Laser Pumping Requirements and Techniques

1. Laser Pumping Requirements and Techniques

2. Excitation or Pumping Threshold Requirements • Let the density of pumping states be N and the rate of excitation Γ i.e. NΓ. • Any amount of population that is pumped into level u will decay within the lifetime associated with that level. • The pumping process to sufficiently fill level u effectively starts over for each lifetime duration τu of that level.

3. In athree level laser with the upper laser level as the highest level the population density of upper laser level under steady state can given by Where Njis the density in the state j of the species from which the energy is to be transferred, Γju is the pumping rate to the upper laser level u and γu is the decay rate of level u, from which we have τu = 1/γu (γul + γuo has been replaced by γu).

4. Thus it can be seen from (1) that longer the lifetime of the level , the more population will build up in that level. • It is well known that the exponential gain factor is expressed by σul[Nu-(gu/gl)Nl]L; the first portion of the factor leading to gain is the product σulNuL, whereas the factor - σul (gu/gl)NlL associated with the population density Nl in the lower laser level l. • It is detrimental to producing gain. • Thus to determine the minimum pumping flux required, we will only deal with Nu. • More pumping flux would be required if Nlbecomes significant compared to Nu.

5. Thus minimum threshold condition for making a laser will be given by σul NuL = σulL ≈ 12 ±5 ………(2) with no mirrors. σul NuL = σul L = ½ ln(1/R1R2) with mirrors ………………………….(3) • If l has a significant population, then one or more of the pumping factors of (2) and (3) would have to be increased in order to make up for the absorption loss due to the population in level l.

6. In order to maintain a significant power from a laser, the pumping must significantly exceed these threshold requirements. • In a steady state laser the gain coefficient g will be reduced to gth as the power is extracted, owing to the fact that the stimulated emission rate will increase the population decay of level u until the net gain is zero. Thus, the stimulated emission rate is an automatic adjusting parameter that keeps the net gain at a zero value.

7. For pulsed lasers, the threshold pumping requirements can be different than those summarized. • The population Nu was obtained from a steady state solution of the rate equations. • For pulsed conditions, the duration and time dependence of the excitation pulse must be considered in determining the desired value of Nu.

8. Indirect Pumping Direct Pumping Pumping Pathways

9. u Laser γul Γou = I Bou/cΔν l o Excitation by Direct Pumping • In the direct pumping process, the excitation flux is sent directly to the upper laser level u from a source or target state j in which the source state is the highly populated ground state o of the laser species. • This direct pumping process is shown in figure below

10. The pumping rate Γou can be described in general in terms for either optical pumping or particle pumping. Optical Pumping • It is the process most often used for solid state and organic dye lasers. The excitation involves absorption of the pumping light within the gain medium, so we can write Γou as I is theoptical pumping intensity within the absorption linewidth Δν of the absorbing species.

11. Particle Pumping • It is the process generally used for gas lasers and also semiconductor lasers. For gas lasers, Γou can be written as Γou = Np kou …………… (2) where Np is the pumping particle density ( equivalent to the intensity factor I in eqn.(1) for optical pumping) and kou is the reaction probability for causing a transition from level o to u when a particle p collides with laser species in level o; kou has dimensions of volume per unit time.

12. This probability kou is often broken down into the more useful factors σou, the cross section or probability for the transfer of energy from level o to level u , and vpo, the average relative velocity between the colliding species p and the target species o. • The relation between these terms can be expressed as kou = vpoσou …………………..(3) • Thus the population flux rate into level u from level o can be expressed as ΓouNo = Np vpo σouNo ………………… (4)

13. In the case of gaseous discharge, where the particles labeled p are electrons, (4) can be expressed as Γou = ne ve σoue ………………(5) Here ne is the electron density, ve is the average electron velocity, and σoue is the velocity averaged electron excitation cross section from level o to level u. • The minimum pumping power per unit volume to achieve laser action will be given by Pou= ΓouNoΔEou

14. Excitation by Indirect Pumping These processes involve an intermediate level q and can be considered in three general categories as diagrammed in figures below: u u q Transfer Transfer Laser Laser q l Pumping l Pumping o o Transfer from below Transfer across

15. q Transfer u Laser Pumping l o Transfer from above Although these are simplified descriptions, they can be used to categorize, in a reasonably systematic way, almost all of the laser excitation processes other than direct pumping.

