  We study the formation and propagation of chirped elliptic and solitary waves
in cubic-quintic nonlinear Helmholtz (CQNLH) equation. This system describes
nonparaxial pulse propagation in a planar waveguide with Kerr-like and quintic
nonlinearities along with spatial dispersion originating from the nonparaxial
effect that becomes dominant when the conventional slowly varying envelope
approximation (SVEA) fails. We first carry out the modulational instability
(MI) analysis of a plane wave in this system by employing the linear stability
analysis and investigate the influence of different physical parameters on the
MI gain spectra. In particular, we show the nonparaxial parameter suppresses
the conventional MI gain spectrum and also leads to a nontrivial monotonic
increase in the gain spectrum near the tails of the conventional MI band, a
qualitatively distinct behaviour from the standard nonlinear Schr\"odinger
(NLS) system. We then study the MI dynamics by direct numerical simulations
which demonstrate production of ultra-short nonparaxial pulse trains with
internal oscillations and slight distortions at the wings. Following the MI
dynamics, we obtain exact elliptic and solitary wave solutions using the
integration method by considering physically interesting chirped traveling wave
ansatz. In particular, we show that the system features intriguing chirped
anti-dark, bright, gray and dark solitary waves depending upon the nature of
nonlinearities. We also show that the chirping is inversely proportional to the
intensity of the optical wave. Especially, the bright and dark solitary waves
exhibit unusual chirping behaviour which will have applications in nonlinear
pulse compression process.
