  The photoprodution of doubly heavy baryon ($\Xi_{cc},\Xi_{bb},\Xi_{bc}$) is
investigated in the context of future high-energy and high-luminosity $e^+e^-$
colliders. The study incorporates two sources of initial photons, namely the
LBS photon and the WWA photon. Alongside the direct photoproduction via the
sub-process $\gamma+\gamma \rightarrow \Xi_{QQ^{'}} +\bar{Q}+\bar{Q^{'}}$
($Q^{(')}=c,b$), the resolved photoproduction channels are specifically
considered, encompassing the sub-processes $\gamma + g \rightarrow \Xi_{QQ^{'}}
+\bar{Q}+\bar{Q^{'}}$, $g + g \rightarrow \Xi_{QQ^{'}} +\bar{Q}+\bar{Q^{'}}$,
and $q + \bar{q} \rightarrow \Xi_{QQ^{'}} +\bar{Q}+\bar{Q^{'}}$ with $q=u,d,s$.
Within the framework of non-relativistic QCD, two $(cc(bb))$-diquark
configurations, ${}_{\bar{\textbf{3}}}[{}^3S_1]$ and
${}_{\textbf{6}}[{}^1S_0]$, and four $(bc)$-diquark configurations,
$(bc)_{\bar{\textbf{3}}}[{}^3S_1]$, $(bc)_{\textbf{6}}[{}^1S_0]$,
$(bc)_{\textbf{6}}[{}^3S_1]$ and $(bc)_{\bar{\textbf{3}}}[{}^1S_0]$, are
considered in the calculations. Numerical results show that the single resolved
photoproduction processes provide dominant contributions under certain
collision configuration. At the future $e^+e^-$ colliders, the doubly heavy
baryon generated via the photoproduction mechanism is promisingly observable
and can be well studied.
