Theoretical studies of modulation instability, Fermi–Pasta–Ulam recurrence and pattern formation in an ultra-silicon-rich-nitride Bragg grating

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.