# Engineering of Ti:Sapphire Lasers for Dermatology and Aesthetic Medicine
## 2 Experimental Results and Discussion
### The Influence of Pump Fluence Distribution on Ti:Sapphire Laser Operation
If the representative size of nonuniformities is large (or spatial frequencies are small), like in patterns (a) and (b) in Figure 9, then scattering angles should be small. On the contrary, scattering angles produced by patterns (c) and (d) should be large. We suppose that the scattering of generated light in the Ti:Sapphire laser can lead to synchronization of the generation over large areas of aperture if scattering intensity and angles are sufficiently large. It is noteworthy that the natural intrinsic scattering in high-quality Ti:Sapphire crystals is very small--the scattering coefficient is less than 0.001 cm\({}^{-1}\)--which does not influence laser generation. Direct observation of pump-induced scattering is a complicated task because this process is non-stationary and requires high \(\mathrm{W_{PUMP}}\) for excitation, so it is difficult to separate and register the scattered part of the probe light on the pump light's background. To confirm the existence of pump-induced scattering, we used another approach. We studied the angular distribution of the Ti:Sapphire laser radiation at different levels of \(\mathrm{W_{PUMP}}\), using pump patterns with various \(\mathrm{w(x,y)}\) distribution, shown in Figure 9. It was observed that the angular characteristics of the Ti:Sapphire laser with MLA and DD, under pumping at a high \(\mathrm{W_{PUMP}}\) level, acquired features associated with intracavity scattering. To explain this, we refer to the results obtained in [27; 28; 29], which demonstrate the influence of intracavity scattering on laser generation. Later results [27; 28; 29] were summarized in a monograph [30]. A short explanation, based on [30], is provided below. The initial reason for light scattering is phase modulation \(\mathrm{\delta\Psi(x,y)}\) obtained by the light wave after transmission through transparent media with small-scale (in the lateral direction) optical nonuniformities. For small \(\mathrm{\delta\Psi}\), a part of the light, which is scattered after a single pass through nonuniform media, can be calculated as the squared standard deviation [\(\mathrm{StD}\) [\(\mathrm{\delta\Psi(x,y)}\)]]\({}^{2}\). In flat resonators with large \(\mathrm{N_{F}}\), even weak light scattering can increase the angular divergence of laser radiation manifold (in our case, \(\mathrm{N_{F}}\geq 1000\)). The reason for the high sensitivity of such resonators to scattering is due to a very small frequency difference between different order transversal modes. As a result, even weak coupling between such modes leads to the junction of generated light into complexes of modes with the same frequency. Such complexes, which consist of a large number of undistorted flat cavity high-order transversal modes, with random phase and intensity, are real modes of large N\({}_{\rm F}\) flat resonators with intracavity scattering. At a high pump level, these complexes predominate in laser generation, resulting in a large angular divergence of radiation. The mode structure and angular distribution of laser light depends on the characteristics of scattering: intensity, determined by integral scattering coefficient \(\alpha\), and scattering angle \(2\vartheta_{0}\). If \(\vartheta_{0}\geq(\lambda/\LgQ)^{0.5}\), where \(\lambda\) is the light wavelength and \(\LgQ\) is the equivalent resonator length, then the far-field radiation distribution, in addition to a central spot, will include O-rings with an angular diameter of \(2(\beta\lambda/\LgQ)^{0.5}\), where \(\beta\) = 1, 2, 3... These O-rings might contain a considerable amount of laser energy, giving rise to the wings of angular distribution. We should mention that the abovementioned results only reveal some general features of laser angular characteristics. The properties of active media (except scattering), the dynamics of generation and pump characteristics have not been considered here.