The Sparse Intermediate Case

We conclude that a simple exponential decay is an adequate description of the time dependence of Pemission(t) provided that coupling between all resonance levels (or optically active zero-order states) undergoing transitions may be ignored. 

The radiative damping matrix F is of greater importance for discussing radiative transitions and is closely related to the Fermi Golden Rule. It is defined in a manner that accounts for some type of interference effects (i.e., anticrossing-type interference effects)  

In Equation 6.33, there is a sum over the zero-photon excited states a (after radiative decay) as well as a sum over the polarization e and an integration over the direction Q t of the emitted photon. Qph(rfc) is the density of photon states. F( ) is generally nondiagonal, as will be illustrated in the next section. In the ills, tpj representation however, it is easy to verify from Equation 6.15 that 

The off-diagonal contribution will be important only in the case of near-degeneracy when these terms are comparable to the energy spacing between the energy levels, that is, 

In such a case, it is known [80, 144] that the two states a) and a ) do not decay independently and the radiation coupling leads to a mixing of states. 

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