Wave scattering properties in complex scattering systems have been of great interest to both the physics and engineering communities because of their useful characterizations of such systems and significant value for applications. The most common tool for studying such properties – the scattering (S)-matrix, can be fully represented by its zeros and poles in the complex energy/frequency plane. There has been substantial effort to understand the scattering properties and wave phenomena inside complex systems in the past, both theoretical and experimental, which in turn has led to significant advancement in many applications: wavefront shaping (WFS), coherent perfect absorption (CPA), wireless power transfer, electromagnetic interference (EMI), etc.

In this dissertation, I will summarize the recent progress and interest regarding an intriguing wave phenomenon – coherent perfect absorption (CPA) in complex scattering systems. We have successfully implemented CPA protocols in generic complex scattering systems without any geometric or hidden symmetries, which greatly extends CPA beyond its initial concept as the time-reversal of a laser cavity. Under such efforts, we have also established a convenient approach for control of the local losses inside the network system, which helped us to uncover the mystery of matching the imaginary part of the S-matrix zero to the uniform loss of the system. We thus developed the theoretical representation of the S-matrix by its zeros and poles, and generalized the traditional Wigner time delay to a complex quantity in sub-unitary scattering systems. We have revealed the inherent connection between the complex Wigner time delay and coherent perfect absorption, and can utilize the new complex Wigner time delay idea for extracting S-matrix zeros and poles in a practical system. We have also studied the statistical properties of the complex generalization of Wigner time delay for subunitary wave-chaotic scattering systems, and demonstrated excellent agreement between theory and experiments. Finally, we have extended this scheme to a comprehensive time delay analysis framework, including Wigner, transmission, and reflection time delays. This approach offers us the capability to systematically analyze the poles and zeros of the scattering matrix of any complex scattering system. We then apply the new transmission time delay method on a two-channel microwave graph realization of the Aharonov--Bohm ring from mesoscopic physics, and demonstrate the dependence of non-reciprocal transport behavior on the de-phasing rate.

The ultimate goal is to completely control the scattering properties of complex systems by manipulating the zeros and poles of the S-matrix, for example by adding losses in the system or changing the coupling of the scattering channels, etc. Such a capability will be extremely useful for understanding the wave properties of complex scattering systems, and for controlling the wave behavior in optics, electromagnetics, acoustics, quantum transport in condensed matter systems, etc.