Abstract
Soliton states in three coupled optical waveguide systems were studied: two
linearly coupled waveguides with quadratic nonlinearity, two linearly coupled
waveguides with cubic nonlinearity and Bragg gratings, and a quadratic nonlinear
waveguide with resonant gratings, which enable three-wave interaction. The
methods adopted to tackle the problems were both analytical and numerical. The
analytical method mainly made use of the variational approximation. Since no exact
analytical method is available to find solutions for the waveguide systems under
study, the variational approach was proved to be very useful to find accurate
approximations. Numerically, the shooting method and the relaxation method were used.
The numerical results verified the results obtained analytically. New asymmetric
soliton states were discovered for the coupled quadratically nonlinear waveguides,
and for the coupled waveguides with both cubic nonlinearity and Bragg gratings.
Stability of the soliton states was studied numerically, using the Beam Propagation
Method. Asymmetric couplers with quadratic nonlinearity were also studied.
The bifurcation diagrams for the asymmetric couplers were those unfolded from the
corresponding diagrams of the symmetric couplers. Novel stable two-soliton bound
states due to three-wave interaction were discovered for a quadratically nonlinear
waveguide equipped with resonant gratings. Since the coupled optical waveguide
systems are controlled by a larger number of parameters than in the corresponding
single waveguide, the coupled systems can find a much broader field of applications.
This study provides useful background information to support these applications.