Abstract

Photonic crystal fibers (PCFs) are the specialized optical waveguides that led to many interesting applications ranging from nonlinear optical signal processing to high-power fiber amplifiers. In this paper, machine learning techniques are used to compute various optical properties including effective index, effective mode area, dispersion and confinement loss for a solid-core PCF. These machine learning algorithms based on artificial neural networks are able to make accurate predictions of above-mentioned optical properties for usual parameter space of wavelength ranging from 0.5-1.8 µm, pitch from 0.8-2.0 µm, diameter by pitch from 0.6-0.9 and number of rings as 4 or 5 in a silica solid-core PCF. We demonstrate the use of simple and fast-training feed-forward artificial neural networks that predicts the output for unknown device parameters faster than conventional numerical simulation techniques. Computation runtimes required with neural networks (for training and testing) and Lumerical MODE solutions are also compared.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (7)

M. De, T. K. Gangopadhyay, and V. K. Singh, “Prospects of photonic crystal fiber as physical sensor: An overview,” Sensors 19(3), 464 (2019).
[Crossref]

A. Tittl, A. John-Herpin, A. Leitis, E. R. Arvelo, and H. Altug, “Metasurface-based molecular biosensing aided by artificial intelligence,” Angewandte Chemie Int. Ed. 58(42), 14810–14822 (2019).
[Crossref]

C. C. Nadell, B. Huang, J. M. Malof, and W. J. Padilla, “Deep learning for accelerated all-dielectric metasurface design,” Opt. Express 27(20), 27523–27535 (2019).
[Crossref]

J. Jiang, D. Sell, S. Hoyer, J. Hickey, J. Yang, and J. A. Fan, “Free-form diffractive metagrating design based on generative adversarial networks,” ACS Nano 13(8), 8872–8878 (2019).
[Crossref]

F. Musumeci, C. Rottondi, A. Nag, I. Macaluso, D. Zibar, M. Ruffini, and M. Tornatore, “An overview on application of machine learning techniques in optical networks,” IEEE Commun. Surv. Tutorials 21(2), 1383–1408 (2019).
[Crossref]

J. Baxter, A. C. Lesina, J.-M. Guay, A. Weck, P. Berini, and L. Ramunno, “Plasmonic colours predicted by deep learning,” Sci. Rep. 9(1), 8074 (2019).
[Crossref]

F. N. Khan, Q. Fan, C. Lu, and A. P. T. Lau, “An optical communication’s perspective on machine learning and its applications,” J. Lightwave Technol. 37(2), 493–516 (2019).
[Crossref]

2018 (5)

2017 (1)

M. R. Karim, H. Ahmad, and B. M. A. Rahman, “All-normal dispersion chalcogenide PCF for ultraflat mid-infrared supercontinuum generation,” IEEE Photonics Technol. Lett. 29(21), 1792–1795 (2017).
[Crossref]

2013 (1)

R. A. Norton and R. Scheichl, “Planewave expansion methods for photonic crystal fibres,” Appl. Numer. Math. 63, 88–104 (2013).
[Crossref]

2005 (1)

S. S. A. Obayya, B. M. A. Rahman, and K. T. V. Grattan, “Accurate finite element modal solution of photonic crystal fibres,” IEE Proc.: Optoelectron. 152(5), 241–246 (2005).
[Crossref]

2004 (3)

S. Shi, C. Chen, and D. W. Prather, “Plane-wave expansion method for calculating band structure of photonic crystal slabs with perfectly matched layers,” J. Opt. Soc. Am. A 21(9), 1769–1775 (2004).
[Crossref]

C.-P. Yu and H.-C. Chang, “Applications of the finite difference mode solution method to photonic crystal structures,” Opt. Quantum Electron. 36(1-3), 145–163 (2004).
[Crossref]

F. Benabid, G. Bouwmans, J. C. Knight, P. St. J. Russell, and F. Couny, “Ultrahigh efficiency laser wavelength conversion in a gas-filled hollow core photonic crystal fiber by pure stimulated rotational Raman scattering in molecular hydrogen,” Phys. Rev. Lett. 93(12), 123903 (2004).
[Crossref]

2002 (3)

F. Benabid, J. C. Knight, G. Antonopoulos, and P. St. J. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298(5592), 399–402 (2002).
[Crossref]

W. J. Wadsworth, A. Ortigosa-Blanch, J. C. Knight, T. A. Birks, T.-P. M. Man, and P. St. J. Russell, “Supercontinuum generation in photonic crystal fibers and optical fiber tapers: a novel light source,” J. Opt. Soc. Am. B 19(9), 2148–2155 (2002).
[Crossref]

A. Cucinotta, S. Selleri, L. Vincetti, and M. Zoboli, “Holey fiber analysis through the finite-element method,” IEEE Photonics Technol. Lett. 14(11), 1530–1532 (2002).
[Crossref]

2001 (3)

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8(3), 173–190 (2001).
[Crossref]

P. K. Cheo, A. Liu, and G. G. King, “A high-brightness laser beam from a phase-locked multicore Yb-doped fiber laser array,” IEEE Photonics Technol. Lett. 13(5), 439–441 (2001).
[Crossref]

T. M. Monro, W. Belardi, K. Furusawa, J. C. Baggett, N. G. R. Broderick, and D. J. Richardson, “Sensing with microstructured optical fibres,” Meas. Sci. Technol. 12(7), 854–858 (2001).
[Crossref]

2000 (1)

R. Holzwarth, Th. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett. 85(11), 2264–2267 (2000).
[Crossref]

1996 (1)

Abdollahramezani, S.

