Abstract

Vertical coupling using a diffraction grating is a convenient way to couple light into an optical waveguide. Several optimization approaches have been suggested in order to design such a coupler; however, most of them are implemented using algorithm-based modelling. In this paper, we suggest an intuitive method based on S-matrix formalism for analytically optimize 3-port vertical grating coupler devices. The suggested method is general and can be applied to any 3-port coupler device in order to achieve an optimal design based on user constrains. The simplicity of the model allows reduction of the optimization to two variables and the location of an absolute optimal operation point in a 2D contour map. Accordingly, in an ideal device near 100% coupling efficiency and insignificant return loss could be achieved. Our model results show good agreement with numerical finite difference time domain (FDTD) simulations and can predict the general tendencies and sensitivities of the device’s behavior to changes in design parameters. We further apply our model to a previously reported high contrast uni-directional grating coupler device and show that additional improvement in the coupling efficiency is achievable for that layout.

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

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References

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]

2018 (2)

2017 (3)

2016 (2)

2015 (2)

2007 (1)

2005 (1)

2002 (1)

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38(7), 949–955 (2002).
[Crossref]

Baets, R.

G. Roelkens, D. Van Thourhout, and R. Baets, “High efficiency grating coupler between silicon-on-insulator waveguides and perfectly vertical optical fibers,” Opt. Lett. 32(11), 1495–1497 (2007).
[Crossref] [PubMed]

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38(7), 949–955 (2002).
[Crossref]

Bienstman, P.

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38(7), 949–955 (2002).
[Crossref]

Bogaerts, W.

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38(7), 949–955 (2002).
[Crossref]

Bunkowski, A.

Burmeister, O.

Chang-Hasnain, C.

Chen, E.

Chen, H.

Z. Zhang, B. Huang, Z. Zhang, C. Cheng, H. Liu, H. Li, and H. Chen, “Highly efficient vertical fiber interfacing grating coupler with bilayer anti-reflection cladding and backside metal mirror,” Opt. Laser Technol.  90(December 2015), 136–143 (2017)

Chen, K.

Chen, Y.

Cheng, C.

Z. Zhang, B. Huang, Z. Zhang, C. Cheng, H. Liu, H. Li, and H. Chen, “Highly efficient vertical fiber interfacing grating coupler with bilayer anti-reflection cladding and backside metal mirror,” Opt. Laser Technol.  90(December 2015), 136–143 (2017)

Dai, M.

Danzmann, K.

De Mesel, K.

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38(7), 949–955 (2002).
[Crossref]

Demeter-Finzi, A.

A. Demeter-Finzi and S. Ruschin, “Back-reflecting interferometeric sensor based on a single grating on a planar waveguide,” J. Opt. 18(1), 015801 (2016).
[Crossref]

Gong, C.

He, S.

Huang, B.

Z. Zhang, B. Huang, Z. Zhang, C. Cheng, H. Liu, H. Li, and H. Chen, “Highly efficient vertical fiber interfacing grating coupler with bilayer anti-reflection cladding and backside metal mirror,” Opt. Laser Technol.  90(December 2015), 136–143 (2017)

Jin, C.

Krauss, T. F.

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38(7), 949–955 (2002).
[Crossref]

Li, H.

Z. Zhang, B. Huang, Z. Zhang, C. Cheng, H. Liu, H. Li, and H. Chen, “Highly efficient vertical fiber interfacing grating coupler with bilayer anti-reflection cladding and backside metal mirror,” Opt. Laser Technol.  90(December 2015), 136–143 (2017)

Liu, H.

Z. Zhang, B. Huang, Z. Zhang, C. Cheng, H. Liu, H. Li, and H. Chen, “Highly efficient vertical fiber interfacing grating coupler with bilayer anti-reflection cladding and backside metal mirror,” Opt. Laser Technol.  90(December 2015), 136–143 (2017)

Liu, L.

Liu, X.

Lu, M.

Ma, L.

Michaels, A.

Moerman, I.

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38(7), 949–955 (2002).
[Crossref]

Na, N.

Piggott, A. Y.

Roelkens, G.

Rong, H.

Ruschin, S.

A. Demeter-Finzi and S. Ruschin, “Back-reflecting interferometeric sensor based on a single grating on a planar waveguide,” J. Opt. 18(1), 015801 (2016).
[Crossref]

Sapra, N. V.

