Gold nanorods are extensively used for single-molecule fluorescence enhancement as they are easy to synthesize, bio-compatible, and provide high light confinement at their nanometer-sized tips. The current way to estimate fluorescence enhancement relies on binned time traces or on fluorescence correlation spectroscopy. We report on novel ways to extract the enhancement factor in a single-molecule enhancement experiment, avoiding the arbitrary selection of one or a few high-intensity burst(s). These new estimates for the enhancement factor make use of the whole distribution of intensity bursts or of the interphoton delay distribution, which avoids the arbitrary binning of the fluorescence intensity time traces. We present experimental results on the bi-dimensional case, experimentally achieved using a lipid bilayer to support the diffusion of fluorophores. We support our findings with histograms of fluorescence bursts and with an analytical derivation of the interphoton delay distribution of (nearly) immobilized emitters from the fluorescence intensity profile.
The usual denomination is microtime but we opt for nanotime to avoid confusion with the macrotime.
Note that the Laplace transformation is usually applied to time-dependent functions, giving rate-dependent functions. Here, we apply it to a function of the rate and thus obtain a time-dependent transform.