When a low-power, monochromatic Gaussian beam is focused by a thin lens in air and the waist of the beam is in the plane of the lens, there is a shift of the focus position if the waist of the beam is much smaller than the size of the lens. The point of maximum intensity relative to the geometrical focal point shifts closer to the lens. We show that for ultra-intense light beams, when the Kerr effect is unavoidable, there is a nonlinear focal shift. The nonlinear focus position shifts closer to the lens for laser powers below the critical power. To avoid the nonlinear focal shift below the critical power, the correct combination of Gaussian beam waist and focal system has to be used in the experimental setup. It will be shown that as the Fresnel number N w associated with the Gaussian beam radius increases, the nonlinear focal shift first increases and then begins to decrease.

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In this work, we study the effects of noise present on spectral interferometry signals, for femtosecond pulse retrieval such as in the SPIDER technique (spectral phase interferometry for direct e-field reconstruction). Although previous works report SPIDER robustness, we have found that noisy signals with low signal-to-noise ratio (SNR), in the acquired spectral interferogram, could cause variations in the temporal pulse intensity retrieval. We demonstrate that even in a filtered SPIDER signal, following standard procedures, at some point the noise on the spectral interferogram could affect the spectral phase retrieval. As a novel alternative for spectral interferograms filtering, we have applied the wavelet transform and propose a target criterion to automatize the optimization algorithm. We apply this method on SPIDER signals and analyze its effectiveness on the spectral phase retrieval. We present numerical and experimental results to show the improvement in the phase retrieval and the temporal pulse reconstruction after applying this filtering method and compare the results with a standard method.