  We investigate, based on the coupled dipole model, collective properties of
dense Sr ensembles trapped in a three-dimensional (3D) optical lattice in the
presence of dipole-dipole interactions induced on the
5$s5p^{3}$P$_{0}\to5s4d^{3}$D$_{1}$ transition. Our results reveal that the
collective scattering properties, such as the scattered light intensity,
frequency shift and linewidth, strongly depend on the interatomic distance and
the atom number in the lattice. Moreover, the emission intensity is strongly
dependent on the atomic distribution in lattices, the laser polarization and
the detection position. The results not only offer the understanding of
collective behaviors of lattice-trapped ensembles with an atom number
equivalent to the experimental scale, but also provide an excellent platform
for exploring many-body physics, thereby, opening a new window for applications
like quantum information processing and quantum simulation.
