[1] Kitching, J. et al. NIST on a Chip: realizing SI units with microfabricated alkali vapour cells. J. Phys. Conf. Ser. 723, 012056 (2016). doi: 10.1088/1742-6596/723/1/012056
[2] Hummon, M. et al. Photonic chip for laser stabilization to an atomic vapor with 10−11 instability. Optica 5, 443–449 (2018). doi: 10.1364/OPTICA.5.000443
[3] Mehta, K. K. et al. Integrated optical addressing of an ion qubit. Nat. Nanotechnol. 11, 1066–1070 (2016). doi: 10.1038/nnano.2016.139
[4] Kohnen, M. et al. An array of integrated atom–photon junctions. Nat. Photonics 5, 35–38 (2011). doi: 10.1038/nphoton.2010.255
[5] Kippenberg, T. J., Holzwarth, R. & Diddams, S. A. Microresonator-based optical frequency combs. Science 332, 555–559 (2011). doi: 10.1126/science.1193968
[6] Spencer, D. T. et al. An optical-frequency synthesizer using integrated photonics. Nature 557, 81–85 (2018). doi: 10.1038/s41586-018-0065-7
[7] Li, Q. et al. Stably accessing octave-spanning microresonator frequency combs in the soliton regime. Optica 4, 193–203 (2017). doi: 10.1364/OPTICA.4.000193
[8] Kim, S. et al. Dispersion engineering and frequency comb generation in thin silicon nitride concentric microresonators. Nat. Commun. 8, 372 (2017). doi: 10.1038/s41467-017-00491-x
[9] Liang, F., Clarke, N., Patel, P., Loncar, M. & Quan, Q. M. Scalable photonic crystal chips for high sensitivity protein detection. Opt. Express 21, 32306–32312 (2013). doi: 10.1364/OE.21.032306
[10] Fan, X. D. & White, I. M. Optofluidic microsystems for chemical and biological analysis. Nat. Photonics 5, 591–597 (2011). doi: 10.1038/nphoton.2011.206
[11] Xu, D. X. et al. Folded cavity SOI microring sensors for high sensitivity and real time measurement of biomolecular binding. Opt. Express 16, 15137–15148 (2008). doi: 10.1364/OE.16.015137
[12] Jokerst, N. et al. Chip scale integrated microresonator sensing systems. J. Biophotonics 2, 212–226 (2009). doi: 10.1002/jbio.200910010
[13] Lin, S. Y. & Crozier, K. B. Trapping-assisted sensing of particles and proteins using on-chip optical microcavities. ACS Nano 7, 1725–1730 (2013). doi: 10.1021/nn305826j
[14] Thomson, D. et al. Roadmap on silicon photonics. J. Opt. 18, 073003 (2016). doi: 10.1088/2040-8978/18/7/073003
[15] Agrell, E. et al. Roadmap of optical communications. J. Opt. 18, 063002 (2016). doi: 10.1088/2040-8978/18/6/063002
[16] Jahani, S. et al. Controlling evanescent waves using silicon photonic all-dielectric metamaterials for dense integration. Nat. Commun. 9, 1893 (2018). doi: 10.1038/s41467-018-04276-8
[17] Doylend, J. K. et al. Two-dimensional free-space beam steering with an optical phased array on silicon-on-insulator. Opt. Express 19, 21595–21604 (2011). doi: 10.1364/OE.19.021595
[18] Sun, J., Timurdogan, E., Yaacobi, A., Hosseini, E. S. & Watts, M. R. Large-scale nanophotonic phased array. Nature 493, 195–199 (2013). doi: 10.1038/nature11727
[19] Poulton, C. V. et al. Large-scale silicon nitride nanophotonic phased arrays at infrared and visible wavelengths. Opt. Lett. 42, 21–24 (2017). doi: 10.1364/OL.42.000021
[20] Yariv, A. & Yeh, P. Photonics: Optical Electronics in Modern Communications. 6th edn, (Oxford University Press, Oxford, 2006).
[21] Chrostowski, L. & Hochberg, M. Silicon Photonics Design: From Devices to Systems. (Cambridge University Press, Cambridge, 2015).
