I think a multimode fiber de-speckler is simply a device that rapidly perturbs either the fiber (e.g., using a small piezo vibrator) or the beam leaving the fiber (e.g., using a moving diffuser) in order to produce a rapidly varying speckle output.  A time average then yields a smoother beam.  However, at any instance in time the light is still coherent and a speckle pattern exists.  If the beam perturbation is rapid compared to the camera/detector bandwidth, then the speckle appears to be suppressed. See: Methods and Devices of Speckle-Noise Suppression.

To model this case requires first generating a speckle pattern with a set of randomly-phased set of coherent sources.  Then simply select a new set of random relative phases, and re-compute the speckle.  Add this new speckle pattern to the first one and divide the irradiance by two to form an average speckle pattern.  Continue doing this for some number of iterations N that mimics the number of perturbations induced by the de-speckler during the detection time (which could, for example, be the exposure time associated with a single frame of a camera, i.e., one over the frame rate).  The speckle contrast should diminish as 1/sqrt(N) where N is the number of uncorrelated speckle patterns being averaged (see Goodman, Eq. 3.92).

This simulation can be done using either sequential mode (POP) or non-sequential mode using a set of randomly-phased point sources combined with coherent irradiance detection.  The non-sequential approach may be easier, as generating a coherent set of randomly-phased LP modes for use in POP will likely take more effort.  However, the non-sequential approach would be more of an approximation since, in the simplest case, it wouldn’t directly take into account the fiber modes, but instead utilizes a rough approximation of the fiber output as a collection of randomly-phased point sources.

Regards,

Jeff