Measuring the transmission matrix for microwave radiation propagating through random waveguides: fundamentals and applications

This thesis describes the measurement and analysis of the transmission matrix (TM) for microwave radiation propagating through multichannel random waveguides in the crossover to Anderson localization. Eigenvalues of the transmission matrix and the associated eigenchannels are obtained via a singular value decomposition of the TM. The sum of the transmission eigenvalues yields the transmittance $\it T$, which is the classical analog of the dimensionless conductance $\textsl g$. The dimensionless conductance $\textsl g$ is the electronic conductance in units of the quantum conductance, $G/(e^2/h)$.