Abstract

Coupling light between an optical fiber and a silicon nanophotonic waveguide is a challenge facing the field of silicon photonics to which various mode converters have been proposed. Inverted tapers stand out as a practical solution enabling efficient and broadband mode conversion. Current design approaches often use linearly-shaped tapers and two dimensional approximations; however, these approaches have not been rigorously verified and there is not an overarching design framework to guide the design process. Here, using a Lagrangian formulation, we propose an original, constant-loss framework for designing shape-controlled photonic devices and apply this formalism to derive an ideal constant-loss taper (CLT). We specifically report on the experimental demonstration of a fabrication-tolerant, 15-µm-long CLT coupler, that produces 0.56 dB fiber-chip coupling efficiency, the highest efficiency-per-length ratio ever reported.

© 2016 Optical Society of America

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References

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    [Crossref]
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2015 (2)

2014 (2)

2012 (2)

X. Xu, H. Subbaraman, J. Covey, D. Kwong, A. Hosseini, and R. T. Chen, “Complementary metal–oxide–semiconductor compatible high efficiency subwavelength grating couplers for silicon integrated photonics,” Appl. Phys. Lett. 101(3), 031109 (2012).
[Crossref]

I.D. Rukhlenko, M. Premaratne, and G. P. Agrawal, “Effective mode area and its optimization in silicon-nanocrystal waveguides,” Opt. Lett. 37(12), 2295–2297 (2012).
[Crossref] [PubMed]

2010 (2)

2008 (1)

2006 (2)

D. Taillaert, F. Van Laere, M. Ayre, and W. Bogaert, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45(1–8A), 6071–6077 (2006).
[Crossref]

R. Soref, “The past, present, and future of silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1678–1687 (2006).
[Crossref]

2004 (2)

F. Grillot, L. Vivien, S. Laval, D. Pascal, and E. Cassan, “Size influence on the propagation loss induced by sidewall roughness in ultrasmall SOI waveguides,” IEEE Photonics Technol. Lett. 16(7), 1661–1663 (2004)
[Crossref]

Y. A. Vlasov and S. J. McNab, “Losses in single-mode silicon-on-insulator strip waveguides and bends,” Opt. Express 12(8), 1622–1631 (2004).
[Crossref] [PubMed]

2003 (2)

2002 (1)

T. Shoji, T. Tsuchizawa, T. Watanabe, K. Yamada, and H. Morita, “Low loss mode size converter from 0.3 mu m square si wire waveguides to singlemode fibres,” Electron. Lett. 38(25), 1669–1670 (2002).
[Crossref]

1998 (1)

1970 (1)

D. Marcuse, “Radiation losses of tapered dielectric slab waveguides,” Opt. Express 49(2), 279–290 (1970).

Agrawal, G. P.

Almeida, V. R.

Ayre, M.

D. Taillaert, F. Van Laere, M. Ayre, and W. Bogaert, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45(1–8A), 6071–6077 (2006).
[Crossref]

Bock, P. J.

Bogaert, W.

D. Taillaert, F. Van Laere, M. Ayre, and W. Bogaert, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45(1–8A), 6071–6077 (2006).
[Crossref]

Bona, G-L.

Butkov, E.

E. Butkov, Mathematical Physics (Addison Wesley, 1968).

Cassan, E.

F. Grillot, L. Vivien, S. Laval, D. Pascal, and E. Cassan, “Size influence on the propagation loss induced by sidewall roughness in ultrasmall SOI waveguides,” IEEE Photonics Technol. Lett. 16(7), 1661–1663 (2004)
[Crossref]

Cheben, P.

Chen, R. T.

X. Xu, H. Subbaraman, J. Covey, D. Kwong, A. Hosseini, and R. T. Chen, “Complementary metal–oxide–semiconductor compatible high efficiency subwavelength grating couplers for silicon integrated photonics,” Appl. Phys. Lett. 101(3), 031109 (2012).
[Crossref]

Chu, T.

Covey, J.

X. Xu, H. Subbaraman, J. Covey, D. Kwong, A. Hosseini, and R. T. Chen, “Complementary metal–oxide–semiconductor compatible high efficiency subwavelength grating couplers for silicon integrated photonics,” Appl. Phys. Lett. 101(3), 031109 (2012).
[Crossref]

Delage, A.

Densmore, A.

Fu, Y.

Germann, R.

Grillot, F.

