Scattering singularities of optical waveguides under complex modulation

We employ complex index modulation to manipulate light scattering in a waveguide and achieve different kinds of singularities in the system. The singularities refer to poles or zeros in the scattering and transfer matrices. By using spatially complex index modulation, we realize unidirectional zero-reflection singularities, which can be manipulated by adjusting the modulation phase difference between the real and imaginary parts. Laser-coherent perfect absorber singularities with both diverging reflectance and transmittance are also achieved by cascading two waveguides with different modulation phases. Meanwhile, bidirectional zero-reflection singularities with reflectionless light transporting on both sides of the waveguides are also demonstrated. In addition, we utilize temporally complex modulation to obtain transfer matrix singularities and achieve nonreciprocal light transmission. The study may find great applications in light amplification, attenuation, and absorption, as well as constructing nonreciprocal optical devices.