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The Purcell effect, it's influence on the lifetime and quantum yield (of fluorophores)

Physics Asked by Bob van de Voort on September 26, 2021

So I’ve been looking into the Purcell effect and how it interacts with fluorophores (fluorescent molecules). The Purcell arises when you have a dipole in a cavity or even just near a dielectric or metal interface. It can then enhance the emission of the dipole in comparison to free space.

Now for fluorophores two factors are affected by the Purcell effect, the quantum yield and the decay time (aka, relaxation time or lifetime). Now what I don’t know is when and by how much either is affected. This is important for me to know because fluorophores are intrinsically limited as they can only emit 1 photon and absorb one at the same time. Being a bit more specific, they have a saturation in the sense that they can not absorb a new photon if they’re still in the exited state. Now I know that for high quantum yield fluorophores the Purcell effect should mostly affect the decay time.
Now what I would like to know is there a good way to find how much both quantum yield and decay time are affected (approximation). What happens to a saturation curve of fluorophores, what changes, slope, offset, something else?

Also any sources of information (fundamental) are also very much appreciated, especially the fundamentals of the Purcell effect. Like I can understand why there’s an enhancement of the power emitted if the dipole is in a resonant cavity, as that intuitively makes sense, however I have more trouble understanding this if a dipole is just very close to a dielectric interface.

Ps I have a good understanding of optics/photonics but as good as none about quantum.

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