F. Grillot, L. Vivien, S. Laval, D. Pascal, and E. Cassan, “Size influence on the propagation loss induced by sidewall roughness in ultrasmall SOI waveguides,” IEEE Photonics Technol. Lett. 16(7), 1661–1663 (2004)
[Crossref]

Hall, T. J.

Hosseini, A.

X. Xu, H. Subbaraman, J. Covey, D. Kwong, A. Hosseini, and R. T. Chen, “Complementary metal–oxide–semiconductor compatible high efficiency subwavelength grating couplers for silicon integrated photonics,” Appl. Phys. Lett. 101(3), 031109 (2012).
[Crossref]

Hvam, J. M.

M. Pu, L. Liu, H. Ou, K. Yvind, and J. M. Hvam, “Ultra-low-loss inverted taper coupler for silicon-on-insulator ridge waveguide,” Opt. Commun. 283(19), 3678–3682 (2010).
[Crossref]

Janz, S.

Kwong, D.

X. Xu, H. Subbaraman, J. Covey, D. Kwong, A. Hosseini, and R. T. Chen, “Complementary metal–oxide–semiconductor compatible high efficiency subwavelength grating couplers for silicon integrated photonics,” Appl. Phys. Lett. 101(3), 031109 (2012).
[Crossref]

Lamontagne, B.

Lapointe, J.

Laval, S.

F. Grillot, L. Vivien, S. Laval, D. Pascal, and E. Cassan, “Size influence on the propagation loss induced by sidewall roughness in ultrasmall SOI waveguides,” IEEE Photonics Technol. Lett. 16(7), 1661–1663 (2004)
[Crossref]

Lee, D. L.

D. L. Lee, Electromagnetic Principles of Integrated Optics (Wiley, 1986).

Lipson, M.

Liu, L.

M. Pu, L. Liu, H. Ou, K. Yvind, and J. M. Hvam, “Ultra-low-loss inverted taper coupler for silicon-on-insulator ridge waveguide,” Opt. Commun. 283(19), 3678–3682 (2010).
[Crossref]

Marcuse, D.

D. Marcuse, “Radiation losses of tapered dielectric slab waveguides,” Opt. Express 49(2), 279–290 (1970).

McNab, S. J.

McNab, S.J.

Menon, R.

B. Shen, P. Wang, R. Polson, and R. Menon, “An integrated-nanophotonics polarization beamsplitter with 2.4um2 footprint,” Nat. Photonics 9(6), 378–382 (2015).
[Crossref]

Moll, N.

Morita, H.

T. Shoji, T. Tsuchizawa, T. Watanabe, K. Yamada, and H. Morita, “Low loss mode size converter from 0.3 mu m square si wire waveguides to singlemode fibres,” Electron. Lett. 38(25), 1669–1670 (2002).
[Crossref]

Newmann, E.-G.

E.-G. Newmann, Single-Mode Fibers (Springer, 1988).
[Crossref]

Offrein, B.J.

Ou, H.

M. Pu, L. Liu, H. Ou, K. Yvind, and J. M. Hvam, “Ultra-low-loss inverted taper coupler for silicon-on-insulator ridge waveguide,” Opt. Commun. 283(19), 3678–3682 (2010).
[Crossref]

Painchaud, Y.

Painter, O.

Panepucci, R. R.

Pascal, D.

F. Grillot, L. Vivien, S. Laval, D. Pascal, and E. Cassan, “Size influence on the propagation loss induced by sidewall roughness in ultrasmall SOI waveguides,” IEEE Photonics Technol. Lett. 16(7), 1661–1663 (2004)
[Crossref]

Picard, M.-J.

Polson, R.

B. Shen, P. Wang, R. Polson, and R. Menon, “An integrated-nanophotonics polarization beamsplitter with 2.4um2 footprint,” Nat. Photonics 9(6), 378–382 (2015).
[Crossref]

Premaratne, M.

Preston, K.

Pu, M.

M. Pu, L. Liu, H. Ou, K. Yvind, and J. M. Hvam, “Ultra-low-loss inverted taper coupler for silicon-on-insulator ridge waveguide,” Opt. Commun. 283(19), 3678–3682 (2010).
[Crossref]

Rickman, A.

A. Rickman, “The commercialization of silicon photonics,” Nat. Photonics 8, 579–582 (2014).
[Crossref]

Robinson, J. T.

Rukhlenko, I.D.

Schmid, J. H.

Shen, B.

