  The nonlinear absorption of two-dimensional molybdenum disulfide was analyzed
using the Z-scan technique. Sample size corresponding to a number of layer
determines the band gap in the materials which play the key role for
nonlinearity. Exciton dipole transition from ground state to excited state for
monolayer and bilayer/multilayer is determined by the excitation source, ESA
and GSA values. If the band gap is wider than the excitation source, two-photon
excitation process is dominant which requires the larger ESA than GSA. For
narrower bandgap, one-photon excitation is favorable because of the larger GSA
than ESA. In addition, defects, the temperature may alter the band gap.
Therefore, the transition from RSA to SA and vice versa is determined by the
number of layers in materials, temperature, and defects for a given excitation
energy.
