Abstract

In this paper, we propose a novel approach to achieve spectrum prediction, parameter fitting, inverse design, and performance optimization for the plasmonic waveguide-coupled with cavities structure (PWCCS) based on artificial neural networks (ANNs). The Fano resonance and plasmon-induced transparency effect originated from the PWCCS have been selected as illustrations to verify the effectiveness of ANNs. We use the genetic algorithm to design the network architecture and select the hyperparameters for ANNs. Once ANNs are trained by using a small sampling of the data generated by the Monte Carlo method, the transmission spectra predicted by the ANNs are quite approximate to the simulated results. The physical mechanisms behind the phenomena are discussed theoretically, and the uncertain parameters in the theoretical models are fitted by utilizing the trained ANNs. More importantly, our results demonstrate that this model-driven method not only realizes the inverse design of the PWCCS with high precision but also optimizes some critical performance metrics for the transmission spectrum. Compared with previous works, we construct a novel model-driven analysis method for the PWCCS that is expected to have significant applications in the device design, performance optimization, variability analysis, defect detection, theoretical modeling, optical interconnects, and so on.

© 2019 Chinese Laser Press

Full Article  |  PDF Article
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2018 (10)

S. Inampudi and H. Mosallaei, “Neural network based design of metagratings,” Appl. Phys. Lett. 112, 241102 (2018).
[Crossref]

J. Peurifoy, Y. Shen, L. Jing, Y. Yang, F. Canorenteria, B. Delacy, M. Tegmark, J. D. Joannopoulos, and M. Soljacic, “Nanophotonic particle simulation and inverse design using artificial neural networks,” Sci. Adv. 4, eaar4206 (2018).
[Crossref]

D. Liu, Y. Tan, E. Khoram, and Z. Yu, “Training deep neural networks for the inverse design of nanophotonic structures,” ACS Photon. 5, 1365–1369 (2018).
[Crossref]

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

T. W. Hughes, M. Minkov, I. A. Williamson, and S. Fan, “Adjoint method and inverse design for nonlinear nanophotonic devices,” ACS Photon. 5, 4781–4787 (2018).
[Crossref]

P.-H. Fu, S.-C. Lo, P.-C. Tsai, K.-L. Lee, and P.-K. Wei, “Optimization for gold nanostructure-based surface plasmon biosensors using a microgenetic algorithm,” ACS Photon. 5, 2320–2327 (2018).
[Crossref]

A. da Silva Ferreira, C. H. da Silva Santos, M. S. Gonçalves, and H. E. H. Figueroa, “Towards an integrated evolutionary strategy and artificial neural network computational tool for designing photonic coupler devices,” Appl. Soft Comput. 65, 1–11 (2018).
[Crossref]

M. Turduev, E. Bor, C. Latifoglu, I. H. Giden, Y. S. Hanay, and H. Kurt, “Ultra-compact photonic structure design for strong light confinement and coupling into nano-waveguide,” J. Lightwave Technol. 36, 2812–2819 (2018).
[Crossref]

E. Bor, O. Alparslan, M. Turduev, Y. S. Hanay, H. Kurt, S. I. Arakawa, and M. Murata, “Integrated silicon photonic device design by attractor selection mechanism based on artificial neural networks: optical coupler and asymmetric light transmitter,” Opt. Express 26, 29032–29044 (2018).
[Crossref]

E. Bor, C. Babayigit, H. Kurt, K. Staliunas, and M. Turduev, “Directional invisibility by genetic optimization,” Opt. Lett. 43, 5781–5784 (2018).
[Crossref]

2017 (8)

H. Lu, X. Gan, D. Mao, and J. Zhao, “Graphene-supported manipulation of surface plasmon polaritons in metallic nanowaveguides,” Photon. Res. 5, 162–167 (2017).
[Crossref]

H. Cui, X. Sun, and Z. Yu, “Genetic-algorithm-optimized wideband on-chip polarization rotator with an ultrasmall footprint,” Opt. Lett. 42, 3093–3096 (2017).
[Crossref]

Z. Yu, H. Cui, and X. Sun, “Genetically optimized on-chip wideband ultracompact reflectors and Fabry-Perot cavities,” Photon. Res. 5, B15–B19 (2017).
[Crossref]

