# Nonlinear Wave Chaos: Statistics of Second Harmonic Fields

## TL;DR

This paper extends wave chaos statistical models to nonlinear systems by analyzing second harmonic fields generated by a nonlinear frequency-doubling circuit in a chaotic electromagnetic environment, showing good agreement between theory and experiment.

## Contribution

It introduces a nonlinear extension of the Random Coupling Model to predict second harmonic field statistics in wave chaotic systems.

## Key findings

- Good agreement between measurements, simulations, and theory over many decades of power.
- The second harmonic field strength is modeled as a product of two statistical quantities and nonlinearity characteristics.
- The approach successfully extends wave chaos statistical analysis to nonlinear regimes.

## Abstract

Concepts from the field of wave chaos have been shown to successfully predict the statistical properties of linear electromagnetic fields in electrically large enclosures. The Random Coupling Model (RCM) describes these properties by incorporating both universal features described by Random Matrix Theory and the system-specific features of particular system realizations. In an effort to extend this approach to the nonlinear domain, we add an active nonlinear frequency-doubling circuit to an otherwise linear wave chaotic system, and we measure the statistical properties of the resulting second harmonic fields. We develop an RCM-based model of this system as two linear chaotic cavities coupled by means of a nonlinear transfer function. The harmonic field strengths are predicted to be the product of two statistical quantities and the nonlinearity characteristics. Statistical results from measurement-based calculation, RCM-based simulation, and direct experimental measurements are compared and show good agreement over many decades of power.