Robust Optimization of Adiabatic Tapers for Coupling to Slow-Light Photonic-Crystal Waveguides
A Oskooi, A. Mutapcic, S. Noda, J. Joannopulos, S. Boyd, and S. Johnson
Optics Express, 20(19):21558–21575, September 2012.
We investigate the design of taper structures for coupling to slow-light modes
of various photonic-crystal waveguides while taking into account parameter
uncertainties inherent in practical fabrication. Our short-length (11 periods)
robust tapers designed for m
and a slow-light group velocity of
have a total loss less than 20 dB even in the presence of
nanometer-scale surface
roughness, which outperform the corresponding non-robust designs by an order of
magnitude. We discover a posteriori that the robust designs have smooth
profiles that can be parameterized by a few-term (intrinsically smooth) sine
series which helps the optimization to further boost the performance slightly.
We ground these numerical results in an analytical foundation by deriving the
scaling relationships between taper length, taper smoothness, and group
velocity with the help of an exact equivalence with Fourier analysis.
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