T. Zhang, J. Dai, Y. Dai, Y. Fan, X. Han, J. Li, F. Yin, Y. Zhou, and K. Xu, “Dynamically tunable plasmon induced absorption in graphene-assisted metallodielectric grating,” Opt. Express 25, 26221–26233 (2017).
[Crossref]

T. Zhang, J. Dai, Y. Dai, Y. Fan, X. Han, J. Li, F. Yin, Y. Zhou, and K. Xu, “Tunable plasmon induced transparency in a metallodielectric grating coupled with graphene metamaterials,” J. Lightwave Technol. 35, 5142–5149 (2017).
[Crossref]

M. Qin, L. Wang, X. Zhai, D. Chen, and S. Xia, “Generating and manipulating high quality factors of Fano resonance in nanoring resonator by stacking a half nanoring,” Nano. Res. Lett. 12, 578 (2017).
[Crossref]

G. Carleo and M. Troyer, “Solving the quantum many-body problem with artificial neural networks,” Science 355, 602–606 (2017).
[Crossref]

Y. Shen, N. C. Harris, S. Skirlo, M. Prabhu, T. Baehr-Jones, M. Hochberg, X. Sun, S. Zhao, H. Larochelle, D. Englund, and M. Soljačić, “Deep learning with coherent nanophotonic circuits,” Nat. Photonics 11, 441–446 (2017).
[Crossref]

2016 (8)

B. Shahriari, K. Swersky, Z. Wang, R. P. Adams, and N. De Freitas, “Taking the human out of the loop: a review of Bayesian optimization,” Proc. IEEE 104, 148–175 (2016).
[Crossref]

Z. Chai, X. Hu, H. Yang, and Q. Gong, “All-optical tunable on-chip plasmon-induced transparency based on two surface-plasmon-polaritons absorption,” Appl. Phys. Lett. 108, 151104 (2016).
[Crossref]

X. Han, T. Wang, B. Liu, Y. He, and Y. Zhu, “Tunable triple plasmon-induced transparencies in dual T-shaped cavities side-coupled waveguide,” IEEE Photon. Technol. Lett. 28, 347–350 (2016).
[Crossref]

Z. Lin, X. Liang, M. Lončar, S. G. Johnson, and A. W. Rodriguez, “Cavity-enhanced second-harmonic generation via nonlinear-overlap optimization,” Optica 3, 233–238 (2016).
[Crossref]

R. R. Andrawis, M. A. Swillam, M. A. El-Gamal, and E. A. Soliman, “Artificial neural network modeling of plasmonic transmission lines,” Appl. Opt. 55, 2780–2790 (2016).
[Crossref]

L. F. Frellsen, Y. Ding, O. Sigmund, and L. H. Frandsen, “Topology optimized mode multiplexing in silicon-on-insulator photonic wire waveguides,” Opt. Express 24, 16866–16873 (2016).
[Crossref]

J. C. Mak, C. Sideris, J. Jeong, A. Hajimiri, and J. K. Poon, “Binary particle swarm optimized 2 × 2 power splitters in a standard foundry silicon photonic platform,” Opt. Lett. 41, 3868–3871 (2016).
[Crossref]

A. Ahmadivand, R. Sinha, B. Gerislioglu, M. Karabiyik, N. Pala, and M. Shur, “Transition from capacitive coupling to direct charge transfer in asymmetric terahertz plasmonic assemblies,” Opt. Lett. 41, 5333–5336 (2016).
[Crossref]

2015 (6)

P. Ghamisi and J. A. Benediktsson, “Feature selection based on hybridization of genetic algorithm and particle swarm optimization,” IEEE Geosci. Remote Sens. Lett. 12, 309–313 (2015).
[Crossref]

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

B. Shen, P. Wang, R. Polson, and R. Menon, “An integrated-nanophotonics polarization beamsplitter with 2.4 × 2.4 μm2 footprint,” Nat. Photonics 9, 378–382 (2015).
[Crossref]

Y. LeCun, Y. Bengio, and G. Hinton, “Deep learning,” Nature 521, 436–444 (2015).
[Crossref]

X. Han, T. Wang, X. Li, B. Liu, Y. He, and J. Tang, “Ultrafast and low-power dynamically tunable plasmon-induced transparencies in compact aperture-coupled rectangular resonators,” J. Lightwave Technol. 33, 5133–5139 (2015).
[Crossref]

