Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Review Article
  • Published:

Inverse design in nanophotonics

Nature Photonics volume 12, pages 659–670 (2018)Cite this article

Subjects

Abstract

Recent advancements in computational inverse-design approaches — algorithmic techniques for discovering optical structures based on desired functional characteristics — have begun to reshape the landscape of structures available to nanophotonics. Here, we outline a cross-section of key developments in this emerging field of photonic optimization: moving from a recap of foundational results to motivation of applications in nonlinear, topological, near-field and on-chip optics.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Progression of photonic design templates.
Fig. 2: Nonlinear optics.
Fig. 3: Exceptional and topological photonics.
Fig. 4: Growth of applications.
Fig. 5: Metasurface photonics.
Fig. 6: Experimental inverse design.

Similar content being viewed by others

References

  1. Koenderink, A. F., Alù, A. & Polman, A. Nanophotonics: shrinking light-based technology. Science 348, 516–521 (2015).

    Article  ADS  Google Scholar 

  2. Baba, T. Slow light in photonic crystals. Nat. Photon. 2, 465–473 (2008).

    Article  ADS  Google Scholar 

  3. Caldwell, J. D. et al. Sub-diffractional volume-confined polaritons in the natural hyperbolic material hexagonal boron nitride. Nat. Commun. 5, 5221 (2014).

    Article  Google Scholar 

  4. Spillane, S. et al. Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics. Phys. Rev. A 71, 013817 (2005).

    Article  ADS  Google Scholar 

  5. Hashemi, H., Rodriguez, A. W., Joannopoulos, J., Soljačić, M. & Johnson, S. G. Nonlinear harmonic generation and devices in doubly resonant Kerr cavities. Phys. Rev. A 79, 013812 (2009).

    Article  ADS  Google Scholar 

  6. Yu, Z. Fundamental limit of nanophotonic light trapping in solar cells. Proc. Natl Acad. Sci. USA 107, 17491–17496 (2010).

    Article  ADS  Google Scholar 

  7. Miller, O. D., Johnson, S. G. & Rodriguez, A. W. Shape-independent limits to near-field radiative heat transfer. Phys. Rev. Lett. 115, 204302 (2015).

    Article  ADS  Google Scholar 

  8. Arabi, A. & Faraon, A. Fundamental limits of ultrathin metasurfaces. Sci. Rep. 7, 43722 (2017).

  9. Alaeian, H., Atre, A. C. & Dionne, J. A. Optimized light absorption in Si wire array solar cells. J. Opt. 14, 024006 (2012).

    Article  ADS  Google Scholar 

  10. Ganapati, V., Miller, O. D. & Yablonovitch, E. Light trapping textures designed by electromagnetic optimization for subwavelength thick solar cells. IEEE J. Photovolt. 4, 175–182 (2014).

    Article  Google Scholar 

  11. Wang, P. & Menon, R. Optimization of periodic nanostructures for enhanced light-trapping in ultra-thin photovoltaics. Opt. Express 21, 6274–6285 (2013).

    Article  ADS  Google Scholar 

  12. Dühring, M. B. & Sigmund, O. Optimization of extraordinary optical absorption in plasmonic and dielectric structures. J. Opt. Soc. Am. B 30, 1154–1160 (2013).

    Article  ADS  Google Scholar 

  13. Xiao, T. P. et al. Diffractive spectral-splitting optical element designed by adjoint-based electromagnetic optimization and fabricated by femtosecond 3D direct laser writing. ACS Photon. 3, 886–894 (2016).

    Article  Google Scholar 

  14. Ilic, O. et al. Tailoring high-temperature radiation and the resurrection of the incandescent source. Nat. Nanotech. 11, 320–324 (2016).

    Article  ADS  Google Scholar 

  15. Jin, W., Messina, R. & Rodriguez, A. W. Overcoming limits to near-field radiative heat transfer in uniform planar media through multilayer optimization. Opt. Express 25, 14746–14759 (2017).

    Article  ADS  Google Scholar 

  16. Liu, D., Gabrielli, L. H., Lipson, M. & Johnson, S. G. Transformation inverse design. Opt. Express 21, 14223–14243 (2013).

    Article  ADS  Google Scholar 

  17. Frellsen, L. F., Ding, Y., Sigmund, O. & Frandsen, L. H. Topology optimized mode multiplexing in silicon-on-insulator photonic wire waveguides. Opt. Express 24, 16866–16873 (2016).

