Speckled output of a multi-mode optical fibre and sensitivity to fibre perturbations

Multimode fibres are now finding applications in the transport of complex modes and spatial information, such as images. Key to their use is recognising that fibres can be characterised in terms of a transmission matrix, relating any complex input field to the output field. Unfortunately, bending, stressing, or changing the temperature of the fibre changes this matrix, which traditionally then requires a time-consuming re-calibration. In this work, we characterize the stability of this transmission matrix by examining the changes in the transmitted speckle field as the fibre is substantially perturbed. We consider both step-index and graded-index fibres for three different types of fibre bend. Specifically, we examine both step- and graded-index fibres each supporting over one thousand transverse modes and show that, when averaged over the whole numerical aperture, the transmission matrix associated with the graded index fibres is significantly more stable than those for step index, for all types of fibre bend. Furthermore, the higher numerical aperture modes are always more stable than the low-numerical aperture ones. This work is important for selecting fibre type, bend constraints, and calibration bend positions for those using multimode fibres in data transmission or imaging applications.