# Could someone explain the Forster Resonance Energy Transfer?

My understanding of it so far is rather messy, and I haven't found a good source yet that describes WHAT it is rather than just stating lots of equations! I have read a source that mentioned it having something to do with the alignment of magnetic fields with an external vector (unfortunately I have lost this link, but I will include it here of I find it again). Although I am not sure why this would be the case as there isn't a magnetic field in, for example, a photosystem in the chloroplast is there?

Wikipedia said that it had to do with transfer of virtual photos in a situation analogous to energy transfer by light whose wavelength exceeds the distance between source and receiver. I thought this was an interesting concept and have never heard of it before...

So any insight without too much math would be much appreciated!

## 2 Answers

I will try to give a simple explanation.

Imagine there is an emitter (atom/molecule/quantum dot) in an excited state. Usually it can return to the ground state by releasing a photon.

Now consider an absorber with a similar energy gap between its ground and excited states. If we could somehow excite this absorber with the photon from the previous emitter, it would absorb.

In FRET, the emitter and absorber are placed very close to each other (relative to the wavelength of the photon). Thus the energy transfer occurs through near field coupling. Consider the emitter as an oscillating electric dipole with the transition dipole moment. In the near field of the emitter, the electric field is much stronger than the $1/r$ decay in the far field. As a result this strong electric field has a much higher probability of causing a transition in the absorber than in the far field. Since we are using an energy channel that we would not be able to tap through "real photons" in the far field, we can think of the energy transfer as happening through virtual photons. But the essential underlying physics is the same: the emitter causes local field at the location of the absorber, resulting in the deexcitation of the emitter and the excitation of the absorber.

So , basically Förster Resonance Energy Transfer or FRET is a process of Energy Transfer. Basically I have worked with Quantum Dot Polymer nanocomposites and hence can explain the concept to you in that respect. Suppose I mix two materials (A:B for example QD:polymer/polymer:polymer/QD:QD) which have interesting optical properties and if the emission spectrum of A co-incides with the absorption spectrum of B, then a photoluminescence test of the composite A:B would lead to the a heightened emission only from B. The reason is because an emission from A would be absorbed/transferred by/to B via energy transfer and then the emission of B would obviously be slightly red shifted to its absorption. Hence the composite material would have a higher B emission. I mean suppose you have $\beta_1$ moles of $A$ and had a emission function per mole of $f_1(\lambda)$ and similarly $\beta_2$ moles of $B$ with a molar emission function of $f_2(\lambda)$ where $\lambda$ is the wavelength of emission. Then the composite $A:B$ will have a net molar function $f_{net}(\lambda)\neq\beta_1f_1(\lambda)+\beta_2f_2(\lambda)$. If the ratios are iterated backwards from the net emission $f_{net}(\lambda)$ then the ratio of $B$ wrt $A$ calculated will be higher than the actual ratio. These optical non-linear effects are signatorial evidences of energy transfer.

The Förster transfer competes against other radiative and non-radiative path ways of decay hence the yield of Energy Transfer is defined as $Q=\frac{R_{ET}}{R_{ET}+\sum_{i}{R_{RD}}_i+\sum_{j}{R_{NRD}}_j}$. In the example described above, if $g_1(\lambda)$ and $g_2(\lambda)$ are the molar absorptivities of $A$ and $B$ then the overlap integral $S=\frac{\int_{-\infty}^{+\infty}f_1(\lambda)g_2(\lambda)\lambda^k\mathrm{d}\lambda}{\int_{-\infty}^{+\infty}f_1(\lambda)\mathrm{d}\lambda}$. Here $k$ is mostly derived from experimental fits. The higher the overlap integral, the greater the distance across which the energy transfer could be executed with considerable probabilities.

The part of energy transfer due to virtual photons is in my opinion just a mathematically modellable way to explain the energy transfer. We know that the lower the distance between the elements of the composites $A$ and $B$, the higher the chances of energy transfer. For energy transfer via real photons, two things needed to be justified, the conservation of energy and the conservation of momentum, that is the distance between $A$ and $B$ in my opinion should be $\frac{n\lambda}{2}$, or else the Transfer process wouldn't resonate efficiently. This leads to a conservation of momentum and this would be true if there was real photon exchange, but what transpires is that it is found from distances $d<<\frac{\lambda}{2}$, the energy transfer probabilities keep increasing undauntedly and hence a conservation of momentum is not required. So a transfer process where a conservation of energy is obviously required but not a conservation of momentum is basically modeled as a transfer via a virtual photon.