Population inversion steady state

Note that operation of a two-level laser system requires inversion of the population of the upper laser level with respect to the ground state—a theoretical impossibility under steady-state conditions if optical excitation is employed. 

An interesting development in molecular rotational relaxation has been the microwave double-resonance method176-178. The technique permits the exploration of the fine detail of the processes which occur in collisions of polyatomic molecules, and results for a number of symmetric tops have been reported. For example, Oka has described experiments on NH3 in which inversion doublets for selected J values were pumped by high microwave power. Pumping disturbs the population of the inversion doublet, and also that of other doublets which are populated from the original pair by collision processes. By absorption measurements of other inversion doublets with steady state irradiation, Oka has shown that in NH3/NH3 collisions, transitions which are allowed by the electric dipole selection rules (A/ = 0, 1, + - —) are preferred. Oka s analysis indicates that relaxation is most favourable in collision with molecules having similar J values, which are termed rotational resonances (R-R transfer). For example the process... 

Figure 1 Simplified age distribution pattern for a steady state extant population. In this case, the natality/mortality rate is 35% of the total population for a 10-yr interval (fc = 35 X 10 yr ). r ax is defined as the fifth percentile. In practice r ax is the age at which the resolution of the database becomes indistinguishable from the background. The b value for the same population is inversely proportional to the available time resolution T (Equation (2)). Today s instantaneous rates of deposition and erosion of sediments exceed those calculated from the geological record based on time resolution of 10 -10 yr (Sadler, 1981). It is therefore essential to stipulate the resolution T in consideration of rates (after Veizer and Jansen, 1985).

The steady-state population distribution g can then be obtained by inversion of the truncated matrix. 

In Fig. 2, we present the steady-state population inversion between the upper state 1) and the ground state 2), computed from the master equation (73), for r = 0 and different values of the phase difference 5<(> and the interference parameter p. It is seen that in the presence of quantum interference the population can be inverted on the 1) —> 2) transition and the inversion can be controlled by the phase difference between the driving laser fields [27],... 

Large steady-state population inversions can occur between vibrational modes with minimum laser excitation energy. ... 

Both loop gain and output power increase, until the loop gain reaches his maximum value at t. At this point the laser output power is increasing at its maximum rate. As laser operation extends past stimulated emission removes population from the upper laser level to the lower laser level faster than it can be replaced by pumping. Thus, the population inversion is reduced and, consequently, both amplifier gain and loop gain decrease. At f4, the laser stabilizes to steady-state output power and a loop gain of Gl = 1 This value needs to be maintained for CW steady-state laser operation. 

Mflii-steady-state concentration of triplets during the population inversion. There are now many laser dyes available which cover the full spectral range from the IR to the UV, and the best sources of up to date information are manufacturer s catalogues. However there are a few dye classes which are particularly useful as laser dyes, where the basic chemical skeleton is retained but changes in substituent are used to shift absorption and emission wavelengths, e.g. basic structures of 2.1, 4.1, 4.2, 4.6. 

Those spontaneously emitted photons which travel into the right direction (namely parallel to the resonator axis) have the longest path through the active medium and therefore the greater chance of creating new photons by induced emission. Above threshold they induce a photon avalanche which grows until the depletion of the population inversion just compensates the repopulation by the pump. Under steady state conditions the inversion has decreased to the threshold value the saturated net gain is zero and... 

If the relaxation processes are sufficiently fast, they rapidly damp the oscillatory fluctuations of the population inversion and a steady-state inversion is reached which equals the threshold inversion (see Sect,5.7). 

The main purpose of this chapter is to examine the mechanisms by which population inversions are created in the most important of currently available gas laser systems. First, however, we derive detailed expressions for the gain coefficient in gas discharges and consider the conditions that must be satisfied by the radiative lifetimes and collision rates involved to ensure that gain should exist in steady state systems. 

In order to derive the conditions necessary for steady state population inversion in a gas discharge, let the upper level be populated by collisions and radiative cascade from higher excited levels at the total rate atoms m s, as shown schematically in Fig.11.2. The corresponding rate for the lower laser level, S, specifically excludes the cascade contribution from level k to level i since, as we shall see later, this particular mechanism plays a significantly different role from those of the other contributing processes. 

Thus a steady state population inversion, N /gj > i Si> will be obtained only if the rates of excitation and decay satisfy the condition... 

Unfortunately the excitation rate to the lower level can never be zero since even in the absence of collisions with atoms and electrons, the lower laser level is populated by spontaneous emission from the upper level k at the rate k ki" minimum requirement which must be satisfied for a steady state inversion to be possible may be obtained in this case by substituting S =0 into equation (11.15) giving... 

In a helium-cadmium discharge, selective excitation by charge-transfer reactions produces steady-state population inversions between the levels of the (4d 6g - 4d 4f) and (4d °6f - 4d °6d) configurations, producing C.W. laser oscillation on the lines listed in Table 11.3 and shown dia-... 

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