16. For all three cases, the flux transfer rate from a level q to the upper laser level u can be written as NpvpσquNq …………………. (6) for particle transfer, such electrons and heavy particles, and as Nq………….. (7) for transfer by photons.

17. Advantages of Indirect Pumping • In some cases, the intermediate level q has a lifetime τq that is much longer than the lifetime τu of level u. Hence level q can serve as reservoir of population that is energetically near level u, with possibility of transfer from q to u being much simpler than direct transfer from o to u(owing to much smaller energy separation). • Transfer from q to u can be quite selective, in many cases, which implies that it occurs much more favourably to the upper laser level than to the lower laser level. This can often happen in situation where direct pumping from o to u would not be selective or might even be detrimental to the generation of an inversion.

18. Level q can have very broad width and thus accept pumping flux of intensity I over a broad range of energies, in contrast with the upper laser level u, which might be quite narrow in order to provide a high stimulated emission cross section. This q level capability is particularly advantageous for solid state lasers in which the pump bands are broad enough to collect the flux from a flash lamp having a broad spectral output. Examples Transfer from below: Argon ion laser, He-Cd laser, Ar++ laser etc. Transfer across: He-Ne laser, CO2 laser, He-Se laser etc. Transfer from above: Ruby laser, Semiconductor laser, dye laser etc.

19. Specific Excitation Parameters Associated with Optical Pumping Pumping Geometries • Optical pumping can be accomplished by many different light sources, including flashlamps, lasers, solar flux and laser produced plasmas. • In all cases the same pumping considerations apply. In order for pumping to occur, the light from the pumping source must be absorbed by the gain medium.

20. Flash lamp Gain medium Direct Flash lamp Gain medium Elliptical cavity Reflectors Gain medium Gain medium Flash lamps Flash lamps Double Elliptical cavity Slab laser amplifier • This can be accomplished by a number of techniques, few of them have been shown in the figure below

21. Pumping Requirements • Considerations for optical pumping can be described in terms of how the gain medium can best be designed to take advantage of the pumping flux. • Let us assume that the pumping flux is incident upon the gain medium with an intensity Io. • It would be desirable to use as much of the pumping flux as possible in order to make the pumping process efficient.

22. That absorption process is described by an equation of the form of Beer’s Law. The change in intensity within the rod thus varies as • The direction of pump beam is designated as x, and the direction of the laser beam has been assumed earlier along z axis. • However the pump beam can be in any direction including the direction of laser beam.

23. As the pumping flux penetrates the gain medium and populates the upper laser level u, the population in the upper level would have a distribution in the x direction that follows Beer’s law. • We can express the desired gain coefficient go within the medium we are attempting to pump optically as go=σulΔNul≈σulNu ………… (3) This would provide the absolute minimum pumping flux. We also know that

24. Using we get:

25. The term inside the bracket is recognized as the stimulated emission cross section σuo on the pumping transitions from level u to level o. Thus (5) can be written as Now solving for the pump intensity I that would produce a specific small gain coefficient go to be used in (1) and (2), we get:

26. Thus the pumping intensity within the absorption bandwidth of the absorbing transition is determined by the photon energy hνuo of the pump beam, the laser transition probability Aul, the desired gain coefficient go at the center of the desired laser transition, the absorption coefficient αou at the center of the pumping transition. • We can see from (7) that gain will vary in proportion to the pumping intensity. It will thus vary exponentially within the medium in the x direction during the pumping process according to (1) and (2).

28. Carbon Dioxide Laser The CO2 laser operates analogously. N2 is pumped, transferring the energy to CO2.

29. The Ruby Laser Invented in 1960 by Ted Maiman at Hughes Research Labs, it was the first laser. Ruby is a three-level system, so you have to hit it hard.