| Topic: |
Science > Physics |
| User: |
"" |
| Date: |
09 Mar 2005 03:27:26 PM |
| Object: |
spontaneous emission equation-energy density |
My 3 texts on the spontaneous emission of light in a laser, all
represent the transition rates between state 1 and 2 as:
W'21 = B21 r(v) and W'12 = B12 r(v) (read r as rho and v as the
frequency nu)
Perhaps this is the original form in Einstein's paper. My problem with
this, is that the transitions from 1 to 2 can only occur at absolutely
one energy increment: E2-E1 = hv
(I presume homogenous and inhomogenous broadening are neglected here)
So why is the energy density given as a function of v in the equations?
This would imply that any energy of photon could stimulate emission?
TNX
Fritz
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| User: "Bjoern Feuerbacher" |
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| Title: Re: spontaneous emission equation-energy density |
10 Mar 2005 04:11:23 AM |
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wrote:
My 3 texts on the spontaneous emission of light in a laser, all
represent the transition rates between state 1 and 2 as:
W'21 = B21 r(v) and W'12 = B12 r(v) (read r as rho and v as the
frequency nu)
Perhaps this is the original form in Einstein's paper. My problem with
this, is that the transitions from 1 to 2 can only occur at absolutely
one energy increment: E2-E1 = hv
(I presume homogenous and inhomogenous broadening are neglected here)
So why is the energy density given as a function of v in the equations?
This would imply that any energy of photon could stimulate emission?
What is meant by r(v) is "the energy density for the frequency v (=
(E2-E1)/h) which can cause the transition".
Bye,
Bjoern
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| User: "Fritz" |
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| Title: Re: spontaneous emission equation-energy density |
11 Mar 2005 02:00:35 PM |
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OK and thanks Bjoem.
I note that the author, Jariv in this case, goes on later to introduce
rather empirically, g(v), the guassian distribution due to spectral
broadening. I presume in that presentation of the equations, one uses
r(v)xg(v) were v can be integrated over all v. I expect that the
perturbations which induce the broadening (molecular vibrations etc)
cause a slight shift in the eigenvalues E2 and E1 hence the laser can
function over a small range of stimulating EM field.
Regards and thanks again
Fritz
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