Theory for the measurement of the linear and nonlinear refractive indices of double-clad fibers using an interferometric technique

Multiple-beam Fizeau fringes are formed across a liquid silvered wedge when it is illuminated by a collimated beam of monochromatic light. Inserting the fiber into the liquid silvered wedge causes the fringes to shift across the fiber region with respect to the fringes at the liquid region. Fringe shift is a function in the geometry of the different regions of the fiber and the refractive index profile of the fiber. In this paper, theoretical models for the fringe shift across double-clad fibers (DCFs) with rectangular, elliptical, circular, and D-shaped inner cladding are developed. An algorithm to reconstruct the linear and nonlinear terms of the refractive index profile of the DCF is outlined. Numerical examples are provided and discussed.