Calculating the spontaneous emission rate for a material

[Lior Fa]

Hi,
Suppose I have a 1D material of length L, and I want to calculate the spontanious emission rate Γ at ressonance frequeny.
From my understanding, when light passes in a material at ressonance frequency it gets absorved by an electron in the atom, and after a spontaneous emission time t_spont the electron emits a photon by geting down to the last energy level. This photon gets to the next atom nearby, and the electron of that atom absorves it (in some propabilty) and after the same t_spont emits it again, and so on for the rest of the atoms.
My question is, if I know the atom density per meter N (1D material) and the refractive index n, I can calculate the time t_material-t_vaccum which is the time difference of light coming out of the L length material in contrast to the time of the light to travel L in the speed of light in vacuum (L/c), can I calculate the spontaneous emission time of the material from:
t_spont = time_difference/N = (L*(1/c)-(n/c))/N
where N is the density of atoms per unit length.
I have an assumption here that the light interacts with each atom, but I can upgrade this formula for N= atom densitiy times the propabilty that the photon interacts with the electron in the atom.

 

[Buzz Bloom]

Hi Lior:

Since no one has responded to your post, I thought I would post the reference below that might possibly be of some help to you.

https://en.wikipedia.org/wiki/Einstein_coefficients​

Regards,
Buzz

 

[Khashishi]

tspont = time_difference/N = (L*(1/c)-(n/c))/N

From where did you get this equation?
The units don't look right. Time can't equal time divided by density.

Are you using the Lorentz oscillator model for the material? Are you using a complex number to represent n?
You might be able to calculate the spontaneous emission using the Fermi golden rule, if you can obtain densities of states.