Inverted population

Note that is the population difference between the upper and lower states having all the population in the lower state corresponds to = -1 while having a completely inverted population (i.e. no population in the lower state) corresponds to f3 = +1. 

It was shown above that the normal two-level system (ground to excited state) will not produce lasing but that a three-level system (ground to excited state to second excited state) can enable lasing. Some laser systems utilize four- or even five-level systems, but all need at least one of the excited-state energy levels to have a relatively long lifetime to build up an inverted population. 

A dye molecule has one or more absorption bands in the visible region of the electromagnetic spectrum (approximately 350-700 nm). After absorbing photons, the electronically excited molecules transfer to a more stable (triplet) state, which eventually emits photons (fluoresces) at a longer wavelength (composing three-level system.) The delay allows an inverted population to build up. Sometimes there are more than three levels. For example, the europium complex (Figure 18.15) has a four-level system. 

If the flash lamp is pulsed very rapidly, the emergent beam appears at a rate governed by the lifetime of the inverted population. The resulting laser beam becomes almost continuous because the pulses follow each other so rapidly. However, such a solid-state laser should not be pulsed too rapidly because, if it is, the rod heats to an unacceptable extent, causing distortion and even fracture. Generally, solid-state lasers are not used in continuous mode because of this heating aspect. Liquid or gas lasers do not suffer from this problem. 

Lasers act as sources and sometimes as amplifiers of coherent k—uv radiation. Excitation in lasers is provided by external particle or photon pump sources. The high energy densities requked to create inverted populations often involve plasma formation. Certain plasmas, eg, cadmium, are produced by small electric discharges, which act as laser sources and amplifiers (77). Efforts that were dkected to the improvement of the energy conversion efficiencies at longer wavelengths and the demonstration of an x-ray laser in plasma media were successful (78). 

Other methods of excitation are effective or necessary for certain gain media. For example, certain energetic chemical reactions produce molecules in excited states. These excited molecules may then comprise the upper laser level of an inverted-population system. A specific example is the hydrogen fluoride "chemical laser" wherein excitation is provided by the reaction of hydrogen gas with atomic fluorine. Another method of excitation is simply the passage of an electric current through a semiconductor device. This serves as the exciter for diode lasers. 

Indeed, the laser oscillation itself frequently is a transient emission that falls into the broad definition of fluorescent lifetimes. In particular, spiking phenomena (5) and Q Switching (4) clearly bear a close relationship to relaxation times and processes. One could say that laser phenomena are associated with the study of fluorescent decays of inverted populations. 

The voltage-current curve is now asymmetric, a large step corresponds to the resonant level with inverted population. 

Hydrogen and other one-electron atoms can be made into lasers because the state lifetimes vary so greatly. For example, an X-ray laser can be built by blasting carbon rods with an intense field, stripping off all the electrons. When the first electrons recombine with the nuclei, one-electron C5+ atoms are created in a wide variety of stationary states. Any population in the 2p states rapidly decays to the ground state population in 3s or 3 d decays more slowly. Thus the 3s —> 2p and 3d —> 2p transitions develop an inverted population distribution, and lase at the energy difference between the two states (A, = 13.6 nm). 

The reactions, 0(3P) + CS and 0(3P) + C Se, are very similar in their dynamics [450—452]. They are both direct reactions producing CO in high vibrational states with inverted population distributions ( 80 and 70%, respectively). The similarity of the dynamics is illustrated by the virtual identity of the CO vibrational population distributions for the two reactions when plotted against Fv [452]. It seems most likely in view of the direct nature of the reactions that they take place on a repulsive triplet surface without a crossing to the lower singlet surface corresponding to the stable species, OCS or OCSe. 

Figure 11.4. Effect of spin state populations (indicated by the relative thickness of the lines) on NMR signal intensity, (a) Larger than normal excess in lower state, giving enhanced absorption (b) normal slight excess in lower state, giving normal signal intensity (c) saturation, giving zero signal and (d) inverted population (excess in upper state), giving net emission.

The best prospect for creating a chemically driven electronic transition laser is to use a transition where the upper laser level is metastable. Chemical methods that generate high yields of certain metastables have been developed, but so far it has not been possible to achieve lasing on the primary products. For example, inverted populations of the metastables NF(a A) and NCl(a A) can be generated by chemical means, but the a A —... 

A generalized energy level scheme for laser action is shown in Fig. 1. If the terminal laser level is the ground state and the initial and final laser states have equal degeneracies, then more than one-half of the ions must be excited to obtain an inverted population and 3-level laser action. If, instead, the terminal level 2 is above the ground state, then only an excited-state population in level 3 sufficient to overcome the Boltzmann population in level 2 is needed for population inversion. This drastically reduces the pumping requirements. Phonon-terminated or vibronic lasers are those in which level 2 is a vibrational-electronic state. 

If a sample of molecules with inverted populations is placed in an optical cavity which may consist, for instance, of two suitably aligned mirrors (see next section), induced radiation can change the densities N and N of Eq. (1). The interaction of a system with population inversion with a radiation field of the right frequency v can be described in the so-called rate equation approximation. The simplified rate equations for the laser are obtained as follows if two states Ni, Na are considered with the energy difference AE =hvia connected by a radiational transition (13). 

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