Computational Bounds for Photonic Design

Angeris, Guillermo; Vučković, Jelena; Boyd, Stephen

doi:10.1021/acsphotonics.9b00154

Cited by 61 publications

(72 citation statements)

References 21 publications

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“…The imaginary (reactive) part of the resistivity ρ i does not enter into this constraint and may be considered to be chosen freely. This implies that, under only the constraint of (20), the conservation of reactive power in (21) may always be satisfied by a suitable a posteriori choice of bulk reactivity ρ i . When both the conservation of real power (20) and of reactive power (21) are used, an optimization problem with two constraints is formed which is always more restrictive then the former, since now the reactance part of resistivity ρ i is prescribed prior to the optimization.…”

Section: Formulating Bounds Using Optimal Currentsmentioning

confidence: 99%

“…3.1 and Sec. 3.2 an optimization problem is formulated for upper bounds on radiation intensity U (r,ê) using the power constraints (20) and (21). The first constraint would be used when only real part of material resistivity is prescribed, while both constraints should be used to enforce both real and imaginary components of the complex resistivity.…”

Section: Directional Scatteringmentioning

confidence: 99%

“…Shape dependent bounds adapted in this way for maximum radiative heat transfer are given in [1,19]. Shape dependent bounds for maximum absorption are given in [20] and for photonic design in [21].…”

Section: Introductionmentioning

confidence: 99%

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Upper bounds on absorption and scattering

et al. 2020

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C Radiation modes 30 D Material models 33Abstract A general framework for determining fundamental bounds in nanophotonics is introduced in this paper. The theory is based on convex optimization of dual problems constructed from operators generated by electromagnetic integral equations. The optimized variable is a contrast current defined within a prescribed region of a given material constitutive relations. Two power conservation constraints analogous to the optical theorem are utilized to tighten the bounds and to prescribe either losses or material properties. Thanks to the utilization of matrix rank-1 updates, modal decompositions, and model order reduction techniques, the optimization procedure is computationally efficient even for complicated scenarios. No dual gaps are observed. The method is well-suited to accommodate material anisotropy and inhomogeneity. To demonstrate the validity of the method, bounds on scattering, absorption, and extinction cross sections are derived first and evaluated for several canonical regions. The tightness of the bounds is verified by comparison to optimized spherical nanoparticles and shells. The next metric investigated is bi-directional scattering studied closely on a particular example of an electrically thin slab. Finally, the bounds are established for Purcell's factor and local field enhancement where a dimer is used as a practical example.

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Section: Formulating Bounds Using Optimal Currentsmentioning

confidence: 99%

Section: Directional Scatteringmentioning

confidence: 99%

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Upper bounds on absorption and scattering

et al. 2020

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“…Sometimes it is not clear that it is physically possible to achieve the desired behavior in a given design region. To date, rigorously bounding performance of devices is only possible in very limited cases and is not necessarily tight [18,19]. For a rough estimate of an upper bound, one can simply optimize the device without any fabrication constraints, including the top-down lithographic constraint.…”

Section: Device Performance Boundsmentioning

confidence: 99%

Nanophotonic inverse design with SPINS: Software architecture and practical considerations

Vercruysse

Skarda

et al. 2020

Applied Physics Reviews

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128

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A computational nanophotonic design library for gradient-based optimization called SPINS is presented. Borrowing the concept of computational graphs, SPINS is a design framework that emphasizes flexibility and reproducible results. The mathematical and architectural details to achieve these goals are presented, and practical considerations and heuristics for using inverse design are discussed, including the choice of initial condition and the landscape of local minima. arXiv:1910.04829v2 [physics.app-ph] 31 Oct 2019 design. These include the design of objective functions and the choice of initial condition based on an analysis of the local minima reached by the optimization process.The paper outline is as follows. Section 2 provides a mathematical overview of inverse design, and Section 3 provides an overview of the framework and how the inverse design formulation is implemented. Section 4 presents an example of designing wavelength demultiplexers and discusses salient points in the overall design process. Finally, Section 5 discusses practical considerations and analyzes key properties of gradient-based nanophotonic optimization.

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“…Gradient-based optimization from different starting points (a "multistart" algorithm) can explore different local optima but in this work, the main goal is to find a structure much better than what could be easily designed by hand. Comparison to theoretical upper bounds is another route to gauging global optimality of TO structures [22,60].…”

Section: Figmentioning

confidence: 99%

Inverse design of nanoparticles for enhanced Raman scattering

Christiansen¹,

Michon²,

Benzaouia³

et al. 2020

Opt. Express

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We show that topology optimization (TO) of metallic resonators can lead to ∼ 10 2 × improvement in surfaceenhanced Raman scattering (SERS) efficiency compared to traditional resonant structures such as bowtie antennas. TO inverse design leads to surprising structures very different from conventional designs, which simultaneously optimize focusing of the incident wave and emission from the Raman dipole. We consider isolated metallic particles as well as more complicated configurations such as periodic surfaces or resonators coupled to dielectric waveguides, and the benefits of TO are even greater in the latter case. Our results are motivated by recent rigorous upper bounds to Raman scattering enhancement, and shed light on the extent to which these bounds are achievable. * Corresponding

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Computational Bounds for Photonic Design

Cited by 61 publications

References 21 publications

Upper bounds on absorption and scattering

Upper bounds on absorption and scattering

Nanophotonic inverse design with SPINS: Software architecture and practical considerations

Inverse design of nanoparticles for enhanced Raman scattering

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