Analytical and numerical investigation of the pulse-shape effect on the longitudinal electric field of a tightly focused ultrafast few-cycle TM01 laser beam

Abstract

AbstractThe effect of temporal pulse-shape on the characterization of the longitudinal electric field resulting from the tight-focusing of an ultrashort few-cycle TM01 laser beam in free space is investigated analytically and numerically. The longitudinal field is found to be sensitive to the pulse-shape of the driving field. The temporal pulse-shapes considered are Gaussian, Lorentzian, and hyperbolic secant having identical full width at half maximum of intensity. Analytical calculations are made beyond the paraxial and slowly varying envelope approximations. From the numerical results we find that due to finite duration of the signal, the evolution of the pulse envelope before the waist is faster (negative time-delay) but slowed down (positive time-delay) after the waist. This time-delay, for single-cycle pulses of wavelength λ0, and for spot-size w0f in the range 0.6λ0 > w0f > 0.25λ0, is pulse-shape dependent. The time delay is maximum for the Gaussian pulse and minimum for the Lorentzian pulse. The carrier frequency shift depends on the temporal profile of the pulse, beam spot size, axial propagating distance and also on the number of cycles in a pulse. In addition, a comparative study of the variation of the corrected axial Gouy- phase of the longitudinal electric field of single-cycle pulse (spot size w0f = 0.5λ0) with normalized retarded time shows that the phase variation is maximum for Gaussian and minimum for the Lorentzian pulse shape.