The dependence of harmonic emission from a solid on the carrier envelope phase (CEP) is discussed by numerically solving the time-dependent Schrödinger equation. The harmonic spectra periodically exhibit three distinct oscillating structures, which indicate the different dependences of the cutoff energies on the CEP. Furthermore, with time-dependent population imaging and the populations of different energy bands, the underlying physical mechanism is explored.

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Controlling paths of high-order harmonic generation from H 2 + is theoretically investigated by numerically solving the time-dependent Schrödinger equation based on the Born–Oppenheimer approximation in orthogonal two-color fields. Our simulations show that the change of harmonic emission paths is dependent on time-dependent distribution of electrons. Compared with one-dimensional linearly polarized long wavelength laser, multiple returns are suppressed and short paths are dominant in the process of harmonic emission by two-dimensional orthogonal ω/2ω laser fields. Furthermore, not only are multiple returns weaken, but also the harmonic emission varies from twice to once in an optical cycle by orthogonal ω/1.5ω laser fields. Combining the time–frequency distributions and the time-dependent electron wave packets probability density, the mechanism of controlling paths is further explained. As a result, a 68-as isolated attosecond pulse is obtained by superposing a proper range of the harmonics.

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