Abstract

We present the use of the Douglas-Gunn Alternating Direction Implicit finite difference method for computationally efficient simulation of the electric field propagation through a wide variety of optical fiber geometries. The method can accommodate refractive index profiles of arbitrary shape and is implemented in a tool called BPM-Matlab. We validate BPM-Matlab by comparing it to published experimental, numerical, and theoretical data and to commercially available state-of-the-art software. It is user-friendly, fast, and is available open-source. BPM-Matlab has a broad scope of applications in modeling a variety of optical fibers for diverse fields such as imaging, communication, material processing, and remote sensing.

Highlights

  • Tailoring light delivery through optical fibers provides the intriguing possibility to dispense with optical elements at the fiber output, opening up avenues towards miniaturized light delivery in fields such as endoscopy, communication, material processing, remote sensing, and beyond [1,2,3,4,5,6,7,8,9,10,11]

  • We present the use of the Douglas-Gunn Alternating Direction Implicit finite difference method for computationally efficient simulation of the electric field propagation through a wide variety of optical fiber geometries

  • We present a numerical simulation tool called Beam Propagation Method (BPM)-Matlab in which the Douglas-Gunn Alternating Direction Implicit (DG-alternating direction implicit (ADI)) method is used to efficiently model the electric field propagation in a wide variety of optical fiber geometries with arbitrary refractive index profiles

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Summary

Introduction

Tailoring light delivery through optical fibers provides the intriguing possibility to dispense with optical elements at the fiber output, opening up avenues towards miniaturized light delivery in fields such as endoscopy, communication, material processing, remote sensing, and beyond [1,2,3,4,5,6,7,8,9,10,11]. Numerical tools must supplement these theoretical methods to accurately simulate beam propagation and to calculate the memory effect, especially for non-trivial fiber structures and for cases in which perturbation theory may no longer be valid Multiple toolboxes such as BeamLab [19] and software packages such as Lumerical [20], based on the Beam Propagation Method (BPM) and/or the Finite-Difference Eigenmode solver and Eigenmode Expansion propagator, are widely used by the scientific community for optical fiber modeling. These simulation tools can model a multitude of applications in the regimes of free-space, waveguide, and non-linear optics, they are neither free as in beer (gratis) nor free as in speech (libre).

Theory
FD-BPM
Douglas-Gunn alternating direction implicit FD-BPM
Implementation in MATLAB
Fiber modes and modal power distribution
Validation
Straight multimode fiber propagation
Bent fiber propagation in multi- and single-mode fibers
Tapering a multimode fiber to a single-mode fiber
Multicore fiber propagation with distal end focusing
Conclusion

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