Schnabel, R.

Shi, Y.

Su, L.

Taillaert, D.

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38(7), 949–955 (2002).
[Crossref]

Trivedi, R.

Tseng, H. L.

Van Daele, P.

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38(7), 949–955 (2002).
[Crossref]

Van Thourhout, D.

Vercruysse, D.

Verstuyft, S.

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38(7), 949–955 (2002).
[Crossref]

Vuckovic, J.

Wang, S.

Xiang, T.

Xu, Y.

Yablonovitch, E.

Yang, W.

Zhang, C.

Zhang, J.

Zhang, Z.

Z. Zhang, B. Huang, Z. Zhang, C. Cheng, H. Liu, H. Li, and H. Chen, “Highly efficient vertical fiber interfacing grating coupler with bilayer anti-reflection cladding and backside metal mirror,” Opt. Laser Technol.  90(December 2015), 136–143 (2017)

Z. Zhang, B. Huang, Z. Zhang, C. Cheng, H. Liu, H. Li, and H. Chen, “Highly efficient vertical fiber interfacing grating coupler with bilayer anti-reflection cladding and backside metal mirror,” Opt. Laser Technol.  90(December 2015), 136–143 (2017)

Zhu, L.

IEEE J. Quantum Electron. (1)

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38(7), 949–955 (2002).
[Crossref]

J. Opt. (1)

A. Demeter-Finzi and S. Ruschin, “Back-reflecting interferometeric sensor based on a single grating on a planar waveguide,” J. Opt. 18(1), 015801 (2016).
[Crossref]

Opt. Express (5)

Opt. Laser Technol (1)

Z. Zhang, B. Huang, Z. Zhang, C. Cheng, H. Liu, H. Li, and H. Chen, “Highly efficient vertical fiber interfacing grating coupler with bilayer anti-reflection cladding and backside metal mirror,” Opt. Laser Technol.  90(December 2015), 136–143 (2017)

Opt. Lett. (4)

Other (1)

A. E. Siegman, Lasers (University Science Books, 1986).

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Figures (4)

Fig. 1
Fig. 1 Schematic drawing of the suggested device. The numbers in the circles represent the ports numbers, the waveguide length is L, and Iin, IR and IWG are the input intensity and output calculated intensities respectively.
Fig. 2
Fig. 2 (a) Contour plot for the back-reflected intensity as a function of the two independent efficiencies parameters ρ,η . (b) Contour plot for the waveguide length as a function of ρ,η . The optimal values are marked on both figures. In (c) the back-reflected intensity as function of wavelength in the telecommunication C-band range is plotted.
Fig. 3
Fig. 3 Plots for the simulated HCG directional vertical coupler device: (a) contour plot of the directional coupling efficiency of the device using our S-matrix model. The purple dot represents the coordinate of the device reported in [5] and the black dot represents the coordinate of the improved design that was achieved using our model guidance. In (b) the electrical power density of the device is displayed.
Fig. 4
Fig. 4 Plots for the right directed coupling intensity as function of (a) ρ and (b)η . The dots in each plot represents the calculated intensity values using the S-matrix analytical model (magenta) and the numerical FDTD (blue) simulations. Optimal line MATLAB fits for both cases are also shown: (a) Spline fits and (b) sinusoidal fits.

Equations (7)

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S=( r 11 t 12 t 13 t 21 r 22 t 23 t 31 t 32 r 33 )
σ| t 12 |=| t 21 |=| t 23 |=| t 32 |,η| t 13 |=| t 31 |,ξ| r 11 |=| r 33 |,ρ| r 22 |.
E R = a 1 t 12 + a 2 r 22 = a 1 σexp(i ϕ σ )+ a 2 ρexp(i ϕ ρ ), E WG = a 1 t 13 + a 2 t 23 = a 1 ηexp(i ϕ η )+ a 2 σexp(i ϕ σ ).
a 1 = σexp(i ϕ σ ) r G exp(2iβL) 1 r G (ξexp(i ϕ ξ ))exp(2iβL) a 2
ρ 2 +2 σ 2 =1, η 2 + σ 2 + ξ 2 =1.
(1ρ) 2 η (1+ρ) 2 .
L opt = L opt + λ 2 n eff m , m=1,2,3,..

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