X. Han, T. Wang, X. Li, S. Xiao, and Y. Zhu, “Dynamically tunable plasmon induced transparency in a graphene-based nanoribbon waveguide coupled with graphene rectangular resonators structure on sapphire substrate,” Opt. Express 23, 31945–31955 (2015).
[Crossref]

2014 (6)

T. Wang, Y. Zhang, Z. Hong, and Z. Han, “Analogue of electromagnetically induced transparency in integrated plasmonics with radiative and subradiant resonators,” Opt. Express 22, 21529–21534 (2014).
[Crossref]

Z. He, H. Li, S. Zhan, G. Cao, and B. Li, “Combined theoretical analysis for plasmon-induced transparency in waveguide systems,” Opt. Lett. 39, 5543–5546 (2014).
[Crossref]

Z. Zhang, L. Zhang, H. Li, and H. Chen, “Plasmon induced transparency in a surface plasmon polariton waveguide with a comb line slot and rectangle cavity,” Appl. Phys. Lett. 104, 231114 (2014).
[Crossref]

Z. Chen and L. Yu, “Multiple Fano resonances based on different waveguide modes in a symmetry breaking plasmonic system,” IEEE Photon. J. 6, 4802208 (2014).
[Crossref]

Y. Zhu, X. Hu, H. Yang, and Q. Gong, “On-chip plasmon-induced transparency based on plasmonic coupled nanocavities,” Sci. Rep. 4, 3752 (2014).
[Crossref]

Z. Chai, X. Hu, Y. Zhu, S. Sun, H. Yang, and Q. Gong, “Ultracompact chip-integrated electromagnetically induced transparency in a single plasmonic composite nanocavity,” Adv. Opt. Mater. 2, 320–325 (2014).
[Crossref]

2013 (2)

A. B. Khanikaev, C. Wu, and G. Shvets, “Fano-resonant metamaterials and their applications,” Nanophotonics 2, 247–264 (2013).
[Crossref]

H. Li, L. Wang, J. Liu, Z. Huang, B. Sun, and X. Zhai, “Investigation of the graphene based planar plasmonic filters,” Appl. Phys. Lett. 103, 211104 (2013).
[Crossref]

2012 (3)

2011 (1)

C. Wu, A. B. Khanikaev, and G. Shvets, “Broadband slow light metamaterial based on a double-continuum Fano resonance,” Phys. Rev. Lett. 106, 107403 (2011).
[Crossref]

2010 (3)

G. C. Cawley and N. L. Talbot, “On over-fitting in model selection and subsequent selection bias in performance evaluation,” J. Mach. Learn. Res. 11, 2079–2107 (2010).

R. D. Kekatpure, E. S. Barnard, W. Cai, and M. L. Brongersma, “Phase-coupled plasmon-induced transparency,” Phys. Rev. Lett. 104, 243902 (2010).
[Crossref]

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4, 83–91 (2010).
[Crossref]

2008 (1)

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008).
[Crossref]

2002 (1)

K. O. Stanley and R. Miikkulainen, “Evolving neural networks through augmenting topologies,” Evol. Comput. 10, 99–127 (2002).
[Crossref]

1972 (1)

P. B. Johnson and R. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[Crossref]

Adams, R. P.

B. Shahriari, K. Swersky, Z. Wang, R. P. Adams, and N. De Freitas, “Taking the human out of the loop: a review of Bayesian optimization,” Proc. IEEE 104, 148–175 (2016).
[Crossref]

Ahmadivand, A.

Alparslan, O.

Andrawis, R. R.

Arakawa, S. I.

Arieli, U.

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

Babayigit, C.

Babinec, T. M.

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

Baehr-Jones, T.

Y. Shen, N. C. Harris, S. Skirlo, M. Prabhu, T. Baehr-Jones, M. Hochberg, X. Sun, S. Zhao, H. Larochelle, D. Englund, and M. Soljačić, “Deep learning with coherent nanophotonic circuits,” Nat. Photonics 11, 441–446 (2017).
[Crossref]

Baker, B.

B. Baker, O. Gupta, N. Naik, and R. Raskar, “Designing neural network architectures using reinforcement learning,” arXiv:1611.02167 (2016).

Barnard, E. S.