Y. Kiarashinejad, S. Abdollahramezani, M. Zandehshahvar, O. Hemmatyar, and A. Adibi, “Deep learning reveals underlying physics of light-matter interactions in nanophotonic devices,” arXiv preprint arXiv:1905.06889 (2019).

Y. Kiarashinejad, M. Zandehshahvar, S. Abdollahramezani, O. Hemmatyar, R. Pourabolghasem, and A. Adibi, “Knowledge discovery in nanophotonics using geometric deep learning,” arXiv preprint arXiv:1909.07330 (2019).

Adibi, A.

Y. Kiarashinejad, M. Zandehshahvar, S. Abdollahramezani, O. Hemmatyar, R. Pourabolghasem, and A. Adibi, “Knowledge discovery in nanophotonics using geometric deep learning,” arXiv preprint arXiv:1909.07330 (2019).

Y. Kiarashinejad, S. Abdollahramezani, M. Zandehshahvar, O. Hemmatyar, and A. Adibi, “Deep learning reveals underlying physics of light-matter interactions in nanophotonic devices,” arXiv preprint arXiv:1905.06889 (2019).

Ahmad, H.

M. R. Karim, H. Ahmad, and B. M. A. Rahman, “All-normal dispersion chalcogenide PCF for ultraflat mid-infrared supercontinuum generation,” IEEE Photonics Technol. Lett. 29(21), 1792–1795 (2017).
[Crossref]

Altug, H.

A. Tittl, A. John-Herpin, A. Leitis, E. R. Arvelo, and H. Altug, “Metasurface-based molecular biosensing aided by artificial intelligence,” Angewandte Chemie Int. Ed. 58(42), 14810–14822 (2019).
[Crossref]

Antiga, L.

A. Paszke, S. Gross, S. Chintala, G. Chanan, E. Yang, Z. DeVito, Z. Lin, A. Desmaison, L. Antiga, and A. Lerer, “Automatic differentiation in PyTorch,” in NIPS Autodiff Workshop, (2017).

Antonopoulos, G.

F. Benabid, J. C. Knight, G. Antonopoulos, and P. St. J. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298(5592), 399–402 (2002).
[Crossref]

Arvelo, E. R.

A. Tittl, A. John-Herpin, A. Leitis, E. R. Arvelo, and H. Altug, “Metasurface-based molecular biosensing aided by artificial intelligence,” Angewandte Chemie Int. Ed. 58(42), 14810–14822 (2019).
[Crossref]

Asano, T.

Atkin, D. M.

Ba, J. L.

D. P. Kingma and J. L. Ba, “Adam: A method for stochastic optimization,” arXiv preprint arXiv:1412.6980 (2014).

Baggett, J. C.

T. M. Monro, W. Belardi, K. Furusawa, J. C. Baggett, N. G. R. Broderick, and D. J. Richardson, “Sensing with microstructured optical fibres,” Meas. Sci. Technol. 12(7), 854–858 (2001).
[Crossref]

Baxter, J.

J. Baxter, A. C. Lesina, J.-M. Guay, A. Weck, P. Berini, and L. Ramunno, “Plasmonic colours predicted by deep learning,” Sci. Rep. 9(1), 8074 (2019).
[Crossref]

Bayvel, P.

Belardi, W.

T. M. Monro, W. Belardi, K. Furusawa, J. C. Baggett, N. G. R. Broderick, and D. J. Richardson, “Sensing with microstructured optical fibres,” Meas. Sci. Technol. 12(7), 854–858 (2001).
[Crossref]

Benabid, F.

F. Benabid, G. Bouwmans, J. C. Knight, P. St. J. Russell, and F. Couny, “Ultrahigh efficiency laser wavelength conversion in a gas-filled hollow core photonic crystal fiber by pure stimulated rotational Raman scattering in molecular hydrogen,” Phys. Rev. Lett. 93(12), 123903 (2004).
[Crossref]

F. Benabid, J. C. Knight, G. Antonopoulos, and P. St. J. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298(5592), 399–402 (2002).
[Crossref]

Berini, P.

J. Baxter, A. C. Lesina, J.-M. Guay, A. Weck, P. Berini, and L. Ramunno, “Plasmonic colours predicted by deep learning,” Sci. Rep. 9(1), 8074 (2019).
[Crossref]

Birks, T. A.

Borhani, N.

Bouwmans, G.

F. Benabid, G. Bouwmans, J. C. Knight, P. St. J. Russell, and F. Couny, “Ultrahigh efficiency laser wavelength conversion in a gas-filled hollow core photonic crystal fiber by pure stimulated rotational Raman scattering in molecular hydrogen,” Phys. Rev. Lett. 93(12), 123903 (2004).
[Crossref]

Broderick, N. G. R.

T. M. Monro, W. Belardi, K. Furusawa, J. C. Baggett, N. G. R. Broderick, and D. J. Richardson, “Sensing with microstructured optical fibres,” Meas. Sci. Technol. 12(7), 854–858 (2001).
[Crossref]

Bülow, H.

Chagnon, M.

Chanan, G.

A. Paszke, S. Gross, S. Chintala, G. Chanan, E. Yang, Z. DeVito, Z. Lin, A. Desmaison, L. Antiga, and A. Lerer, “Automatic differentiation in PyTorch,” in NIPS Autodiff Workshop, (2017).

