled nonlinear
processes was also proposed, which demonstrated the optimal conversion ratio
between two coupled nonlinear processes at each place along the crystal. In
addition, by applying the semidefinite programming, the upper bound on the
effective nonlinear coefficients deff for different fundamental wavelengths
were calculated. The research can be extended to any coupled dual \c{hi}(2)
process and will help us to understand better the dynamics of coupled nonlinear
interactions based on QPM crystals.
