Signal-to-Noise Ratio and Minimum Detectable Number of Photons

3 Signal-to-Noise Ratio and Minimum Detectable Number of Photons 

We now follow the usual procedure used for the single-quantum case [7.4-6,10] to calculate the approximate SNR for fc-photon sinusoidal heterodyne detection. We begin with two-quantum photomixing, neglecting the double-difference-frequency component and assuming that the ac signal is at the fundamental- 

We now assume that one of the waves (which we call the local oscillator or LO) is strong, i.e., in which case 

The noise power can be obtained from the two-quantum photocurrent spectrum [7.39] which, in turn, is related to the stochastic nature of the radiation source. For a coherent and strong LO, however, the /c-quantum counting statistics will be Poisson [7.41,42], and the two-quantum (shot) noise power is then 

Using the relationship between the two-quantum yield and the two-quantum efficiency t/2 given in (7.4), we finally obtain 

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