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Generation and Coherent Control of Pulsed Quantum Frequency Combs

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Beam wave two-frequency mutual-coherence function and pulse propagation in random media: an analytic solution.

I Sreenivasiah, A Ishimaru

|March 10, 2010

Summary

Researchers present an exact analytic solution for beam wave propagation in random media. This study details how turbulence affects beam coherence and pulse shape, offering insights into wave propagation characteristics.

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Area of Science:

Optics and Photonics
Wave Propagation in Random Media
Electromagnetic Theory

Background:

Pulse propagation in random media is governed by the two-frequency mutual coherence function.
Previous studies focused on numerical solutions for plane waves and analytical solutions for specific refractive-index fluctuation spectra.
A need exists for analytical solutions for more general beam wave cases.

Purpose of the Study:

To derive an exact analytic solution for the mutual coherence function of a beam wave in a random medium.
To investigate the propagation characteristics of beam waves, including coherence and pulse shape variations.
To analyze the effects of turbulence on beam collimation and focus.

Main Methods:

Developed an exact analytic solution for the parabolic equation governing the two-frequency mutual coherence function.
Applied an approximation based on a Gaussian spectrum of refractive-index fluctuations.
Studied the time variation of pulse shape for delta function input on and off the beam axis.

Main Results:

Obtained simple expressions describing the decollimating and defocusing effects of turbulence on beam waves.
Analyzed the beam wave mutual coherence function at single and two frequencies.
Presented results for both collimated and focused beams, detailing pulse shape evolution.

Conclusions:

The derived analytic solution provides a powerful tool for understanding beam wave propagation in turbulent media.
Turbulence significantly impacts beam coherence and can cause decollimation and defocusing.
The study offers qualitative insights into the temporal and spatial characteristics of propagating pulses.