  Susskind-Glogower coherent states, whose Fock expansion coefficients include
Bessel functions, have recently attracted considerable attention for their
optical properties. Nevertheless, identity resolution is still an open
question, which is an essential mathematical property that defines an
overcomplete basis in the Fock space and allows a coherent state quantization
map. In this regard, the modified Susskind-Glogower coherent states have been
introduced as an alternative family of states that resolve the identity
resolution. In the present manuscript, the quantization map related to the
modified Susskind-Glogower coherent states is exploited, which naturally leads
to a particular representation of the $\mathfrak{su}(1,1)$ Lie algebra in its
discrete series. The latter provides evidence about further generalizations of
coherent states, built from the Susskind-Glogower ones by extending the indexes
of the Bessel functions of the first kind and, alternatively, by employing the
modified Bessel functions of the second kind. In this form, the new families of
Susskind-Glogower-I and Susskind-Glogower-II coherent states are introduced.
The corresponding quantization maps are constructed so that they lead to
general representations of elements of the $\mathfrak{su}(1,1)$ and
$\mathfrak{su}(2)$ Lie algebras as generators of the SU$(1,1)$ and SU$(2)$
unitary irreducible representations respectively. For completeness, the optical
properties related to the new families of coherent states are explored and
compared with respect to some well-known optical states.
