Active laser medium
The active laser medium (also called gain medium or lasing medium) is the source of optical gain within a laser. The gain results from the stimulated emission of photons through electronic or molecular transitions to a lower energy state from a higher energy state previously populated by a pump source. Examples of active laser media include: In order to fire a laser, the active gain medium must be in a nonthermal energy distribution known as a population inversion. The preparation of this state requires an external energy source and is known as laser pumping. Pumping may be  achieved with electrical currents (e.g. semiconductors, or gases via high-voltage discharges) or with light, generated by discharge lamps or by other lasers (semiconductor lasers). More exotic gain media can be pumped by chemical reactions, nuclear fission, or with high-energy electron beams. Example of a model of gain medium. The simplest model of optical gain in real systems includes just two, energetically well separated, groups of sub-levels. Within each sub-level group, fast transitions ensure that thermal equilibrium is reached quickly."(fig.1)". Stimulated emissions between upper and lower groups, essential for gain, require the upper levels to be  more populated than the corresponding lower ones. This is more readily achieved if unstimulated transition rates between the two groups are slow, i.e. the upper levels are metastable. Population inversions are more easily produced when only the lowest sublevels are occupied, requiring either low temperatures or well energetically split groups. In the case of amplification of optical signals, the lasing frequency is called "signal frequency." If the externally provided energy required for the signal's amplification is optical, it would necessarily be at the same or higher "pump" frequency. Cross-sections. The simple medium can be characterized with effective cross -sections of absorption and emission at frequencies formula_1 and formula_2. The relative concentrations can be defined as formula_7 and formula_8. The rate of transitions of an active center from ground state to the excited state can be expressed with formula_9 and The rate of transitions back to the ground state can be expressed with formula_10, where formula_11 and formula_12 are effective cross-sections of absorption at the frequencies of the signal and the pump. formula_13 and formula_14 are the same for stimulated emission; formula_15 is rate of the spontaneous decay of the upper level. Then, the kinetic equation for relative  populations can be written as follows: formula_16 The dynamic saturation intensities can be defined: formula_17, formula_18. The absorption at strong signal: formula_19. The gain at strong pump: formula_20, where formula_21 is determinant of cross-section. Gain never exceeds value formula_22, and absorption never exceeds value formula_23. At given intensities formula_24, formula_25 of pump and signal, the gain and absorption can be expressed as follows: formula_26, formula_27, where formula_28, formula_29, formula_30, formula_31 . Identities. The following identities take place: formula_32, formula_33 The state of gain medium can be characterized with a single parameter, such as population of the upper level, gain or  absorption. Efficiency of the gain medium. The efficiency of a gain medium can be defined as formula_34. Within the same model, the efficiency can be expressed as follows: formula_35. For the efficient operation both intensities, pump and signal should exceed their saturation intensities; formula_36, and formula_37. The estimates above are valid for a medium uniformly filled with pump and signal light. Spatial hole burning may slightly reduce the efficiency because some regions are pumped well, but the pump is not efficiently withdrawn by the signal in the nodes of the interference of counter-propagating waves.