    Article  ADS  Google Scholar 

  18. Shen, B., Wang, P., Polson, R. & Menon, R. Ultra-high-efficiency metamaterial polarizer. Optica 1, 356–360 (2014).

    Article  Google Scholar 

  19. Su, L., Piggott, A. Y., Sapra, N. V., Petykiewicz, J. & Vuckovic, J. Inverse design and demonstration of a compact on-chip narrowband three-channel wavelength demultiplexer. ACS Photon 5, 301–305 (2017).

    Article  Google Scholar 

  20. Chadan, K. & Sabatier, P. C. Inverse Problems in Quantum Scattering Theory (Springer Science & Business Media, Berlin, Heidelberg, New York, 2012).

  21. Bendsøe, M. P. & Sigmund, O. Topology Optimization: Theory, Methods and Applications (Springer, Berlin, Heidelberg, New York, 2003).

  22. Georgieva, N. K., Glavic, S., Bakr, M. H. & Bandler, J. W. Feasible adjoint sensitivity technique for EM design optimization. IEEE Trans. Microw. Theory Tech. 50, 2751–2758 (2002).

    Article  ADS  Google Scholar 

  23. Pratt, R. G. & Worthington, M. Inverse theory applied to multi-source cross-hole tomography. Part 1: acoustic wave-equation method. Geophys. Prospect. 38, 287–310 (1990).

    Article  ADS  Google Scholar 

  24. Jensen, J. S. & Sigmund, O. Topology optimization for nano-photonics. Laser Photon. Rev. 5, 308–321 (2011).

    Article  ADS  Google Scholar 

  25. Sigmund, O. On the usefulness of non-gradient approaches in topology optimization. Struct. Multidiscipl. Optim. 43, 589–596 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  26. Spühler, M. M. et al. A very short planar silica spot-size converter using a nonperiodic segmented waveguide. J. Light. Technol. 16, 1680–1685 (1998).

    Article  ADS  Google Scholar 

  27. Dobson, D. C. & Cox, S. J. Maximizing band gaps in two-dimensional photonic crystals. SIAM J. Appl. Math. 59, 2108–2120 (1999).

    Article  MathSciNet  MATH  Google Scholar 

  28. Back, T., Hammel, U. & Schwefel, H.-P. Evolutionary computation: comments on the history and current state. IEEE Trans. Evol. Comput. 1, 3–17 (1997).

    Article  Google Scholar 

  29. Fu, M. C., Glover, F. W. & April, J. Simulation optimization: a review, new developments, and applications. In 2005 Proc. Winter Simulation Conference 83–95 (IEEE, 2005).

  30. Boyd, S. & Vandenberghe, L. Convex Optimization (Cambridge Univ. Press, Cambridge, 2004).

  31. Baumert, T., Brixner, T., Seyfried, V., Strehle, M. & Gerber, G. Femtosecond pulse shaping by an evolutionary algorithm with feedback. Appl. Phys. B 65, 779–782 (1997).

    Article  ADS  Google Scholar 

  32. Doosje, M., Hoenders, B. J. & Knoester, J. Photonic bandgap optimization in inverted fcc photonic crystals. JOSA B 17, 600–606 (2000).

    Article  ADS  Google Scholar 

  33. Cox, S. J. & Dobson, D. C. Band structure optimization of two-dimensional photonic crystals in H-polarization. J. Comput. Phys. 158, 214–224 (2000).

    Article  ADS  MATH  Google Scholar 

  34. Felici, T. & Engl, H. W. On shape optimization of optical waveguides using inverse problem techniques. Inverse Probl. 17, 1141–1162 (2001).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  35. Geremia, J., Williams, J. & Mabuchi, H. Inverse-problem approach to designing photonic crystals for cavity QED experiments. Phys. Rev. E 66, 066606 (2002).

    Article  ADS  Google Scholar 

  36. Jiang, J., Cai, J., Nordin, G. P. & Li, L. Parallel microgenetic algorithm design for photonic crystal and waveguide structures. Opt. Lett. 28, 2381–2383 (2003).

    Article  ADS  Google Scholar 

  37. Kiziltas, G., Psychoudakis, D., Volakis, J. L. & Kikuchi, N. Topology design optimization of dielectric substrates for bandwidth improvement of a patch antenna. IEEE Trans. Antennas Propag. 51, 2732–2743 (2003).

