Determination of the statistical distribution of electromagnetic-field amplitudes in complex cavities

We describe an analytic technique to predict the statistical distribution of field amplitudes in complex cavities, which result from the simultaneous excitation of hundreds of modes. We have been able to determine that the electromagnetic-field amplitudes in a complex cavity are statistically distributed according to a {Γ} distribution. The shape of the distribution depends on a dimensionless parameter, the specific mode density, which is a measure of the number of modes excited simultaneously in the cavity. In the limit of large cavity volume, measured in cubic wavelengths, and of moderate to low Q, the distribution becomes a χ² distribution with a uniform shape, independent of cavity parameters. Comparison with experimental data is included for four real systems widely varying in size, shape, and Q, and with a laboratory experiment which varied the cavity Q in a controlled manner over two orders of magnitude. In all these cases the data fell within the 90% confidence bounds of the theory. The theory further provides a quantitative measure capable of distinguishing to what extent experimental data have been distorted by the finite dynamic range of the measurement instrumentation, and of restoring the correct statistics in spite of large distortions in the data. This measure does not depend on knowledge of the instrumentation system. Errors less than several decibels appear detectable.