Gaussian beam profile

A commercial fs-laser (CPA-10 Clark-MXR, MI, USA) was used for ablation. The parameters used for the laser output pulses were central wavelength 775 nm pulse energy -0.5 mj pulse duration 170-200 fs and repetition rate from single pulse operation up to 10 Hz. In these experiments the laser with Gaussian beam profile was used because of the lack of commercial beam homogenizers for femtosecond lasers. 

It is useful for illustrative purposes to consider a laser beam with a Gaussian spatial profile and a square pulse time profile. If the laser has a Gaussian spatial beam profile the temperature at the surface of the Irradiated solid (z=0) at a time t after the laser pulse is started is given by(4) ... 

The driving fields in nonlinear coherent microscopy can be dressed with alternative phase profiles. One of the simplest phase masks is a one-dimensional r-phase step across the transverse Gaussian beam profile. The resulting phase pattern resembles... 

The analysis of Z-scans relies on Gaussian spatial beam profiles. For short laser pulses the beam profile is frequently not completely Gaussian and the unbiased use of the standard anlaysis of Z-scan can lead to large experimental errors. For reliable Z-scan measurements the spatial beam profile has to be well... 

Chappie et al thourougly discussed the critical parameter of Z-scan and Mian et al. [35] showed the influence of beam ellipticity on the Z-scan measurements. A solution to overcome the troubles with non-Gaussian beams is the employment of top-hat beams [36,37]. An aperture is placed in the expanded beam in front of the focusing lens, so that the beam profile is uniform in the aperture. The analysis follows an analogous approach as for Gaussian beams and results in similar curves but with a magnitude that is about 2.5 times larger. 

In the experiment above the light was collimated with a lens. Therefore, the Gaussian shaped beam profile introduced weaker illumination of the camera at the edges than in the center. Figure 6b shows the reference profile fin for this geometry. For optimum performance the reference hne should be positioned in close proximity to the LVF hue. 

For the indication of absolute laser fluence values, e.g., for ablation, modification, melting etc. of a material, the determination of the spot size is crucial. Fluence values allow the comparison of laser treatment with different types of lasers showing various spatial beam characteristics like a square (e.g., excimer laser) or a Gaussian beam profile (e.g., Tksapphire laser). In the following, the determination of the Gaussian beam radius is described. 

Fig. 8 Scheme of a spatially Gaussian beam profile. F0 and Fth denote the maximum laser fluence and the ablation threshold fluence, respectively. The distance 2w0 represents the 1/e2-Gaussian beam diameter... 

Assuming a Gaussian spatial beam profile, the relation between the crater diameter D and the maximum laser fluence F0 can be written as [17]... 

In the estimation of the dissociation excimer laser flux, we assume that the mildly focused laser beam has a Gaussian beam profile [121]. The photodissociation laser spot size has also been checked by examining the burn spots on thermal papers at various distances from the focusing lens. The variation of the laser beam spot size with distance from the focusing lens is consistent with that predicted by the Gaussian beam profile. In the photodissociation region the ionization laser beam spot is smaller than the photodissociation laser beam spot. 

The volumes of product S atoms sampled by the ionization detector in the pulsed beam mode and in the gas mode are different. The determination of the intersection volume of the ionization laser beam and the CH3SCH3 beam, as well as that of the ionization laser beam and the CS molecules in the gas cell, is necessary for the calibration. The ionization dye laser beam profile is again assumed to conform with the Gaussian profile. The size of the CH3SCH3 beam is determined by the skimmer opening and the nozzle-skimmer distance. 

Figure 7. Beam profile for a Gaussian beam truncated at its center by an electrode. (x ) is the beam amplitude relative to its center, and x is the distance from the electrode (downward in Figure 4). The dashed line shows the profile for the beam before any chromophore is generated, and the solid line is the beam cross-section after 10 sec of chromophore generation.

Since the temperature dependences of M and have been experimentally determined one has to make assumptions regarding the radial temperature distribution in the heated spot to find the corresponding radial distribution of M and R. If the intensity distribution of the laser beam is Gaussian the temperature distribution in the film can be represented by means of isotherms of elhpsoidal character (Umer-Wille et al., 1980) such as schematically indicated in fig. 53. A Gaussian laser beam profile was also used in the numerical calculations of Huth (1974), presented below. 

Fig, 53. Isotherms representing the temperature in a thin amorphous film 1 jas after an instantaneous heat pulse induced by a laser beam of Gaussian intensity profile (after Urner-Wille et al 1980). 

The main advantage of LA is the direct ablation capability from preselected areas of a sample, thereby avoiding laborious sample preparation and contamination. The focal spot size achieved with UV lasers of adequate (Gaussian) beam profile can be reduced to a few micrometers or less, which enables the microanalysis of solids. Quasicontinuous sampling is possible if the laser is operated with an adequate repetition rate. 

Transverse electric field mode indicates that the electric field of the laser beam is perpendicular to its direction of propagation. TEMqo imphes a Gaussian beam profile. 

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