R. D. Kekatpure, E. S. Barnard, W. Cai, and M. L. Brongersma, “Phase-coupled plasmon-induced transparency,” Phys. Rev. Lett. 104, 243902 (2010).
[Crossref]

Benediktsson, J. A.

P. Ghamisi and J. A. Benediktsson, “Feature selection based on hybridization of genetic algorithm and particle swarm optimization,” IEEE Geosci. Remote Sens. Lett. 12, 309–313 (2015).
[Crossref]

Bengio, Y.

Y. LeCun, Y. Bengio, and G. Hinton, “Deep learning,” Nature 521, 436–444 (2015).
[Crossref]

Bor, E.

Bozhevolnyi, S. I.

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Z. Chai, X. Hu, Y. Zhu, S. Sun, H. Yang, and Q. Gong, “Ultracompact chip-integrated electromagnetically induced transparency in a single plasmonic composite nanocavity,” Adv. Opt. Mater. 2, 320–325 (2014).
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Y. Shen, N. C. Harris, S. Skirlo, M. Prabhu, T. Baehr-Jones, M. Hochberg, X. Sun, S. Zhao, H. Larochelle, D. Englund, and M. Soljačić, “Deep learning with coherent nanophotonic circuits,” Nat. Photonics 11, 441–446 (2017).
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D. Liu, Y. Tan, E. Khoram, and Z. Yu, “Training deep neural networks for the inverse design of nanophotonic structures,” ACS Photon. 5, 1365–1369 (2018).
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Tegmark, M.

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Figures (12)

Fig. 1.
Fig. 1. Schematic diagrams of the (a) THRC system, (b) FORC system, and (c) FIRC system.
Fig. 2.
Fig. 2. (a) Simulated transmission spectrum of the THRC system for Ag with loss (red solid line) and without loss (orange solid line), and theoretical transmission spectrum of the THRC system (blue dashed line); (b) group index and loss factor of the THRC system. The insets are simulated magnetic field distributions for the incident light at wavelengths of (A) 851 nm, (B) 893 nm, (C) 955 nm, (D) 1005 nm, and (E) 1048 nm.
Fig. 3.
Fig. 3. (a) Simulated transmission spectrum of the FORC system for g3=20  nm (red solid line) and 30 nm (orange solid line); theoretical transmission spectrum of the FORC system (blue circles); simulated transmission spectrum of the FORC system, which includes only cavities 1, 2, 4 (orange dashed line) and cavities 1, 2 (blue dashed line); (b) group index of the FORC system. The insets are calculated magnetic field distributions for the incident light at wavelengths of (A) 0.851 μm, (B) 0.893 μm, (C) 0.953 μm, (D) 1.01 μm, (E) 1.056 μm, (F) 1.168 μm, and (G) 1.18 μm.
Fig. 4.
Fig. 4. (a) Simulated transmission spectrum of the FIRC system for g4=40  nm (red solid line) and 60 nm (orange solid line); theoretical transmission spectrum of the FIRC system (blue dashed line); (b) group index of the FIRC system. The insets are calculated magnetic field distributions for the incident light at wavelengths of (A) 851 nm, (B) 893 nm, (C) 954 nm, (D) 1010 nm, (E) 1056 nm, (F) 1151 nm, (G) 1160 nm, (H) 1178 nm, and (I) 1189 nm.
Fig. 5.
Fig. 5. (a) Diagram of the ANNs applied in the spectrum prediction; (b) fitness for different generations in the spectrum prediction; (c) training losses for different iterations in the spectrum prediction; FDTD simulated transmission spectra and ANN-predicted transmission spectra for the (d) THRC, (e) FORC, and (f) FIRC systems; (g) fitness for different generations in the parameter fitting. The inset reveals the training losses for different iterations in the parameter fitting.
Fig. 6.
Fig. 6. (a) Diagram of the ANNs applied in the inverse design and performance optimization problems; comparison results between the real structure parameters and ANN-predicted structure parameters for the (b) THRC, (c) FORC, and (d) FIRC systems. The insets in (b)–(d) are the FDTD-simulated transmission spectra corresponding to the real structures (red solid line) and ANN-predicted structure parameters (blue dashed line); (e) transmittance optimization for the THRC system; (f) bandwidth optimization for the FORC system; (g) transmittance optimization for the FIRC system.
Fig. 7.
Fig. 7. Prediction accuracies for different numbers of training instances in the (a) spectrum prediction and (b) inverse design.
Fig. 8.
Fig. 8. (a) The dispersion of Ag described by using the Drude model (red and blue solid lines) and experimental data (red and blue diamond-shaped markers), respectively; (b) transmission of THRC system when εAg is described by the Drude model (cyan solid line) and is set as a constant equal to 22.217+0.26i (orange solid line), 49.187+0.758i (yellow solid line), and 85.667+1.665i (purple solid line), corresponding to the εAg obtained by the Drude model at λ=0.7, 1, and 1.3 μm, respectively; (c) theoretically (triangle and inverted triangle markers) and numerically (blue solid and dashed lines) obtained nMDM of SPP mode supported by the MDM waveguide in the 2D case, and the numerically obtained nMDM in the 3D case at tcavity=300  nm (cyan solid and dashed lines), tcavity=500  nm (red solid and dashed lines), tcavity=700  nm (purple solid and dashed lines), and tcavity=900  nm (orange solid and dashed lines), respectively. The inset is the schematic of the 3D MDM cavity.
Fig. 9.
Fig. 9. Schematic diagram of the THRC system.
Fig. 10.
Fig. 10. Schematic of the FORC system.
Fig. 11.
Fig. 11. Schematic of the FIRC system.
Fig. 12.
Fig. 12. (a) Fitness of GA (blue) and PSO (black) for different generations in the inverse design; (b) comparison results between the ANN-predicted parameters, GA-optimized, and PSO-optimized structure parameters; (c) FDTD-simulated transmission spectra calculated for the ANN-predicted, GA-optimized, and PSO-optimized structure parameters.