Chang, H.-C.

C.-P. Yu and H.-C. Chang, “Applications of the finite difference mode solution method to photonic crystal structures,” Opt. Quantum Electron. 36(1-3), 145–163 (2004).
[Crossref]

Chen, C.

Cheng, F.

W. Ma, F. Cheng, and Y. Liu, “Deep-learning-enabled on-demand design of chiral metamaterials,” ACS Nano 12(6), 6326–6334 (2018).
[Crossref]

Cheo, P. K.

P. K. Cheo, A. Liu, and G. G. King, “A high-brightness laser beam from a phase-locked multicore Yb-doped fiber laser array,” IEEE Photonics Technol. Lett. 13(5), 439–441 (2001).
[Crossref]

Chintala, S.

A. Paszke, S. Gross, S. Chintala, G. Chanan, E. Yang, Z. DeVito, Z. Lin, A. Desmaison, L. Antiga, and A. Lerer, “Automatic differentiation in PyTorch,” in NIPS Autodiff Workshop, (2017).

Chugh, S.

S. Chugh, S. Ghosh, A. Gulistan, and B. M. A. Rahman, “Machine learning regression approach to the nanophotonic waveguide analyses,” http://dx.doi.org/10.1109/JLT.2019.2946572 (2019).

Couny, F.

F. Benabid, G. Bouwmans, J. C. Knight, P. St. J. Russell, and F. Couny, “Ultrahigh efficiency laser wavelength conversion in a gas-filled hollow core photonic crystal fiber by pure stimulated rotational Raman scattering in molecular hydrogen,” Phys. Rev. Lett. 93(12), 123903 (2004).
[Crossref]

Cucinotta, A.

A. Cucinotta, S. Selleri, L. Vincetti, and M. Zoboli, “Holey fiber analysis through the finite-element method,” IEEE Photonics Technol. Lett. 14(11), 1530–1532 (2002).
[Crossref]

da Silva Ferreira, A.

De, M.

M. De, T. K. Gangopadhyay, and V. K. Singh, “Prospects of photonic crystal fiber as physical sensor: An overview,” Sensors 19(3), 464 (2019).
[Crossref]

Desmaison, A.

A. Paszke, S. Gross, S. Chintala, G. Chanan, E. Yang, Z. DeVito, Z. Lin, A. Desmaison, L. Antiga, and A. Lerer, “Automatic differentiation in PyTorch,” in NIPS Autodiff Workshop, (2017).

DeVito, Z.

A. Paszke, S. Gross, S. Chintala, G. Chanan, E. Yang, Z. DeVito, Z. Lin, A. Desmaison, L. Antiga, and A. Lerer, “Automatic differentiation in PyTorch,” in NIPS Autodiff Workshop, (2017).

Eriksson, T. A.

Fan, J. A.

J. Jiang, D. Sell, S. Hoyer, J. Hickey, J. Yang, and J. A. Fan, “Free-form diffractive metagrating design based on generative adversarial networks,” ACS Nano 13(8), 8872–8878 (2019).
[Crossref]

Fan, Q.

Furusawa, K.

T. M. Monro, W. Belardi, K. Furusawa, J. C. Baggett, N. G. R. Broderick, and D. J. Richardson, “Sensing with microstructured optical fibres,” Meas. Sci. Technol. 12(7), 854–858 (2001).
[Crossref]

Gangopadhyay, T. K.

M. De, T. K. Gangopadhyay, and V. K. Singh, “Prospects of photonic crystal fiber as physical sensor: An overview,” Sensors 19(3), 464 (2019).
[Crossref]

Ghosh, S.

S. Chugh, S. Ghosh, A. Gulistan, and B. M. A. Rahman, “Machine learning regression approach to the nanophotonic waveguide analyses,” http://dx.doi.org/10.1109/JLT.2019.2946572 (2019).

Grattan, K. T. V.

S. S. A. Obayya, B. M. A. Rahman, and K. T. V. Grattan, “Accurate finite element modal solution of photonic crystal fibres,” IEE Proc.: Optoelectron. 152(5), 241–246 (2005).
[Crossref]

Gross, S.

A. Paszke, S. Gross, S. Chintala, G. Chanan, E. Yang, Z. DeVito, Z. Lin, A. Desmaison, L. Antiga, and A. Lerer, “Automatic differentiation in PyTorch,” in NIPS Autodiff Workshop, (2017).

Guay, J.-M.

J. Baxter, A. C. Lesina, J.-M. Guay, A. Weck, P. Berini, and L. Ramunno, “Plasmonic colours predicted by deep learning,” Sci. Rep. 9(1), 8074 (2019).
[Crossref]

Gulistan, A.

S. Chugh, S. Ghosh, A. Gulistan, and B. M. A. Rahman, “Machine learning regression approach to the nanophotonic waveguide analyses,” http://dx.doi.org/10.1109/JLT.2019.2946572 (2019).

Hänsch, T. W.

R. Holzwarth, Th. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett. 85(11), 2264–2267 (2000).
[Crossref]

Hemmatyar, O.

Y. Kiarashinejad, S. Abdollahramezani, M. Zandehshahvar, O. Hemmatyar, and A. Adibi, “Deep learning reveals underlying physics of light-matter interactions in nanophotonic devices,” arXiv preprint arXiv:1905.06889 (2019).

