  We present a detailed calculation of the linear and nonlinear optical
response of four types of monolayer Two-Dimensional (2D) Transition-Metal
Dichalcogenides (TMDCs), having the formula $\textrm{MX}_2$ with M=Mo,W and
X=S,Se. The calculations are based on 6-band tight-binding model of TMDCs, and
then performing a semiclassical perturbation analysis of response functions. We
numerically calculate the linear $\chi_{\mu\nu}^{(1)}(-\omega;\omega)$ and
nonlinear surface susceptibility tensors $\chi_{\mu\nu\zeta\eta}^{(3)}
(-\omega_\Sigma;\omega_r,\omega_s,\omega_t)$ with
$\omega_\Sigma=\omega_r+\omega_s+\omega_t$. Both non-degenerate and degenerate
cases are studied for third-harmonic generation and nonlinear refractive index,
respectively. Computational results obtained \textit{with no external fitting
parameters} are discussed regarding two recent reported experiments on ${\rm
MoS}_2$, and thus we can confirm the extraordinarily strong optical
nonlinearity of TMDCs. As a possible application, we demonstrate generation of
a $\frac{\pi}{4}-$rotated squeezed state by means of nonlinear response of
TMDCs, in a silica micro-disk resonator covered with the 2D material. Our
proposed method will enable accurate calculations of nonlinear optical
response, such as four-wave mixing and high-harmonic generation in 2D materials
and their heterostructures, thus enabling study of novel functionalities of 2D
photonic integrated circuits.
