M5L23o.txt

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Now we have to make the connection that the statement
that we need inversion for lasing was related
to absorption, but now we've cancelled absorption.
So now what we want to do is we want
to create a situation where we have lasing.
We want to put population into the excited state,
but the population in this excited state
will be much, much smaller than the population in the ground
state, so you're not even close to inversion.
So let me draw the diagram.
We have lots and lots and lots and lots of population
in the ground state.
We have zero population in e1, and in e2
we just have a little bit.
And now you would say, well, you don't have inversion,
how can you get lasing?
But if you have now a cavity at frequency omega 0,
then you can say the Lorentzian profile of the excited state e2
overlaps with omega 0, so at least you
have some possibility for the excited state e2
to decay into the cavity mode.
And therefore, a very weak field in the cavity mode
will be amplified by stimulated emission
without suffering any absorption,
so therefore, it will be amplified and we have gain.

So if you have a cavity at omega 0,
we have gain because we have some stimulated emission
at omega 0, but no absorption.
Of course, if you would tune your cavity
to be in a resonance with e2, you
would have more stimulated emission.
But you would have much more absorption,
and you would not be able to get a net gain
for a small [? probe ?] field, so you would not have a lasing.
So you can say that what we have achieved here in a three level
system, we have accomplished destructive interference
for absorption.
But the way how we've population just in e2,
we have not any destructive interference
for the stimulated gain.
So we have tweaked on the lasing equation, the laser equation,
the absorption part, but not the stimulated emission
part by interference in a three level system.