Using the Time-Transformation Approach to Generate Free Ballistic Acceleration and Inversion of the Airy Pulse in Dynamic Optical Media

In this study, the time-transformation approach (TTA) is applied to investigate two key phenomena in dynamic optical media: free ballistic acceleration (FBA) and asymmetric Airy pulse inversion (AAPI). These effects arise from either the interplay between input chirp and group-velocity dispersion (GVD) or from dominant positive third-order dispersion (TOD) on a truncated Airy profile (TAP) electric field. By modeling a linear dynamic medium that includes GVD and TOD, an impulse response is derived with an intrinsic Airy structure. Nonlinear effects, particularly the Kerr effect, are incorporated via a Jacobian-based transit time expression. In the linear regime, these results closely match those obtained with the split-step Fourier method (SSFM), while being approximately 14 times faster due to TTA's direct field mapping. In the Kerr nonlinear regime, TTA remains reliable, especially for AAPI driven by chirp-GVD interaction. These findings highlight TTA as a powerful hybrid analytical-numerical tool for simulating asymmetric optical signals like TAPs in time-varying media.