Analysis and measurement of the modal-noise probability distribution for a step-index optical fiber

With a sufficiently narrow source spectrum, and either fiber movement or source frequency shift, a changing speckle pattern exists at a multimode-fiber output plane that results in modal noise. Daino and co-workers [Electron. Lett. 15, 755 (1979)] have obtained the noise probability density function (PDF) for a fiber of arbitrary refractive-index profile in the limiting cases in which the number of speckles seen by the detector is either very small or very large. We show that, in the special case of a step-index fiber, the PDF is a gamma distribution of argument M′, where M′ is the number of degrees of freedom in the speckle pattern. We report measurements of the PDF that show good agreement with calculated gamma distributions.