Y. Kiarashinejad, M. Zandehshahvar, S. Abdollahramezani, O. Hemmatyar, R. Pourabolghasem, and A. Adibi, “Knowledge discovery in nanophotonics using geometric deep learning,” arXiv preprint arXiv:1909.07330 (2019).

Hernández-Figueroa, H. E.

Hickey, J.

J. Jiang, D. Sell, S. Hoyer, J. Hickey, J. Yang, and J. A. Fan, “Free-form diffractive metagrating design based on generative adversarial networks,” ACS Nano 13(8), 8872–8878 (2019).
[Crossref]

Hinton, G.

Y. LeCun, D. Touresky, G. Hinton, and T. Sejnowski, “A theoretical framework for back-propagation,” in Proceedings of the 1988 Connectionist Models Summer School, vol. 1 (CMU, Pittsburgh, Pa: Morgan Kaufmann, 1988), pp. 21–28.

Holzwarth, R.

R. Holzwarth, Th. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett. 85(11), 2264–2267 (2000).
[Crossref]

Hoyer, S.

J. Jiang, D. Sell, S. Hoyer, J. Hickey, J. Yang, and J. A. Fan, “Free-form diffractive metagrating design based on generative adversarial networks,” ACS Nano 13(8), 8872–8878 (2019).
[Crossref]

Huang, B.

Jiang, J.

J. Jiang, D. Sell, S. Hoyer, J. Hickey, J. Yang, and J. A. Fan, “Free-form diffractive metagrating design based on generative adversarial networks,” ACS Nano 13(8), 8872–8878 (2019).
[Crossref]

Joannopoulos, J. D.

John-Herpin, A.

A. Tittl, A. John-Herpin, A. Leitis, E. R. Arvelo, and H. Altug, “Metasurface-based molecular biosensing aided by artificial intelligence,” Angewandte Chemie Int. Ed. 58(42), 14810–14822 (2019).
[Crossref]

Johnson, S. G.

Kakkava, E.

Karanov, B.

Karim, M. R.

M. R. Karim, H. Ahmad, and B. M. A. Rahman, “All-normal dispersion chalcogenide PCF for ultraflat mid-infrared supercontinuum generation,” IEEE Photonics Technol. Lett. 29(21), 1792–1795 (2017).
[Crossref]

Khan, F. N.

Kiarashinejad, Y.

Y. Kiarashinejad, S. Abdollahramezani, M. Zandehshahvar, O. Hemmatyar, and A. Adibi, “Deep learning reveals underlying physics of light-matter interactions in nanophotonic devices,” arXiv preprint arXiv:1905.06889 (2019).

Y. Kiarashinejad, M. Zandehshahvar, S. Abdollahramezani, O. Hemmatyar, R. Pourabolghasem, and A. Adibi, “Knowledge discovery in nanophotonics using geometric deep learning,” arXiv preprint arXiv:1909.07330 (2019).

King, G. G.

P. K. Cheo, A. Liu, and G. G. King, “A high-brightness laser beam from a phase-locked multicore Yb-doped fiber laser array,” IEEE Photonics Technol. Lett. 13(5), 439–441 (2001).
[Crossref]

Kingma, D. P.

D. P. Kingma and J. L. Ba, “Adam: A method for stochastic optimization,” arXiv preprint arXiv:1412.6980 (2014).

Knight, J. C.

F. Benabid, G. Bouwmans, J. C. Knight, P. St. J. Russell, and F. Couny, “Ultrahigh efficiency laser wavelength conversion in a gas-filled hollow core photonic crystal fiber by pure stimulated rotational Raman scattering in molecular hydrogen,” Phys. Rev. Lett. 93(12), 123903 (2004).
[Crossref]

F. Benabid, J. C. Knight, G. Antonopoulos, and P. St. J. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298(5592), 399–402 (2002).
[Crossref]

W. J. Wadsworth, A. Ortigosa-Blanch, J. C. Knight, T. A. Birks, T.-P. M. Man, and P. St. J. Russell, “Supercontinuum generation in photonic crystal fibers and optical fiber tapers: a novel light source,” J. Opt. Soc. Am. B 19(9), 2148–2155 (2002).
[Crossref]

R. Holzwarth, Th. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett. 85(11), 2264–2267 (2000).
[Crossref]

J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21(19), 1547–1549 (1996).
[Crossref]

Lau, A. P. T.

Lavery, D.

LeCun, Y.

Y. LeCun, D. Touresky, G. Hinton, and T. Sejnowski, “A theoretical framework for back-propagation,” in Proceedings of the 1988 Connectionist Models Summer School, vol. 1 (CMU, Pittsburgh, Pa: Morgan Kaufmann, 1988), pp. 21–28.

Leitis, A.

A. Tittl, A. John-Herpin, A. Leitis, E. R. Arvelo, and H. Altug, “Metasurface-based molecular biosensing aided by artificial intelligence,” Angewandte Chemie Int. Ed. 58(42), 14810–14822 (2019).
[Crossref]

Lerer, A.

A. Paszke, S. Gross, S. Chintala, G. Chanan, E. Yang, Z. DeVito, Z. Lin, A. Desmaison, L. Antiga, and A. Lerer, “Automatic differentiation in PyTorch,” in NIPS Autodiff Workshop, (2017).

Lesina, A. C.

J. Baxter, A. C. Lesina, J.-M. Guay, A. Weck, P. Berini, and L. Ramunno, “Plasmonic colours predicted by deep learning,” Sci. Rep. 9(1), 8074 (2019).
[Crossref]

Lin, Z.

