Optical Imaginary Directional Couplers

We investigate the light propagation in a double-waveguide coupler with imaginary-valued coupling coefficient. The imaginary coupling is realized by incorporating an additional waveguide between the coupled waveguides and considering both gain and loss. Both symmetric and asymmetric couplers with imaginary coupling are analyzed. The coupling strength can be controlled by varying the dielectric gain and loss. As the coupling is imaginary, the energy of the system is no longer conserved and the light intensities in individual waveguides should oscillate in phase. It is also found that the exceptional points can emerge in the asymmetric couplers, which are reflected from the beat length of the intensity oscillation. The study may find great applications in optical switches and splitters.