In this study, we propose an ideal structure for lossless bends in optical waveguides for the first time. The ideal structure is obtained by applying a series of conformal mappings to transform a single-mode straight waveguide into the equivalent bend configuration. The expressions used to determine the waveguide path and the refractive index are derived for the lossless bends with arbitrary bend angles, even up to 90°. Also, variations in the waveguide path and the refractive index are illustrated by adopting lossless bends with six different bend angles (4, 10, 30, 45, 60, and 90°). The simulated results show that the refractive-index distribution can be controlled within the range of interest for the practical bend structure. Moreover, the characteristics of the phase front for the modal field in a lossless bend are thoroughly discussed to verify that no transmitted power would be lost by conversion to radiation modes.
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