Abstract

Nanophotonic chip coupling using an optical thin-film stack forming a micro graded-refractive-index (GRIN) lens with a super-high numerical aperture (NA) that is highly compact (tens of micron long) and can be directly integrated is presented. We explore the lens’ integration on the surface of Silicon-On-Insulator (SOI) platform with an asymmetric GRIN profile. We show that to achieve high efficiency for optical coupling between an optical fiber and a nanophotonic waveguide with a sub-wavelength (λ/n) beam size, conventional asymmetric parabolic GRIN profile is no longer adequate due to the super-high NA needed (>3.1), which results in severe spatial beam aberration at the focal plane. We present an efficient algorithm to computationally generate the ideal GRIN profile that is completely aberration free even at super-high NA, which improves the coupling efficiency from ~66% (parabolic case) to ~95%. A design example involving an optical thin-film stack using an improved dual-material approach is given. The performance of the thin-film stack is analyzed. This thin-film stack based GRIN lens is shown to be high in coupling efficiency, wavelength insensitive and compatible with standard thin-film process.

©2010 Optical Society of America

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References

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  1. V. R. Almeida, R. R. Panepucci, and M. Lipson, “Nanotaper for compact mode conversion,” Optic. Lett. Vol. 28, pp. 1302–1304, 2003.
  2. L. Vivien, X. L. Roux, S. Laval, E. Cassan, and D. Marris-Morini, “Design, Realization, and characterization of 3-D Taper for Fiber/Micro- Waveguide Coupling,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1354–1358 (2006).
    [Crossref]
  3. 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 coupling for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38(7), 949–955 (2002).
    [Crossref]
  4. D. Tailaert, W. Bogaerts, and R. Baets, “Efficient coupling between submicron SOI-waveguides and single-mode fibers”, Proc. Symposium IEEE/LEOS, 2003.
  5. B. Wang, J. Jiang, and G. P. Nordin, “Embedded slanted grating for vertical coupling between fibers and silicon-insulator planar waveguides,” IEEE Photon. Technol. Lett. 17(9), 1884–1886 (2005).
    [Crossref]
  6. N. Izhaky, M. T. Morse, S. Koehl, O. Cohen, D. Rubin, A. Barkai, G. Sarid, R. Cohen, and M. J. Paniccia, “Development of CMOS-Compatible integrated silicon photonics devices,” IEEE Sel. Top. Quantum Electron. 12(6), 1688–1698 (2006).
    [Crossref]
  7. D. Dai, S. He, and H. Tsang, “Bilevel mode converter between a silicon nanowire waveguide and a larger waveguide,” J. Lightwave Technol. 24(6), 2428–2433 (2006).
    [Crossref]
  8. Y. Huang and S. T. Ho, “Superhigh numerical aperture (NA>1.5) micro gradient-index lens based on a dual-material approach,” Opt. Lett. 30(11), 1291–1293 (2005).
    [Crossref] [PubMed]
  9. R. Sun, V. Nguyen, A. Agarwal, C. Hong, J. Yasaitis, and L. Kimerling. AndJ. Michel, “High performance asymmetric graded index coupler with integrated lens for high index waveguides,” Appl. Phys. Lett. 90, 1–3 (2007).
  10. A. Delâge, S. Janz, B. Lamontagne, A. Bogdanov, D. Dalacu, D.-X. Xu, and K. P. Yap, “Monolithically integrated asymmetric graded and step-index couplers for microphotonic waveguides,” Opt. Express 14(1), 148–161 (2006).
    [Crossref] [PubMed]
  11. A. Taflove and S. C. Hagness, Computational electrodynamics: the finite-difference time-domain method (Artech House Inc, 2000).
  12. G. R. Hadley, “Multistep method for wide-angle beam propagation,” Opt. Lett. 17(24), 1743–1745 (1992).
    [Crossref] [PubMed]

2007 (1)

R. Sun, V. Nguyen, A. Agarwal, C. Hong, J. Yasaitis, and L. Kimerling. AndJ. Michel, “High performance asymmetric graded index coupler with integrated lens for high index waveguides,” Appl. Phys. Lett. 90, 1–3 (2007).

R. Sun, V. Nguyen, A. Agarwal, C. Hong, J. Yasaitis, and L. Kimerling. AndJ. Michel, “High performance asymmetric graded index coupler with integrated lens for high index waveguides,” Appl. Phys. Lett. 90, 1–3 (2007).

