1. Atomic transitions and electromagnetic waves
The interaction of an assembly of identical atoms with a radiation field
spontaneous emission
stimulated emission
absorption

2. Transition rates
the photon energy density per unit frequency
The interaction of an assembly of identical atoms with a radiation field
transition rates
the population densities of levels 1 and 2
spontaneous emission
stimulated emission
absorption

3. Determination of the Einstein coefficients
We consider the case where the atoms are in a thermal equilibrium with a blackbody radiation field
(Planck’s law)
(total downward transition rate = total upward transition rate)
(Boltzmann statistics)

4. Conclusions for the LASER
We need a large photon concentration, this is achieved in an optical cavity
We need population inversion, i.e., The LASER principle is based on non-thermal equilibrium.

5. Induced transitions
Induced transition rate per atom (stimulated emission, absorption):
the spontaneous lifetime of the atom
Including the spectral lineshape function leads to (for details, see Yariv-Yeh, page 227)
(monochromatic field)
intensity [watts/square meter]
energy density [Joule/volume]

6. Absorption and amplification
Induced transition rate per atom
The net power generated within a unit volume
For plane wave propagating in z
gain coefficient

7. Absorption and amplification
gain coefficient

8. Ytterbium-Doped Fiber Amplifiers

9. Ytterbium-Doped Fiber Amplifiers

10. Ytterbium-Doped Fiber Amplifiers
(for the signal power)
(for the pump power)

11. Ytterbium-Doped Fiber Amplifiers
(for the signal power)
(for the pump power)