Theoretical studies of modulation instability, Fermi-Pasta-Ulam recurrence and pattern formation in an...

Ultra-silicon-rich nitride Bragg gratings provide a powerful platform for precise light manipulation in photonic chips. Their exceptionally high nonlinearity and strong grating-induced dispersion near the stop-band edges significantly reduce the power and length required for chip-scale light-matter interactions. Using computational methods, we theoretically investigate modulational instability, Fermi-Pasta-Ulam recurrence, and pattern formation in this platform within the framework of the Akhmediev breather. We assess their experimental feasibility and show that this platform can generate a high-quality pulse train at the output. We demonstrate that modulational instability can be triggered in the gratings as short as 1-2 mm, leading to Akhmediev breather formation. By analyzing the full dispersion profile, we identify pump wavelengths that generate new frequencies and show that the grating also can produce a comb-like discrete spectrum. Furthermore, we reveal that even with high loss, parametric amplification at the grating output is possible, highlighting its potential as a nonlinear platform for frequency comb generation, wavelength-multiplexed data transmission, and high-precision pulse processing.