  Coupled waveguides are convenient at implementing useful optical
transformations. In this letter, we investigate the uncertainty of
transformation by two coupled waveguides that stems from the perturbations of
waveguide's mode indices~--- the effect that may be imposed by a non-ideal
fabrication process, in particular, those of femtosecond direct laser writing.
In our analysis, the perturbations are assumed to be samples of a stationary
random process, characterized by an intensity and a correlation scale
parameter. We have derived analytical equations that link these parameters with
relevant statistical characteristics and applied them to analyse how the
uncertainty evolves with field propagation length. We have shown that the
interaction length over which the expectation value of power becomes evenly
distributed among the waveguides is crucially dependent on the random process
correlation scale and perturbation intensity.
