Study of a dynamic-shape-curve function for a fused tapering optical fiber

For the fused tapering optical fibers, a physics-mathematics equation of dynamic-shape curves is deduced. The closed-form solution of the equation can be acquired by use of its initial, boundary, and volume-conserved conditions. The shape curves in different tapering processes can be described by the solution conveniently, accurately, and integratively. A large quantity of experimental data has been provided and shown to have a coincidence with the theoretical results properly. Especially, the initial length of the fused zone is known, and the solution can predict the whole tapering shape curve with an arbitrary elongating length.