3,663 research outputs found
Fabrication-Adaptive Optimization, with an Application to Photonic Crystal Design
It is often the case that the computed optimal solution of an optimization
problem cannot be implemented directly, irrespective of data accuracy, due to
either (i) technological limitations (such as physical tolerances of machines
or processes), (ii) the deliberate simplification of a model to keep it
tractable (by ignoring certain types of constraints that pose computational
difficulties), and/or (iii) human factors (getting people to "do" the optimal
solution). Motivated by this observation, we present a modeling paradigm called
"fabrication-adaptive optimization" for treating issues of
implementation/fabrication. We develop computationally-focused theory and
algorithms, and we present computational results for incorporating
considerations of implementation/fabrication into constrained optimization
problems that arise in photonic crystal design. The fabrication-adaptive
optimization framework stems from the robust regularization of a function. When
the feasible region is not a normed space (as typically encountered in
application settings), the fabrication-adaptive optimization framework
typically yields a non-convex optimization problem. (In the special case where
the feasible region is a finite-dimensional normed space, we show that
fabrication-adaptive optimization can be re-cast as an instance of modern
robust optimization.) We study a variety of problems with special structures on
functions, feasible regions, and norms, for which computation is tractable, and
develop an algorithmic scheme for solving these problems in spite of the
challenges of non-convexity. We apply our methodology to compute
fabrication-adaptive designs of two-dimensional photonic crystals with a
variety of prescribed features
Robust topology optimization of three-dimensional photonic-crystal band-gap structures
We perform full 3D topology optimization (in which "every voxel" of the unit
cell is a degree of freedom) of photonic-crystal structures in order to find
optimal omnidirectional band gaps for various symmetry groups, including fcc
(including diamond), bcc, and simple-cubic lattices. Even without imposing the
constraints of any fabrication process, the resulting optimal gaps are only
slightly larger than previous hand designs, suggesting that current photonic
crystals are nearly optimal in this respect. However, optimization can discover
new structures, e.g. a new fcc structure with the same symmetry but slightly
larger gap than the well known inverse opal, which may offer new degrees of
freedom to future fabrication technologies. Furthermore, our band-gap
optimization is an illustration of a computational approach to 3D dispersion
engineering which is applicable to many other problems in optics, based on a
novel semidefinite-program formulation for nonconvex eigenvalue optimization
combined with other techniques such as a simple approach to impose symmetry
constraints. We also demonstrate a technique for \emph{robust} topology
optimization, in which some uncertainty is included in each voxel and we
optimize the worst-case gap, and we show that the resulting band gaps have
increased robustness to systematic fabrication errors.Comment: 17 pages, 9 figures, submitted to Optics Expres
Aperiodic nano-photonic design
The photon scattering properties of aperiodic nano-scale dielectric
structures can be tailored to closely match a desired response by using
adaptive algorithms for device design. We show that broken symmetry of
aperiodic designs provides access to device functions not available to
conventional periodic photonic crystal structures.Comment: 23 pages, LaTex, 8 postscript figure
One-shot ultraspectral imaging with reconfigurable metasurfaces
One-shot spectral imaging that can obtain spectral information from thousands
of different points in space at one time has always been difficult to achieve.
Its realization makes it possible to get spatial real-time dynamic spectral
information, which is extremely important for both fundamental scientific
research and various practical applications. In this study, a one-shot
ultraspectral imaging device fitting thousands of micro-spectrometers (6336
pixels) on a chip no larger than 0.5 cm, is proposed and demonstrated.
Exotic light modulation is achieved by using a unique reconfigurable
metasurface supercell with 158400 metasurface units, which enables 6336
micro-spectrometers with dynamic image-adaptive performances to simultaneously
guarantee the density of spectral pixels and the quality of spectral
reconstruction. Additionally, by constructing a new algorithm based on
compressive sensing, the snapshot device can reconstruct ultraspectral imaging
information (/~0.001) covering a broad (300-nm-wide)
visible spectrum with an ultra-high center-wavelength accuracy of 0.04-nm
standard deviation and spectral resolution of 0.8 nm. This scheme of
reconfigurable metasurfaces makes the device can be directly extended to almost
any commercial camera with different spectral bands to seamlessly switch the
information between image and spectral image, and will open up a new space for
the application of spectral analysis combining with image recognition and
intellisense
Astronomical photonics in the context of infrared interferometry and high-resolution spectroscopy
We review the potential of Astrophotonics, a relatively young field at the
interface between photonics and astronomical instrumentation, for
spectro-interferometry. We review some fundamental aspects of photonic science
that drove the emer- gence of astrophotonics, and highlight the achievements in
observational astrophysics. We analyze the prospects for further technological
development also considering the potential synergies with other fields of
physics (e.g. non-linear optics in condensed matter physics). We also stress
the central role of fiber optics in routing and transporting light, delivering
complex filters, or interfacing instruments and telescopes, more specifically
in the context of a growing usage of adaptive optics.Comment: SPIE Astronomical Telescopes and Instrumentation conference, June
2016, 21 pages, 10 Figure
Designing Phononic Crystals With Convex Optimization
Designing phononic crystals by creating frequency bandgaps is of particular interest in the engineering of elastic and acoustic microstructured materials. Mathematically, the problem of optimizing the frequency bandgaps is often nonconvex, as it requires the maximization of the higher indexed eigenfrequency and the minimization of the lower indexed eigenfrequency. A novel algorithm [1] has been previously developed to reformulate the original nonlinear, nonconvex optimization problem to an iteration-specific semidefinite program (SDP). This algorithm separates two consecutive eigenvalues — effectively maximizing bandgap (or bandwidth) — by separating the gap between two orthogonal subspaces, which are comprised columnwise of “important” eigenvectors associated with the eigenvalues being bounded. By doing so, we avoid the need of computation of eigenvalue gradient by computing the gradient of affine matrices with respect to the decision variables. In this work, we propose an even more efficient algorithm based on linear programming (LP). The new formulation is obtained via approximation of the semidefinite cones by judiciously chosen linear bases, coupled with “delayed constraint generation”. We apply the two convex conic formulations, namely, the semidefinite program and the linear program, to solve the bandgap optimization problems. By comparing the two methods, we demonstrate the efficacy and efficiency of the LP-based algorithm in solving the category of eigenvalue bandgap optimization problems.United States. Air Force Office of Scientific Research (FA9550-11- 1-0141
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