Statistical analysis of interferometric crosstalk: Theory and optical network examples

General, statistical properties of accumulation of interferometric crosstalk due to a number of interfering signals are analyzed. The probability density function of the total crosstalk is derived as function of the sum of the incoherent crosstalk contributions associated with the interfering signals. Because the total crosstalk level can be expected to vary only slowly as compared to the time duration of one bit, the probability p that the total crosstalk exceeds a maximum tolerable value is introduced as a parameter in the crosstalk and bit error rate analysis of optical networks. General computations show that the crosstalk requirement on optical network elements may be significantly relaxed if it can be accepted that it is possible, although most unlikely, that the total crosstalk may exceed this maximum tolerable value. The statistical crosstalk model is then illustrated by investigation of optical network examples with respect to their crosstalk and transmission properties, and, finally, compared with previous crosstalk models.