Fiber Taper for Coupling of Space Beam to Single Mode Fiber

Coupling between fiber modes due to imperfections is proportional to the overlap integral of the modes and inversely proportional to the difference between their propagation constants (Deltabeta). To that effect a detailed study of core and cladding modes for finite cladding fiber using analytical and numerical techniques and simulation with finite element method is presented. The respective characteristic equations for both the core and cladding modes are obtained. The normalized propagation constant versus normalized frequency is numerically obtained for different clad to core radii ratios. This is done for fixed cladding diameter of 126 mum and increasing core diameter from 3 to 9 mum with core and cladding refractive indices corresponding to a normalized frequency V range from 0.774 to 2.322 at wavelength lambda = 1.55 mum. It was observed that the overlap integral and the inverse of the difference of the propagation constants (1/ Deltabeta) are both high at small core radius ´a´ and diminish as the core radius increases. To affect power coupling from the cladding modes to the core mode, a core taper is considered with small radius at its input end, increasing to constant normal core size. Simulation of wave propagation in such fiber shows clearly the increase of the field inside the core with propagation in the tapered section. Analytical treatment of mode coupling is also given under the assumption of adiabatic core radius increase. Perturbation technique is used to solve the coupled mode equations. The results confirmed the basic finding of the simulation.