Dissertations, Theses, and Capstone Projects

Date of Degree


Document Type


Degree Name





Azriel Z. Genack

Committee Members

Andrea Alù

Chushun Tian

Victor A. Gopar

Mohammad-Ali Miri

Subject Categories

Condensed Matter Physics | Optics | Statistical, Nonlinear, and Soft Matter Physics


time delay, density of states, energy density, quasi-normal mode, absorption, universality


This thesis presents studies of the field and energy excited in disordered systems as well as the dynamics of scattering.

Dynamic and steady state aspects of wave propagation are deeply connected in lossless open systems in which the scattering matrix is unitary. There is then an equivalence among the energy excited within the medium through all channels, the Wigner time delay, which is the sum of dwell times in all channels coupled to the medium, and the density of states. But these equivalences fall away in the presence of material loss or gain. In this paper, we use microwave measurements, numerical simulations, and theoretical analysis to discover the changing relationships among the internal field, transmission, transmission time, dwell time, total excited energy, and the density of states in with loss and gain, and their dependence upon dimensionality and spectral overlap. The field, including the contribution of the still coherent incident wave, is a sum over modal partial fractions with amplitudes that are independent of loss and gain. Specifically, we demonstrate in a unitary system that wave statistics within samples of any dimension are independent of the detailed structure of a material and depend only on the net strengths of scattering and reflection between the observation point and each of the boundaries. The total energy excited is proportional to the dwell time. When modes are spectrally isolated, the energy is proportional to the sum of products of the modal contribution to the density of states and the ratio of the linewidth without and with absorption. When modes overlap, however, the total energy is further reduced by loss and enhanced by gain.

In 1D, the average transmission time is independent of loss, gain, and scattering strength. In higher dimensions, however, the average transmission time falls with loss, scattering strength and channel number, and increases with gain. It is the sum over Lorentzian functions associated with the zeros as well as the poles of the transmission matrix. This endows transmission zeros with topological characteristics: in unitary media, zeros occur either singly on the real axis or as conjugate pairs in the complex frequency plane. The transmission zeros are moved down or up in the complex plane by an amount equal to the internal rate of decay or growth of the field. In weakly absorbing media, the spectrum of the transmission time of the lowest transmission eigenchannel is the sum of Lorentzians due to transmission zeros plus a background due to far-off-resonance poles. As the scattering strength increases, conjugate pairs of zeros are brought to the real axis and converted to two single zeros which are constrained to move on the real axis until they combine and leave the real axis as a conjugate pair. The average density of transmission zeros in the complex plane is found from the fall of the average transmission time with absorption as zeros are swept into the lower half of the complex frequency plane. As a sample is deformed, two single zeros and a conjugate pair of zeros may interconvert on the real axis with a square root singularity in the sensitivity of the spacing between transmission zeros to structural change. Thus, the disposition of poles and zeros in the complex frequency plane provides a framework for understanding and controlling wave propagation in non-Hermitian systems.

Waves propagating through random media experience multiple scattering and give rise to random fluctuations of transmission and reflection. We show using a random-matrix model, microwave experiments, and numerical simulations that the location and reflectivity of an object inside a 1D random medium can be extracted from the transmitted and reflected fields.