A. Paszke, S. Gross, S. Chintala, G. Chanan, E. Yang, Z. DeVito, Z. Lin, A. Desmaison, L. Antiga, and A. Lerer, “Automatic differentiation in PyTorch,” in NIPS Autodiff Workshop, (2017).

Liu, A.

P. K. Cheo, A. Liu, and G. G. King, “A high-brightness laser beam from a phase-locked multicore Yb-doped fiber laser array,” IEEE Photonics Technol. Lett. 13(5), 439–441 (2001).
[Crossref]

Liu, Y.

W. Ma, F. Cheng, and Y. Liu, “Deep-learning-enabled on-demand design of chiral metamaterials,” ACS Nano 12(6), 6326–6334 (2018).
[Crossref]

Lu, C.

Ma, W.

W. Ma, F. Cheng, and Y. Liu, “Deep-learning-enabled on-demand design of chiral metamaterials,” ACS Nano 12(6), 6326–6334 (2018).
[Crossref]

Macaluso, I.

F. Musumeci, C. Rottondi, A. Nag, I. Macaluso, D. Zibar, M. Ruffini, and M. Tornatore, “An overview on application of machine learning techniques in optical networks,” IEEE Commun. Surv. Tutorials 21(2), 1383–1408 (2019).
[Crossref]

Malheiros-Silveira, G. N.

Malof, J. M.

Man, T.-P. M.

Monro, T. M.

T. M. Monro, W. Belardi, K. Furusawa, J. C. Baggett, N. G. R. Broderick, and D. J. Richardson, “Sensing with microstructured optical fibres,” Meas. Sci. Technol. 12(7), 854–858 (2001).
[Crossref]

Moser, C.

Musumeci, F.

F. Musumeci, C. Rottondi, A. Nag, I. Macaluso, D. Zibar, M. Ruffini, and M. Tornatore, “An overview on application of machine learning techniques in optical networks,” IEEE Commun. Surv. Tutorials 21(2), 1383–1408 (2019).
[Crossref]

Nadell, C. C.

Nag, A.

F. Musumeci, C. Rottondi, A. Nag, I. Macaluso, D. Zibar, M. Ruffini, and M. Tornatore, “An overview on application of machine learning techniques in optical networks,” IEEE Commun. Surv. Tutorials 21(2), 1383–1408 (2019).
[Crossref]

Noda, S.

Norton, R. A.

R. A. Norton and R. Scheichl, “Planewave expansion methods for photonic crystal fibres,” Appl. Numer. Math. 63, 88–104 (2013).
[Crossref]

Obayya, S. S. A.

S. S. A. Obayya, B. M. A. Rahman, and K. T. V. Grattan, “Accurate finite element modal solution of photonic crystal fibres,” IEE Proc.: Optoelectron. 152(5), 241–246 (2005).
[Crossref]

Ortigosa-Blanch, A.

Padilla, W. J.

Paszke, A.

A. Paszke, S. Gross, S. Chintala, G. Chanan, E. Yang, Z. DeVito, Z. Lin, A. Desmaison, L. Antiga, and A. Lerer, “Automatic differentiation in PyTorch,” in NIPS Autodiff Workshop, (2017).

Pourabolghasem, R.

Y. Kiarashinejad, M. Zandehshahvar, S. Abdollahramezani, O. Hemmatyar, R. Pourabolghasem, and A. Adibi, “Knowledge discovery in nanophotonics using geometric deep learning,” arXiv preprint arXiv:1909.07330 (2019).

Prather, D. W.

Psaltis, D.

Rahman, B. M. A.

M. R. Karim, H. Ahmad, and B. M. A. Rahman, “All-normal dispersion chalcogenide PCF for ultraflat mid-infrared supercontinuum generation,” IEEE Photonics Technol. Lett. 29(21), 1792–1795 (2017).
[Crossref]

S. S. A. Obayya, B. M. A. Rahman, and K. T. V. Grattan, “Accurate finite element modal solution of photonic crystal fibres,” IEE Proc.: Optoelectron. 152(5), 241–246 (2005).
[Crossref]

S. Chugh, S. Ghosh, A. Gulistan, and B. M. A. Rahman, “Machine learning regression approach to the nanophotonic waveguide analyses,” http://dx.doi.org/10.1109/JLT.2019.2946572 (2019).

Ramunno, L.

J. Baxter, A. C. Lesina, J.-M. Guay, A. Weck, P. Berini, and L. Ramunno, “Plasmonic colours predicted by deep learning,” Sci. Rep. 9(1), 8074 (2019).
[Crossref]

Richardson, D. J.

T. M. Monro, W. Belardi, K. Furusawa, J. C. Baggett, N. G. R. Broderick, and D. J. Richardson, “Sensing with microstructured optical fibres,” Meas. Sci. Technol. 12(7), 854–858 (2001).
[Crossref]

Rottondi, C.

F. Musumeci, C. Rottondi, A. Nag, I. Macaluso, D. Zibar, M. Ruffini, and M. Tornatore, “An overview on application of machine learning techniques in optical networks,” IEEE Commun. Surv. Tutorials 21(2), 1383–1408 (2019).
[Crossref]

Ruffini, M.

F. Musumeci, C. Rottondi, A. Nag, I. Macaluso, D. Zibar, M. Ruffini, and M. Tornatore, “An overview on application of machine learning techniques in optical networks,” IEEE Commun. Surv. Tutorials 21(2), 1383–1408 (2019).
[Crossref]

Russell, P. St. J.