    Article  ADS  Google Scholar 

  38. Erni, D. et al. Application of evolutionary optimization algorithms in computational optics. ACES 15, 43–60 (2000).

  39. Veronis, G., Dutton, R. W. & Fan, S. Method for sensitivity analysis of photonic crystal devices. Opt. Lett. 29, 2288–2290 (2004).

    Article  ADS  Google Scholar 

  40. Jiao, Y., Fan, S. & MillYer, D. A. Systematic photonic crystal device design: global and local optimization and sensitivity analysis. IEEE J. Quantum Electron. 42, 266–279 (2006).

    Article  ADS  Google Scholar 

  41. Borel, P. I. et al. Topology optimization and fabrication of photonic crystal structures. Opt. Express 12, 1996–2001 (2004).

    Article  ADS  Google Scholar 

  42. Jensen, J. S. & Sigmund, O. Systematic design of photonic crystal structures using topology optimization: low-loss waveguide bends. Appl. Phys. Lett. 84, 2022–2024 (2004).

    Article  ADS  Google Scholar 

  43. Jensen, J. S. & Sigmund, O. Topology optimization of photonic crystal structures: a high-bandwidth low-loss T-junction waveguide. JOSA B 22, 1191–1198 (2005).

    Article  ADS  Google Scholar 

  44. Kao, C.-Y., Osher, S. & Yablonovitch, E. Maximizing band gaps in two-dimensional photonic crystals by using level set methods. Appl. Phys. B 81, 235–244 (2005).

    Article  ADS  Google Scholar 

  45. Burger, M. A framework for the construction of level set methods for shape optimization and reconstruction. Interfaces Free Bound. 5, 301–329 (2003).

    Article  MathSciNet  MATH  Google Scholar 

  46. Burger, M., Osher, S. J. & Yablonovitch, E. Inverse problem techniques for the design of photonic crystals. IEICE Trans. Electron. 87, 258–265 (2004).

    Google Scholar 

  47. Gerken, M. & Miller, D. A. Multilayer thin-film structures with high spatial dispersion. Appl. Opt. 42, 1330–1345 (2003).

    Article  ADS  Google Scholar 

  48. Håkansson, A. & Sánchez-Dehesa, J. Inverse designed photonic crystal de-multiplex waveguide coupler. Opt. Express 13, 5440–5449 (2005).

    Article  ADS  Google Scholar 

  49. Sanchis, L., Håkansson, A., López-Zanón, D., Bravo-Abad, J. & Sánchez-Dehesa, J. Integrated optical devices design by genetic algorithm. Appl. Phys. Lett. 84, 4460–4462 (2004).

    Article  ADS  Google Scholar 

  50. Preble, S., Lipson, M. & Lipson, H. Two-dimensional photonic crystals designed by evolutionary algorithms. Appl. Phys. Lett. 86, 061111 (2005).

    Article  ADS  Google Scholar 

  51. Burger, M. & Osher, S. J. A survey on level set methods for inverse problems and optimal design. Eur. J. Appl. Math. 16, 263–301 (2005).

    Article  MathSciNet  MATH  Google Scholar 

  52. Novotny, A. A. & Sokołowski, J. Topological Derivatives in Shape Optimization (Springer Science & Business Media, Heidelberg, New York, 2012).

  53. van Dijk, N. P., Maute, K., Langelaar, M. & Van Keulen, F. Level-set methods for structural topology optimization: a review. Struct. Multidiscipl. Optim. 48, 437–472 (2013).

    Article  MathSciNet  Google Scholar 

  54. Tortorelli, D. A. & Michaleris, P. Design sensitivity analysis: overview and review. Inverse Probl. Eng. 1, 71–105 (1994).

    Article  Google Scholar 

  55. Miller, O. D. et al. Fundamental limits to extinction by metallic nanoparticles. Phys. Rev. Lett. 112, 123903 (2014).

    Article  ADS  Google Scholar 

  56. Giles, M. B. & Pierce, N. A. An introduction to the adjoint approach to design. Flow Turbul. Combust. 65, 393–415 (2000).

    Article  MATH  Google Scholar 

  57. Riishede, J. & Sigmund, O. Inverse design of dispersion compensating optical fiber using topology optimization. JOSA B 25, 88–97 (2008).

