Full-Quantum Numerical Scheme of Finite Difference Time Domain Method for High-Order Harmonic Generation

This paper presents a complete full-quantum numerical scheme for the analysis of high-order harmonic generation from a gaseous medium by an intense laser field. With respect to the previous theoretical understanding and semiclassical theory, the main contribution is that the entire process of high-order harmonic generation is strictly full-quantum solved by the finite difference time domain method. With the Crank-Nicolson central differencing formula applied into the time-dependent Schrödinger equation in the length gauge, wave functions of the valence electron can be achieved simultaneously, including both the real and imaginary parts. The stability analysis of the employed differencing formula is also derived in detail with the equation of error transmission. Numerical results are given to demonstrate the accuracy and feasibility of the proposed method. This method provides an efficient and promising approach for the evaluation of high-order harmonic generation generated from the gaseous medium and further optimization of isolated attosecond pulse.