Exponential Control of Adiabatic Time Reflection by Complex-Time Singularities

Nearly identical temporal switching profiles can produce very different reflections even when both have small local adiabatic measures. In a lossless dielectric, we obtain this difference by adding a weak feature that changes the complex-time singularities while preserving monotonicity, endpoints, and central slope. A perturbation bounded by $0.6\%$ of the total inverse-permittivity change raises the reflected mode amplitude from $8.02\times10^{-10}$ to $1.28\times10^{-3}$. The complex action and pole residue predict this amplitude to within $0.32\%$. Within this waveform family, deviation and monotonicity constraints select three design regimes. At fixed deviation bound, reoptimization keeps the central feature's time scale comparable to the inverse incident angular frequency. The optimal amplitude is then proportional to $1/T$ as the switching time $T$ tends to infinity. Stretching a fixed profile gives exponential suppression. Full-wave Maxwell simulations resolve the backward packet, and filtering calculations quantify its sensitivity to modulation bandwidth.