# Amplification

 The fundamental principle behind generating any laser beam is amplification of light. A material or device is put in such a state that when light of the right wavelength travels through it, that light grows in intensity. All of the light that is added to the beam by the device or material has exactly the same characteristics as the original light - the same direction, the same wavelength, the same polarization, and the same phase. When the light traversing the amplifying medium or device has low intensity, the amount of light added to the beam through amplification is proportional to the amount of light already present. Whenever the change in a quantity is proportional to the quantity being changed, you get an exponential change in the quantity. For the light beam, this means that the intensity I will grow with the distance x traversed as I = I0 exp(x/a) where I0 is the intensity at x=0, and a is the characteristic amplification length of the medium. At high intensity, the gain saturates and all the energy stored in a given length of the amplification medium is delivered to the beam. In this limit, the intensity increases linearly with distance I = dE/dx x where dE/dx is the energy stored in a given length of the gain medium. Many varieties of amplifiers that can be used to generate laser beams only work at one highly specific wavelength. Others work at a broader range of wavelengths, but work best at a given wavelength. There are still other gain media that can operate well over a wide range of wavelengths. While amplification is a necessary part of any scheme to generate a laser beam, as described in subsequent sections, it is also often used to increase the intensity of an already existing beam. Just put your energized amplifier in the path of the beam you want to pump up, and it increases the intensity of the beam as it goes through.