Generation-Resolved Signatures in QED Cascades: Diagnostics for Ultraintense Laser Parameters

We present a generation-resolved analysis of shower-type, spin- and polarization-dependent quantum electrodynamics (QED) cascades initiated by head-on collisions of ultraintense laser pulses ($a_0 = 200$--$1000$) with $10$~GeV electron bunches. Using a Monte Carlo model that tracks cascade evolution across distinct generations, we shows that radiation reaction strongly suppresses high-generation yields. The positron energy spectrum exhibits a systematic softening with increasing $a_0$, and the average photon polarization $\overline{\xi}_3$ increases with pulse duration $\tau$ due to polarization-selective depletion in nonlinear Breit--Wheeler pair production. We identify a scaling relation $a_0^2\tau$ that governs both the maximum cascade generation $G_{\max}$ and the fraction of backward-emitted photons $F_r$, thereby establishing experimentally accessible diagnostics for laser intensity and pulse duration using two observables: $F_r$ and the positron peak energy $\varepsilon_+^{\rm peak}$. These generation-dependent signatures suggest a potential shot-resolved, post-interaction approach for characterization of ultraintense laser parameters in the strong-field QED regime.