Geometrical representation of coherent tunneling process in two-waveguide and three-waveguide coupler

We propose an identical geometrical representation scheme for both Landau-Zener (LZ) tunneling process in two-waveguide coupler with a cubically bent structure and stimulated Raman adiabatic passage (STIRAP) in three-waveguide coupler, similar to the geometrical representation of sum frequency process. The results show that although the two-waveguide coupler with a cubically bent axis has not aperiodic structure, it acts as a chirped quasi-phase-matching (QPM) grating and corrects the relative phase between the two supermodes in the curved coupler system. We present a scheme about how to choose the parameters to design the curved beam splitter.