Spectrum Conversion and Mode Preservation of Airyprime Pulses under Dynamically Modulated Time-Dependent Potential Fractional Systems in OPPC Fibers

We theoretically analyze the transmission properties of Airyprime pulses based on a fractional Schrödinger equation (FSE) in an Optical Phase Conductor (OPPC) fiber. In the absence of an external potential, both time and frequency domain pulses propagate in a mode invariant manner. The dispersion effect alters the tilt angle of the time domain pulses, while the evolution of the frequency domain pulses remains unaffected. When the Moiré lattice modulates the time-varying harmonic oscillator (HO) potential, the time domain pulse preserves its Airyprime pattern during transmission. In contrast, the corresponding frequency domain pulse undergoes several spectral transitions between saddle and Airyprime profiles, with the system parameters governing these transitions. The pulse undergoes spectral transition and tunneling under the influence of a time-varying HO potential with hyperbolic secant modulation, which position depends on the modulation parameters. By modulating the time-varying HO potential with Dirac’s delta functions, the pulse exhibits an abrupt spectral transition and a two-step spectral shift. Our results provide valuable insights into the modulation of Airyprime pulses in OPPC fibers, broadening the potential application scenarios for pulses and time-varying potentials.