F. Benabid, G. Bouwmans, J. C. Knight, P. St. J. Russell, and F. Couny, “Ultrahigh efficiency laser wavelength conversion in a gas-filled hollow core photonic crystal fiber by pure stimulated rotational Raman scattering in molecular hydrogen,” Phys. Rev. Lett. 93(12), 123903 (2004).
[Crossref]

F. Benabid, J. C. Knight, G. Antonopoulos, and P. St. J. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298(5592), 399–402 (2002).
[Crossref]

W. J. Wadsworth, A. Ortigosa-Blanch, J. C. Knight, T. A. Birks, T.-P. M. Man, and P. St. J. Russell, “Supercontinuum generation in photonic crystal fibers and optical fiber tapers: a novel light source,” J. Opt. Soc. Am. B 19(9), 2148–2155 (2002).
[Crossref]

R. Holzwarth, Th. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett. 85(11), 2264–2267 (2000).
[Crossref]

J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21(19), 1547–1549 (1996).
[Crossref]

P. St. J. Russell, “Photonic crystal fibers: Basics and applications,” in Optical Fiber Telecommunications VA, (Elsevier, 2008), pp. 485–522.

Scheichl, R.

R. A. Norton and R. Scheichl, “Planewave expansion methods for photonic crystal fibres,” Appl. Numer. Math. 63, 88–104 (2013).
[Crossref]

Schmalen, L.

Sejnowski, T.

Y. LeCun, D. Touresky, G. Hinton, and T. Sejnowski, “A theoretical framework for back-propagation,” in Proceedings of the 1988 Connectionist Models Summer School, vol. 1 (CMU, Pittsburgh, Pa: Morgan Kaufmann, 1988), pp. 21–28.

Sell, D.

J. Jiang, D. Sell, S. Hoyer, J. Hickey, J. Yang, and J. A. Fan, “Free-form diffractive metagrating design based on generative adversarial networks,” ACS Nano 13(8), 8872–8878 (2019).
[Crossref]

Selleri, S.

A. Cucinotta, S. Selleri, L. Vincetti, and M. Zoboli, “Holey fiber analysis through the finite-element method,” IEEE Photonics Technol. Lett. 14(11), 1530–1532 (2002).
[Crossref]

Shi, S.

Singh, V. K.

M. De, T. K. Gangopadhyay, and V. K. Singh, “Prospects of photonic crystal fiber as physical sensor: An overview,” Sensors 19(3), 464 (2019).
[Crossref]

Thouin, F.

Tittl, A.

A. Tittl, A. John-Herpin, A. Leitis, E. R. Arvelo, and H. Altug, “Metasurface-based molecular biosensing aided by artificial intelligence,” Angewandte Chemie Int. Ed. 58(42), 14810–14822 (2019).
[Crossref]

Tornatore, M.

F. Musumeci, C. Rottondi, A. Nag, I. Macaluso, D. Zibar, M. Ruffini, and M. Tornatore, “An overview on application of machine learning techniques in optical networks,” IEEE Commun. Surv. Tutorials 21(2), 1383–1408 (2019).
[Crossref]

Touresky, D.

Y. LeCun, D. Touresky, G. Hinton, and T. Sejnowski, “A theoretical framework for back-propagation,” in Proceedings of the 1988 Connectionist Models Summer School, vol. 1 (CMU, Pittsburgh, Pa: Morgan Kaufmann, 1988), pp. 21–28.

Udem, Th.

R. Holzwarth, Th. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett. 85(11), 2264–2267 (2000).
[Crossref]

Vincetti, L.

A. Cucinotta, S. Selleri, L. Vincetti, and M. Zoboli, “Holey fiber analysis through the finite-element method,” IEEE Photonics Technol. Lett. 14(11), 1530–1532 (2002).
[Crossref]

Wadsworth, W. J.

W. J. Wadsworth, A. Ortigosa-Blanch, J. C. Knight, T. A. Birks, T.-P. M. Man, and P. St. J. Russell, “Supercontinuum generation in photonic crystal fibers and optical fiber tapers: a novel light source,” J. Opt. Soc. Am. B 19(9), 2148–2155 (2002).
[Crossref]

R. Holzwarth, Th. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett. 85(11), 2264–2267 (2000).
[Crossref]

Weck, A.

J. Baxter, A. C. Lesina, J.-M. Guay, A. Weck, P. Berini, and L. Ramunno, “Plasmonic colours predicted by deep learning,” Sci. Rep. 9(1), 8074 (2019).
[Crossref]

Yang, E.

A. Paszke, S. Gross, S. Chintala, G. Chanan, E. Yang, Z. DeVito, Z. Lin, A. Desmaison, L. Antiga, and A. Lerer, “Automatic differentiation in PyTorch,” in NIPS Autodiff Workshop, (2017).

Yang, J.

J. Jiang, D. Sell, S. Hoyer, J. Hickey, J. Yang, and J. A. Fan, “Free-form diffractive metagrating design based on generative adversarial networks,” ACS Nano 13(8), 8872–8878 (2019).
[Crossref]

Yu, C.-P.

C.-P. Yu and H.-C. Chang, “Applications of the finite difference mode solution method to photonic crystal structures,” Opt. Quantum Electron. 36(1-3), 145–163 (2004).
[Crossref]

Zandehshahvar, M.

