1. PUMPING SCHEMES how to produce a population inversion in a given material? To achieve this an interaction of the material with a sufficiently strong em wave, perhaps coming from a sufficiently intense lamp, at the frequency ν = ν 0. Since at thermal equilibrium (N 1 /g 1 ) > (N 2 /g 2 ), absorption in fact predominates over stimulated emission. The incoming wave then produces more transitions 1→2 than transitions 2→1, so one would hope in this way to end up with a population inversion. When in fact g 2 N 2 = g 1 N 1, absorption and stimulated emission processes compensate one another, and, according to Eq. (1.2.1), the material becomes transparent. This situation is often referred to as two-level saturation. With just two levels, 1 and 2, it is therefore impossible to produce a population inversion.

2. is it possible using more than two levels of the infinite set of levels of a given atomic system? the answer in this case is positive, so we accordingly speak of a three-level or four-level laser, depending on the number of levels used (Fig. 1.4). In a three-level laser: atoms are in some way raised from level 1 (ground) to level 3. If the material is such that, after an atom is raised to level 3, it decays rapidly to level 2 (perhaps by a rapid nonradiative decay), then a population inversion can be obtained between levels 2 and 1.

3. In a four-level laser: atoms are again raised from the ground level (for convenience we now call this level 0) to level 3. If the atom then decays rapidly to level 2 (e.g., again by rapid nonradiative decay), a population inversion can again be obtained between levels 2 and 1. Once oscillation starts in such a four-level laser however, atoms are transferred to level 1 through stimulated emission. For continuous wave operation, it is therefore necessary for the transition 1→0 also to be very rapid (this again usually occurs by rapid nonradiative decay).

4. We could of course ask why one should bother with a four- level scheme when a three-level scheme already seems to offer a suitable way of producing a population inversion. The answer is that one can, in general, produce a population inversion much more easily in a four-level than in a three-level laser. We should seek a material that can be operated as a four- level rather than a three-level system. It is of course also possible to use more than four levels. In the so-called quasi-three-level lasers case the ground level consists of many sublevels, the lower laser level being one of these sublevels. the ground level and level 0 is the lowest sublevel of the ground level. The process by which atoms are raised from ground level to level 3 is known as pumping

5. There are several ways in which this process can be realized in practice, e.g., by some sort of lamp of sufficient intensity or by an electrical discharge in the active medium. the threshold is reached when the population inversion given by We can write: Take Where g(ν) the line shape function and we can write an expiration for the gain : or σ is the absorption cross section of the active medium and is the length of the cavity both values are constant for the system.

6. Now the gain is a constant multiplied by the line profile function. As we discussed before the maximum amount of energy gain at the frequency ν o where: Divide both equations we get: For homogenous broadening g(v) is given by, Substitute to get This equation gave the gain at any frequency nit only at ν o

7. Now we are going to get the where the condition of getting the laser is fulfilled and its relation with width range of the Gain ∆v. For the laser action the gain at frequency v o should be greater than the losses α( where α is the loss), i.e. Or Where N is integer represent the ratio between losses and gain

8. From the figure a = g o (v 1 ) Bandwidth for the laser action between two energy levels given by this equation which can be represented graphically by the curve

9. Summary: For large N the amount of the gain is greater than the loss this is best efficiency for the laser. For N=2 the laser frequency range is equal to the width range of the Gain ∆v and the gain twice the amount of loss For N=1 the amount of the gain is equal the amount of loss Bandwidth for the laser action is zero ν 2 -ν 1 =0 For N<1 the loss will be greater than the gain and there is no laser