Stimulated emission in Nd:silica glass, energy levels broadening and lasers It is known that due to absence of uniform crystalline structure in Nd-doped glasses (comparing to Nd:YAG and Nd:YVO4 crystals) energy levels of Nd+ are significantly broadened. 
This means that we have broadened absorption and emission peaks. Broadened absorption peak seems favorable, as it allows us better utilize energy of flash lamps or diode sources.
But we still have wide emission peak (up to 30nm wide). What happens when 1065nm photon reaches excited atom ready to emit 1055nm and vice-versa? I understand that excess energy will go to heat/be extracted from heat, but what is typical gain bandwidth we can completely deplete in single-frequency laser?
Are we doomed to have super-wide emission spectra from Nd:glass laser or have terrible efficiency when trying to make it narrow-bandwidth (or even single-frequency) by missing energy levels of 99% of excited atoms? Will we be able to excite 100% of Nd+ atoms in Nd:silica glass using 808nm laser, or only small fraction of them which happen to have their individual absorption peak overlaping 808nm laser emission (which is ~2nm wide)?
So to recap: Can someone clarify how does Nd:silica glass behave when a) pumped by narrow-band source, like 808nm laser b) excited in single-frequency laser with narrow-band pumping c) excited in single-frequency laser with wide-band pumping (flashlamp)
 A: (This is only a partial answer to one-third of your question.)
I'm sure you already know this but ...


*

*Inhomogeneous broadening is what you're talking about where different Nd atoms are in different microscopic environments and therefore emit at different wavelengths.

*Homogeneous broadening is where even a single Nd atom can emit at some range of different frequencies because of natural linewidth.
Even if a gain medium has inhomogeneous broadening, it also has homogeneous broadening!
After searching for 30 seconds I couldn't find data on Nd:silica but I did find info on erbium-doped silica fibers here. Let's use that as an example.
This book says that the inhomogeneous broadening (for Er) is ~30nm and the homogeneous broadening is ~6nm. Therefore if you have a broadband (flashlamp) pump for a monochromatic laser...


*

*About 20% of the Er atoms will be great for helping the laser via stimulated emission

*Maybe another 0-60% will be kinda bad at stimulated emission at the laser frequency, but will do it anyway if the laser light is strong enough and the competing decay channels are slow enough (I made up those numbers. The point is, the natural lineshape is a smooth gradual decay, the "width" is not a sharp line)

*The rest of the Er atoms are useless for the laser.
That's the Er version of your question (c) I think.
For your other questions (a) and (b), I have no idea because now you're talking about inhomogeneous broadening of the pump absorption frequency rather than broadening of the emission frequency, in this three-level system. I have no idea how they relate. I hope someone answers.
