  Higgs-boson pair production is well known being capable to probe the
trilinear self-coupling of the Higgs boson, which is one of the important
ingredients of the Higgs sector itself. Pair production then depends on the
top-quark Yukawa coupling $g_t^{S,P}$, Higgs trilinear coupling $\lambda_{3H}$,
and a possible dim-5 contact-type $ttHH$ coupling $g_{tt}^{S,P}$, which may
appear in some higher representations of the Higgs sector. We take into account
the possibility that the top-Yukawa and the $ttHH$ couplings involved can be CP
violating. We calculate the cross sections and the interference terms as
coefficients of the square or the 4th power of each coupling $(g_t^{S,P},
\lambda_{3H}, g_{tt}^{S,P})$ at various stages of cuts, such that the desired
cross section under various cuts can be obtained by simply inputing the
couplings. We employ the $H H \to \gamma\gamma b \bar b$ decay mode of the
Higgs-boson pair to investigate the possibility of disentangle the triangle
diagram from the box digram so as to have a clean probe of the trilinear
coupling at the LHC. We found that the angular separation between the $b$ and
$\bar b$ and that between the two photons is useful. We obtain the sensitivity
reach of each pair of couplings at the 14 TeV LHC and the future 100 TeV pp
machine. Finally, we also comment on using the $b\bar b \tau^+ \tau^-$ decay
mode in Appendix.