Y. Kiarashinejad, S. Abdollahramezani, M. Zandehshahvar, O. Hemmatyar, and A. Adibi, “Deep learning reveals underlying physics of light-matter interactions in nanophotonic devices,” arXiv preprint arXiv:1905.06889 (2019).

Y. Kiarashinejad, M. Zandehshahvar, S. Abdollahramezani, O. Hemmatyar, R. Pourabolghasem, and A. Adibi, “Knowledge discovery in nanophotonics using geometric deep learning,” arXiv preprint arXiv:1909.07330 (2019).

Zibar, D.

F. Musumeci, C. Rottondi, A. Nag, I. Macaluso, D. Zibar, M. Ruffini, and M. Tornatore, “An overview on application of machine learning techniques in optical networks,” IEEE Commun. Surv. Tutorials 21(2), 1383–1408 (2019).
[Crossref]

Zoboli, M.

A. Cucinotta, S. Selleri, L. Vincetti, and M. Zoboli, “Holey fiber analysis through the finite-element method,” IEEE Photonics Technol. Lett. 14(11), 1530–1532 (2002).
[Crossref]

ACS Nano (2)

W. Ma, F. Cheng, and Y. Liu, “Deep-learning-enabled on-demand design of chiral metamaterials,” ACS Nano 12(6), 6326–6334 (2018).
[Crossref]

J. Jiang, D. Sell, S. Hoyer, J. Hickey, J. Yang, and J. A. Fan, “Free-form diffractive metagrating design based on generative adversarial networks,” ACS Nano 13(8), 8872–8878 (2019).
[Crossref]

Angewandte Chemie Int. Ed. (1)

A. Tittl, A. John-Herpin, A. Leitis, E. R. Arvelo, and H. Altug, “Metasurface-based molecular biosensing aided by artificial intelligence,” Angewandte Chemie Int. Ed. 58(42), 14810–14822 (2019).
[Crossref]

Appl. Numer. Math. (1)

R. A. Norton and R. Scheichl, “Planewave expansion methods for photonic crystal fibres,” Appl. Numer. Math. 63, 88–104 (2013).
[Crossref]

IEE Proc.: Optoelectron. (1)

S. S. A. Obayya, B. M. A. Rahman, and K. T. V. Grattan, “Accurate finite element modal solution of photonic crystal fibres,” IEE Proc.: Optoelectron. 152(5), 241–246 (2005).
[Crossref]

IEEE Commun. Surv. Tutorials (1)

F. Musumeci, C. Rottondi, A. Nag, I. Macaluso, D. Zibar, M. Ruffini, and M. Tornatore, “An overview on application of machine learning techniques in optical networks,” IEEE Commun. Surv. Tutorials 21(2), 1383–1408 (2019).
[Crossref]

IEEE Photonics Technol. Lett. (3)

A. Cucinotta, S. Selleri, L. Vincetti, and M. Zoboli, “Holey fiber analysis through the finite-element method,” IEEE Photonics Technol. Lett. 14(11), 1530–1532 (2002).
[Crossref]

M. R. Karim, H. Ahmad, and B. M. A. Rahman, “All-normal dispersion chalcogenide PCF for ultraflat mid-infrared supercontinuum generation,” IEEE Photonics Technol. Lett. 29(21), 1792–1795 (2017).
[Crossref]

P. K. Cheo, A. Liu, and G. G. King, “A high-brightness laser beam from a phase-locked multicore Yb-doped fiber laser array,” IEEE Photonics Technol. Lett. 13(5), 439–441 (2001).
[Crossref]

J. Lightwave Technol. (3)

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

Meas. Sci. Technol. (1)

T. M. Monro, W. Belardi, K. Furusawa, J. C. Baggett, N. G. R. Broderick, and D. J. Richardson, “Sensing with microstructured optical fibres,” Meas. Sci. Technol. 12(7), 854–858 (2001).
[Crossref]

Opt. Express (3)

Opt. Lett. (1)

Opt. Quantum Electron. (1)

C.-P. Yu and H.-C. Chang, “Applications of the finite difference mode solution method to photonic crystal structures,” Opt. Quantum Electron. 36(1-3), 145–163 (2004).
[Crossref]

Optica (1)

Phys. Rev. Lett. (2)

R. Holzwarth, Th. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett. 85(11), 2264–2267 (2000).
[Crossref]

F. Benabid, G. Bouwmans, J. C. Knight, P. St. J. Russell, and F. Couny, “Ultrahigh efficiency laser wavelength conversion in a gas-filled hollow core photonic crystal fiber by pure stimulated rotational Raman scattering in molecular hydrogen,” Phys. Rev. Lett. 93(12), 123903 (2004).
[Crossref]

Sci. Rep. (1)

J. Baxter, A. C. Lesina, J.-M. Guay, A. Weck, P. Berini, and L. Ramunno, “Plasmonic colours predicted by deep learning,” Sci. Rep. 9(1), 8074 (2019).
[Crossref]

Science (1)

F. Benabid, J. C. Knight, G. Antonopoulos, and P. St. J. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298(5592), 399–402 (2002).
[Crossref]

Sensors (1)

M. De, T. K. Gangopadhyay, and V. K. Singh, “Prospects of photonic crystal fiber as physical sensor: An overview,” Sensors 19(3), 464 (2019).
[Crossref]

Other (7)

P. St. J. Russell, “Photonic crystal fibers: Basics and applications,” in Optical Fiber Telecommunications VA, (Elsevier, 2008), pp. 485–522.

