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

Dense and Sharp Resonance Peaks in Stretched Moir\'e Waveguides