Statistical coupling characteristics of optical directional couplers subject to random irregularities are studied theoretically by means of coupled mode theory. A new method is used for solving coupled mode equations in which random components of coupling coefficients and phase constants are assumed to be Gaussian random processes with an arbitrary correlation length. Mean values, variances, and probability distributions of coupled powers in 0-dB and 3-dB directional couplers are presented. The influence of random parameters is made clear. It is seen that tolerance requirements can be relaxed by a proper choice of the average parameters. Discussions about the film waveguide couplers for integrated optics applications are presented.
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