a) Recollision-resolved M 3C energy spectra (CEP-averaged, I=3 × 10 13 W cm −2) and respective SMM cutoffs for direct and rescattering electrons for 400 nm spheres. The index n indicates the number of recollisions with the sphere. The M 3C cutoff (red circular symbol) is assigned to the energy where the spectrum of single recollision electrons (solid red curve) has dropped by a factor of 10 3. ( b) CEP-resolved M 3C energy spectra ( n=1, colour coded) for the same parameters as in ( a) for emission into the upper half space. Vertical dotted, dashed, and solid black curves indicate the SMM result for the CEP-dependent cutoff energy. The grey horizontal line marks the critical phase predicted by M 3C. ( c) Evolution of the linear (Mie solution) and full M 3C near field at the outer surface for the critical phase and sampled under the critical angle; all other parameters are the same as in ( a). ( d) Radially resolved evolution of the nonlinear near-field for the same parameters as in ( c) and critical radial trajectories from SMM and M 3C (average over trajectories with E= E c±1%). ( e) CEP-dependent distributions of birth and recollision times of the M 3C trajectories with E>0.8 E c, see blue box in ( b), and their time averages (red lines); black lines show the SMM prediction for cutoff electrons; the M 3C recollision time refers to the mean of re-entry and exit, see zoomed region of panel ( d); the x=0 passage of the peak of the unperturbed field envelope defines the time reference.