Interactions Between Laser Beam and Glass

To understand why laser radiation of the visible wavelength range is also used nowadays for absorption by transparent glass, non-linear optical effects and multi photon absorption need to be considered. 

However, for real absorbing materials the polarisation does not respond instantaneously to an applied field, which causes dielectric loss. This is expressed by a permittivity that is both complex and frequency dependent. Taking these aspects into consideration a complex index of refraction n can be defined, see (8.3)  

In a transparent medium such as gfass U2 is afmost 0. In absorbing materials, however, the intensity of the transmitted light I decreases with increase in penetration depth, which is described by the Lambert Beer law, see (8.6)  

The amplitude of the electron oscillation increases so it is not able anymore to follow the oscillation of the electrical field. This oscillation of the electrons can be described by a series development, see (8.8)  

In this series the first term describes the linear optical effects, i.e. the refractive index n and absorption coefficient / e, whereas the second term describes the optical loses in isotropic materials and the third term the non-linear effects, such as non-linear refractive index n and non-linear absorption coefficient / g. 

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