Abstract:
The versatility of computational design as an alternative
to design by
nanofabrication has made computers a reliable design
tool in
nanophotonics. Given that almost any 2d pattern can
be fabricated at
infrared length scales, there exists a large number
of degrees of
freedom in nanophotonic device design. However current
designs are
ad-hoc and could potentially benefit from optimization
but there are
several outstanding issues regarding PDE-based optimization
for
electromagnetism that must first be addressed: continuously
and
accurately deforming geometric objects represented
on a discrete
uniform grid while avoiding staircasing effects,
reducing the
computational expense of large simulations while
improving accuracy,
resolving the breakdown of standard absorbing boundary
layers for
important problems, finding robust designs that are
impervious to
small perturbations, and finally distinguishing global
from local
minima. We address each of these issues in turn by
developing novel
subpixel smoothing methods that markedly improve
the accuracy of
simulations, demonstrate the failure of perfectly
matched layers (PML) in
several important cases and propose a workaround,
develop a simple
procedure to determine the validity of any PML implementation
and
incorporate these and other enhancements into a flexible,
free
software package for electromagnetic simulations
based on the
finite-difference time-domain (FDTD) method. Next
we investigate two
classes of design problems in nanophotonics. The
first involves
finding cladding structures for holey photonic-crystal
fibers at
low-index contrasts that permit a larger class of
materials to be used
in the fabrication process. The second is the development
of adiabatic
tapers for coupling to slow-light modes of photonic-crystal
waveguides
that are insensitive to manufacturing and operational
variability.
URL: http://ab-initio.mit.edu/~ardavan/stuff/oskooi_scd_2010.pdf
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