Numerical characterization of an ultra-high NA coherent fiber bundle part I: modal analysis

Advances in fiber optics and CCD technology in the last decades have allowed for a large reduction in outer diameter (from centimeters to submillimeter) of endoscopes. Attempts to reduce the outer diameter even further, however, have been hindered by the trade-off, inherent to conventional endoscopes, between outer diameter, resolution and field of view. Several groups have shown the feasibility of further miniaturization towards so called micro-endoscopes, albeit at the cost of a very reduced field of view. In previous work we presented the design of an ultra-high NA (0.928) Coherent FiberBundle (CFB) that, in combination with proximal wave front shaping, could be used to circumvent this trade-off thus paving the way for even smaller endoscopes. In this paper we analyze how the modal properties of such an ultra-high NA CFB determine the required input field to achieve any desired output field. We use the periodicity of the hexagonal lattice which characterizes a CFB, to define a unit cell of which we analyze the eigen-modes. During the modal analysis, we also take into account realistic variations in lattice constant, core size and core shape due to the limitations of the fabrication technology. Realistic values for these types of fabrication-induced irregularities were obtained via SEM images of a CFB fabricated according to the aforementioned design. The presence of these irregularities results, for a desired output, in the required input to be different from the required input for a defect-free CFB. We find that of the different types of fabrication-induced irregularities present in the CFB, variations in core ellipticity have the biggest impact on the required input for a given desired output.