Ph D. Dissertation Defense; Min Zhou

Tuesday, March 26, 2019
3:00 p.m.-5:00 p.m.
AVW 2168
Maria Hoo
301 405 3681

ANNOUNCEMENT: Ph D. Dissertation Defense



Name: Min Zhou

Advisory Committee:

Prof. Steven Anlage, chair/advisor

Prof. Thomas Antonsen, Dean’s representative

Prof. Thomas Murphy

Prof. Christopher Davis

Prof. Phillip Sprangle 


Date/Time: Tuesday, March 26, 2019, at 3:00 pm-5:00 pm

Location: AVW 2168

Nonlinear Wave Chaos and the Random Coupling Model (RCM)


The Random Coupling Model (RCM) has been shown to successfully predict the statistical properties of linear wave chaotic systems in the highly over-moded regime. It is of interest to extend the RCM to nonlinear systems. Nonlinearity manifests as harmonic generation, amplitude dependent responses, etc. My PhD research studies whether or not there are universal statistical properties of nonlinear wave chaotic systems, and how the RCM needs to be modified for those systems. Several microwave chaotic systems are studied by introducing different sources of nonlinearities.


The first experiment studies the statistics of the 2nd harmonic fields in a wave chaotic setting. By adding an active frequency doubling circuit to the ¼ bowtie billiard, the second harmonic fields are generated. The Vector Network Analyzer (VNA) in Frequency Offset Mode (FOM) measures the absolute power of the second harmonic fields with respect to the input fundamental frequency. Taking into account the characteristics of the nonlinear circuit, the RCM is extended to predict the statistics of the second harmonic fields.  It is found that the modified model agrees quite well with the experimental results.


The second experiment is also built on the ¼ bowtie microwave billiard, but studies the nonlinear response of S-parameters for different input amplitudes. A diode is attached between the port and the billiard to construct a nonlinear port. A high power PNA is assembled to measure the S-parameters up to ~+37 dBm. We find the raw statistics of the fields change dramatically with input power. The radiation impedance and short orbits also deviate from that in the linear case.  We have systematically studied the nonlinear port and then utilized the radiation efficiency model to describe the port. The nonlinear response is mainly associated with the port


The previous two systems contained objects that can be approximated as creating a point-like nonlinearity in the system. In addition to circuit nonlinearity, superconducting materials provides nonlinearity through its impedance Z = R + iX. We have two microwave billiards made of superconducting materials. They can be considered as chaotic systems with nonlinear cavity boundaries.

  1. One is made of lead coated copper. It is studied in a dilution refrigerator at temperatures below 1K. We observe the billiard mainly shows nonlinear resistance and quality factor Q changes. The changes in Q are too small to be reflected in the statistical results. In addition the VNA changes its dynamic range and noise level for different powers. The noise effect dominates the changes in measured statistics.
  2. Another superconducting microwave billiard is a thin film coating of TiN on Si wafer, which we proposed.  TiN is reported to be very nonlinear in a reactive manner, hence it is studied as a complementary system to the Pb billiard. We have prepared a test sample and done some preliminary characterization of the experimental setup.  The progress and future work will be reported.


Nonlinear systems are common and may occur in different forms. There are a lot of other sources that can be studied, for example, to create a continuous nonlinear medium.  Possible realizations include putting diodes or nonlinear dielectric/magnetic materials in the microwave billiards. The numerical simulation work we have done to explore other nonlinear sources will also be presented. The work to extend the RCM to nonlinear wave chaotic systems will be summarized, and the future directions will be suggested.


Audience: Graduate  Faculty 


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