Two-photon ionization ofHe+as a nonlinear optical effect in the soft-x-ray region

We present numerical simulations of two-photon ionization of ${\mathrm{He}}^{+}$ by 27th harmonic pulses of a Ti:sapphire laser. This process is chosen as a candidate for the experimental observation of a nonlinear optical effect in the soft-x-ray domain. We solve the time-dependent Schrödinger equation and evaluate the ionization probability as the number of electrons absorbed by the mask function at the outer radial boundary. Our model can address questions concerning possible saturation and quantum interference in ionization at high intensity and ultrashort pulse duration with no ambiguity. According to our results, in spite of saturation of ionization found at intensity higher than ${10}^{13}{\mathrm{W}/\mathrm{c}\mathrm{m}}^2,$ the ionization probability by a 30 fs harmonic pulse with a peak intensity of $(2\mathrm{}–5)\times {10}^{13}{\mathrm{W}/\mathrm{c}\mathrm{m}}^2,$ attainable with the latest progress in high-order harmonic generation, should be sufficiently high to put the second-order nonlinear optical process in the soft-x-ray region within experimental reach, along with desirable properties such as its nearly quadratic dependence on intensity and approximate linearity in pulse width. Our simulations also show that the variation of the yield with the pulse width of the 27th harmonic is no longer linear for a pulse width shorter than 5 fs, while the dependence on intensity is still quadratic. Our analysis on the ionization of ${\mathrm{He}}^{+}$ by a double pulse in such an ultrashort pulse regime shows that the yield is not simply twice as large as that by a single pulse, but exhibits an oscillation of quantum origin with the interval and the phase difference between the two pulses. A simple model of the oscillation is discussed.