Scattering from a waveguide by cycling a non-Hermitian degeneracy

It has been recently shown that by varying the potential parameters in time so that a non-Hermitian degeneracy [exceptional point (EP)] is cycled, the nonadiabatic couplings have a large effect on the dynamics. This cardinal effect does not disappear even when the potential parameter are changed arbitrarily slow ("adiabatic process"). For a specific Hamiltonian this counterintuitive effect has been shown to be associated with the Stokes phenomenon. We study analytically the effects of EP cycling on the transmission and reflection of light in a waveguide with a small complex refractive index modulation. We find that in the adiabatic limit the oscillations in the transmission spectrum are sharply attenuated above a certain frequency where the EP is no longer cycled.