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Shape optimization for the design of passive mid-infrared photonic components

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Abstract

Shape optimization techniques were first developed in the context of mechanical engineering and, more recently, applied to photonic components for data communication. Here, motivated by the growing application potential of mid-infrared photonics driven by chemical sensing and spectroscopy, we present the design by shape optimization of passive components operating in this wavelength range. A focus is placed on the creation of designs that are fabricable and robust to manufacturing uncertainties.

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Notes

  1. We deliberately ignore here the treatment of the radiative modes for convenience, but their consideration does not change the results presented in this section.

  2. In a nutshell this adjoint equation corresponds to a Maxwell equation simulation, where the mode is injected from the output waveguide with a power proportional to the value of \(a_n^*\) (the propagating mode power considered in the objective \(J(\varOmega )\)). For more details see Lebbe et al. (2018).

References

  • Allaire, G., Schoenauer, M.: Conception Optimale de Structures, vol. 58. Springer, Berlin (2007)

    MATH  Google Scholar 

  • Allaire, G., Jouve, F., Toader, A.M.: Structural optimization using sensitivity analysis and a level-set method. J. Comput. Phys. 194(1), 363–393 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  • Bendsøe, M.P., Sigmund, O.: Topology Optimization: Theory, Methods, and Applications. Springer, Berlin (2003)

    MATH  Google Scholar 

  • Berenger, J.P.: A perfectly matched layer for the absorption of electromagnetic waves. J. Comput. Phys. 114(2), 185–200 (1994)

    Article  ADS  MathSciNet  Google Scholar 

  • Brun, M., Labeye, P., Grand, G., Hartmann, J.M., Boulila, F., Carras, M., Nicoletti, S.: Low loss SiGe graded index waveguides for mid-IR applications. Opt. Express 22(1), 508–518 (2014)

    Article  ADS  Google Scholar 

  • Fedeli, J., Nicoletti, S.: Mid-Infrared (Mid-IR) Silicon-Based Photonics. In: Proceedings of the IEEE, pp. 1–11 (2018)

  • Frellsen, L.F., Ding, Y., Sigmund, O., Frandsen, L.H.: Topology optimized mode multiplexing in silicon-on-insulator photonic wire waveguides. Opt. Express 24(15), 16866–16873 (2016)

    Article  ADS  Google Scholar 

  • Jensen, J.S., Sigmund, O.: Topology optimization of photonic crystal structures: a high-bandwidth low-loss t-junction waveguide. JOSA B 22(6), 1191–1198 (2005)

    Article  ADS  Google Scholar 

  • Jin, J.M.: The Finite Element Method in Electromagnetics. Wiley, New York (2015)

    Google Scholar 

  • Lalau-Keraly, C.M., Bhargava, S., Miller, O.D., Yablonovitch, E.: Adjoint shape optimization applied to electromagnetic design. Opt. Express 21(18), 21693–21701 (2013)

    Article  ADS  Google Scholar 

  • Lebbe, N., Dapogny, C., Oudet, E., Hassan, K., Gliere, A.: Robust shape and topology optimization of nanophotonic devices using the level set method. HAL preprint hal-01860882 (2018). https://hal.archives-ouvertes.fr/hal-01860882

  • Lu, J., Vučković, J.: Nanophotonic computational design. Opt. Express 21(11), 13351 (2013)

    Article  ADS  Google Scholar 

  • Molesky, S., Lin, Z., Piggott, A.Y., Jin, W., Vučković, J., Rodriguez, A.W.: Outlook for inverse design in nanophotonics. arXiv preprint arXiv:1801.06715 (2018)

  • Osher, S., Fedkiw, R.: Level Set Methods and Dynamic Implicit Surfaces, vol. 153. Springer, Berlin (2006)

    MATH  Google Scholar 

  • Piggott, A.Y., Lu, J., Lagoudakis, K.G., Petykiewicz, J., Babinec, T.M., Vučković, J.: Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nat. Photonics 9(6), 374–377 (2015)

    Article  ADS  Google Scholar 

  • Piggott, A.Y., Petykiewicz, J., Su, L., Vučković, J.: Fabrication-constrained nanophotonic inverse design. Sci. Rep. 7(1), 1786–1792 (2017)

    Article  ADS  Google Scholar 

  • Pironneau, O.: Optimal shape design for elliptic systems. In: Drenick R.F., Kozin F. (eds.) System Modeling and Optimization. Lecture Notes in Control and Information Sciences, vol 38, pp. 42–66. Springer, Berlin (1982)

  • Sethian, J.A.: Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science, vol. 3. Cambridge University Press, Cambridge (1999)

    MATH  Google Scholar 

  • Shen, B., Wang, P., Polson, R., Menon, R.: An integrated-nanophotonics polarization beamsplitter with 2.4 × 2.4 μm 2 footprint. Nat. Photonics 9(6), 378–382 (2015)

    Article  ADS  Google Scholar 

  • Sigmund, O., Maute, K.: Topology optimization approaches. Struct. Multidiscip. Optim. 48(6), 1031–1055 (2013)

    Article  MathSciNet  Google Scholar 

  • Soref, R.: Mid-infrared photonics in silicon and germanium. Nat. Photonics 4(8), 495–497 (2010)

    Article  ADS  Google Scholar 

  • Yu, Z., Cui, H., Sun, X.: Genetic-algorithm-optimized wideband on-chip polarization rotator with an ultrasmall footprint. Opt. Lett. 42(16), 3093–3096 (2017)

    Article  ADS  Google Scholar 

  • Zhou, W., Cheng, Z., Wu, X., Sun, X., Tsang, H.K.: Fully suspended slot waveguide platform. J. Appl. Phys. 123(6), 063103 (2018)

    Article  ADS  Google Scholar 

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Acknowledgements

This research was partly funded by the European Union Project REDFINCH (E.U. H2020, No. 780240). Moreover, the authors are grateful to J.-M. Fedeli for his expertise regarding the technological platform and for his involvement in the future fabrication of the micro-components.

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Correspondence to Alain Glière.

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This article is part of the Topical Collection on Numerical Simulation of Optoelectronic Devices, NUSOD’ 18.

Guest Edited by Paolo Bardella, Weida Hu, Slawomir Sujecki, Stefan Schulz, Silvano Donati, Angela Traenhardt.

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Lebbe, N., Glière, A., Hassan, K. et al. Shape optimization for the design of passive mid-infrared photonic components. Opt Quant Electron 51, 166 (2019). https://doi.org/10.1007/s11082-019-1849-1

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