Dynamic characteristics of electrons in high-order corrected fields of ultrashort laser pulses

High-order correction to the fields of ultrashort, tightly-focused laser pulses expressed in power series of epsilon = 1/(omega(0)t(0)) and s = 1/(k(0) omega(0)) (omega(0) = ck(0) the central oscillatory frequency, t(0) the pulse duration, w(0) the beam waist radius), are derived. Based on paraxial approximation, the first-order correction terms to the Gaussian pulses are explicitly given. Their corrections of amplitude and phase, are found to be related to the variable of E. Applying them to the study of the electron dynamics in the intense laser pulse field, we found that as long as w(0) t(0) > 20, the zeroth-order approximation ( long pulse approximation) is adequate for describing the in.teraction. For w(0) t(0) < 20, higher-order corrections have to be taken into account.