  The anisotropy of the electronic transition is a well-known characteristic of
low-dimensional transition-metal dichalcogenides, but their layer-thickness
dependence has not been properly in- vestigated experimentally until now. Yet,
it not only determines the optical properties of these low-dimensional
materials, but also holds the key in revealing the underlying character of the
elec- tronic states involved. Here we used both angle-resolved electron
energy-loss spectroscopy and spectral analysis of angle-integrated spectra to
study the evolution of the anisotropic electronic transition involving the low
energy valence electrons in the freestanding MoS$_2$ layers with different
thicknesses. We are able to demonstrate that the well-known direct gap at 1.8
eV is only excited by the in-plane polarized field while the out-of-plane
polarized optical gap is 2.4$\pm$0.2 eV in monolayer MoS$_2$. This contrasts
with the much smaller anisotropic response found for the indirect gap in the
few-layer MoS$_2$ systems. In addition, we determined that the joint density of
states associated with the indirect gap transition in the multilayer systems
and the corresponding indirect transition in the monolayer case has a
characteristic three-dimensional-like character. We attribute this to the
soft-edge behavior of the confining potential and it is an important factor
when considering the dynamical screening of the electric field at the relevant
excitation energies. Our result provides a logical explanation, for the large
sensitivity of the indirect transition to thickness variation compared with
that for the direct transition, in terms of quantum confinement.
