OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 18 — Sep. 9, 2013
  • pp: 21693–21701

Adjoint shape optimization applied to electromagnetic design

Christopher M. Lalau-Keraly, Samarth Bhargava, Owen D. Miller, and Eli Yablonovitch  »View Author Affiliations

Optics Express, Vol. 21, Issue 18, pp. 21693-21701 (2013)

View Full Text Article

Enhanced HTML    Acrobat PDF (1083 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



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.

© 2013 OSA

OCIS Codes
(130.3120) Integrated optics : Integrated optics devices
(230.1360) Optical devices : Beam splitters
(230.7370) Optical devices : Waveguides

ToC Category:
Integrated Optics

Original Manuscript: July 26, 2013
Revised Manuscript: August 19, 2013
Manuscript Accepted: August 20, 2013
Published: September 6, 2013

Christopher M. Lalau-Keraly, Samarth Bhargava, Owen D. Miller, and Eli Yablonovitch, "Adjoint shape optimization applied to electromagnetic design," Opt. Express 21, 21693-21701 (2013)

Sort:  Author  |  Year  |  Journal  |  Reset  


  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. Express21(1), 1310–1316 (2013). [CrossRef] [PubMed]
  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] [PubMed]
  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] [PubMed]
  7. M. P. Bendsøe and N. Kikuchi, “Generating optimal topologies in structural design using a homogenization method,” Comput. Meth. In Appl. M. 71, 197–224 (1988).
  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 Fluids41(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] [PubMed]
  13. V. Liu and S. Fan, “Compact bends for multi-mode photonic crystal waveguides with high transmission and suppressed modal crosstalk,” Opt. Express21(7), 8069–8075 (2013). [CrossRef] [PubMed]
  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] [PubMed]
  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] [PubMed]
  19. Lumerical FDTD Solutions, www.lumerical.com
  20. S. Osher and J. A. Sethian, “Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations,” J. Comput. Phys.79(1), 12–49 (1988). [CrossRef]
  21. http://optoelectronics.eecs.berkeley.edu/PhotonicInverseDesign/

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited