Gaussian beam curve

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. 

Silicon films that were electron beam evaporated at a rate of 5 nm sec-1 on silica substrates at 440°C were subsequently irradiated with an Ar+ laser. The rapidly scanned Gaussian beam formed a smooth lateral temperature gradient in the film hence it provided a simple means to study the crystallization mechanism. The laser-heated track reveals two easily discernible areas. A 1 -//m-thick film showed color changes from black to deep red at the margins of the track to light yellow in the middle of the track. Despite the smooth fall of the laser intensity, the different boundaries are abrupt. Optical absorption measurements of the respective areas are also displayed in Fig. 1. The curve E440 represents the as grown evaporated film and is in... 

Fig. 16. The diffraction efficiency kinetics curves comparison of different kinds of polarization recording holograms in Fulgide/PMMA film written by Gaussian beams (a) Experimentally measured results (b) Theoretically calculated results...

So far, we have assumed that the wave fronts of the laser radiation field are planes and that the molecules move parallel to these planes. However, the phase surfaces of a focused Gaussian beam are curved except at the focus. As Fig. 3.20 illustrates, the spatial phase shift Acf) = x2n/X experienced by an atom moving along the r-direction perpendicular to the laser beam z-axis... 

Illustrated in Fig. 9 is the Z-scan setup using a beam with a top-hat spatial profile. An aperture Al of diameter d is placed in front of a lens L with a focal length /, producing a system with an F number equal to fid. The top-hat beam waist at the focus is dehned as Wq = AF. The remaining components of the setup such as the second aperture A2 and photodetector PD are in the standard Z-scan geometry. The z-scan curve for a top-hat beam is similar to those for a Gaussian beam. 

Shown in Fig. 10 are calculated Z-scan curves for both beam profiles with the same value for d>Q. Here d>o is the nonlinear phase shift at r = 0 when the sample is at the focal point z = 0 and is the on-axis intensity at the focal point. Note that the peak-valley transmittance difference, Tp. = 7 p T, obtained with the top-hat profile is approximately 2.5 times greater than that with the Gaussian beam. 

FIGURE 10 Z-scan curves for the top-hat and Gaussian beams. (From Ref. 17.)... 

Fig. 3.20. Merged beam results for the charge transfer reaction Kr+ + H2O — H2O+ + Kr. The rate coefficient is plotted as a function of the laboratory energy of the ion, E (lower scale). Accounting for the velocity of the water beam which has been seeded in He, one obtains the collision energy Et (upper scale). The two Gaussian-like curves represent the numerically determined energy distributions at the nominal energies 0 and 50 meV. The dashed curve is an empirical fit.

Fig. 10-1 Electric field amplitude (r) and diffraction intensity pattern A (u) for (a) a Gaussian beam and (b) a uniform beam. The dashed curve is the Gaussian beam approximation of Eq. (10-1) for the uniform beam, and is defined by Eq. (10-2).

Figure 9.6. The point spread function of a circular aperture for 4 different values of the edge taper with Gaussian illumination. The four curves are for uniform illumination or 0 db taper, 9, 18 and 27 db taper. The sidelobe level decreases with increasing taper, while the width of the main beam increases slightly.

The time dependence of such a signal is presented in Fig. 3.22. For curves 1-4 the width of the entrance slit l is five times larger than the Gaussian radius of the beam ro for curves 5-8 it is equal to it, and lower... 

A numerical calculation of the line profiles due to the combined effect of the natural lifetime, the light-shift and the saturation has been performed taking into account all possible trajectories of atoms inside the metastable beam. Actually, the study of experimental linewidths shows there are some other stray effects responsible for the broadening of the lines. He have considered their contribution by making a convolution of the line profile with a gaussian curve. 

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