Adjoint shape optimization applied to electromagnetic design
Open accessAbstract
We present an adjoint-based optimization for electromagnetic design. It embeds commercial Maxwell solvers within a steepest-descent inverse-design optimization algorithm. The adjoint approach calculates shape derivatives at all points in space, but requires only two "forward" simulations. Geometrical shape parameterization is by the level set method. Our adjoint design optimization is applied to a Silicon photonics Y-junction splitter that had previously been investigated by stochastic methods. Owing to the speed of calculating shape derivatives within the adjoint method, convergence is much faster, within a larger design space. This is an extremely efficient method for the design of complex electromagnetic components.
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Topology optimization has been used to design photonic crystals, integrated photonics devices, and metamaterials with superior performance metrics than those based on conventional designs.
“This technique has been used to design photonic crystals [15], integrated photonics devices [16,17], and metamaterials [18–24] with superior performance metrics than those based on conventional designs.”
From Robust design of topology-optimized metasurfaces (2019) · cites this paper as [17]
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Research works printed but not linked: 17
- [1]P. Sandborn, N. Quack, N. Hoghooghi, J. B. Chou, J. Ferrara, S. Gambini, B. Behroozpour, L. Zhu, B. Boser, C. Chang-Hasnain, and M. C. Wu, “Linear frequency chirp generation employing opto-electronic feedback loop and integrated Silicon photonics,” in CLEO, (2013) pp. 5–6.
- [2]A. Sakai, T. Fukazawa, and T. Baba, “Low loss ultra-small branches in a silicon photonic wire waveguide,” IEICE Trans. Electron. E85, 1033–1038 (2002).
- [3]Y. Zhang, S. Yang, A. E. J. Lim, G. Q. Lo, C. Galland, T. Baehr-Jones, and M. Hochberg, “A compact and low loss Y-junction for submicron silicon waveguide,” Opt. Express 21(1), 1310–1316 (2013). Crossref
- [4]P. Sanchis, P. Villalba, F. Cuesta, A. Håkansson, A. Griol, J. V. Galán, A. Brimont, and J. Martí, “Highly efficient crossing structure for silicon-on-insulator waveguides,” Opt. Lett. 34(18), 2760–2762 (2009). Crossref
- [5]Y. Zhang, S. Yang, E. J. Lim, G. Lo, T. Baehr-Jones, and M. Hochberg, “A CMOS-compatible, low-loss and low-crosstalk silicon waveguide crossing,” IEEE Photon. Technol. Lett. 25(5), 422–425 (2013). Crossref
- [6]T. Tanemura, K. C. Balram, D. S. Ly-Gagnon, P. Wahl, J. S. White, M. L. Brongersma, and D. A. B. Miller, “Multiple-wavelength focusing of surface plasmons with a nonperiodic nanoslit coupler,” Nano Lett. 11(7), 2693–2698 (2011). Crossref
- [8]M. P. Bendsoe and O. Sigmund, Topology Optimization Theory, Methods and Applications. (Springer, 2003)
- [9]T. Borrvall and J. Petersson, “Topology optimization of fluids in Stokes flow,” Int. J. Numer. Methods Fluids 41(1), 77–107 (2003). Crossref
- [10]J. S. Jensen and O. Sigmund, “Topology optimization for nano-photonics,” Las. Photon. Rev. 5(2), 308–321 (2011). Crossref
- [11]P. Seliger, M. Mahvash, C. Wang, and A. F. J. Levi, “Optimization of aperiodic dielectric structures,” J. Appl. Phys. 100(3), 034310 (2006). Crossref
- [12]W. R. Frei, D. A. Tortorelli, and H. T. Johnson, “Geometry projection method for optimizing photonic nanostructures,” Opt. Lett. 32(1), 77–79 (2007). Crossref
- [13]V. Liu and S. Fan, “Compact bends for multi-mode photonic crystal waveguides with high transmission and suppressed modal crosstalk,” Opt. Express 21(7), 8069–8075 (2013). Crossref
- [14]G. Veronis, R. W. Dutton, and S. Fan, “Method for sensitivity analysis of photonic crystal devices,” Opt. Lett. 29(19), 2288–2290 (2004). Crossref
- [15]A. F. J. Levi and I. G. Rosen, “A novel formulation of the adjoint method in the optimal design of quantum electronic devices,” SIAM J. Contr. Optim. 48(5), 3191–3223 (2010). Crossref
- [16]G. Strang, Computational Science and Engineering , (Wellesley-Cambridge, 2007).
- [17]O. D. Miller, PhD thesis (2012), University of California at Berkeley, http://optoelectronics.eecs.berkeley.edu/ThesisOwenMiller.pdf
- [18]S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(6), 066611 (2002). Crossref
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- Authors
- Lalau-Keraly, C. M., Bhargava, S., Miller, O. D., & Yablonovitch, E.
- Affiliations
- University of California, Berkeley (US)
- Massachusetts Institute of Technology (US)
- Venue
- Optics Express
- Publisher
- Optica Publishing Group
- Published
- 2013-09-06
- Volume
- 21
- Issue
- 18
- Pages
- 21693
- ISSN
- 1094-4087 (ISSN-L)
- OpenAlex
- W2009741032
- Cited by
- 753
- References
- 0
- Citations by year
- 2026: 88 · 2025: 99 · 2024: 109 · 2023: 112 · 2022: 91 · 2021: 68 · 2020: 68 · 2019: 52 · 2018: 25 · 2017: 12 · 2016: 9 · 2015: 13 · 2014: 7
- FWCI
- 5.80
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Locations
- Optics Express (publishedVersion)
- PubMed (publishedVersion)
- Funders
- Defense Advanced Research Projects Agency (DARPA) (HR0011-11-2-0021)
- National Science Foundation (NSF) (0939514)
- Topics
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Photonic and Optical Devices
- Physical Sciences › Engineering › Civil and Structural Engineering › Topology Optimization in Engineering
- Physical Sciences › Materials Science › Electronic, Optical and Magnetic Materials › Metamaterials and Metasurfaces Applications
- Keywords
- electromagnetic design, inverse design, shape derivative, level set method, gradient descent, silicon photonics, Maxwell solver
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