To date, the supersymmetric (SUSY) formalism in optics has been used to engineer the spatial distributions of refractive indices. Here, we use SUSY formalism to engineer the shape of the corrugated dielectric waveguide instead of its refractive index profile to enable the insertion of an arbitrary number of transmission peaks in the stopband. These peaks can be used to make low-power intensity-dependent optical switches. Moreover, at microwave frequencies, the embedded states can be used to design leaky wave antennas, capable of scanning continuously from forward to the backward direction through broadside without degradation in beam quality.
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