After the incredible success of graphene, two-dimensional (2D) semiconductors have become the focus of much theoretical
and experimental investigation. Transition metal dichalcogenides (TMDC), one such class of layered 2D materials,
become the focus of fundamental research and technological applications due to their unique crystal structures, versatile
electronic, optical, mechanical and chemical properties. 2D TMDCs are usually denoted by MX2 , where M represents a
transition metal(Mo, W, Ti etc.) and X represents the chalcogen (S, Se, and Te). This type of semiconductor have also attracted
a great deal of attention in that they exhibit novel and intriguing properties with potentials application in field of transistors,
optoelectronic devices, topological insulators and biosensor. For example, monolayer MoS2 has recently been shown as an
efficient material for low power field effect transistor, phototransistor and biosensor. In this talk, we will present out recent
study on the nonlinear optical and electronic properties of such materials. We demonstrate an effective microspectroscopy
technique by tracing the dispersion of second order nonlinear susceptibility χ(2) in a single atomic layer of tungsten diselenide
(WSe2). Ultra-broadband continuum pulses served as the fundamental beam while its second harmonic spectrum in visible
and ultraviolet (UV) was detected and analyzed with better than 0.3 nm spectral resolution (<2 meV). The obtained results
allowed us to estimate peak second order nonlinearity values that are found to be within 89-104 pm/V range. The resonant
enhancement of the nonlinearity and peak broadening are governed by higher density of states transitions within the split-off
band of the monolayer semiconductor. Sub-structure in the χ(2) dispersion shows a contribution to the nonlinearity due to
exciton transitions with exciton binding energy of 0.181±0.001 meV.