Laser amplification is a process by which a weak laser signal is amplified through the stimulated emission of photons in a gain medium. This process is used in many applications such as telecommunications, medicine, and industry.

Figure 1: Stimulated Emission

The principle of laser amplification is based on the stimulated emission of photons, which was first proposed by Albert Einstein in 1917. Stimulated emission occurs when an atom in an excited state is stimulated by an incident photon of the same frequency and phase, causing the atom to emit a second photon with the same frequency, phase, and direction as the first photon. This process results in the amplification of the original photon signal. Figure 1 shows the energy level diagram in the process of stimulated emission.

Figure 2: Schematic of a laser medium

The amplification process occurs in a laser cavity, which consists of a gain medium, typically a crystal or a gas, placed between two mirrors as shown in figure 2. The gain medium is excited by a pump laser, which raises the atoms in the medium to an excited state to achieve the condition of population inversion. When a photon of the laser signal passes through the gain medium, it stimulates the emission of additional photons by the excited atoms, resulting in an amplification of the signal.

The amplification process is governed by the rate equation, which describes the rate of change of the population inversion of the gain medium as a function of time. It is given by:

where N is the number of atoms in the excited state, B is the rate coefficient for stimulated emission, P is the power density of the laser signal, A is the rate coefficient for absorption, and C is the rate coefficient for spontaneous emission. The terms:

BNP represents the rate of stimulated emission. 

AN represents the rate of absorption. 

CN represents the rate of spontaneous emission. 

The population inversion is the condition in which the number of atoms in the excited state is greater than the number of atoms in the ground state. In order to achieve laser amplification, the population inversion must be maintained above a threshold level.

The amplification factor of the laser cavity depends on several factors, including the length of the gain medium, the strength of the pump laser, and the reflectivity of the mirrors. A high reflectivity mirror at one end of the amplifier will reflect the amplified laser signal back into the gain medium, causing further amplification.