Population Inversion and Laser Operation

Population Inversion and Laser Operation

As discussed above, whenever light is incident on the material, there is competition between absorption, spontaneous emission and stimulated emission processes. Under normal equilibrium conditions, the population of various levels is given by Boltzmann's relationship and thus N2 will always be less than N1. Further, stimulated photon emission is much less than the spontaneous photon emission and the absorption. For a system to work as a laser one requires that stimulated emission should exceed photon absorption; it leads us to the following two conditions:



    N2 > N1: i.e. Population Inversion



    As per equation (6) or (7), the value of ρ (the radiation energy density which is equal to Nhn) should be as large as possible.

First condition cannot be achieved under thermal equilibrium conditions. This implies that in order to create population inversion, one must look for non-thermal equilibrium system and thus the need for special laser materials.

The second condition that requires higher value of r necessitates the use of an additional supply of large amount of energy of correct wavelength to excite the desired transition. The process is known as pumping. Various techniques include optical, electrical, chemical, gas dynamic etc.

Population inversion though is the primary condition, but in itself is not sufficient for producing a laser. As there are certain losses of the emitted photons within the material itself in addition to spontaneous emission, one has to think about the geometry that can overcome these losses and there is overall gain. This requires an optical cavity or resonator.

The principle behind the laser is like this. Suppose we can produce a large number of atoms all in excited states. If one of the atoms emitted spontaneously, then the emitted photon would stimulate other atoms to emit. These emitted photons would, in turn, stimulate further emission. The result would be an intense burst of coherent radiation.

Laser action: Interaction of electromagnetic radiation with matter produces absorption and spontaneous emission. Absorption and spontaneous emission are natural processes. For the generation of laser, stimulated emission is essential. Stimulated emission has to be induced or stimulated and is generated under special conditions as stated by Einstein in his famous paper of 1917. i.e. ?when the population inversion exists between upper and lower levels among atomic systems, it is possible to realize amplified stimulated emission and the stimulated emission has the same frequency and phase as the incident radiation?. Einstein combined Plank? law with Boltzmann?s statistics in formulating the concept of stimulated emission. In electronic, atomic, molecular or ionic systems the upper energy levels are less populated than the lower energy levels under equilibrium conditions. Pumping mechanism excites say, atoms to a higher energy level by absorption (Figs.3a and 3b).

The atom stays at the higher level for a certain duration and decays to the lower stable ground level spontaneously, emitting a photon, with a wavelength decided by the difference between the upper and the lower energy levels. This is referred to as natural or spontaneous emission and the photon is called spontaneous photon. The spontaneous emission or fluorescence has no preferred direction and the photons emitted have no phase relations with each other, thus generating an incoherent light output (Fig.4). But it is not necessary that the atom is always de-excited to ground state. It can go to an intermediate state, called metastable state with a radiation less transition, where it stays for a much longer period than the upper level and comes down to lower level or to the ground state. Since period of stay of atoms in the metastable state is large, it is possible to have a much larger number of atoms in metastable level in comparison to the lower level so that the population of metastable state and the lower or ground state is reversed. i.e. there are more atoms in the upper metastable level than the lower level. This condition is referred to as population inversion. Once this is achieved, laser action is initiated in the following fashion. The atom in the metastable state comes down to the ground state emitting a photon. This photon can stimulate an atom in the metastable state to release its photon in phase with it. The photon thus released is called stimulated photon. It moves in the same direction as the initiating photon, has the same wavelength and polarization and is in phase with it, thus producing amplification. Since there are a large number of initiating photons, it forms an initiating electromagnetic radiation field. An avalanche of stimulated photons is generated, as the photons traveling along the length of the active medium stimulates a number of excited atoms in the metastable state to release their photons. This is referred to as the stimulated emission. These photons are fully reflected by the rear reflector (100% reflective) and the number and consequently the intensity of stimulated photons increases as they traverse through the active medium, thus increasing the intensity of radiation field of stimulated emission. At the output coupler, a part of these photons are reflected and the rest is transmitted as the laser output. This action is repeated and the reflected photons after striking the rear mirror, reach the output coupler in the return path. The intensity of the laser output increases as the pumping continues. When the input pumping energy reduces, the available initiating and subsequently the stimulated photons decrease considerably and the gain of the system is not able to overcome the losses, thus laser output ceases. Since the stimulation process was started by the initiating photons, the emitted photons can combine coherently, as all of them are in phase with each other, unlike in the case of spontaneous emission and coherent laser light is emitted (Fig.5). Though the laser action will continue as long as the energy is given to the active medium, it may be stated that pulsed laser is obtained if the population inversion is available in a transient fashion and continuous wave (CW) laser is possible if the population inversion is maintained in a steady-state basis. If the input energy is given by say a flash lamp, the output will be a pulsed output and the laser is called a pulsed laser.