Abstract
Light transport through a multimode optical waveguide undergoes changes when subjected to bending deformations. We show that optical waveguides with a perfectly parabolic refractive index profile are almost immune to bending, conserving the structure of propagation-invariant modes. Moreover, we show that changes to the transmission matrix of parabolic-index fibers due to bending can be expressed with only two free parameters, regardless of how complex a particular deformation is. We provide detailed analysis of experimentally measured transmission matrices of a commercially available graded-index fiber as well as a gradient-index rod lens featuring a very faithful parabolic refractive index profile. Although parabolic-index fibers with a sufficiently precise refractive index profile are not within our reach, we show that imaging performance with standard commercially available graded-index fibers is significantly less influenced by bending deformations than step-index types under the same conditions. Our work thus predicts that the availability of ultraprecise parabolic-index fibers will make endoscopic applications with flexible probes feasible and free from extremely elaborate computational challenges.
Highlights
Light transport through a multimode optical waveguide undergoes changes when subjected to bending deformations
These measurements lead to the reconstruction of a transmission matrix (TM) [2,13,14,15]—a linear relation between conveniently chosen representations of input and output modes containing the complete information about light transport through the multimode fibers (MMFs)
In 2015, it was shown that commercially available stepindex MMFs, at length scales relevant for imaging applications, are of sufficient quality to allow for prediction of the TM based on numerical simulations [18]
Summary
Especially laser-scanning-based approaches [4,5] including multiphoton excitation [6], superresolution [7], as well as wide-field techniques such as bright-field, dark-field, and light-sheet microscopy [5,8,9], have already been demonstrated These approaches have been treating MMFs as random media [10,11] and they required a calibration step, in which the light transport through MMF is quantitatively analyzed. These measurements lead to the reconstruction of a transmission matrix (TM) [2,13,14,15]—a linear relation between conveniently chosen representations of input and output modes containing the complete information about light transport through the MMF During this procedure and subsequent imaging, the MMF is required to remain locked to the same position (contortion) since any deformation would introduce changes to the TM and as a result affect the imaging quality [5,16,17].
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