Ways to produce and measure atto- and femtosecond soft X-ray pulses

The ways to produce and measure atto-and femtosecond soft X-ray pulses are reported. The laser phase relation of high-order harmonic generation (HHG) shows two different radiation energy distributions in time (or laser phase) domain. These energy-phase relations are helpful for realizing the dynamic processes of HHG. Two presented parameterized formulas can be used to calculate the durations of the energy distributions with a bandwidth of the pulse. These formulas are useful in calculating and simulating pulses transports and interactions with mediums. The time structures of atto-and femtosecond soft X-ray pulses can be directly measured with photoelectron spectrum transfer equations and the related laser phase determination methods without any previous pulse shape and the instantaneous frequency assumptions. These equations and methods can be used to evaluate and improve the technical parameters of the ultra-short X-ray sources. They have wide measurement ranges and high time resolutions, which may enable ultra-fast measurements to reach metrological precisions, and lead to a new tide of scientific researches in physics, chemistry, biochemistry, etc. The application of atto-and femtosecond X-rays as well as the theoretical and technical problems in measurements are briefly discussed.