B. Shen, P. Wang, R. Polson, and R. Menon, “An integrated-nanophotonics polarization beamsplitter with 2.4um2 footprint,” Nat. Photonics 9(6), 378–382 (2015).
[Crossref]

Shoji, T.

T. Shoji, T. Tsuchizawa, T. Watanabe, K. Yamada, and H. Morita, “Low loss mode size converter from 0.3 mu m square si wire waveguides to singlemode fibres,” Electron. Lett. 38(25), 1669–1670 (2002).
[Crossref]

Soref, R.

R. Soref, “The past, present, and future of silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1678–1687 (2006).
[Crossref]

Spuhler, M. M.

Subbaraman, H.

X. Xu, H. Subbaraman, J. Covey, D. Kwong, A. Hosseini, and R. T. Chen, “Complementary metal–oxide–semiconductor compatible high efficiency subwavelength grating couplers for silicon integrated photonics,” Appl. Phys. Lett. 101(3), 031109 (2012).
[Crossref]

Taillaert, D.

D. Taillaert, F. Van Laere, M. Ayre, and W. Bogaert, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45(1–8A), 6071–6077 (2006).
[Crossref]

Tang, W.

Tsuchizawa, T.

T. Shoji, T. Tsuchizawa, T. Watanabe, K. Yamada, and H. Morita, “Low loss mode size converter from 0.3 mu m square si wire waveguides to singlemode fibres,” Electron. Lett. 38(25), 1669–1670 (2002).
[Crossref]

Vachon, M.

Van Laere, F.

D. Taillaert, F. Van Laere, M. Ayre, and W. Bogaert, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45(1–8A), 6071–6077 (2006).
[Crossref]

Vivien, L.

F. Grillot, L. Vivien, S. Laval, D. Pascal, and E. Cassan, “Size influence on the propagation loss induced by sidewall roughness in ultrasmall SOI waveguides,” IEEE Photonics Technol. Lett. 16(7), 1661–1663 (2004)
[Crossref]

Vlasov, Y. A.

Wang, P.

B. Shen, P. Wang, R. Polson, and R. Menon, “An integrated-nanophotonics polarization beamsplitter with 2.4um2 footprint,” Nat. Photonics 9(6), 378–382 (2015).
[Crossref]

Wang, S.

Watanabe, T.

T. Shoji, T. Tsuchizawa, T. Watanabe, K. Yamada, and H. Morita, “Low loss mode size converter from 0.3 mu m square si wire waveguides to singlemode fibres,” Electron. Lett. 38(25), 1669–1670 (2002).
[Crossref]

Xu, D.-X.

Xu, X.

X. Xu, H. Subbaraman, J. Covey, D. Kwong, A. Hosseini, and R. T. Chen, “Complementary metal–oxide–semiconductor compatible high efficiency subwavelength grating couplers for silicon integrated photonics,” Appl. Phys. Lett. 101(3), 031109 (2012).
[Crossref]

Yamada, K.

T. Shoji, T. Tsuchizawa, T. Watanabe, K. Yamada, and H. Morita, “Low loss mode size converter from 0.3 mu m square si wire waveguides to singlemode fibres,” Electron. Lett. 38(25), 1669–1670 (2002).
[Crossref]

Ye, T.

Yvind, K.

M. Pu, L. Liu, H. Ou, K. Yvind, and J. M. Hvam, “Ultra-low-loss inverted taper coupler for silicon-on-insulator ridge waveguide,” Opt. Commun. 283(19), 3678–3682 (2010).
[Crossref]

Appl. Phys. Lett. (1)

X. Xu, H. Subbaraman, J. Covey, D. Kwong, A. Hosseini, and R. T. Chen, “Complementary metal–oxide–semiconductor compatible high efficiency subwavelength grating couplers for silicon integrated photonics,” Appl. Phys. Lett. 101(3), 031109 (2012).
[Crossref]

Electron. Lett. (1)

T. Shoji, T. Tsuchizawa, T. Watanabe, K. Yamada, and H. Morita, “Low loss mode size converter from 0.3 mu m square si wire waveguides to singlemode fibres,” Electron. Lett. 38(25), 1669–1670 (2002).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

R. Soref, “The past, present, and future of silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1678–1687 (2006).
[Crossref]

IEEE Photonics Technol. Lett. (1)

