Skip to main content
SpringerLink
Log in

Prediction of electromagnetic field patterns of optical waveguide using neural network

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

Physical fields represent quantities that vary in space and/or time axes. Understanding the distribution of a field pattern is a key element in scientific discoveries and technological developments. In this article, by picking up the electromagnetic field of an optical waveguide as an example, we demonstrate how field patterns can be uncovered using artificial neural networks. The cross section plane of the optical waveguide is discretized into a set of tiny pixels, and the field values are obtained at these pixels. Deep learning model is created by assuming the field values as outputs, and the geometrical dimensions of the waveguide as inputs. The correlation between the field values in the adjacent pixels is established by mean of feedback using a recurrent neural network. The trained deep learning model enables field pattern prediction for the entire (and usual) parameter space for applications in the field of photonics.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. Nayak J, Bighnaraj B, Behera HS (2015) A comprehensive survey on support vector machine in data mining tasks: applications and challenges. Int J Database Theory Appl 8:169–186

    Google Scholar 

  2. May A et al (2019) Kernel approximation methods for speech recognition. J Mach Learn Res 20:1–36

    MathSciNet  Google Scholar 

  3. Lakin SM et al (2019) Hierarchical hidden Markov models enable accurate and diverse detection of antimicrobial resistance sequences. Commun Biol 2:294

    Google Scholar 

  4. Lee PM (2004) Bayesian statistics: an introduction, 3rd edn. Hodder Education Publishers, London

    MATH  Google Scholar 

  5. Battula BP, RamaKrishna KVSS, Kim T (2015) An efficient approach for knowledge discovery in decision trees using inter quartile range transform. Int J Control Autom 8:325–334

    Google Scholar 

  6. Goodfellow I, Bengio Y, Courville A (2016) Deep learning. MIT Press, New York

    MATH  Google Scholar 

  7. Sharma N, Jain V, Mishra A (2018) An analysis of convolutional neural networks for image classification. Procedia Comput Sci 132:377–384

    Google Scholar 

  8. Kłosowski P (2018) Deep learning for natural language processing and language modelling. In: Signal processing: algorithms, architectures, arrangements, and applications (SPA), Poznan, pp 223–228

  9. Nassif AB, Shahin I, Attili I, Azzeh M, Shaalan K (2019) Speech recognition using deep neural networks: a systematic review. IEEE Access 7:19143–19165

    Google Scholar 

  10. Pierson HA, Gashler MS (2017) Deep learning in robotics: a review of recent research. Adv Robot 31:821–835

    Google Scholar 

  11. Wang J et al (2018) Deep learning for smart manufacturing: methods and applications. J Manuf Syst 48:144–156

    Google Scholar 

  12. Lavecchia A (2019) Deep learning in drug discovery: opportunities, challenges and future prospects. Drug Discov Today 24:2017–2032

    Google Scholar 

  13. Xue D et al (2016) Accelerated search for materials with targeted properties by adaptive design. Nat Commun 7:11241

    Google Scholar 

  14. Sadowski P et al (2015) Deep learning, dark knowledge, and dark matter. Proc Mach Learn Res 42:81–87

    Google Scholar 

  15. Zhu L et al (2008) Deep learning for seismic phase detection and picking in the aftershock zone of 2008 Mw7.9 Wenchuan earthquake. arXiv:1901.06396

  16. Brunton SL, Noack BR, Koumoutsakos P (2020) Machine learning for fluid mechanics. Annu Rev Fluid Mech 52:477–508

    MATH  Google Scholar 

  17. Beerel PA, Pedram M (2018) Opportunities for machine learning in electronic design automation. In: 2018 IEEE international symposium on circuits and systems (ISCAS), Florence, pp 1–5

  18. Landau LD, Lifshitz EM (2015) The classical theory of fields, 4th edn. Butterworth Heinemann Ltd, Oxford

    MATH  Google Scholar 

  19. Acheson DJ (1990) Elementary fluid dynamics. Oxford applied mathematics and computing science series. Oxford University Press, Oxford

