An asymptotic treatment of power transport by guided modes in two parallel, identical planar dielectric waveguides is presented in the weak coupling limit. The small parameter is the factor by which the field amplitude decays from one waveguide to the other. The maximum power is transferred from one waveguide to the other periodically in the propagation direction, the spatial period being known as the interaction length. When the power in one waveguide is a maximum, there is a small amount of residual, undesirable power in the other waveguide. This cross talk is intrinsic to a coupled system. It is shown that the product of the intrinsic cross talk and the interaction length is a constant depending only on the parameters of the corresponding uncoupled waveguide. Also, this constant is identical to the transverse electric mode and the transverse magnetic mode. This cross‐talk relation shows that the intrinsic cross talk can be reduced only at the expense of increasing the device dimensions.