Y. Kiarashinejad, S. Abdollahramezani, M. Zandehshahvar, O. Hemmatyar, and A. Adibi, “Deep learning reveals underlying physics of light-matter interactions in nanophotonic devices,” arXiv preprint arXiv:1905.06889 (2019).

Y. Kiarashinejad, M. Zandehshahvar, S. Abdollahramezani, O. Hemmatyar, R. Pourabolghasem, and A. Adibi, “Knowledge discovery in nanophotonics using geometric deep learning,” arXiv preprint arXiv:1909.07330 (2019).

D. P. Kingma and J. L. Ba, “Adam: A method for stochastic optimization,” arXiv preprint arXiv:1412.6980 (2014).

Y. LeCun, D. Touresky, G. Hinton, and T. Sejnowski, “A theoretical framework for back-propagation,” in Proceedings of the 1988 Connectionist Models Summer School, vol. 1 (CMU, Pittsburgh, Pa: Morgan Kaufmann, 1988), pp. 21–28.

S. Chugh, S. Ghosh, A. Gulistan, and B. M. A. Rahman, “Machine learning regression approach to the nanophotonic waveguide analyses,” http://dx.doi.org/10.1109/JLT.2019.2946572 (2019).

A. Paszke, S. Gross, S. Chintala, G. Chanan, E. Yang, Z. DeVito, Z. Lin, A. Desmaison, L. Antiga, and A. Lerer, “Automatic differentiation in PyTorch,” in NIPS Autodiff Workshop, (2017).

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Figures (11)

Fig. 1.
Fig. 1. Cross-section of a solid-core hexagonal PCF with five rings of air holes.
Fig. 2.
Fig. 2. Artificial neural network (ANN) representation with one input layer (5 input nodes), three hidden layers (50 nodes in each layer), and one output layer (4 output nodes).
Fig. 3.
Fig. 3. The scatter plot of training dataset produced by ANN for different epochs, comparing $\textit {n}_{\textit {eff}}$ values from the simulation (x-axis) and the ANN predictions (y-axis) along with the ideal linear model (y = x). Inset shows the mean squared error (${\textrm{MSE}}$) obtained with epochs when training the ANN model.
Fig. 4.
Fig. 4. Comparing actual (simulation) and predicted (ANN model) $\textit {n}_{\textit {eff}}$ for different epochs at an unknown pitch, $\Lambda $ = 1.5 µm, $\textit {d}$/$\Lambda $ = 0.7, and $\textit {N}_{\textit {r}}$ = 4.
Fig. 5.
Fig. 5. (a) The scatter plot of training dataset produced by ANN for different epochs, comparing $\textit {A}_{\textit {eff}}$ values from the simulation (x-axis) and the ANN predictions (y-axis) along with the ideal linear model (y = x), (b) Comparing actual (simulation) and predicted (ANN model) $\textit {A}_{\textit {eff}}$ for different epochs at an unknown pitch, $\Lambda $ = 1.5 µm, $\textit {d}$/$\Lambda $ = 0.7, and $\textit {N}_{\textit {r}}$ = 4.
Fig. 6.
Fig. 6. Comparing actual (simulation) and predicted (ANN model) $\textit {A}_{\textit {eff}}$ for different datasets at an unknown pitch, $\Lambda $ = 1.5 µm, $\textit {d}$/$\Lambda $ = 0.7, and $\textit {N}_{\textit {r}}$ = 4.
Fig. 7.
Fig. 7. (a) The scatter plot of training dataset produced by ANN for different epochs, comparing $\textit {D}$ values from the simulation (x-axis) and the ANN predictions (y-axis) along with the ideal linear model (y = x), (b) Comparing actual (simulation) and predicted (ANN model) $\textit {D}$ for different epochs at an unknown pitch, $\Lambda $ = 1.5 µm, $\textit {d}$/$\Lambda $ = 0.7, and $\textit {N}_{\textit {r}}$ = 4.
Fig. 8.
Fig. 8. The scatter plot of training dataset produced by ANN for different epochs, comparing $\alpha_{\textit {c}}$ values from the simulation (x-axis) and the ANN predictions (y-axis) along with the ideal linear model (y = x).
Fig. 9.
Fig. 9. Actual values of $\alpha_{\textit {c}}$ from the simulation and in logarithm with wavelength for a general case.
Fig. 10.
Fig. 10. (a) The scatter plot of training dataset produced by ANN for different epochs, comparing $\alpha_{\textit {c}}$ values in logarithm from the simulation (x-axis) and the ANN predictions (y-axis) along with the ideal linear model (y = x), (b) Comparing actual (simulation) and predicted (ANN model) $\alpha_{\textit {c}}$ in logarithm for different epochs at an unknown pitch, $\Lambda $ = 1.5 µm, $\textit {d}$/$\Lambda $ = 0.7, and $\textit {N}_{\textit {r}}$ = 4.
Fig. 11.
Fig. 11. Comparing actual values from the simulation and ANN model for different epochs at an unknown pitch, $\Lambda $ = 1.5 µm, $\textit {d}$/$\Lambda $ = 0.7, and $\textit {N}_{\textit {r}}$ = 4 or 5.

Tables (1)

Tables Icon

Table 1. Simulation times with Lumerical Mode Solutions and ANN model.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

A eff = ( Ω | H t | 2   dxdy ) 2 Ω | H t | 4   dxdy
D = λ c d 2   Re ( n eff ) d   λ 2
α c = 8.686 × 10 6   k 0   Im ( n eff )         dB / m