# Scattering Statistics in Nonlinear Wave Chaotic Systems

## TL;DR

This paper investigates how a nonlinear port affects the scattering statistics in wave chaotic systems, extending the Random Coupling Model to account for nonlinear effects using high power measurements and diode components.

## Contribution

It introduces a nonlinear extension to the RCM and demonstrates how a diode port influences the statistical electromagnetic properties in chaotic enclosures.

## Key findings

- Diode admittance increases with excitation amplitude.
- Nonlinear port reduces power entering the cavity.
- Extended RCM accounts for nonlinear effects.

## 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.