| Effects of curvature on the optical modes of slab waveguides and simple one-dimensional photonic crystals are theoretically studied. We found that for both transverse electric and transverse magnetic modes, curving waveguide perpendicular to the propagation direction induces the optical field peak intensity move toward the center of the curvature. This results in a blueshift of the optical mode frequency as compared to the same mode propagating on a flat slab waveguide. For the waveguide curved in the direction parallel to the propagation direction, the opposite effects are observed. Applying curvature effects to the design of the photonic crystals, we demonstrate that the photonic bandgap as well as cavity modes can be modified. This theoretical works could be extended to experimentally realizable rolled-up photonic crystals. |
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