A Theoretical Study on Special Ti:LiNbO $_{3}$ Structure of an Array of Strip Waveguides Embedded in a Planar Waveguide

A theoretical study was performed on waveguiding characteristics of a special Ti:LiNbO₃ structure that an array of strip waveguides is embedded in a planar waveguide. First, a special Ti:LiNbO₃ structure was fabricated by diffusion of homogeneously coated Ti film at first and then photolithographically patterned Ti-strips with different widths of 4, 5, 6, 7, and 8 μ m, and the transverse magnetic (TM) mode guided in the strip waveguides of the special structure was characterized by near-field measurements. Second, a 2-D refractive index profile is supposed for the special structure. Third, based upon this supposed index profile model and the experimentally determined mode field profile type, the mode sizes of the strip waveguides were calculated using variational method and compared with the experimental results to verify the validity of the index model supposed and the numerical method adopted. Finally, the mode sizes and effective indexes of several lowest order TM modes guided in the strip waveguides were calculated as a function of the initial Ti-strip width for different waveguide parameters that include the surface index increment and depth (width) of both the planar and strip waveguides. The numerical results show that the field profile in the width direction is influenced by many factors such as the initial Ti-strip width, waveguide width and depth, and the surface index increment of the strip waveguide. Instead, the mode field in the depth direction is only influenced by three factors that include the depth of strip waveguide and the surface index increments of both planar and strip waveguides. The single-mode condition depends on all of these parameters.