    Article  ADS  MathSciNet  Google Scholar 

  58. Dobson, D. C. & Simeonova, L. B. Optimization of periodic composite structures for sub-wavelength focusing. Appl. Math. Optim. 60, 133–150 (2009).

    Article  MathSciNet  MATH  Google Scholar 

  59. Borel, P. I. et al. Imprinted silicon-based nanophotonics. Opt. Express 15, 1261–1266 (2007).

    Article  ADS  Google Scholar 

  60. Elesin, Y., Lazarov, B. S., Jensen, J. S. & Sigmund, O. Design of robust and efficient photonic switches using topology optimization. Photon. Nanostruct. 10, 153–165 (2012).

    Article  ADS  Google Scholar 

  61. Tsuji, Y. & Hirayama, K. Design of optical circuit devices using topology optimization method with function-expansion-based refractive index distribution. IEEE Photon. Technol. Lett. 20, 982–984 (2008).

    Article  ADS  Google Scholar 

  62. Sigmund, O. & Petersson, J. Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Struct. Multidiscipl. Optim. 16, 68–75 (1998).

    Article  Google Scholar 

  63. Wang, F., Jensen, J. S. & Sigmund, O. High-performance slow light photonic crystal waveguides with topology optimized or circular-hole based material layouts. Photon. Nanostruct. 10, 378–388 (2012).

    Article  ADS  Google Scholar 

  64. Sigmund, O. Manufacturing tolerant topology optimization. Acta Mech. Sin. 25, 227–239 (2009).

    Article  ADS  MATH  Google Scholar 

  65. Oskooi, A. et al. Robust optimization of adiabatic tapers for coupling to slow-light photonic-crystal waveguides. Opt. Express 20, 21558–21575 (2012).

    Article  ADS  Google Scholar 

  66. Frei, W., Tortorelli, D. & Johnson, H. Geometry projection method for optimizing photonic nanostructures. Opt. Lett. 32, 77–79 (2007).

    Article  ADS  Google Scholar 

  67. Frei, W. R., Johnson, H. & Choquette, K. D. Optimization of a single defect photonic crystal laser cavity. J. Appl. Phys. 103, 033102 (2008).

    Article  ADS  Google Scholar 

  68. Lu, J., Boyd, S. & Vučković, J. Inverse design of a three-dimensional nanophotonic resonator. Opt. Express 19, 10563–10570 (2011).

    Article  ADS  Google Scholar 

  69. Boyd, S., Parikh, N., Chu, E., Peleato, B. & Eckstein, J. Distributed optimization and statistical learning via the alternating direction method of multipliers Found. Trend. Mach. Learn. 3, 1–122 (2011).

    MATH  Google Scholar 

  70. Englund, D., Fushman, I. & Vucković, J. General recipe for designing photonic crystal cavities. Opt. Express 13, 5961–5975 (2005).

    Article  ADS  Google Scholar 

  71. Men, H., Nguyen, N. C., Freund, R. M., Parrilo, P. A. & Peraire, J. Bandgap optimization of two-dimensional photonic crystals using semidefinite programming and subspace methods. J. Comput. Phys. 229, 3706–3725 (2010).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  72. Liang, X. & Johnson, S. G. Formulation for scalable optimization of microcavities via the frequency-averaged local density of states. Opt. Express 21, 30812–30841 (2013).

    Article  ADS  Google Scholar 

  73. Elesin, Y., Lazarov, B. S., Jensen, J. S. & Sigmund, O. Time domain topology optimization of 3D nanophotonic devices. Photon. Nanostruct. 12, 23–33 (2014).

    Article  ADS  Google Scholar 

  74. Chen, H., Chan, C. T. & Sheng, P. Transformation optics and metamaterials. Nat. Mater. 9, 387–396 (2010).

    Article  ADS  Google Scholar 

  75. Men, H., Lee, K. Y., Freund, R. M., Peraire, J. & Johnson, S. G. Robust topology optimization of three-dimensional photonic-crystal band-gap structures. Opt. Express 22, 22632–22648 (2014).

    Article  ADS  Google Scholar 

  76. Maldovan, M. & Thomas, E. L. Diamond-structured photonic crystals. Nat. Mater. 3, 593–600 (2004).

    Article  ADS  Google Scholar 

  77. Sigmund, O. & Hougaard, K. Geometric properties of optimal photonic crystals. Phys. Rev. Lett. 100, 153904 (2008).

    Article  ADS  Google Scholar 

  78. Ou, Z. & Kimble, H. J. Enhanced conversion efficiency for harmonic generation with double resonance. Opt. Lett. 18, 1053–1055 (1993).

