Population differences inverting

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. 

Consider the 13C— H bond as a two-spin system. CH coupling occurs between one nucleus with small population difference (13C) and another one with large polarization (1H). Fig. 2.43(a) illustrates this situation by the number of dots on the energy levels. Population inversion of the proton levels 1 and 3 connected by the transition 1H1 is achieved by an appropriate 180° pulse, which turns the double cone of precession shown in Fig. 2.1 upside down. Thereafter, the inverted proton population difference controls both carbon-13 transitions (Fig. 2.43(b)). This is the polarization or population transfer making up an enhanced absorption signal for one transition (e.g. 13Ci in Fig. 2.43 (b)) and an enhanced emission on the other (e.g. 13C2 in Fig. 2.43(b)). 

The induced transitions change the populations of the different energy levels. After a 90° pulse the populations are equalised, and after a 180° pulse the populations are inverted so that for a spin- /2 nucleus the + h state now contains the population excess. 

Although once popular, this experimental approach is rather less used nowadays and as such shall be considered no further. The more common approach to obtaining kinetic data is to instantaneously perturb a spin system not by saturation but by inverting the target resonance(s) (that is, inverting the population differences across the corresponding transitions) and then allowing the NOE to develop in the absence of further external interference. The new populations are then sampled with a 90° pulse as usual (Fig. 8.20). In this case the NOE is seen initially to build for some time but ultimately fades away as spin relaxation restores the equilibrium condition these enhancements are thus termed transient NOEs. 

If the inverted population difference A A of the active medium is larger than AAthr, a wave that is reflected back and forth between the mirrors will be amplified in spite of losses, therefore its intensity will increase. 

In the case of a homogeneous profile g(v —vo)> all molecules in the upper level can contribute to stimulated emission at the laser frequency Ua with the probability Bikpgiva I d), see (5.8). Although the laser may oscillate only with a single frequency v, the whole homogeneous gain profile a(v) = ANa v) saturates until the inverted population difference AN has decreased to the threshold value AAthr (Fig- 5.23a). The saturated amplification coefficient asat(v) at the intracavity laser intensity / is, according to Sect. 3.6,... 

A laser is a little more complicated than a LED in which an inverted population of excited states must be created so that stimulated emission can occur. One way of accomplishing this is by doping the Fermi level on the n-side above the conduction band and the p-side below the valence band as shown in Figure 21.18a. Now when the jimction is biased, the filled states in the n-materials are lifted above the empty states in the p-material and the population is inverted as seen in Figure 21.18b. The battery continues to supply electrons to the n-material to replace those that fell into the unfilled state by emitting photons with energy equal to the difference between the conduction band and the imfilled states near the valence band. 

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