Refractive index profile of fused-fiber couplers cross-section

We investigate the refractive index profile of the cross-section of fused type fiber-optic couplers by solving the convective diffusion equation. We assume the refractive index to be a linear function of the dopant concentration. The viscous sintering of the optical fibers is considered as the motion of an incompressible Newtonian fluid which is driven by the surface tension acting at the free boundary. The internal velocity field is obtained using conformal mapping methods. We present numerical solutions of the resulting equations and compare them with experimental observations.