    Article  ADS  Google Scholar 

  79. Lin, Z., Liang, X., Lončar, M., Johnson, S. G. & Rodriguez, A. W. Cavity-enhanced second-harmonic generation via nonlinear-overlap optimization. Optica 3, 233–238 (2016).

    Article  Google Scholar 

  80. Fürst, J. et al. Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator. Phys. Rev. Lett. 104, 153901 (2010).

    Article  ADS  Google Scholar 

  81. Bi, Z.-F. et al. High-efficiency second-harmonic generation in doubly-resonant χ 2 microring resonators. Opt. Express 20, 7526–7543 (2012).

    Article  ADS  Google Scholar 

  82. Khurgin, J. B. How to deal with the loss in plasmonics and metamaterials. Nat. Nanotech. 10, 2–6 (2015).

    Article  ADS  Google Scholar 

  83. Sitawarin, C., Jin, W., Lin, Z. & Rodriguez, A. W. Inverse-designed photonic fibers and metasurfaces for nonlinear frequency conversion. Photon. Res. 6, B82–B89 (2018).

    Article  Google Scholar 

  84. Lin, Z., Lončar, M. & Rodriguez, A. W. Topology optimization of multi-track ring resonators and 2D microcavities for nonlinear frequency conversion. Opt. Lett. 42, 2818–2821 (2017).

    Article  ADS  Google Scholar 

  85. Takahashi, Y. et al. A micrometre-scale Raman silicon laser with a microwatt threshold. Nature 498, 470–474 (2013).

    Article  ADS  Google Scholar 

  86. Halir, R. et al. Ultrabroadband supercontinuum generation in a CMOS-compatible platform. Opt. Lett. 37, 1685–1687 (2012).

    Article  ADS  Google Scholar 

  87. Pelton, M. et al. Efficient source of single photons: a single quantum dot in a micropost microcavity. Phys. Rev. Lett. 89, 233602 (2002).

    Article  ADS  Google Scholar 

  88. Bi, L. et al. On-chip optical isolation in monolithically integrated non-reciprocal optical resonators. Nat. Photon. 5, 758–762 (2011).

    Article  ADS  Google Scholar 

  89. Lu, L., Joannopoulos, J. D. & Soljačić, M. Topological photonics. Nat. Photon. 8, 821–829 (2014).

    Article  ADS  Google Scholar 

  90. Heiss, W. The physics of exceptional points. J. Phys. Math. Theor. 45, 444016 (2012).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  91. Pick, A. et al. General theory of spontaneous emission near exceptional points. Opt. Express 25, 12325–12348 (2017).

    Article  ADS  Google Scholar 

  92. Regensburger, A. et al. Parity-time synthetic photonic lattices. Nature 488, 167–171 (2012).

    Article  ADS  Google Scholar 

  93. Peng, B. et al. Loss-induced suppression and revival of lasing. Science 346, 328–332 (2014).

    Article  ADS  Google Scholar 

  94. Hodaei, H. et al. Enhanced sensitivity at higher-order exceptional points. Nature 548, 187–191 (2017).

    Article  ADS  Google Scholar 

  95. Pick, A., Lin, Z., Jin, W. & Rodriguez, A. W. Enhanced nonlinear frequency conversion and Purcell enhancement at exceptional points. Phys. Rev. B 96, 224303 (2017).

    Article  ADS  Google Scholar 

  96. Peng, B. et al. Parity-time-symmetric whispering-gallery microcavities. Nat. Phys. 10, 394–398 (2014).

    Article  Google Scholar 

  97. Rüter, C. E. et al. Observation of parity–time symmetry in optics. Nat. Phys. 6, 192–195 (2010).

    Article  Google Scholar 

  98. Zhen, B. et al. Spawning rings of exceptional points out of Dirac cones. Nature 525, 354–358 (2015)

    Article  ADS  Google Scholar 

  99. Bhargava, S. & Yablonovitch, E. Lowering HAMR near-field transducer temperature via inverse electromagnetic design. IEEE Trans. Magn. 51, 1–7 (2015).

