The loss properties of multimode -branch waveguides are analyzed using coupled mode theory combined with two-dimensional Padé (1,1) approximation finite-difference beam propagation method. The radiation losses of zeroth-order mode propagating in single-mode and multimode turning channel waveguides are compared. Mode conversion in the symmetric five-layer waveguide for multimode -branch configuration is analyzed. Then the relations between radiation loss and the branching angle for single-mode and multimode -branch waveguides are obtained and explained. It is found that when there is not much coupling from zeroth-order mode to other higher-order modes in a multimode -branch waveguide, radiation loss of zeroth-order mode propagating in the waveguide is lower than that in a single mode one. For a multimode -branch waveguide, the radiation loss curve fluctuates as the result of mode coupling and influence of the turning points of the waveguide structure. By making use of the fluctuation of the radiation loss curve, optimizing the structural parameters such as branching angle and the width of waveguide and trying to eliminate the generation of the second-order mode at the turning points, a design of a multimode -branch waveguide with low loss and wide branching angle is obtained.
A compact integrated 1310/1550nm Y-branch waveguide wavelength demultiplexing coupler based on multimode interference is demonstrated. Theoretical analysis and simulation results for the demultiplexer configuration are presented. The structure performance can be optimized with an appropriate choice of some structural parameters such as input and output waveguide widths, refractive index profiles and coupler length. The contrasts achieve 9.8 and 9.4dB for a graded-index Y-branch wavelength demultiplexer at 1310 and 1550nm, and the corresponding insertion losses are 0.60 and 0.73dB at 1310 and 1550nm, respectively. For a step-index Y-branch wavelength demultiplexer, contrasts are 7.6 and 7.5dB, and insertion losses are 0.75 and 0.83dB at 1310 and 1550nm, respectively.
Theoretic characteristics of Er<sup>3+</sup>-Yb<sup>3+</sup> co-doped phosphate glass waveguide amplifier are studied by resolving rate-propagation equations with overlapping integral method. Considering the effect of the up-conversion and ASE, the amplifier gain and ASE spectrum are obtained. The relations between the amplifier gain and several parameters are analyzed, such as the waveguide length, pump power, up-conversion coefficient, propagation loss and so on. The experiment result agrees well with the numerical result.