  We study third-harmonic generation (THG) in an excitonic insulator (EI)
described in a two-band correlated electron model. Employing the perturbative
expansion with respect to the external electric field, we derive the THG
susceptibility taking into account the collective dynamics of the excitonic
order parameter. In the inversion-symmetric EI, the collective order parameter
motion is activated at second order of the external field and its effects arise
in THG. We find three peaks in the THG susceptibility at energies $\hbar \Omega
= \Delta_g/3$, $\Delta_g/2$, and $\Delta_g$, where $\Delta_g$ is the band gap.
While the THG response at $\Delta_g/3$ is caused by bare three-photon
excitation of the independent particle across the band gap, the latter two
peaks involve the motion of the order parameter activated at second order. The
resulting resonant peaks are prominent in particular in the BCS regime but they
become less significant in the BEC regime. We demonstrate that the resonant
peak originated by the collective excitation is observable in the temperature
profile of the THG intensity. Our study suggests that the THG measurement
should be promising for detecting the excitonic collective nature of materials.
