Can Laser be generated with only rapid decay levels?

dimanche 1 septembre 2013

I'm new to laser technology and learning it from some lecture videos and a textbook "Optics & Lasers".

When I came to the light amplifier part, I got stuck in understanding the difference between "rapid decay" and "metastable state" -- what I can recite now is that "rapid decay" cannot generate laser emission while "metastable state" can.

Basically I understand the Professor's description on why a 2-level system is not capable of laser emission in this lecture video (starting from around 05:00) : https://www.youtube.com/watch?v=Re07gHGEZNo

However, what if I have a 3-level system just like the Ruby Laser (depicted in the attachment) but all inter-level transitions are "rapid decay"? Can I generate laser with such a system?

To be specific, if I want to use some material to make a light amplifier and I have:

3 energy levels a, b, c where a is the lowest level and b is the highest with the material;

[itex]n_a, \; n_b, \; n_c[/itex] indicate the number of atoms at each level in the amplifier respectively;

the amplifier starts with [itex]n_a = N, \; n_b=n_c=0[/itex] where [itex]N[/itex] is an integer;

atoms at level a will be continually pumped to level b, and I have an infinite energy pump (does the power of the pump matter here?)

atoms at level b will decay rapidly (generally in nano-seconds as said in the lecture video) to level c

atoms at level c [itex]ALSO[/itex] decay rapidly to level a!

Can I generate laser with this setting? I expect a continuous rapid decay between level b and level c would occur and laser would be generated by that.

I also have another question with my assumed setting, may I achieve the situation that [itex]n_c > n_a[/itex] at some time? Will "rapid decay" occur when [itex] 0< n_c < n_a[/itex] or is "rapid decay" independent of population difference?

Any help will be appreciated :)

Attached Images