Jeudi 10 avril 2014
Some new elements about the debate whether Förster resonance energy transfer can be tuned (or not) with the photonic environment have been recently published in Nature Communications.The authors use a model system of nanocrystals co-doped with Ce3+ donors and Tb3+ acceptors.To tune the photonic environment and the local density of optical
states (LDOS), the authors change the refractive index n of the solvent. The experiments conclude that the donor emission rate increases linearly with the refractive index n, while the energy
transfer rate does not.This brings the authors to the general conclusion that "FRET rates are independent of the photonic environment". I feel this conclusion so abrupt that it deserves
at least a comment here.
First, let's look back at Förster theory as derived in the late 40s. On wikipedia, one can readily find that the rate
of spontaneous emission can be described by Fermi's golden rule, and that under the dipole approximation the radiative rate is given by:
which directly shows that the emission rate scales linearly with the refractive index n of the environment. This is what the authors observe for their donor emission. Turning to FRET, the
well-established Förster theory states that the energy transfer rate scales as the product of
the donor emission rate in absence of the acceptor time the sixth power of the Förster radius Ro, which is given by:
Here, the Förster formalism indicates that Ro scales with the refractive index as (1/n4)1/6 so 1/n2/3, which is almost constant for most refractive indexes of
common solvents. So the Förster radius is not expected to vary noticeably as the refractive index is changed, which is again what the authors observe.
The expected evolution of the energy transfer rate ΓFRET = Γ rad (R0/r)6 can be deduced from the two equations above as function of the refractive index. The FRET rate
then evolves as n/n4 = 1/n3, so the energy transfer rate actually decreases when the refractive index is increased. Nothing really special here, just the standard Förster theory from 1948.
Based on the above observations, how can one conclude that FRET rates are independent of the photonic environment? What is true (and well within the Förster theory) is that increasing the
refractive index increases the radiative decay rate and reduces the energy transfer rate. However, the authors skip that the refractive index comes as some sort of prefactor in the
porportionality relationship between the emission rate and the LDOS. There are actually two ways to tune the LDOS and the photonic environment. The obvious way is to change the medium refractive
index (or the emission wavelength). The second (and physically relevant) way is to play with the secondary local field Es that is back-scattered by the (inhomogeneous) environment onto
the emitter (equivalent to Green's dydadic approach). This is the only way to enhance the LDOS by more a hundred times, and requires photonic crystals or plasmonic antennas.
This is not simply a pure theory debate, FRET has huge applications in bioimaging, lighting sources and photovoltaics, and plays a key role in photosynthesis. Only complex photonic environments can assess the relationship of FRET with the LDOS and unlock the application of the nanophotonics toolbox to enhance FRET.
Do not get me wrong: I don't say/think the paper is wrong, I don't say/think the reviewers or editors took a bad decision, I don't go into personal debate. I simply discuss the scientific
conclusion that one can draw from this study, they are far away from "settling the debate about conversion of light".