F. Grillot, L. Vivien, S. Laval, D. Pascal, and E. Cassan, “Size influence on the propagation loss induced by sidewall roughness in ultrasmall SOI waveguides,” IEEE Photonics Technol. Lett. 16(7), 1661–1663 (2004)
[Crossref]

J. Lightwave Technol. (1)

Jpn. J. Appl. Phys. (1)

D. Taillaert, F. Van Laere, M. Ayre, and W. Bogaert, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45(1–8A), 6071–6077 (2006).
[Crossref]

Nat. Photonics (2)

B. Shen, P. Wang, R. Polson, and R. Menon, “An integrated-nanophotonics polarization beamsplitter with 2.4um2 footprint,” Nat. Photonics 9(6), 378–382 (2015).
[Crossref]

A. Rickman, “The commercialization of silicon photonics,” Nat. Photonics 8, 579–582 (2014).
[Crossref]

Opt. Commun. (1)

M. Pu, L. Liu, H. Ou, K. Yvind, and J. M. Hvam, “Ultra-low-loss inverted taper coupler for silicon-on-insulator ridge waveguide,” Opt. Commun. 283(19), 3678–3682 (2010).
[Crossref]

Opt. Express (5)

Opt. Lett. (3)

Photon. Res. (1)

Other (3)

E.-G. Newmann, Single-Mode Fibers (Springer, 1988).
[Crossref]

D. L. Lee, Electromagnetic Principles of Integrated Optics (Wiley, 1986).

E. Butkov, Mathematical Physics (Addison Wesley, 1968).

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Figures (6)

Fig. 1
Fig. 1 In (a), the effective mode area and effective index (neff) of the fundamental quasi-TE mode is plotted for λ = 1550 nm for varying waveguide core width a core thickness of 220 nm. The solid line shows the results calculated using a full-vectorial (FULL) mode solver while the dashed line corresponds to the effective medium theory (EMT). Top-left inset shows the cross-section of the waveguide, bottom inset shows a close-up of the effective mode area as a function of waveguide width. The major component of the electric field of the guided mode is shown at three points on interest: w =150 nm, (b); 450 nm, (c); and 1000 nm, (d).
Fig. 2
Fig. 2 The overlap integral between the modes of a 4.9 µm MFD fiber and the taper tip of varying widths for quasi-TE and -TM polarization. (a) Fabricated 15-µm-long constant-loss taper optimized for TE coupling, (b) distinctive feature of the constant-loss taper (CLT) that abruptly expands near the final 450 nm width, and (c) the taper tip.
Fig. 3
Fig. 3 Top three pictograms show various monotonically increasing tapering functions. (a) and (c) present the limit cases of potential taper functions; (b) presents an example of a taper function, the linear taper. (d) presents a method of deriving the constant-loss taper; at step 0 the taper tip is defined by maximizing the overlap intergral with the fiber, in step 1 a waveguide step, δz1, is selected that produces a constant mode mismatch loss, αthreshold. Recursively, the following ith steps can be defined by selection a waveguide step δzi−1,i leading to αi−1,i = αthreshold.
Fig. 4
Fig. 4 (a) The width of the linear, parabolic and constant-loss taper as calculated using the constant-loss methodology. (b) The power in the guided mode (Pmode) at a position z within the taper is tracked for the various taper functions. The bottom figures (c)–(f) show the major component of the electric field at 4 different positions; (c) and (f) show the input (155 nm) and output (450 nm) modes.
Fig. 5
Fig. 5 Coupler efficiency as a function of the taper length with a 4.9 µm MFD fiber using a 3D FDTD simulation and measured efficiency for 15 µm long tapers.
Fig. 6
Fig. 6 Distribution of the coupler loss efficiency given roughness perturbations for a linear, parabolic, and constant-loss taper; the median coupler efficiency are 5.0, 4.6, and 3.5 dB, respectively. Vertical annotatted line show the reference coupler efficiency of an unperturbed taper.

Equations (6)

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

E M A = ( S z d x d y ) 2 / S z 2 d x d y
η = | E i × H j * d x d y | 2 | E i × H i * d x d y | | E j × H j * d x d y | .
L { w } = 0 L α ( w , w ˙ , z ) d z .
α w d d z ( α w ˙ ) = 0.
α = w ˙ α w ˙ = cst .
T i 1 , i = η i 1 , i R i 1 , i = | n e f f i 1 n e f f i n e f f i 1 + n e f f i | 2 α i 1 , i = ( 1 R T ) ( 1 T ) = α t h r e s h o l d = cst .

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