High-Order Temporal Corrected Fields of Ultra-Short Laser Pulses and Laser-Driven Acceleration

Up to third-order temporal correction in terms of a small dimensionless temporal parameter ε =1/(ω₀ t₀) (ω₀ = ck₀ the central oscillatory frequency, t₀ the pulse duration of half period), the field expressions of ultra-short focused laser pulses are explicitly presented. To evaluate the correction efficacy, electric amplitudes of zeroth-order and higher-order corrected fields are compared for different pulse durations. Furthermore, electron interaction with ultra-short laser pulses is simulated using both the zeroth-order and higher-order corrected field equations. Our simulation results show that the third-order correction terms should be considered for investigating the interaction if the laser pulse duration decreases to a few optical periods.