  Using the superlattice (SL) eigenvalues $E_{\mu ,\nu }^{c,v}$ and
eigenfunctions $\varphi_{\mu\nu}^{c,v}(z) $, obtained within the theory of
finite periodic systems, where $\mu$ indicates the subbands and $\nu$ the
intra-subband levels, we calculate optical transitions in SLs and periodic
systems. Based on the eigenfunction parity symmetries, studied in the previous
paper, new symmetry selection rules (SSR) are derived and photoluminescence and
infrared spectra for different types of SLs are calculated. The narrow peaks
clustered in groups that couldn't be explained before in Nakamura's et al. for
blue emitting devices, are now fully understood. Among the various properties
and differences that we discuss in the paper, we notice that many transitions
that were experimentally observed but theoretically forbidden, are now
perfectly possible. Since the number of matrix-elements allowed by the SSR is
generally too large, we devote the second part of this paper to show that one
can obtain the same spectra when, besides the SSR, other leading order
selection rules closely related to intra-subband symmetries are introduced.
These rules reduce the number of matrix evaluations from $\sim n^2$$n_cn_v/2$
to $\sim n$$n_cn_v/2$, i.e., depending on the SL, from about 1000 to 100. We
comment also on a third rule, that picks up the contributions of the surface
and edge states, and show that it reduces further the number of transitions to
$N_s\leq n_cn_v$. With these rules, the main peaks are conserved and their
number practically matches with that of the actual spectrum. Excellent
agreements with experimental results are found.
