Appropriate Gate Time for Single Molecular Photon Detection Based on Optimal Signal-to-Noise Ratio Analyses

Signal-to-noise ratio of fluorescence detection from a single molecule is analysed by using time-gated techniques. It is found that the optimal signal-to-noise ratio can be obtained by choosing an appropriate gate time with a certain optical background. The dependences of molecular fluorescence lifetime and the optimal signal-to-noise ratio on the appropriate gate time are respectively discussed with two kinds of background sources, chaotic state with uniform distribution and coherent state with exponential distribution in time domain. For chaotic state background we find that a certain range for appropriate gate time can be obtained with a definite fluorescence lifetime, larger fluorescence lifetime would lower the value of optimal signal-to-noise
ratios. For coherent state background we find that there is also a narrow range of appropriate gate time when lifetime of single molecule is less than that of background photons.