    Article  Google Scholar 

  100. Lee, Y. E., Miller, O. D., Reid, M. H., Johnson, S. G. & Fang, N. X. Computational inverse design of non-intuitive illumination patterns to maximize optical force or torque. Opt. Express 25, 6757–6766 (2017).

    Article  ADS  Google Scholar 

  101. Deng, Y. & Korvink, J. G. Topology optimization for three-dimensional electromagnetic waves using an edge element-based finite-element method. Proc. R. Soc. A 472, 20150835 (2016).

    Article  ADS  Google Scholar 

  102. Andkjær, J., Asger Mortensen, N. & Sigmund, O. Towards all-dielectric, polarization-independent optical cloaks. Appl. Phys. Lett. 100, 101106 (2012).

    Article  ADS  Google Scholar 

  103. Andkjær, J., Johansen, V. E., Friis, K. S. & Sigmund, O. Inverse design of nanostructured surfaces for color effects. JOSA B 31, 164–174 (2014).

    Article  ADS  Google Scholar 

  104. Sell, D., Yang, J., Doshay, S., Yang, R. & Fan, J. A. Large-angle, multifunctional metagratings based on freeform multimode geometries. Nano Lett. 17, 3752–3757 (2017).

    Article  ADS  Google Scholar 

  105. Callewaert, F., Velev, V., Kumar, P., Sahakian, A. & Aydin, K. Inverse-designed broadband all-dielectric electromagnetic metadevices. Sci. Rep. 8, 1358 (2018).

    Article  ADS  Google Scholar 

  106. Okoro, C., Kondakci, H. E., Abouraddy, A. F. & Toussaint, K. C. Demonstration of an optical-coherence converter. Optica 4, 1052–1058 (2017).

    Article  Google Scholar 

  107. Garnett, E. & Yang, P. Light trapping in silicon nanowire solar cells. Nano Lett. 10, 1082–1087 (2010).

    Article  ADS  Google Scholar 

  108. Lee, W.-K. et al. Concurrent design of quasi-random photonic nanostructures. Proc. Natl Acad. Sci. USA 114, 8734–8739 (2017).

    Article  ADS  Google Scholar 

  109. Kim, G., Dominguez-Caballero, J. A., Lee, H., Friedman, D. J. & Menon, R. Increased photovoltaic power output via diffractive spectrum separation. Phys. Rev. Lett. 110, 123901 (2013).

    Article  ADS  Google Scholar 

  110. Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nat. Photon. 9, 374–377 (2015).

    Article  ADS  Google Scholar 

  111. Shen, B., Wang, P., Polson, R. & Menon, R. An integrated-nanophotonics polarization beamsplitter with 2.4 × 2.4 μm2 footprint. Nat. Photon. 9, 378–382 (2015).

    Article  ADS  Google Scholar 

  112. Mak, J. C., Sideris, C., Jeong, J., Hajimiri, A. & Poon, J. K. Binary particle swarm optimized 2 × 2 power splitters in a standard foundry silicon photonic platform. Opt. Lett. 41, 3868–3871 (2016).

    Article  ADS  Google Scholar 

  113. Piggott, A. Y., Petykiewicz, J., Su, L. & Vučković, J. Fabrication-constrained nanophotonic inverse design. Sci. Rep. 7, 1786 (2017).

  114. Shen, B., Wang, P., Polson, R. & Menon, R. Integrated metamaterials for efficient and compact free-space-to-waveguide coupling. Opt. Express 22, 27175–27182 (2014).

    Article  ADS  Google Scholar 

  115. Niederberger, A. C., Fattal, D. A., Gauger, N. R., Fan, S. & Beausoleil, R. G. Sensitivity analysis and optimization of sub-wavelength optical gratings using adjoints. Opt. Express 22, 12971–12981 (2014).

    Article  ADS  Google Scholar 

  116. Frandsen, L. H. & Sigmund, O. Inverse design engineering of all-silicon polarization beam splitters. Proc. SPIE 9756, 97560Y (2016).

    Google Scholar 

  117. Michaels, A. & Yablonovitch, E. Inverse design of near unity efficiency perfectly vertical grating couplers. Opt. Express 26, 4766–4779 (2018).

    Article  ADS  Google Scholar 

  118. Lazarov, B. S., Wang, F. & Sigmund, O. Length scale and manufacturability in density-based topology optimization. Arch. Appl. Mech. 86, 189–218 (2016).

