Two-dimensional refractive index and stresses profiles of a homogenous bent optical fiber

We present a significant contribution to the theory of determining the refractive index profile of a bent homogenous optical fiber. In this theory we consider two different processes controlling the index profile variations. The first is the linear index variation due to stress along the bent radius, and the second is the release of this stress on the fiber surface. This release process is considered to have radial dependence on the fiber radius. These considerations enable us to construct the index profile in two dimensions normal to the optical axis, considering the refraction of light rays traversing the fiber. This theory is applied to optical homogenous bent fiber with two bending radii when they are located orthogonal to the light path of the object arm in the holographic setup (like the Mach-Zehnder interferometer). Digital holographic phase shifting interferometry is employed in this study. The recorded phase shifted holograms have been combined, reconstructed, and processed to extract the phase map of the bent optical fiber. A comparison between the extracted optical phase differences and the calculated one indicates that the refractive index profile variation should include the above mentioned two processes, which are considered as a response for stress distribution across the fiber's cross section. The experimentally obtained refractive index profiles provide the stress induced birefringence profile. Thus we are able to present a realistic induced stress profile due to bending.