The directional coupler based on the GaAs/GaAlAs optical strip waveguide is analyzed using three-dimensional beam propagation method based on the series expansion method (3D-SEM-BPM).The even and odd modes supported by this coupler are obtained

respectively

and the coupling length exponentially increases with the increasing of the waveguide separation.The simulation results for the injected field through the present device are also gotten

and the excitation selected as the fundamental mode supported by the single optical strip waveguide at left channel is transferred into the right channel after propagatiny 2.62mm

thus the cross state is obtained.The 3D-SEM-BPM reduces the basic BPM equation to the first-order normal differential equation system.Consequently

the computational program is simple.Moreover

the calculation is efficient due to the small matrix derived from the present method.In dealing with the boundary conditions

a tangent-type function is applied to map the infinite space into a unit square.As a result

the boundary truncation is eliminated.