The driving electric field (red lines) of (a) a “perfect wave” and (b) an optimized waveform consisting of the first four harmonics of 1/T and a field with a period of 2T. Trajectories of the returning electrons with the maximum kinetic energies are also shown (green lines). ε_opt = (e²/m)(FT/4ɛ₀c) is the maximum returning electron energy generated by the “perfect wave”, where e and m are the electron charge and mass, respectively, T is the oscillation period, and F is per period fluence. Reprinted with permission from Ref. [95]. © (2009) by the American Physical Society.