Jen-Hao Yeh

Universal and nonuniversal properties of wave-chaotic scattering systems

Prediction of the statistics of scattering in typical wave-chaotic systems requires combining system-specific information with universal aspects of chaotic scattering as described by random matrix theory. This Rapid Communication shows that the average impedance matrix, which characterizes such system-specific properties, can be semiclassically calculated in terms of ray trajectories between ports. Theoretical predictions are compared with experimental results for a microwave billiard, demonstrating that the theory successfully uncovered universal statistics of wave-chaotic scattering systems.

Experimental examination of the effect of short ray trajectories in two-port wave-chaotic scattering systems

Predicting the statistics of realistic wave-chaotic scattering systems requires, in addition to random matrix theory, introduction of system-specific information. This paper investigates experimentally one aspect of system-specific behavior, namely, the effects of short ray trajectories in wave-chaotic systems open to outside scattering channels. In particular, we consider ray trajectories of limited length that enter a scattering region through a channel (port) and subsequently exit through a channel (port). We show that a suitably averaged value of the impedance can be computed from these trajectories and that this can improve the ability to describe the statistical properties of the scattering systems. We illustrate and test these points through experiments on a realistic two-port microwave scattering billiard.

In situ broadband cryogenic calibration for two-port superconducting microwave resonators.

We introduce an improved microwave calibration method for use in a cryogenic environment, based on a traditional three-standard calibration, the Thru-Reflect-Line (TRL) calibration. The modified calibration method takes advantage of additional information from multiple measurements of an ensemble of realizations of a superconducting resonator, as a new pseudo-Open standard, to correct errors in the TRL calibration. We also demonstrate an experimental realization of this in situ broadband cryogenic calibration system utilizing cryogenic switches. All calibration measurements are done in the same thermal cycle as the measurement of the resonator (requiring only an additional 20 min), thus avoiding 4 additional thermal cycles for traditional TRL calibration (which would require an additional 12 days). The experimental measurements on a wave-chaotic microwave billiard verify that the new method significantly improves the measured scattering matrix of a high-quality-factor superconducting resonator.

First-principles model of time-dependent variations in transmission through a fluctuating scattering environment.

Fading is the time-dependent variation in transmitted signal strength through a complex medium due to interference or temporally evolving multipath scattering. In this paper we use random matrix theory (RMT) to establish a first-principles model for fading, including both universal and nonuniversal effects. This model provides a more general understanding of the most common statistical models (Rayleigh fading and Rice fading) and provides a detailed physical basis for their parameters. We also report experimental tests on two ray-chaotic microwave cavities. The results show that our RMT model agrees with the Rayleigh and Rice models in the high-loss regime, but there are strong deviations in low-loss systems where the RMT approach describes the data well.

Application of the Random Coupling Model to Electromagnetic Statistics in Complex Enclosures

The effectiveness of the random coupling model (RCM) in predicting electromagnetic wave coupling to targeted electronic components within a complex enclosure is examined. In the short-wavelength limit with respect to the characteristic length of the enclosure, electromagnetic wave propagation within a large enclosure is sensitive to small changes to the interior, or to the boundaries of the enclosure. Such changes can reduce or invalidate the applicability of deterministic predictions of the electromagnetic fields at radiofrequencies (RF) in large enclosures. Under such circumstances, a statistical approach is needed to provide a better understanding of RF coupling to components within large enclosures. In this paper, we experimentally demonstrate the applicability of a statistical technique, the RCM, to estimate the probabilistic magnitudes of RF fields on electrically large components (i.e., long cables, etc.) that are partially shielded within a complex, 3-D enclosure.

Wave chaotic analysis of weakly coupled reverberation chambers

In this paper, we analyze the field fluctuations in weakly coupled complex cavities by using a random matrix theory to model the chaotic scattering within each cavity. Universal (chaotic) and non-universal are separated. In particular, non-universal are found to be conveniently described by the radiation impedance concept. Inherently, the development of the random field regime is accounted for by taking each mode of the cavity as a random plane wave expansion. Sources and sinks inside the cavities are assumed to be electrically small. A model for the cascaded cavities scenario is derived through the electric network theory and random matrix theory for both lossy and lossless cases. The adopted physical framework is a linear chain of two-port cavities terminated by a one-port cavity. The field flowing into this last cavity is related to the current excitation on the first cavity through the coupling radiation impedance. Closed-form expressions are derived for two interconnected cavities, mimicking the nested reverberation chamber scenario. Finally, the practical issue of measurements in a nested reverberation chamber is presented and discussed. Accordingly, based on physical arguments, the small fluctuations theory applies. Results are of interest in interference propagation through complex electromagnetic environment or planar circuits, EMC immunity tests, and reverberation chambers.

Impedance and Scattering Variance Ratios of Complicated Wave Scattering Systems in the Low Loss Regime

Random matrix theory (RMT) successfully predicts universal statistical properties of complicated wave scattering systems in the semiclassical limit, while the random coupling model offers a complete statistical model with a simple additive formula in terms of impedance to combine the predictions of RMT and nonuniversal system-specific features. The statistics of measured wave properties generally have nonuniversal features. However, ratios of the variances of elements of the impedance matrix are predicted to be independent of such nonuniversal features and thus should be universal functions of the overall system loss. In contrast with impedance variance ratios, scattering variance ratios depends on nonuniversal features unless the system is in the high loss regime. In this paper, we present numerical tests of the predicted universal impedance variance ratios and show that an insufficient sample size can lead to apparent deviation from the theory, particularly in the low loss regime. Experimental tests are carried out in three two-port microwave cavities with varied loss parameters, including a novel experimental system with a superconducting microwave billiard, to test the variance-ratio predictions in the low loss time-reversal-invariant regime. It is found that the experimental results agree with the theoretical predictions to the extent permitted by the finite sample size.

Broadband cryogenic calibration two-port superconducting resonators

Superconducting resonators are useful for precision electromagnetic measurements, so broadband cryogenic calibration of these resonators are important. We found that a traditional three standards calibration, the Thru-Reflection-Line calibration, fails to calibrate the transmission lines between a vector network analyzer and a cryogenic two-port resonator. Here we introduce a modified calibration method that replaces the Reflection standard by a pseudo-Open standard. Experimental measurements show the new method significantly improves the calibrated results.