We use an inverse-scattering (IS) approach to design single-mode waveguides with controlled linear and higher-order
dispersion. The technique is based on a numerical solution to the Gelfand-Levitan-Marchenko integral equation, for the
inversion of rational reflection coefficients with arbitrarily large number of leaky poles. We show that common features
of dispersion-engineered waveguides such as trenches, rings and oscillations in the refractive index profile come
naturally from the IS algorithm without any a priori assumptions. Increasing the leaky-pole number increases the
dispersion map granularity and allows design of waveguides with identical low order and differing higher order
dispersion coefficients.
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