Equations (25)

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

1J2=1i=0N(ytrueiypredi)2i=0N(ytrueiypredi/N)2,
damdt=(jωmγm)am+jγm(s(m1)++sm),
s(m1)=sm+jγmam,
sm+=s(m1)++jγmam.
s(m1)=γmpmγmsm+pm2γmpmγmsm+,
s(m1)+=pmpmγmsm+γmpmγmsm+,
(s(m1)s(m1)+)=Mm(smsm+),
Mm=1pmγm(pm2γmγmγmpm).
(s0s0+)=M1(ejφ100ejφ1)M2(ejφ200ejφ2)M3(s3s3+),
tanh(wπnMDM2εaλ)=εanMDM2εmεmnMDM2εa.
MallTHRC=M1(ejφ100ejφ1)M2(ejφ200ejφ2)M3.
TTHRC=[(p1γ1)(p2γ2)(p3γ3)γ1γ3(2γ2p2)ej(φ1+φ2)p1γ2γ3ej(φ2φ1)γ1γ2p3ej(φ1φ2)+p1p2p3ej(φ1+φ2)]2.
da3dt=(jω3γ3γ4)a3+jγ3(s2++s3)+jγ4a4,
da4dt=(jω4γ4)a4+jγ4a3.
M3FORC=1p3FORCγ3(p3FORC2γ3γ3γ3p3FORC),
TFORC=[(p1γ1)(p2γ2)(p3FORCγ3)γ1γ3(2γ2p2)ej(φ1+φ2)p1γ2γ3ej(φ2φ1)γ1γ2p3FORCej(φ1φ2)+p1p2p3FORCej(φ1+φ2)]2.
da3dt=(jω3γ3γ4)a3+jγ3(s2++s3)+jγ4a4,
da4dt=(jω4γ4γ5)a4+jγ4a3+jγ5a5,
da5dt=(jω5γ5)a5+jγ5a4.
M3FIRC=1p3FIRCγ3(p3FIRC2γ3γ3γ3p3FIRC),
p3FIRC=j(ωω3)+γ3+γ4+γ4j(ωω4)+γ4+γ5+γ5j(ωω5)+γ5.
TFIRC=[(p1γ1)(p2γ2)(p3FIRCγ3)γ1γ3(2γ2p2)ej(φ1+φ2)p1γ2γ3ej(φ2φ1)γ1γ2p3FIRCej(φ1φ2)+p1p2p3FIRCej(φ1+φ2)]2.
F=λminλmax|S0(λ)S(λ)|.
Vik+1=WVik+c1r1(pikXik)+c2r2(gkdXik),
Xik+1=Xik+Vik+1.