Inverse design of nanophotonic structures using complementary convex optimization

Fig. 1 shows the result of applying our method to a one-dimensional problem. The algorithm was executed for 100 iterations, which took 3 minutes on a generic desktop computer. The target field, which started as a sinusoid in a Gaussian-envelope, closely matches the field obtained from simulating the dielectric structure using FDTD. Additionally, the values of Y were strictly constrained to be between 1 and 10, which resulted in a nearly binary dielectric structure. This is important, since feasible nanophotonic devices are almost universally binary and discrete in values of ∈

[1]  W. Marsden.  I and J , 2012 .

[2]  K. Yee.  Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media , 1966 .

[3]  A. Louisa,et al.  コロイド混合体における有効力 空乏引力から集積斥力へ | 文献情報 | J-GLOBAL 科学技術総合リンクセンター , 2002 .

[4]  Ilya Fushman,et al.  General recipe for designing photonic crystal cavities. , 2005, Optics express.

[5]  土屋 一郎,et al.  Ultra-High-Q Photonic Double-Heterostructure Nanocavity , 2005 .

[6]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[7]  Susumu Noda,et al.  Fine-tuned high-Q photonic-crystal nanocavity. , 2005, Optics express.

[8]  P. Bernardi,et al.  A Numerical Method Based on the Discretization of Maxwell Equations in Integral Form (Short Papers) , 1974 .

[9]  Andreas Håkansson,et al.  Inverse designed photonic crystal de-multiplex waveguide coupler. , 2005, Optics express.

[10]  Michal Lipson,et al.  Low modal volume dipole-like dielectric slab resonator. , 2008, Optics express.

[11]  Jakob S. Jensen,et al.  Topology optimization and fabrication of photonic crystal structures. , 2004, Optics express.

[12]  E. L. Hu,et al.  Tuning photonic nanocavities by atomic force microscope nano-oxidation , 2006 .

[13]  M. Ausloos,et al.  Absorption spectrum of clusters of spheres from the general solution of Maxwell's equations. The long-wavelength limit , 1980 .

[14]  Steven G. Johnson,et al.  Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis. , 2001, Optics express.

[15]  T. Asano,et al.  High-Q photonic nanocavity in a two-dimensional photonic crystal , 2003, Nature.

[16]  Jelena Vucković,et al.  Second harmonic generation in gallium phosphide photonic crystal nanocavities with ultralow continuous wave pump power. , 2009, Optics express.

[17]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[18]  P. Deotare,et al.  High quality factor photonic crystal nanobeam cavities , 2009, 0901.4158.

[19]  Jelena Vucković,et al.  Design of photonic crystal microcavities for cavity QED. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.