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Are there examples of “loss-less” Forster Resonance Energy Transfer (FRET)?

When I think of a Forster Resonance Energy Transfer (FRET) process, I typically imagine the initial excitation of an absorbing chromophore with a photon followed by the subsequent emission of a lower ...
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What is the “direction” of the transition dipole moment? (Understanding Eq. 9.29, Charge and Energy Transfer 3rd Ed, May & Kuhn)

For a real vector $\mathbf{r}$, the direction is given by: $\hat{\mathbf{n}}=\mathbf{r}/\left|\mathbf{r}\right|$. The transition dipole moment is a complex vector. How do you define its direction? ...