Scattering statistics in nonlinear wave chaotic systems

Abstract

The Random Coupling Model (RCM) is a statistical approach for studying the scattering properties of linear wave chaotic systems in the semi-classical regime. Its success has been experimentally verified in various over-moded wave settings, including both microwave and acoustic systems. It is of great interest to extend its use to nonlinear systems. This paper studies the impact of a nonlinear port on the measured statistical electromagnetic properties of a ray-chaotic complex enclosure in the short wavelength limit. A Vector Network Analyzer is upgraded with a high power option which enables calibrated scattering (S) parameter measurements up to +43 dBm. By attaching a diode to the excitation antenna, amplitude-dependent S-parameters are observed. We have systematically studied how the key components in the RCM are affected by this nonlinear port, including the radiation impedance, short ray orbit corrections, and statistical properties. By applying the newly developed radiation efficiency extension to the RCM, we find that the diode admittance increases with excitation amplitude. This reduces the amount of power entering the cavity through the port, so that the diode effectively acts as a protection element.

Wave scattering properties of multiple weakly coupled complex systems

“…Over the last decade, the Random Coupling Model has been introduced, studied extensively and compared with single chaotic enclosure experiments with various cavity losses, dimensions, and non-linear elements inside the cavity [43,50,73]. Here, we apply an RCMbased model which can be used to make statistical predictions of impedance values in inter-connected systems of chaotic cavities.…”

Short-wavelength Reverberant Wave Systems for Enhanced Reservoir Computing

“…into analog waveforms by an AWG (arbitrary waveform generator) and stored for both the training and testing time-series data sets. After appropriate time scaling, the input signal is then amplified and injected into a wave chaotic microwave cavity [25][26][27][28][29][30].…”

“…The waveform is amplified by the RF-Lambda 2-18GHz amplifier (RFLUPA0218G5). The output ports consist of SMA dipole antennas with high switching speed diodes (Infineon BAS7004) connected between the center pin and the cavity top plate (Fig.1b)[27]. The voltage signals are measured with an oscilloscope (Agilent DSO91304A) with a sampling rate of 40Gs/s.…”

Eigenfunction and eigenmode-spacing statistics in chaotic photonic crystal graphs

“…The statistical properties of many system quantities, such as the closed system eigenvalues and the open system scattering/impedance matrices, exhibit universal characteristics, which only depend on general symmetries (e.g., time-reversal, symplectic) and the degree of system loss. The Random Coupling Model (RCM) has found great success in characterizing the statistical properties of a variety of experimental systems by removing the non-universal effects induced by port coupling and short-orbit effects [9,13,14,16,17,[19][20][21][22][23][24]. Chaotic microwave graphs support complex scattering phenomena despite their relatively simple structure, and allow for various useful circuit components (such as phase shifters and attenuators) to be incorporated into the structure [3][4][5].…”