Review on typical applications and computational optimizations based on semiclassical methods in strong-field physics

The semiclassical method based on Feynman’s path-integral is in favor of uncovering the quantum tunneling effect,the classical trajectory description of the electron, and the quantum phase information, which can present an intuitive and transparent physical image of electron’s propagation in comparison with the ab initio time-dependent Schr ¨odinger equation.In this review, we introduce the basic theoretical concepts and development of several semiclassical methods as well as some of their applications in strong-field physics. Special emphasis is placed on extracting time delay on attosecond scale by the combination of the semiclassical method with phase of phase method. Hundreds of millions of trajectories are generally adopted to obtain a relatively high-resolution photoelectron spectrum, which would take a large amount of time. Here we also introduce several optimization approaches of the semiclassical method to overcome the time-consuming problem of violence calculation.