The Transmitting Theory And Experimental Verification Of The Single Mode Laser Limited Temporal Coherence In A SIMMF

The study of the transmission of partially coherent light in a Multi-Mode Fiber (MMF) is important in understanding mode noises in optical communication, astronomical optical imaging and the speckle characteristics. Since the spatial coherence of output light in MMF is limited by the temporal coherence of the input light except that has something to do with the illuminant itself, the physical laws governing the propagation of partially coherent light in free space and general imaging system are no longer applicable. In this paper, we study the change of spatial coherence when the single-mode laser with partially temporal coherent through the MMF. First of all, establish a correlation matrix for output light based on the coherence function between modes of MMF. Under weakly guiding, far from cutoff frequency and mode fully coupled, we can assume that the amplitude of each mode fields are equal as well as real number and the time delay during adjacent modes are equal too at the exit end when the partially coherent light coupled to optical fiber and then transmission. Secondly, diagonalize the correlation matrix, and then obtain a decorrelation eigenvalue spectrum. Next, put forward a gaussian approximation for the eigenvalue spectrum and a assumption that space translation invariance for output light because it is difficult and complex to solve the eigen function and so that the complex coherence factor of output light cannot be obtained actually. Therefore, the complex coherence factor of output light and the contrast of speckle can be gained base on eigen-function methodology. In order to test and verify the rationality of approximate theory, we do two experiments. First, use Young’s double-hole interference experiment to study the change rule that coherence along with the space to Step-Index Multi-Mode Fiber (SIMMF). And second, use CCD to measure the change of the speckle contrast of silica SIMMF and plastic SIMMF along with the length of their own respectively. Experimental results validated the rationality of the approximation theory basically. Finally, do a semi phenomenological correction for the approximate theory based on the deviation of speckle measurement results and the approximate theoretical analysis.