A design method for fully adiabatic waveguide branches is developed for the first time. Mode conversion between local normal modes is entirely suppressed through the explicit decoupling of the modes, where novel parametric and graphical representations of the self-consistent orthogonal coupled-mode theory are utilized to describe the strongly coupled part of the waveguide branches. A closed-form expression for an adiabatic condition is derived, and the significance of degenerated waveguide patterns with nonuniform waveguide widths is clarified. Validity of the method is tested by numerical simulations, and L<sup>-2</sup> dependence of the converted power to a circuit length is found. These results raise a fundamental question about the meaning of the adiabaticity in the waveguide branches.
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