2006 (4)

A. Delâge, S. Janz, B. Lamontagne, A. Bogdanov, D. Dalacu, D.-X. Xu, and K. P. Yap, “Monolithically integrated asymmetric graded and step-index couplers for microphotonic waveguides,” Opt. Express 14(1), 148–161 (2006).
[Crossref] [PubMed]

D. Dai, S. He, and H. Tsang, “Bilevel mode converter between a silicon nanowire waveguide and a larger waveguide,” J. Lightwave Technol. 24(6), 2428–2433 (2006).
[Crossref]

L. Vivien, X. L. Roux, S. Laval, E. Cassan, and D. Marris-Morini, “Design, Realization, and characterization of 3-D Taper for Fiber/Micro- Waveguide Coupling,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1354–1358 (2006).
[Crossref]

N. Izhaky, M. T. Morse, S. Koehl, O. Cohen, D. Rubin, A. Barkai, G. Sarid, R. Cohen, and M. J. Paniccia, “Development of CMOS-Compatible integrated silicon photonics devices,” IEEE Sel. Top. Quantum Electron. 12(6), 1688–1698 (2006).
[Crossref]

2005 (2)

B. Wang, J. Jiang, and G. P. Nordin, “Embedded slanted grating for vertical coupling between fibers and silicon-insulator planar waveguides,” IEEE Photon. Technol. Lett. 17(9), 1884–1886 (2005).
[Crossref]

Y. Huang and S. T. Ho, “Superhigh numerical aperture (NA>1.5) micro gradient-index lens based on a dual-material approach,” Opt. Lett. 30(11), 1291–1293 (2005).
[Crossref] [PubMed]

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 coupling for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38(7), 949–955 (2002).
[Crossref]

1992 (1)

Agarwal, A.

R. Sun, V. Nguyen, A. Agarwal, C. Hong, J. Yasaitis, and L. Kimerling. AndJ. Michel, “High performance asymmetric graded index coupler with integrated lens for high index waveguides,” Appl. Phys. Lett. 90, 1–3 (2007).

Baets, R.

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 coupling for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38(7), 949–955 (2002).
[Crossref]

Barkai, A.

N. Izhaky, M. T. Morse, S. Koehl, O. Cohen, D. Rubin, A. Barkai, G. Sarid, R. Cohen, and M. J. Paniccia, “Development of CMOS-Compatible integrated silicon photonics devices,” IEEE Sel. Top. Quantum Electron. 12(6), 1688–1698 (2006).
[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 coupling 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 coupling for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38(7), 949–955 (2002).
[Crossref]

Bogdanov, A.

Cassan, E.

L. Vivien, X. L. Roux, S. Laval, E. Cassan, and D. Marris-Morini, “Design, Realization, and characterization of 3-D Taper for Fiber/Micro- Waveguide Coupling,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1354–1358 (2006).
[Crossref]

Cohen, O.

N. Izhaky, M. T. Morse, S. Koehl, O. Cohen, D. Rubin, A. Barkai, G. Sarid, R. Cohen, and M. J. Paniccia, “Development of CMOS-Compatible integrated silicon photonics devices,” IEEE Sel. Top. Quantum Electron. 12(6), 1688–1698 (2006).
[Crossref]

Cohen, R.

N. Izhaky, M. T. Morse, S. Koehl, O. Cohen, D. Rubin, A. Barkai, G. Sarid, R. Cohen, and M. J. Paniccia, “Development of CMOS-Compatible integrated silicon photonics devices,” IEEE Sel. Top. Quantum Electron. 12(6), 1688–1698 (2006).
[Crossref]

Dai, D.

Dalacu, D.

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 coupling for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38(7), 949–955 (2002).
[Crossref]

Delâge, A.

Hadley, G. R.

He, S.

Ho, S. T.

Hong, C.

R. Sun, V. Nguyen, A. Agarwal, C. Hong, J. Yasaitis, and L. Kimerling. AndJ. Michel, “High performance asymmetric graded index coupler with integrated lens for high index waveguides,” Appl. Phys. Lett. 90, 1–3 (2007).

Huang, Y.

Izhaky, N.

N. Izhaky, M. T. Morse, S. Koehl, O. Cohen, D. Rubin, A. Barkai, G. Sarid, R. Cohen, and M. J. Paniccia, “Development of CMOS-Compatible integrated silicon photonics devices,” IEEE Sel. Top. Quantum Electron. 12(6), 1688–1698 (2006).
[Crossref]

Janz, S.

Jiang, J.

B. Wang, J. Jiang, and G. P. Nordin, “Embedded slanted grating for vertical coupling between fibers and silicon-insulator planar waveguides,” IEEE Photon. Technol. Lett. 17(9), 1884–1886 (2005).
[Crossref]

Kimerling, L.

R. Sun, V. Nguyen, A. Agarwal, C. Hong, J. Yasaitis, and L. Kimerling. AndJ. Michel, “High performance asymmetric graded index coupler with integrated lens for high index waveguides,” Appl. Phys. Lett. 90, 1–3 (2007).

Koehl, S.