    Article  ADS  Google Scholar 

  119. Lalau-Keraly, C. M., Bhargava, S., Miller, O. D. & Yablonovitch, E. Adjoint shape optimization applied to electromagnetic design. Opt. Express 21, 21693–21701 (2013).

    Article  ADS  Google Scholar 

  120. Zhou, M., Lazarov, B. S. & Sigmund, O. Topology optimization for optical projection lithography with manufacturing uncertainties. Appl. Opt. 53, 2720–2729 (2014).

    Article  ADS  Google Scholar 

  121. Menon, R., Rogge, P. & Tsai, H.-Y. Design of diffractive lenses that generate optical nulls without phase singularities. J. Opt. Soc. Am. A 26, 297–304 (2009).

    Article  ADS  Google Scholar 

  122. Rosenbluth, A. E. et al. Optimum mask and source patterns to print a given shape. J. MicroNanolithogr. MEMS MOEMS 1, 13–31 (2002).

    Article  ADS  Google Scholar 

  123. Kasahara, K. et al. Recent progress in nanoparticle photoresists development for EUV lithography. Proc. SPIE 9776, (977604 (2016).

    Google Scholar 

  124. Urness, A. C., Anderson, K., Ye, C., Wilson, W. L. & McLeod, R. R. Arbitrary GRIN component fabrication in optically driven diffusive photopolymers. Opt. Express 23, 264–273 (2015).

    Article  ADS  Google Scholar 

  125. Zibar, D., Wymeersch, H. & Lyubomirsky, I. Machine learning under the spotlight. Nat. Photon. 11, 749–751 (2017).

    Article  ADS  Google Scholar 

  126. Painter, O. et al. Two-dimensional photonic band-gap defect mode laser. Science 284, 1819–1821 (1999).

    Article  Google Scholar 

  127. Knight, J. C. Photonic crystal fibres. Nature 424, 847–851 (2003).

    Article  ADS  Google Scholar 

  128. Xu, Q., Fattal, D. & Beausoleil, R. G. Silicon microring resonators with 1.5-μm radius. Opt. Express 16, 4309–4315 (2008).

    Article  ADS  Google Scholar 

  129. Eichenfield, M., Chan, J., Camacho, R. M., Vahala, K. J. & Painter, O. Optomechanical crystals. Nature 462, 78–82 (2009).

    Article  ADS  Google Scholar 

  130. Liu, N., Mesch, M., Weiss, T., Hentschel, M. & Giessen, H. Infrared perfect absorber and its application as plasmonic sensor. Nano Lett. 10, 2342–2348 (2010).

    Article  ADS  Google Scholar 

  131. Otomori, M., Yamada, T., Izui, K., Nishiwaki, S. & Andkjær, J. Topology optimization of hyperbolic metamaterials for an optical hyperlens. Struct. Multidiscipl. Optim. 55, 913–923 (2017).

    Article  MathSciNet  MATH  Google Scholar 

  132. Yu, Z., Cui, H. & Sun, X. Genetically optimized on-chip wideband ultracompact reflectors and Fabry–Perot cavities. Photon. Res. 5, B15–B19 (2017).

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Science Foundation under Grant No. DMR-1454836, Grant No. DMR 1420541, and Award EFMA-1640986; and the National Sciences and Engineering Research Council of Canada under PDF-502958-2017. All authors acknowledge helpful comments made during the preparation of this manuscript by D. A. B. Miller.

Author information

Authors and Affiliations

  1. Department of Electrical Engineering, Princeton University, Princeton, NJ, USA

    Sean Molesky, Weiliang Jin & Alejandro W. Rodriguez

  2. John A. Paulson School of Engineering and Applied Sciences Harvard University, Cambridge, MA, USA

    Zin Lin

  3. Ginzton Laboratory, Stanford University, Stanford, CA, USA

    Alexander Y. Piggott & Jelena Vucković

Authors
  1. Sean Molesky
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zin Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Alexander Y. Piggott
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Weiliang Jin
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Jelena Vucković
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Alejandro W. Rodriguez
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alejandro W. Rodriguez.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Molesky, S., Lin, Z., Piggott, A.Y. et al. Inverse design in nanophotonics. Nature Photon 12, 659–670 (2018). https://doi.org/10.1038/s41566-018-0246-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41566-018-0246-9

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing