  This paper studies the interaction of laser-driven $\gamma$-photons and high
energy charged particles with high-Z targets through Monte-Carlo simulations.
The interacting particles are taken from particle-in-cell simulations of the
interaction of a tightly-focused ultraintense laser pulse with a titanium
target. Lead is chosen as the secondary high-Z target owing to its high cross
section of the giant dipole resonance and electron-positron pair production.
The results reveal an ultra-short ultra-relativistic collimated positron
population and their energy spectra, angular distribution, and temporal profile
are found. We investigate the target thickness dependence of the resulting
total numbers and total kinetic energies of various particle species emitted
from the lead target irradiated with laser-generated $\gamma$-photons and
charged particles separately. We plot the charts of residual high-Z nuclides
generated by irradiation of the lead target. Owing to the short pulse duration,
the $\gamma$-photon, electron-positron, and neutron sources can find
applications in material science, nuclear physics, laboratory astrophysics, and
as injectors in laser-based accelerators of charged particles.