N. Izhaky, M. T. Morse, S. Koehl, O. Cohen, D. Rubin, A. Barkai, G. Sarid, R. Cohen, and M. J. Paniccia, “Development of CMOS-Compatible integrated silicon photonics devices,” IEEE Sel. Top. Quantum Electron. 12(6), 1688–1698 (2006).
[Crossref]

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 coupling for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38(7), 949–955 (2002).
[Crossref]

Lamontagne, B.

Laval, S.

L. Vivien, X. L. Roux, S. Laval, E. Cassan, and D. Marris-Morini, “Design, Realization, and characterization of 3-D Taper for Fiber/Micro- Waveguide Coupling,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1354–1358 (2006).
[Crossref]

Marris-Morini, D.

L. Vivien, X. L. Roux, S. Laval, E. Cassan, and D. Marris-Morini, “Design, Realization, and characterization of 3-D Taper for Fiber/Micro- Waveguide Coupling,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1354–1358 (2006).
[Crossref]

Michel, J.

R. Sun, V. Nguyen, A. Agarwal, C. Hong, J. Yasaitis, and L. Kimerling. AndJ. Michel, “High performance asymmetric graded index coupler with integrated lens for high index waveguides,” Appl. Phys. Lett. 90, 1–3 (2007).

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 coupling for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38(7), 949–955 (2002).
[Crossref]

Morse, M. T.

N. Izhaky, M. T. Morse, S. Koehl, O. Cohen, D. Rubin, A. Barkai, G. Sarid, R. Cohen, and M. J. Paniccia, “Development of CMOS-Compatible integrated silicon photonics devices,” IEEE Sel. Top. Quantum Electron. 12(6), 1688–1698 (2006).
[Crossref]

Nguyen, V.

R. Sun, V. Nguyen, A. Agarwal, C. Hong, J. Yasaitis, and L. Kimerling. AndJ. Michel, “High performance asymmetric graded index coupler with integrated lens for high index waveguides,” Appl. Phys. Lett. 90, 1–3 (2007).

Nordin, G. P.

B. Wang, J. Jiang, and G. P. Nordin, “Embedded slanted grating for vertical coupling between fibers and silicon-insulator planar waveguides,” IEEE Photon. Technol. Lett. 17(9), 1884–1886 (2005).
[Crossref]

Paniccia, M. J.

N. Izhaky, M. T. Morse, S. Koehl, O. Cohen, D. Rubin, A. Barkai, G. Sarid, R. Cohen, and M. J. Paniccia, “Development of CMOS-Compatible integrated silicon photonics devices,” IEEE Sel. Top. Quantum Electron. 12(6), 1688–1698 (2006).
[Crossref]

Roux, X. L.

L. Vivien, X. L. Roux, S. Laval, E. Cassan, and D. Marris-Morini, “Design, Realization, and characterization of 3-D Taper for Fiber/Micro- Waveguide Coupling,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1354–1358 (2006).
[Crossref]

Rubin, D.

N. Izhaky, M. T. Morse, S. Koehl, O. Cohen, D. Rubin, A. Barkai, G. Sarid, R. Cohen, and M. J. Paniccia, “Development of CMOS-Compatible integrated silicon photonics devices,” IEEE Sel. Top. Quantum Electron. 12(6), 1688–1698 (2006).
[Crossref]

Sarid, G.

N. Izhaky, M. T. Morse, S. Koehl, O. Cohen, D. Rubin, A. Barkai, G. Sarid, R. Cohen, and M. J. Paniccia, “Development of CMOS-Compatible integrated silicon photonics devices,” IEEE Sel. Top. Quantum Electron. 12(6), 1688–1698 (2006).
[Crossref]

Sun, R.

R. Sun, V. Nguyen, A. Agarwal, C. Hong, J. Yasaitis, and L. Kimerling. AndJ. Michel, “High performance asymmetric graded index coupler with integrated lens for high index waveguides,” Appl. Phys. Lett. 90, 1–3 (2007).

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 coupling for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38(7), 949–955 (2002).
[Crossref]

Tsang, H.

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 coupling for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38(7), 949–955 (2002).
[Crossref]

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 coupling for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38(7), 949–955 (2002).
[Crossref]

Vivien, L.

L. Vivien, X. L. Roux, S. Laval, E. Cassan, and D. Marris-Morini, “Design, Realization, and characterization of 3-D Taper for Fiber/Micro- Waveguide Coupling,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1354–1358 (2006).
[Crossref]

Wang, B.

B. Wang, J. Jiang, and G. P. Nordin, “Embedded slanted grating for vertical coupling between fibers and silicon-insulator planar waveguides,” IEEE Photon. Technol. Lett. 17(9), 1884–1886 (2005).
[Crossref]

Xu, D.-X.

Yap, K. P.

Yasaitis, J.

R. Sun, V. Nguyen, A. Agarwal, C. Hong, J. Yasaitis, and L. Kimerling. AndJ. Michel, “High performance asymmetric graded index coupler with integrated lens for high index waveguides,” Appl. Phys. Lett. 90, 1–3 (2007).

