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We have investigated and analyzed the modulation instability (MI) of finite energy Airy pulse (FEAP) in an optical fiber in order to reveal the impact of truncation coefficient on the nonlinear propagation dynamics of FEAP with or without amplitude perturbation. We have also characterized the difference between the propagation process of smooth FEAP and that of modulated FEAP. It is shown that, for a smooth FEAP, the side lobes prior to the main lobe first undergo compression and then break up into multiple sub-pulses during propagation in the case of small truncation coefficient; while the opposite occurs in the case of large truncation coefficient. For a FEAP with amplitude modulation, the breakup of the main lobe induced by MI precedes that of side lobes for arbitrary values of truncation coefficients; but the evolution of secondary lobes is made by a transition from splitting process to a simple compression process with increasing truncation coefficient. The propagation dynamics of secondary lobes with number symbol larger 2, marked the secondary lobes starting number 1 from near to far according the distance between itself and the main lobe, is insensitive to the truncation coefficients variation in both cases. Finally, the MI gain spectra of FEAP with different truncation coefficients are obtained by numerically solving the nonlinear Schrödinger equation and the results have been compared with the theoretical predictions.

The propagation of decelerating Airy pulses in non-instantaneous cubic medium is investigated both theoretically and numerically. In a Debye model, at variance with the case of accelerating Airy and Gaussian pulses, a decelerating Airy pulse evolves into a single soliton for weak and general non-instantaneous response. Airy pulses can hence be used to control soliton generation by temporal shaping. The effect is critically dependent on the response time, and could be used as a way to measure the Debye type response function. For highly non-instantaneous response, we theoretically find a decelerating Airy pulse is still transformed into Airy wave packet with deceleration. The theoretical predictions are confirmed by numerical simulations.

A novel group velocity mismatch (GVM) absent scheme for nonlinear optical parametric procedure in mid-infrared was developed with type-I quasi phase matching by use of an off-digital nonlinear optical coefficient d31. This was achieved by matching of the group velocities of the pump and the signal waves, while the phase velocities were quasi phase matched. The system employs MgO-doped periodically poled LiNbO3 as the nonlinear medium. Desired group-velocity dispersion would be obtained via appropriately temperature regulation. To demonstrate its potential applications in ultrafast mid-infrared pulses generation, aiming at a typical mid-infrared wavelength of ~3.2 μm, design examples of two basic nonlinear frequency conversion procedures are studied for both the narrow-band seeding mid-IR optical parametric amplification (OPA) and the synchronously pumped femtosecond optical parametric oscillation (SPOPO). Compared with the conventional scheme of type-0 QPM, the quantum-efficiency can be more than doubled with nearly unlimited bandwidth. The proposed GVM- absent phase matching design may provide a promising route to efficient and broadband sub-100 fs mid-infrared ultrafast pulses generation without group-velocity walk-off.