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Suppose I have a 1D material of lenght 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 vaccum (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.