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Transmission statistics and focusing in single disordered samples.

Matthieu Davy¹, Zhou Shi, Jing Wang

¹Department of Physics, Queens College of the City University of New York, Flushing, NY 11367, USA.

|April 24, 2013

Summary

In samples with many channels, transmission statistics depend on a single parameter, the participation number (M). This parameter governs relative transmission variance and focusing contrast, offering a new framework for transmission and imaging.

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Area of Science:

Wave physics
Statistical mechanics
Condensed matter physics

Background:

Understanding wave transmission through complex media is crucial for various applications.
Characterizing the statistical properties of transmission in multi-channel systems remains a challenge.

Purpose of the Study:

To identify a key parameter governing transmission statistics in multi-channel systems.
To establish a framework for analyzing and predicting wave transmission and focusing.

Main Methods:

Microwave experiments were conducted on complex samples.
Random matrix theory calculations were employed to analyze transmission eigenvalues.

Main Results:

The participation number (M) of transmission matrix eigenvalues was identified as the sole determinant of relative transmission statistics.

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The inverse of M (M(-1)) correlates with the variance of relative total transmission.

Maximal focusing contrast is directly equal to M.

The distribution of relative total transmission transitions from Gaussian to negative exponential as M(-1) varies from 0 to 1.

Conclusions:

The participation number (M) provides a unified framework for understanding wave transmission and focusing in complex, multi-channel systems.
This finding simplifies the analysis of transmission statistics and opens avenues for improved imaging techniques.