Degree of Second-order Coherence
Note that this is not a generalization of the first-order coherence
If the electric fields are considered classical, we can reorder them to express in terms of intensities. A plane parallel wave in a stationary state will have
The above expression is even, For classical fields, one can apply Cauchy-Schwarz inequality to the intensities in the above expression (since they are real numbers) to show that and that . Nevertheless the second-order coherence for an average over fringe of complementary interferometer outputs of a coherent state is only 0.5 (even though for each phase). And (calculated from averages) can be reduced down to zero with a proper discriminating trigger level applied to the signal (within the range of coherence).
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