Gaussian beam distribution

The crater surfaces obtained in the LA-TOF-MS experiment on the TiN-TiAlN-Fe sample were remarkably smooth and clearly demonstrated the Gaussian intensity distribution of the laser beam. Fig. 4.45 shows an SEM image of the crater after 100 laser pulses (fluence 0.35 J cm ). The crater is symmetrical and bell-shaped. There is no significant distortion of the single layers. Fig. 4.45 is an excellent demonstration of the potential of femtosecond laser ablation, if the laser beam had a flat-top, rather than Gaussian, intensity profile. 

Droplet size may be determined with the use of a laser interferometer. This technique is an extension of the laser Doppler anemometry (LDA) technique commonly used to measure velocities of small particles in a flowing stream. Two equal-intensity Gaussian beams are made to intersect at their focal waists to form a standing electromagnetic wave distribution in the intersection (probe) volume. This standing wave can be visualized conceptually as a set of planar fringes perpendicular to the... 

Initially the signals were displayed on a fast storage oscilloscope, and a typical particle scattering trace for 8°, 6°, and 12 is shown in Figure 4. A nearly Gaussian intensity distribution was always observed, and the particle velocity can be estimated from the known beam width divided by the measmed transit time. 

The dependence of the sample volume size on the particle s apparent diameter since larger particles have a larger effective sample volume due to the Gaussian intensity distribution of the laser beam. 

Here, T is the linear transmissivity independent of f(0), and 7) the non-linear transmissivity dependent on 7(0). From Eq. (16) the non-linear absorption coefficient P can be experimentally determined easily by measuring the non-linear transmissivity T for a given input intensity 7 and a given sample thickness L. If the beam is focused nearby the sample and a Gaussian transverse distribution in the non-linear medium can be assumed, the non-linear transmissivity T, should be modified as [23] ... 

A two-dimensional Gaussian beam exhibits a fluence distribution F(x,y) according to... 

FIGURE 18.1 Schematic of (a) beam-surface interaction and the coordinate system and (b) the elliptical Gaussian beam intensity distribution. 

Consider the case where a Gaussian beam is directed normal to a moving solid as shown in Fig. 18.1. The solid absorbs the beam power, either on its surface or volumetrically. The Gaussian beam intensity distribution (after reflection) is [18] ... 

Pulsed sources can be used to tailor the material s internal temperature distribution. Pulsing is typically used to sharpen spatial temperature gradients. Solutions to Eq. 18.9 involving a single pulse for Pe = 0, p = 1 have been obtained by a number of researchers, and consideration of the general case of pulsed irradiation of a moving material with elliptical Gaussian beams is presented by Sanders [27],... 

Analytical solutions for thermoelastic stress distributions within moving material, irradiated with two-dimensional CW Gaussian beams (P 1 = 0), have also been obtained [24], For a material characterized by k = 50.2 W/mK, p = 7880 kg/m3, c = 502 J/kgK, PI2r = 105 W/m, 7 = 4 mm/s, P = 10 5 K-1, v = 0.3, and p = 105 MPa (the material shear modulus), the dimensionless surface stress component varies with Pe as shown in Fig. 18.9. Here, Pe was varied by changing the beam radius, and the beam moves relative to the surface in the positive x direction. At large Pe, stresses are relatively uniform, while, at extremely small Pe, stress gradients... 

FIGURE 18.9 Dimensionless surface stress distributions within a moving solid material irradiated by a two-dimensional Gaussian beam [24],... 

The interpretation of PDA principles based on geometrical optics is valid only for particles considerably larger than the wavelength and also when only one scattering mode is present on the detector aperture. Extensions can be introduced to account for the Gaussian beam intensity distribution (Sankar and Bachalo 1991). 

Fig. 8. Normalized residence time curves for ions of different mass accelerated to a fixed ion exit energy of 6.8 eV under conditions of a dc repeller field. Plotted is the relative ion intensity having a relative residence time greater than r/t, where t is the average residence time. Theory predicts that the shape of the curve is not mass-dependent, and experiment confirms this. The theoretical curve is computed for a Gaussian electron-beam distribution, with a full-width at half-maximum equal to the dimension of the slit through which the electron beam enters the source. Corrections resulting from the initial Maxwellian velocity distribution of the ions are ignored since they are negligible.

Gaussian Beam Illumination The Gaussian beam intensity distribution is... 

Figure 12.11 shows the CCD images of the lens at three voltage states V=0, 23, and 35 Vrms- At V = 0, the observed He-Ne laser beam is not very uniform due to its Gaussian intensity distribution. The peak intensity is -6x10 arbitrary units. As the voltage reaches 23 Vi. ,s... 

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