  In the current quest for efficient and experimentally feasible platforms for
implementation of multimode squeezing and entanglement in the continuous
variable regime, we underpin and complement our results on the generation of
versatile multimode entanglement and cluster states in nonlinear waveguide
arrays presented by Barral et al., Phys. Rev. Appl. $\bf{14}$, 044025 (2020).
We present detailed derivations of the equations that describe the propagation
of light through this system, and then we focus on parameter regimes where
these equations can be solved analytically. These analytical solutions build an
intuition for the wide landscape of quantum states that are accessible through
the activation of pumping, coupling and measurement schemes. Furthermore, we
showcase the acquired insights by using one of the identified analytical
solutions to exhibit the generation, optimization and scalability of spatial
linear cluster states.