Appl. Phys. Lett. (1)

R. Sun, V. Nguyen, A. Agarwal, C. Hong, J. Yasaitis, and L. Kimerling. AndJ. Michel, “High performance asymmetric graded index coupler with integrated lens for high index waveguides,” Appl. Phys. Lett. 90, 1–3 (2007).

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 coupling for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38(7), 949–955 (2002).
[Crossref]

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

L. Vivien, X. L. Roux, S. Laval, E. Cassan, and D. Marris-Morini, “Design, Realization, and characterization of 3-D Taper for Fiber/Micro- Waveguide Coupling,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1354–1358 (2006).
[Crossref]

IEEE Photon. Technol. Lett. (1)

B. Wang, J. Jiang, and G. P. Nordin, “Embedded slanted grating for vertical coupling between fibers and silicon-insulator planar waveguides,” IEEE Photon. Technol. Lett. 17(9), 1884–1886 (2005).
[Crossref]

IEEE Sel. Top. Quantum Electron. (1)

N. Izhaky, M. T. Morse, S. Koehl, O. Cohen, D. Rubin, A. Barkai, G. Sarid, R. Cohen, and M. J. Paniccia, “Development of CMOS-Compatible integrated silicon photonics devices,” IEEE Sel. Top. Quantum Electron. 12(6), 1688–1698 (2006).
[Crossref]

J. Lightwave Technol. (1)

Opt. Express (1)

Opt. Lett. (2)

Other (3)

A. Taflove and S. C. Hagness, Computational electrodynamics: the finite-difference time-domain method (Artech House Inc, 2000).

V. R. Almeida, R. R. Panepucci, and M. Lipson, “Nanotaper for compact mode conversion,” Optic. Lett. Vol. 28, pp. 1302–1304, 2003.

D. Tailaert, W. Bogaerts, and R. Baets, “Efficient coupling between submicron SOI-waveguides and single-mode fibers”, Proc. Symposium IEEE/LEOS, 2003.

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Figures (13)

Fig. 1
Fig. 1 a) Schematic of the optical thin-film based GRIN lens for optical coupling between nanophotonic chip and fiber; b) optical thin-film stack with a binary refractive index profile (nH and nL) acts equivalent to an asymmetric GRIN lens with a graded refractive index profile from n0 to nR.

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Fig. 2
Fig. 2 Requirement of refractive index contrast for collimating the light beam within the GRIN lens.

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Fig. 3
Fig. 3 Simulation of light propagation in the parabolic GRIN lens with a super-high NA; a) Ray-tracing; b) FDTD simulation.

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Fig. 4
Fig. 4 Transverse intensity profiles of singlemode fiber, and output field from the GRIN lens with a parabolic profile.

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Fig. 5
Fig. 5 a) Schematic for the targeted trajectories of the rays emitted from the nano-waveguide in the aberration-free GRIN lens; b) Ray-tracing for calculating the refractive index of the second layer; c) Ray-racing for calculating the refractive index for the i-th layer.

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Fig. 6
Fig. 6 The refractive index profile generated for the asymmetric GRIN lens with an aberration-free focusing; conventional parabolic profile is given for comparison.

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Fig. 7
Fig. 7 Light propagation results in the aberration-free super-GRIN lens; a) Ray-tracing in the asymmetric aberration-free GRIN lens; b) 2D FDTD simulation of light propagation in the same lens.

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Fig. 8
Fig. 8 Transverse field profile at the facet of aberration-free GRIN lens and eigenmode of the optical fiber.

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Fig. 9
Fig. 9 a) Optical design of thin-film stack to have equivalent graded refractive index profile; b) replace a thin-film layer having a particular refractive index with two thin-film layers that effectively approximate this refractive index.

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Fig. 10
Fig. 10 a) FDTD simulation of light propagation within the dual-material thin-film stack when a) f=300 nm; b) f=250 nm; c) f=200 nm, d) f=150 nm.

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Fig. 11
Fig. 11 Coupling efficiency between the fiber and nano-waveguide with thin-film stack based GRIN lens

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Fig. 12
Fig. 12 Layout of the optical thin-film stack designed by Eq. (2) when f=150 nm.

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Fig. 13
Fig. 13 Coupling efficiency between nanophotonic waveguide and optical fiber using the thin-film stack based GRIN lens under different wavelengths.

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Tables (1)

Tables Icon

Table 1 Beam’s spot size and divergence angle that encompasses 95% energy; the required refractive index nR and NA for the GRIN lens to confine the light beam

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Equations (2)

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L f = ∑ k = 1 i − 1 h n k 2 n i 2 − 1
f H j = n j 2 − n L 2 n H 2 − n L 2 f T j

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