    MATH  Google Scholar 

  20. Griffiths DJ (2017) Introduction to electrodynamics, 4th edn. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  21. Turduev M, Bor E, Latifoglu C, Giden IH, Hanay YS, Kurt H (2018) Ultracompact photonic structure design for strong light confinement and coupling into nanowaveguide. J Lightw Technol 36:2812–2819

    Google Scholar 

  22. Malkiel I, Nagler A, Mrejen M, Arieli U, Wolf L, Suchowski H (2017) Deep learning for design and retrieval of nanophotonic structures. arXiv:1702.07949

  23. Ma W, Cheng F, Liu Y (2018) Deep-learning-enabled on-demand design of chiral metamaterials. ACS Nano 12:6326–6334

    Google Scholar 

  24. Liu D, Tan Y, Khoram E, Yu Z (2018) Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5:1365–1369

    Google Scholar 

  25. Alagappan G, Png CE (2019) Deep learning models for effective refractive indices in silicon nitride waveguides. J Opt 21:035801

    Google Scholar 

  26. Alagappan G, Png CE (2018) Modal classification in optical waveguides using deep learning. J Mod Opt 66:557–561

    Google Scholar 

  27. Okamato K (2006) Fundamental of optical waveguides. Elsevier Inc., Amsterdam

    Google Scholar 

  28. Yariv A, Yeh P (2007) Photonics: optical electronics in modern communications. Oxford University Press, Oxford

    Google Scholar 

  29. Gondarenko A, Levy JS, Lipson M (2009) High confinement micron-scale silicon nitride high Q ring resonator. Opt Express 17:11366–11370

    Google Scholar 

  30. Sun X, Alam MZ, Aitchison JS, Mojahedi M (2016) Compact and broadband polarization beam splitter based on a silicon nitride augmented low-index guiding structure. Opt Lett 41:163–166

    Google Scholar 

  31. Chen L, Doerr CR, Chen Y-K (2011) Compact polarization rotator on silicon for polarization-diversified circuits. Opt Lett 36:469–471

    Google Scholar 

  32. Levy JS, Foster MA, Gaeta AL, Lipson M (2011) Harmonic generation in silicon nitride ring resonators. Opt Express 19:11415–11421

    Google Scholar 

  33. Rahman BMA, Fernandez FA, Davies JB (1991) Review of finite element methods for microwave and optical waveguides. Proc IEEE 79:1442–1448

    Google Scholar 

  34. Mabaya N, Lagasse PE, Vandenbulcke P (1981) Finite element analysis waveguides of optical. IEEE Trans Microw Theory Tech 29:600–605

    Google Scholar 

  35. Yu CP, Chang HC (2004) Yee-mesh-based finite difference eigenmode solver with PML absorbing boundary conditions for optical waveguides and photonic crystal fibers. Opt Express 12:6165–6177

    Google Scholar 

  36. Yao K, Unni R, Zheng Y (2019) Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8:339

    Google Scholar 

  37. Peng H-T, Nahmias MA, de Lima TF, Tait AN, Shastri BJ, Prucnal PR (2018) Neuromorphic photonic integrated circuits. IEEE J Sel Top Quantum Electron 24:6101715

    Google Scholar 

  38. Prucnal PR, Shastri BJ (2017) Neuromorphic photonics. CRC Press, Boca Raton

    Google Scholar 

  39. de Lima TF, Shastri BJ, Tait AN, Nahmias MA, Prucnal PR (2017) Progress in neuromorphic photonics. Nanophotonics 6:577

    Google Scholar 

  40. Dory C et al (2019) Inverse-designed diamond photonics. Nat Commun 10:3309

    Google Scholar 

  41. Liu Y et al (2018) Very sharp adiabatic bends based on an inverse design. Opt Lett 43:2482

    Google Scholar 

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

    Google Scholar 

  43. Zhang Y, Yang S, Lim AEJ, Lo GQ, Galland C, Baehr-Jones T, Hochberg M (2013) A compact and low loss Y-junction for submicron silicon waveguide. Opt Express 21:1310–1316

    Google Scholar 

  44. Zejie Yu, Feng A, Xi X, Sun X (2019) Inverse-designed low-loss and wideband polarization-insensitive silicon waveguide crossing. Opt Lett 44:77–80

