70,356 research outputs found
Programming of inhomogeneous resonant guided wave networks
Photonic functions are programmed by designing the interference of local waves in inhomogeneous resonant guided wave networks composed of power-splitting elements arranged at the nodes of a nonuniform waveguide network. Using a compact, yet comprehensive, scattering matrix representation of the network, the desired photonic function is designed by fitting structural parameters according to an optimization procedure. This design scheme is demonstrated for plasmonic dichroic and trichroic routers in the infrared frequency range
A Subgradient Method for Free Material Design
A small improvement in the structure of the material could save the
manufactory a lot of money. The free material design can be formulated as an
optimization problem. However, due to its large scale, second-order methods
cannot solve the free material design problem in reasonable size. We formulate
the free material optimization (FMO) problem into a saddle-point form in which
the inverse of the stiffness matrix A(E) in the constraint is eliminated. The
size of A(E) is generally large, denoted as N by N. This is the first
formulation of FMO without A(E). We apply the primal-dual subgradient method
[17] to solve the restricted saddle-point formula. This is the first
gradient-type method for FMO. Each iteration of our algorithm takes a total of
foating-point operations and an auxiliary vector storage of size O(N),
compared with formulations having the inverse of A(E) which requires
arithmetic operations and an auxiliary vector storage of size . To
solve the problem, we developed a closed-form solution to a semidefinite least
squares problem and an efficient parameter update scheme for the gradient
method, which are included in the appendix. We also approximate a solution to
the bounded Lagrangian dual problem. The problem is decomposed into small
problems each only having an unknown of k by k (k = 3 or 6) matrix, and can be
solved in parallel. The iteration bound of our algorithm is optimal for general
subgradient scheme. Finally we present promising numerical results.Comment: SIAM Journal on Optimization (accepted
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