Two-dimensional refractive index and birefringence profiles of a graded index bent optical fibre

A theory to recover refractive index profile of the bent graded index (GRIN) optical fibre, in core region, is proposed. This theory is applied to the bent GRIN optical fibre when it is located orthogonal in the light path of the object arm in digital holographic phase shifting interferometer; like Mach–Zehnder interferometer. In the experiment, the fibre is bent with two different bending radii and fixed on a microscope slide keeping it immersed in matching liquid. The produced phase shifted holograms, with the presence of the fibre, are recorded using an attached CCD camera. Two different processes controlling the index profile shape of the bent GRIN optical fibre are assumed. In the first process, a linear index variation is evolved from stresses in the direction of the bent radius. In the second one, there is a release of these stresses near the fibre surface, which depends on the fibre’s radius. This will affect the outer free surface of the cladding. Based on these assumptions, we are able to construct the index profile in two dimensions normal to the optical axis. We propose two functions to describe the refractive index profiles in cladding and the core regions of the bent GRIN optical fibre. The recorded phase shifted holograms are combined, reconstructed and analyzed to get the phase map of the bent GRIN optical fibre. Comparing the extracted optical phase differences with the calculated ones, a good agreement between them is found. This means that the used two dimensional proposed functions, which are describing cladding and the core indices profiles, are the most proper in this situation. Thus, we are able to determine a realistic induced birefringence profile inside the fibre which is generated by a bending operation, not only in the cladding but also in graded index core region as well.