Light guiding in microstructures of purely imaginary refractive index contrasts

Using a scalar approximation to the Helmholtz equation we investigate periodic complex dielectric microstructures constituting an optical loss or amplification. We demonstrate that the traditional way of depicting bandgaps arising in microstructures is no longer sufficient when dealing with loss or gain in the materials. A new way of mapping the effective indices onto the complex plane is introduced and discussed. Furthermore this mapping is used directly to find modes guided in the microstructure solely by the effects of imaginary refractive index contrasts.