Inverse design in nanophotonics

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.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

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.

References

  1. 1.

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

    ADS  Article  Google Scholar 

  2. 2.

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

    ADS  Article  Google Scholar 

  3. 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. 4.

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

    ADS  Article  Google Scholar 

  5. 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).

    ADS  Article  Google Scholar 

  6. 6.

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

    ADS  Article  Google Scholar 

  7. 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).

    ADS  Article  Google Scholar 

  8. 8.

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

  9. 9.

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

    ADS  Article  Google Scholar 

  10. 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. 11.

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

    ADS  Article  Google Scholar 

  12. 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).

    ADS  Article  Google Scholar 

  13. 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. 14.

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

    ADS  Article  Google Scholar 

  15. 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).

    ADS  Article  Google Scholar 

  16. 16.

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

    ADS  Article  Google Scholar 

  17. 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).

    ADS  Article  Google Scholar 

  18. 18.

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

    Article  Google Scholar 

  19. 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. 20.

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

  21. 21.

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

  22. 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).

    ADS  Article  Google Scholar 

  23. 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).

    ADS  Article  Google Scholar 

  24. 24.

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

    ADS  Article  Google Scholar 

  25. 25.

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

    MathSciNet  MATH  Article  Google Scholar 

  26. 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).

    ADS  Article  Google Scholar 

  27. 27.

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

    MathSciNet  MATH  Article  Google Scholar 

  28. 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. 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. 30.

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

  31. 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).

    ADS  Article  Google Scholar 

  32. 32.

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

    ADS  Article  Google Scholar 

  33. 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).

    ADS  MATH  Article  Google Scholar 

  34. 34.

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

    ADS  MathSciNet  MATH  Article  Google Scholar 

  35. 35.

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

    ADS  Article  Google Scholar 

  36. 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).

    ADS  Article  Google Scholar 

  37. 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).

    ADS  Article  Google Scholar 

  38. 38.

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

  39. 39.

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

    ADS  Article  Google Scholar 

  40. 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).

    ADS  Article  Google Scholar 

  41. 41.

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

    ADS  Article  Google Scholar 

  42. 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).

    ADS  Article  Google Scholar 

  43. 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).

    ADS  Article  Google Scholar 

  44. 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).

    ADS  Article  Google Scholar 

  45. 45.

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

    MathSciNet  MATH  Article  Google Scholar 

  46. 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. 47.

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

    ADS  Article  Google Scholar 

  48. 48.

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

    ADS  Article  Google Scholar 

  49. 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).

    ADS  Article  Google Scholar 

  50. 50.

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

    ADS  Article  Google Scholar 

  51. 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).

    MathSciNet  MATH  Article  Google Scholar 

  52. 52.

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

  53. 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).

    MathSciNet  Article  Google Scholar 

  54. 54.

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

    Article  Google Scholar 

  55. 55.

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

    ADS  Article  Google Scholar 

  56. 56.

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

    MATH  Article  Google Scholar 

  57. 57.

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

    ADS  MathSciNet  Article  Google Scholar 

  58. 58.

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

    MathSciNet  MATH  Article  Google Scholar 

  59. 59.

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

    ADS  Article  Google Scholar 

  60. 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).

    ADS  Article  Google Scholar 

  61. 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).

    ADS  Article  Google Scholar 

  62. 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. 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).

    ADS  Article  Google Scholar 

  64. 64.

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

    ADS  MATH  Article  Google Scholar 

  65. 65.

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

    ADS  Article  Google Scholar 

  66. 66.

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

    ADS  Article  Google Scholar 

  67. 67.

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

    ADS  Article  Google Scholar 

  68. 68.

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

    ADS  Article  Google Scholar 

  69. 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. 70.

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

    ADS  Article  Google Scholar 

  71. 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).

    ADS  MathSciNet  MATH  Article  Google Scholar 

  72. 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).

    ADS  Article  Google Scholar 

  73. 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).

    ADS  Article  Google Scholar 

  74. 74.

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

    ADS  Article  Google Scholar 

  75. 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).

    ADS  Article  Google Scholar 

  76. 76.

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

    ADS  Article  Google Scholar 

  77. 77.

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

    ADS  Article  Google Scholar 

  78. 78.

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

    ADS  Article  Google Scholar 

  79. 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. 80.

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

    ADS  Article  Google Scholar 

  81. 81.

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

    ADS  Article  Google Scholar 

  82. 82.

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

    ADS  Article  Google Scholar 

  83. 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. 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).

    ADS  Article  Google Scholar 

  85. 85.

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

    ADS  Article  Google Scholar 

  86. 86.

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

    ADS  Article  Google Scholar 

  87. 87.

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

    ADS  Article  Google Scholar 

  88. 88.

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

    ADS  Article  Google Scholar 

  89. 89.

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

    ADS  Article  Google Scholar 

  90. 90.

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

    ADS  MathSciNet  MATH  Article  Google Scholar 

  91. 91.

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

    ADS  Article  Google Scholar 

  92. 92.

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

    ADS  Article  Google Scholar 

  93. 93.

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

    ADS  Article  Google Scholar 

  94. 94.

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

    ADS  Article  Google Scholar 

  95. 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).

    ADS  Article  Google Scholar 

  96. 96.

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

    Article  Google Scholar 

  97. 97.

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

    Article  Google Scholar 

  98. 98.

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

    ADS  Article  Google Scholar 

  99. 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. 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).

    ADS  Article  Google Scholar 

  101. 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).

    ADS  Article  Google Scholar 

  102. 102.

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

    ADS  Article  Google Scholar 

  103. 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).

    ADS  Article  Google Scholar 

  104. 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).

    ADS  Article  Google Scholar 

  105. 105.

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

    ADS  Article  Google Scholar 

  106. 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. 107.

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

    ADS  Article  Google Scholar 

  108. 108.

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

    ADS  Article  Google Scholar 

  109. 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).

    ADS  Article  Google Scholar 

  110. 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).

    ADS  Article  Google Scholar 

  111. 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).

    ADS  Article  Google Scholar 

  112. 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).

    ADS  Article  Google Scholar 

  113. 113.

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

  114. 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).

    ADS  Article  Google Scholar 

  115. 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).

    ADS  Article  Google Scholar 

  116. 116.

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

    Google Scholar 

  117. 117.

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

    ADS  Article  Google Scholar 

  118. 118.

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

    ADS  Article  Google Scholar 

  119. 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).

    ADS  Article  Google Scholar 

  120. 120.

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

    ADS  Article  Google Scholar 

  121. 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).

    ADS  Article  Google Scholar 

  122. 122.

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

    ADS  Article  Google Scholar 

  123. 123.

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

    Google Scholar 

  124. 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).

    ADS  Article  Google Scholar 

  125. 125.

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

    ADS  Article  Google Scholar 

  126. 126.

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

    Article  Google Scholar 

  127. 127.

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

    ADS  Article  Google Scholar 

  128. 128.

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

    ADS  Article  Google Scholar 

  129. 129.

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

    ADS  Article  Google Scholar 

  130. 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).

    ADS  Article  Google Scholar 

  131. 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).

    MathSciNet  MATH  Article  Google Scholar 

  132. 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

Affiliations

Authors

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

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

Further reading

Search

Nature Briefing

Sign up for the Nature Briefing newsletter for a daily update on COVID-19 science.

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