    Google Scholar 

  45. Ke X, Liu L, Wen X, Sun W, Zhang N, Yi N, Sun S, Xiao S, Song Q (2017) Integrated photonic power divider with arbitrary power ratios. Opt Lett 42:855–858

    Google Scholar 

  46. Lebbe N, Glière A, Hassan K (2019) High-efficiency and broadband photonic polarization rotator based on multilevel shape optimization. Opt Lett 44:1960–1963

    Google Scholar 

  47. Lin Z, Liu V, Pestourie R, Johnson SG (2019) Topology optimization of freeform large-area metasurfaces. Opt Express 27:15765–15775

    Google Scholar 

  48. Logan S, Trivedi R, Sapra NV, Piggott AY, Vercruysse D, Vučković J (2018) Fully-automated optimization of grating couplers. Opt Express 26:4023–4034

    Google Scholar 

  49. Logan S, Piggott AY, Sapra NV, Petykiewicz J, Vučković J (2018) Inverse design and demonstration of a compact on-chip narrowband three-channel wavelength demultiplexer. ACS Photonics 5:301

    Google Scholar 

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

    Google Scholar 

  51. Hegde RS (2020) Photonics inverse design: pairing deep neural networks with evolutionary algorithms. IEEE J Sel Top Quantum Electron 26:1

    Google Scholar 

  52. Song J, Tokpanov YS, Chen Y, Fleischman D, Fountaine KT, Atwater HA, Yu Y Optimizing photonic nanostructures via multi-fidelity Gaussian processes. arXiv:1811.07707

  53. Garcia-Santiago X et al (2018) Shape design of a reflecting surface using Bayesian optimization. J Phys: Conf Ser 963:012003

    Google Scholar 

  54. Gabr AM, Featherston C, Zhang C, Bonfil C, Zhang Q-J, Smy TJ (2019) Design and optimization of optical passive elements using artificial neural networks. J Opt Soc Am B 36:999–1007

    Google Scholar 

  55. Alagappan G, Png CE (2019) Universal deep learning representation of effective refractive index for photonics channel waveguides. J Opt Soc Am B 36:2636–2642

    Google Scholar 

  56. Hammond AM, Camacho RM (2019) Designing integrated photonic devices using artificial neural networks. Opt Express 27:29620–29638

    Google Scholar 

  57. Hegde RS (2019) Accelerating optics design optimizations with deep learning. Opt Eng 58:065103

    Google Scholar 

  58. Heaton J (2008) Introduction to neural networks for Java, 2nd edn. Heaton Research Inc, Chesterfield

    Google Scholar 

  59. Moller MF (1993) A scaled conjugate gradient algorithm for fast supervised learning. Neural Netw 6:525

    Google Scholar 

  60. Riedmiller M, Braun H (1993) A direct adaptive method for faster backpropagation learning: The RPROP algorithm. In: Proceedings of the IEEE international conference on neural networks, pp 586–591

  61. James G, Witten D, Hastie T, Tibshirani R (2013) An introduction to statistical learning: with applications in R. Springer, New York

    MATH  Google Scholar 

  62. Chollet F (2018) Deep learning with python. Manning, New York

    Google Scholar 

  63. https://www.mathworks.com/help/matlab/ref/scatteredinterpolant.html

  64. Chapre S (2016) Numerical methods for engineers, 7th edn. McGraw-Hill, New York

    Google Scholar 

  65. Giacomini R, White H (2006) Test of conditional predictive ability. Econometrica 74(6):1545–1578

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work is supported by RGANS1901, “Al-Enabled Electronic-Photonic IC Design”.

Author information

Authors and Affiliations

  1. Institute of High Performance Computing, Agency for Science, Technology, and Research (A-STAR), Fusionopolis, 1 Fusionopolis Way, #16-16, Connexis, 138632, Singapore

    Gandhi Alagappan & Ching Eng Png

Authors
  1. Gandhi Alagappan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ching Eng Png
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gandhi Alagappan.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

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

Alagappan, G., Png, C.E. Prediction of electromagnetic field patterns of optical waveguide using neural network. Neural Comput & Applic 33, 2195–2206 (2021). https://doi.org/10.1007/s00521-020-05061-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-020-05061-9

Keywords

Search

Navigation