  We show that the analogue of the geometric phase for non-Hermitian coupled
waveguides with PT-symmetry and at least one periodically varying parameter can
be purely imaginary, and will consequently result in the manifestation of an
instability in the system. The instability peaks seen in the spectrum of the
system's eigenstates after evolution along the waveguides can be directly
mapped to the spectrum of the derivative of the geometric function. The
instabilities are magnified as the exceptional point of the system is
approached, and non-adiabatic effects begin to appear. As the system cannot
evolve adiabatically in the vicinity of the exceptional point, PT-symmetry will
be observed breaking earlier than theoretically predicted.
