Ideal Waveform to Generate the Maximum Possible Electron Recollision Energy for Any Given Oscillation Period

We present the perfect waveform which, during a strong field interaction, generates the maximum possible electron recollision energy for any given oscillation period, over 3 times as high as that for a pure sinusoidal wave. This ideal waveform has the form of a linear ramp with a dc offset. A genetic algorithm was employed to find an optimized practically achievable waveform composed of a longer wavelength field, to provide the offset, in addition to higher frequency components. This second waveform is found to be capable of generating electron recollision energies as high as those for the perfect waveform while retaining the high recollision amplitudes of a pure sinusoidal wave. Calculations of high harmonic generation demonstrate this enhancement, by increasing the cutoff energy by a factor of 2.5 while maintaining the harmonic yield, providing an enhanced tool for attosecond science.