  Parity-time-symmetric ($\mathcal{PT}$-symmetric) optical waveguide couplers
have become a key component for integrated optics. They offer new possibilities
for fast, ultracompact, configurable, all-optical signal processing. Here, we
study nonlinear properties of finite-size multimode $\mathcal{PT}$-symmetric
couplers and report a peculiar type of dispersion relation in couplers made of
more than one dimer. Moreover, we predict a $\mathcal{PT}$ transition triggered
by nonlinearity in these structures, and we demonstrate that with the increase
of the number of dimers in the system, the transition threshold decreases and
converges to the value corresponding to an infinite array. Finally, we present
a variety of periodic intensity patterns that can be formed in these couplers
depending on the initial excitation.
