Fast dispersion tailoring of multimode photonic crystal resonators

We introduce a numerical procedure which permits us to drastically accelerate the design of multimode
photonic crystal resonators. Specifically, we demonstrate that the optical response of an important class of such
nanoscale structures is reproduced accurately by a simple, one-dimensional model within the entire spectral
range of interest. This model can describe a variety of tapered photonic crystal structures. Orders of magnitude
faster to solve, our approach can be used to optimize certain properties of the nanoscale cavity. Here we consider
the case of a nanobeam cavity, for which the confinement results from the modulation of its width. The profile
of the width is optimized in order to flatten the resonator dispersion profile (so that all modes are equally spaced
in frequency). This result is particularly relevant for miniaturizing parametric generators of nonclassical light,
optical nanocombs, and mode-locked laser sources. Our method can be easily extended to complex geometries,
described by multiple parameters