ABSTRACT
We have developed an algorithm to filter the noise in the spectral intensity of ultrashort laser pulses. The filtering procedure consists of smoothing the noise by using the Savitzky-Golay filter, removing the offset, and using a super-Gaussian window to truncate the frequencies of the spectrum. We have modeled bandwidth-limited ultrashort pulses with Gaussian modulated frequencies to show the estimation of the carrier wavelength, reconstruction of the intensity pulse profile, and pulse duration after applying the algorithm. Theoretical results are presented for pulse durations between 5 fs and 100 fs with a carrier wavelength of 825 nm and three different amounts of signal-to-noise ratio (SNR): 30 dB, 20 dB, and 15 dB, normally found in experiments. The algorithm is also applied to an experimental spectral intensity from a homemade Ti:sapphire laser that produces pulses of about 20 fs at 825 nm at 100 MHz. We will show that using only a low-pass Fourier filter and removing offset is not enough to recover the spectral intensity when a large SNR is present, which may be the case when the ultrashort laser beam has been manipulated to compensate for the group velocity dispersion of an external optical system. In cases like this, the use of the Savitzky-Golay filter prior to the super-Gaussian filter improves the recovery of the carrier wavelength and the spectral intensity. We will also show that the algorithm presented in this paper is suitable for experimental analysis and requires limited user intervention.
ABSTRACT
In this paper, the temporal and spatial intensity pulse distributions are calculated around the focal region of an optical system using a combination of ray tracing and a wave propagation method. We analyze how to measure the width of the intensity pulse distributions to estimate pulse duration and spot size in order to study the impact of the variation of spherical aberration with frequency in a pulse on the intensity distributions. Two experimental techniques used in the laboratory are also modeled: the knife-edge test to measure spatial distribution and the intensity autocorrelation technique to measure the temporal distribution. We use two measuring criteria, the full-width half-maximum (FWHM) and standard deviation (σ), to compare the spatial and temporal intensity distributions of the calculated diffraction patterns and those obtained from the simulated experimental techniques. We show that the FWHM is not a good criterion, since it gives different results in the measured intensity distributions in time and space when they are measured directly from the theoretical modeling and when they are measured from the modeled experimental techniques used in the laboratory. The standard deviation, however, is a consistent criterion, giving the same results for the calculated intensity distributions and the modeled experiments.
ABSTRACT
To pump a solid-state femtosecond laser cavity, a beam from a CW laser is focused by a single lens into the laser crystal. To increase the output power of the laser, the overlap of the laser mode with the pump mode should be maximized. This is particularly important in the so-called mode coupling and the Kerr-lens mode locking (KLM) operation, where the change in beam waist at the position of the gain medium is exploited to enhance the mode overlap with the pump laser in the crystal. In this paper, the astigmatism in the pump beam is reduced by tilting the pump lens. A Gaussian beam is propagated through the complete focusing system-pump lens, tilted spherical mirror, and crystal cut at Brewster's angle-to show the astigmatism inside the crystal as a function of the tilt of the pump lens. A genetic algorithm is presented to optimize the mode coupling between the pump and laser beam inside the crystal by tilting the pump lens. Experimental results are presented to verify the design, showing an increase in the output power of the laser cavity of about 20%.
