Focusing Conditions

To optimize the conversion efficiency, physical focusing conditions need to be optimized. With reference to the SG spectrum shown in Fig. 5.8, for fixed incident laser power and fixed focal length of the lens, the location of the focus point within the 7.5 cm long barium fluoride crystal was found to determine the extent of the white light spectrum. With the focus located f cm inside the crystal, the flattest possible spectrum of white light was obtained (as shown in Fig. 5.8), and the highest conversion efficiency was also achieved. 

---

The natural way to increase the efficiency of such a frequency conversion process is to use a focused fundamental beam (or, alternatively, a waveguide structure). An established theory of SHG using focused cw beams " predicts, for negligible birefringence waUc-off, an optimal focusing condition which is expressed by the ratio L/b 2.83, where b is the confocal parameter (b = k wQ, where Wqi and ky are the focal spot radius and the wave vector of the fundamental wave respectively). However, this theory applies only to the long-pulse or cw case, where GVM is negligible... 

L). Our recently published theoretical model defines, for the first time, the optimum focusing conditions for SHG using focused beams in the ultrashort-pulse regime, where GVM is significant (i.e. where L > ). 

In practical applications, it should be kept in mind that the beam waist itself usually depends on the wavelength (at the diffraction limit, uiq is proportional to >.) and, therefore, that the comparison between IPA and 2PA excitation rates may not be as straightforward as that shown in Fig. 2. In general, the 2PA excitation volume depends on the focusing conditions and beam parameters used for the material excitation. 

An important parameter in order to avoid elemental fractionation in laser ablation ICP-MS is the laser power density ( ) which is a function of laser energy, of laser pulse duration and focusing conditions, as described in the following equation ... 

Figure 1 shows an experimental image of a T-0 layer silicate (lizardite). The 0.7-nm periodicity is clearly apparent, and no subperiodicities (<0.7 nm) or superperiodicities (>0.7 nm) can be detected. This image was obtained at or near Scherzer focus, and the crystal was oriented such that the basal planes were perfectly parallel to the electron beam, as determined by electron diffraction patterns of the areas from which the images were obtained. Thus, this image was taken under nearly ideal conditions in that both the focus conditions and orientation were carefully controlled. 

---