$$\def\ket#1{{\left|{#1}\right\rangle}} \def\bra#1{{\left\langle{#1}\right|}} \def\braket#1#2{{\left\langle{#1}|{#2}\right\rangle}}$$

## Part 2: Bent Fibers

We saw in the first part of the tutorial that the profiles and the propagation constants of the propagation modes of a straight multimode fiber can easily be avulated for an arbitrary index profile by inverting a large but sparse matrix. Under some approximations [1], a portion of fiber with a fixed radius of curvature satisfies a similar problem that can be solved with the same numerical tools, as we illustrate with the PyMMF Python module [2]. Moreover, when the modes are known for the straight fiber, the modes for a fixed radius can be approximate by inverting a square matrix of size the number of propagating modes [1]. It allows fast computation of the modes for different radii of curvature.

$$\def\ket#1{{\left|{#1}\right\rangle}} \def\bra#1{{\left\langle{#1}\right|}}$$