Design of Arbitrary Modal Electric Field in Cylindrical Waveguides

In this paper, we examine for the first time how to design arbitrary shape modal fields within complex refractive index circular waveguides. In order to achieve this flexibility in field shape, we use complex refractive index profile waveguides, where we determine the required refractive index profile on both real and imaginary refractive index. We develop a technique for calculating directly and accurately the refractive index profiles of cylindrical waveguides from knowledge of the desired modal electric field. The method we use to solve this inverse problem is via modeling the waveguide transversely as a transmission line. We demonstrate this algorithm with a number of example reconstructions of different arbitrary modal electric fields. The refractive index profiles generated supporting the required modal electric fields are complex. We reconstruct complex refractive index profiles which support unusual electric field distributions. We expect this technique to be useful in designing special fibers for mode matching between dissimilar waveguides, in designing sensing optical fibers, in mode division multiplexing, in gain flattening optical fiber amplifiers, and also for high power optical fibers.