There are three main effects that affect the femtosecond pulse focusing process near the focal plane of a refractive lens: the group velocity dispersion (GVD), the propagation time difference (PTD), and the aberrations of the lens. In this paper we study in detail these effects generated by nonideal achromatic doublets based on a Fourier-optical analysis and Seidel aberration theory considering lens material, wavelength range, lens surface design, and temporally and spatially uniform and Gaussian intensity distributions. We show that the residual chromatic aberration in achromatic lenses, which has been neglected so far, has a considerable effect on the focusing of pulses shorter than 20 fs in the spectral range between the UV and IR, 300 to 1100 nm, and is particularly important in the blue and UV spectral range. We present a general fitted function for an estimation of the pulse stretching parameter, which depends only on the numerical aperture and focal length of the doublet as well as the wavelength of the carrier of the pulse.

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Gaussian temporal envelope pulses with initial durations of 10 fs, 15 fs and 20 fs and a carrier wavelength of 810 nm were analyzed at the paraxial focal plane of non-ideal achromatic doublet lenses for well-collimated incoming pulses parallel to the optical axis. The wave vector is expanded up to third order, to investigate the effect of third-order group velocity dispersion on the pulse and the results are compared to those obtained when the wave number is expanded up to second order. The propagation time difference and the primary spherical aberration were included in the calculations using the thin lens approximation theory. Results are presented for a homogenous illumination beam.

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