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.

Department of Theoretical Physics and Astrophysics Masaryk University Kotlářská 2 61137 Brno Czechia

Institute of Scientific Instruments of CAS Královopolská 147 612 64 Brno Czech Republic

LaserLaB Amsterdam Department of Physics and Astronomy VU University Amsterdam De Boelelaan 1081 1081 HV Amsterdam The Netherlands

Leibniz Institute of Photonic Technology Albert Einstein Straße 9 07745 Jena Germany

School of Science and Engineering University of Dundee Ewing building Nethergate DD1 4HN Dundee Scotland United Kingdom

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