Fig. 5.

Curved waveguides and skin-depth engineering. a, b Refractive index profile (blue) and the magnetic field profile (green) of a a straight strip waveguide and b a straight e-skid waveguide. c The corresponding bent waveguides c, d can be transformed to straight waveguides with inhomogeneous refractive index profiles in a new coordinate system. If the local refractive index of the cladding exceeds the effective modal index $\left(n\prime \left(u_0\right)>n_{\mathrm{e}ff}\right)$, the waveguide mode starts radiating. This occurs at the radiation condition point denoted by black arrows. The multilayer metamaterial cladding in e-skid waveguides suppresses the evanescent wave field beyond this radiation condition point. Thus, in comparison with conventional bent waveguides, lesser power is radiated owing to curvature effects