A general numerical tool,based on thermal diffusion equation and full-vectorial eigen-mode equation,has been presented for the systematic analysis of graded index channel waveguide fabricated by ion exchange on Er3+ doped glass.Finite difference method with full-vectorial formulation(FV-FDM) is applied to solving the full-vectorial modes of graded index channel waveguide for the first time.The coupled difference equations based on magnetic fields in FV-FDM are derived from the Taylor series expansion and accurate formulation of boundary conditions.Hybrid nature of vectorial guided modes for both pump(980 nm) and signal light(1550 nm) are demonstrated by the simulation.Results show that the fabrication parameters of ion exchange,such as channel opening width and time ratio of second step to first step in ion exchange,have large influence on the properties of waveguide.By optimizing the fabrication parameters,maintenance of monomode for signal light and improvement of the gain dynamics can be achieved in Er3+ doped waveguide amplifier(EDWA) fabricated by ion exchange technique.This theoretical model is significant for the design and fabrication of EDWA with ion exchange technique.Furthermore,a single polarization EDWA,which operates at wavelength from 1528 nm to 1541 nm for HE polarization,is numerically designed. A general numerical tool, based on thermal diffusion equation and full-vectorial eigen-mode equation, has been presented for the systematic analysis of graded index channel waveguide fabricated by ion exchange on Er3 + doped glass. Finite difference method with full-vectorial formulation (FV -FDM) is applied to solve the full-vectorial modes of graded index channel waveguide for the first time. The coupled difference equations based on magnetic fields in FV-FDM are derived from the Taylor series expansion and accurate formulation of boundary conditions. Hybrid nature of vectorial guided modes for both pump (980 nm) and signal light (1550 nm) are demonstrated by the simulation. Results show that the fabrication parameters of ion exchange, such as channel opening width and time ratio of second step to first step in ion exchange, have large influence on the properties of waveguide.By optimizing the fabrication parameters, maintenance of monomode for signal light and improvement of the gain dynamics c an be achieved in Er3 + doped waveguide amplifier (EDWA) fabricated by ion exchange technique. This theoretical model is significant for the design and fabrication of EDWA with ion exchange technique. Futurertherm, a single polarization EDWA, which operates at wavelength from 1528 nm to 1541 nm for HE polarization, is numerically designed.