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

Abstract 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.