  In this study, the linear, third-order nonlinear and total absorption
coefficients (ACs) of multi-layered quantum dot (MLQD) and multi-layered
quantum anti-dot (MLQAD) with a hydrogenic impurity are calculated. The
analytical and numerical solutions of Schr\"{o}dinger equation for both MLQD
and MLQAD, within the effective mass approximation and dielectric continuum
model, are obtained. As our numerical results indicate, an increase in the
optical intensity changes the total AC considerably, but the intensity range
that leads to these changes is different for MLQAD and MLQD. It is observed
that by changing the incident photon energy, the AC curves corresponding to
MLQAD and MLQD are of different shapes and behaviors. The peak heights of AC
curves corresponding to MLQAD are strongly affected by changing the core
antidot radius and the shell thickness values, however in these cases no
considerable changes are observed in peak heights of MLQD. Furthermore, in
contrast to MLQAD, the photon energies corresponding to total AC peaks of MLQD
are more affected by changing the confining potentials (CPs).
