Colloquium, Jan. 17th, 2012
Three Perspectives on Transmission and “Optical” Conductance in Random Systems: Speckle, Modes, and Transmission Eigenchannels
Azriel Z. Genack, Queens College of the City University of New York
The
understanding of electron localization and conductance fluctuations has been
advanced by utilizing notions of speckle, quasi-normal modes, and
transmission eigenchannels. These concepts cannot be probed directly for
electronic systems but can be explored for classical waves utilizing spectra
of field transmission coefficients between arrays of points on the incident
and output surfaces of ensembles of random samples. This is illustrated in
microwave measurements of transmission and “optical” conductance through
random waveguides in the Anderson localization transition. These experiments
supply the link between the statistics of intensity and conductance and show
that the transmitted wave can be decomposed simultaneously into the
underlying quasi-normal modes and transmission eigenchannels of the sample.
The power of each of these approaches and the richness of the links between
them will be illustrated by examples that reveal new aspects of wave
propagation. The delayed onset of transmission following pulse excitation is
shown to be the result of destructive interference between highly correlated
speckle patterns of neighboring modes, while the falling decay rate at later
times reflects the incoherent decay of increasingly prominent long-lived
modes. We determine the individual eigenvalues
tn
of the transmission matrix and achieve nearly complete transmission in
opaque diffusive samples. The speckle pattern of the most strongly
transmitting eigenchannel is close to that of the most prominent resonant
mode. We demonstrate that when reflection at the sample interface is taken
into account, the spacing between average values of lntn
is equal to the inverse of the bare conductance, in accord with predictions
by Dorokhov. We find that the distribution of total transmission relative to
the “optical” conductance is determined by the participation number of
transmission eigenvalues,
.
is
the variance of total transmission relative to its average while M is
equal to the contrast between the peak and background of maximally focused
radiation in the transmitted wave.
In collaboration with Zhou Shi, Jing Wang and Matthieu Davy.