  In this article, we demonstrate dense resonant peaks in the transmission
spectra of a rectangular waveguide inscribed with a stretched moir\'e pattern.
We investigated an array of silicon waveguides with sinusoidally modulated
cladding of varying depth of modulation. The investigation reveals a critical
depth of modulation that splits the geometries into weakly scattering and
strongly scattering regimes. Geometries in the weakly scattering regime
resemble Bragg waveguides with shallow cladding modulation, whereas in the
strongly scattering regime, the geometries resemble chains of isolated
dielectric particles. The guided mode photonic bandgap for geometries in the
strongly scattering regime is much larger than that of the weakly scattering
regime. By inscribing stretched moir\'e patterns in the strongly scattering
regime, we show that a large number of sharp peaks can be created in the
transmission spectra of the waveguide. All periodic stretched moir\'e patterns
can be identified with an R parameter. The R parameter indicates the ratio of
the supercell period of the stretched system to the unstretched system. Our
empirical study shows that the density of peaks linearly increases with R. The
multiple resonance peaks evolve along well-defined trajectories with quality
factor defined by exponential functions of R.
