Figure 5 Spectra a of the time series using even-, odd-, and the ลฝ . left-half excitation, and detailed spectra b near the frequency of 2 = 10 14 Hz steps without losing too much of the fine structure information for the propagation mode. These techniques include w x high-resolution spectrum analysis 11 and the zero-padding w x 12 technique. Those approaches are the subjects of a future study.
IV. CONCLUSION
The wave-coupling mechanism in a dielectric optical waveguide coupler was interpreted using even-and odd-mode analysis. It was determined that the coupling length is inversely proportional to the difference between the even-and odd-mode propagation constants in the coupling section. The 2-D FDTD was implemented to determine the dispersion relations of the propagation modes. Due to the small difference between the even-and odd-mode propagation constants, a large number of the time steps are needed to increase the integration time, and to provide the resolution needed to reveal the fine structure. The calculated coupling length compares well with that obtained using the Marcatili method.
ACKNOWLEDGMENT
The authors would like to thank J. Brandelik and J.B. Tsui of AFRL for their useful discussion. We are also in debt to the Major Shared Resource Center, ASCrMSRC, for its computation time and the related consultations.