[22] Dakss, M. L., Kuhn, L., Heidrich, P. F. & Scott, B. A. Grating coupler for efficient excitation of optical guided waves in thin films. Appl. Phys. Lett. 16, 523–525 (1970). doi: 10.1063/1.1653091
[23] Harris, J. H., Winn, R. K. & Dalgoutte, D. G. Theory and design of periodic couplers. Appl. Opt. 11, 2234–2241 (1972). doi: 10.1364/AO.11.002234
[24] Dalgoutte, D. G. A high efficiency thin grating coupler for integrated optics. Opt. Commun. 8, 124–127 (1973). doi: 10.1016/0030-4018(73)90152-1
[25] Ogawa, K., Chang, W., Sopori, B. & Rosenbaum, F. A theoretical analysis of etched grating couplers for integrated optics. IEEE J. Quantum Electron. 9, 29–42 (1973). doi: 10.1109/JQE.1973.1077337
[26] Taillaert, D., Bienstman, P. & Baets, R. Compact efficient broadband grating coupler for silicon-on-insulator waveguides. Opt. Lett. 29, 2749–2751 (2004). doi: 10.1364/OL.29.002749
[27] Van Laere, F. et al. Compact and highly efficient grating couplers between optical fiber and nanophotonic waveguides. J. Lightwave Technol. 25, 151–156 (2007). doi: 10.1109/JLT.2006.888164
[28] Ding, Y. H., Peucheret, C., Ou, H. Y. & Yvind, K. Fully etched apodized grating coupler on the SOI platform with −0.58 dB coupling efficiency. Opt. Lett. 39, 5348–5350 (2014). doi: 10.1364/OL.39.005348
[29] Roelkens, G. et al. High efficiency diffractive grating couplers for interfacing a single mode optical fiber with a nanophotonic silicon-on-insulator waveguide circuit. Appl. Phys. Lett. 92, 131101 (2008). doi: 10.1063/1.2905260
[30] Vermeulen, D. et al. High-efficiency fiber-to-chip grating couplers realized using an advanced CMOS-compatible Silicon-On-Insulator platform. Opt. Express 18, 18278–18283 (2010). doi: 10.1364/OE.18.018278
[31] Ding, Y. H., Ou, H. Y. & Peucheret, C. Ultrahigh-efficiency apodized grating coupler using fully etched photonic crystals. Opt. Lett. 38, 2732–2734 (2013). doi: 10.1364/OL.38.002732
[32] Zaoui, W. S. et al. Bridging the gap between optical fibers and silicon photonic integrated circuits. Opt. Express 22, 1277–1286 (2014). doi: 10.1364/OE.22.001277
[33] Chen, X., Li, C., Fung, C. K. Y., Lo, S. M. G. & Tsang, H. K. Apodized waveguide grating couplers for efficient coupling to optical fibers. IEEE Photonics Technol. Lett. 22, 1156–1158 (2010). doi: 10.1109/LPT.2010.2051220
[34] Mehta, K. K. & Ram, R. J. Precise and diffraction-limited waveguide-to-free-space focusing gratings. Sci. Rep. 7, 2019 (2017). doi: 10.1038/s41598-017-02169-2
[35] Mekis, A. et al. A grating-coupler-enabled CMOS photonics platform. IEEE J. Sel. Top. Quantum Electron. 17, 597–608 (2011). doi: 10.1109/JSTQE.2010.2086049
[36] Xu, X. C. et al. Complementary metal–oxide–semiconductor compatible high efficiency subwavelength grating couplers for silicon integrated photonics. Appl. Phys. Lett. 101, 031109 (2012). doi: 10.1063/1.4737412
[37] Song, J. H. et al. Polarization-independent nonuniform grating couplers on silicon-on-insulator. Opt. Lett. 40, 3941–3944 (2015). doi: 10.1364/OL.40.003941
[38] Chen, X., Xu, K., Cheng, Z. Z., Fung, C. K. Y. & Tsang, H. K. Wideband subwavelength gratings for coupling between silicon-on-insulator waveguides and optical fibers. Opt. Lett. 37, 3483–3485 (2012). doi: 10.1364/OL.37.003483
[39] Halir, R. et al. Continuously apodized fiber-to-chip surface grating coupler with refractive index engineered subwavelength structure. Opt. Lett. 35, 3243–3245 (2010). doi: 10.1364/OL.35.003243
[40] Caiseda, C., Griva, I., Martinez, L., Shaw, K. & Weingarten, D. Numerical optimization technique for optimal design of the n grooves surface Plasmon grating coupler. Procedia Comput. Sci. 29, 2145–2151 (2014). doi: 10.1016/j.procs.2014.05.199
[41] Michaels, A. & Yablonovitch, E. Inverse design of near unity efficiency perfectly vertical grating couplers. Opt. Express 26, 4766–4779 (2018). doi: 10.1364/OE.26.004766
[42] Su, L. et al. Fully-automated optimization of grating couplers. Opt. Express 26, 4023–4034 (2018). doi: 10.1364/OE.26.004023
[43] Griva, I., Nash, S. G. & Sofer, A. Linear and Nonlinear Optimization. 2nd edn, (SIAM, Philadelphia, 2009).
[44] COMSOL Multiphysics Acoustic Optimization Model. https://www.comsol.com/model/optimizing-the-shape-of-a-horn-4353.
[45] COMSOL Multiphysics Reference Manual, Chapter 18: Deformed Geometry and Moving Mesh. version COMSOL Multiphysics® v. 5.2. COMSOL AB, Stockholm, Sweden, 2015, pp. 865–883.
[46] Gill, P. E., Murray, W. & Saunders, M. A. SNOPT: an SQP algorithm for large-scale constrained optimization. SIAM Rev. 47, 99–131 (2005). doi: 10.1137/S0036144504446096
[47] Optimization Module User's Guide, COMSOL Multiphysics® v. 5.2. COMSOL AB, Stockholm, Sweden, 2015.
[48] Balram, K. C. et al. The nanolithography toolbox. J. Res. Natl Inst. Stand. Technol. 121, 464–475 (2016). doi: 10.6028/jres.121.024