Abstract

The bandwidth of planar waveguide grating couplers is theoretically investigated based on the rigorous grating theory. We observe that the bandwidth behavior is not only determined by the grating coupler intrinsic properties, but also affected by the fiber parameters such as position, beam waist and Numerical Aperture. The rigorous bandwidth formula is derived. By analyzing the formula, several practical guidelines are proposed for grating coupler design and fiber operation in order to achieve wideband performance.

© 2013 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Hochberg and T. Baehr-Jones, “Towards fabless silicon photonics,” Nat. Photonics4(8), 492–494 (2010).
    [CrossRef]
  2. F. Van Laere, G. Roelkens, M. Ayre, J. Schrauwen, D. Taillaert, D. Van Thourhout, T. F. Krauss, and R. Baets, “Compact and highly efficient grating couplers between optical fiber and nanophotonic Waveguides,” J. Lightwave Technol.25(1), 151–156 (2007).
    [CrossRef]
  3. I. A. Avrutsky, A. S. Svakhin, V. A. Sychugov, and O. Parriaux, “High-efficiency single-order waveguide grating coupler,” Opt. Lett.15(24), 1446–1448 (1990).
    [CrossRef] [PubMed]
  4. X. Chen, C. Li, C. K. Y. Fung, S. M. G. Lo, and H. K. Tsang, “Apodized waveguide grating couplers for efficient coupling to optical fibers,” IEEE Photon. Technol. Lett.22(15), 1156–1158 (2010).
    [CrossRef]
  5. G. Roelkens, D. Van Thourhout, and R. Baets, “High efficiency silicon-on-Insulator grating coupler based on a poly-silicon overlay,” Opt. Express14(24), 11622–11630 (2006).
    [CrossRef] [PubMed]
  6. C. R. Doerr, L. Chen, Y. Chen, and L. L. Buhl, “Wide bandwidth silicon nitride grating coupler,” IEEE Photon. Technol. Lett.22(19), 1461–1463 (2010).
    [CrossRef]
  7. X. Chen, K. Xu, Z. Cheng, C. K. Y. Fung, and H. K. Tsang, “Wideband subwavelength gratings for coupling between silicon-on-insulator waveguides and optical fibers,” Opt. Lett.37(17), 3483–3485 (2012).
    [CrossRef] [PubMed]
  8. Z. Xiao, F. Luan, T. Y. Liow, J. Zhang, and P. Shum, “Design for broadband high-efficiency grating couplers,” Opt. Lett.37(4), 530–532 (2012).
    [CrossRef] [PubMed]
  9. T. Tamir, “Beam and waveguide couplers,” in Integrated Optics (Springer, 1975).
  10. T. K. Gaylord and M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE73(5), 894–937 (1985).
    [CrossRef]
  11. R. G. Hunsperger, Integrated Optics: Theory and Technology (Springer, 2008).
  12. J. C. Brazas and L. Li, “Analysis of input-grating couplers having finite lengths,” Appl. Opt.34(19), 3786–3792 (1995).
    [CrossRef] [PubMed]
  13. D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys.45(8A), 6071–6077 (2006).
    [CrossRef]
  14. T. Tamir and S. T. Peng, “Analysis and Design of Grating Couplers,” Appl. Phys. (Berl.)14(3), 235–254 (1977).
    [CrossRef]
  15. S. T. Peng, T. Tamir, and H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microw. Theory Tech.23(1), 123–133 (1975).
    [CrossRef]
  16. S. Miyanaga and T. Asakura, “Intensity profile of outgoing beams from uniform and linearly tapered grating couplers,” Appl. Opt.20(4), 688–695 (1981).
    [CrossRef] [PubMed]

2012 (2)

2010 (3)

M. Hochberg and T. Baehr-Jones, “Towards fabless silicon photonics,” Nat. Photonics4(8), 492–494 (2010).
[CrossRef]

X. Chen, C. Li, C. K. Y. Fung, S. M. G. Lo, and H. K. Tsang, “Apodized waveguide grating couplers for efficient coupling to optical fibers,” IEEE Photon. Technol. Lett.22(15), 1156–1158 (2010).
[CrossRef]

C. R. Doerr, L. Chen, Y. Chen, and L. L. Buhl, “Wide bandwidth silicon nitride grating coupler,” IEEE Photon. Technol. Lett.22(19), 1461–1463 (2010).
[CrossRef]

2007 (1)

2006 (2)

G. Roelkens, D. Van Thourhout, and R. Baets, “High efficiency silicon-on-Insulator grating coupler based on a poly-silicon overlay,” Opt. Express14(24), 11622–11630 (2006).
[CrossRef] [PubMed]

D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys.45(8A), 6071–6077 (2006).
[CrossRef]

1995 (1)

1990 (1)

1985 (1)

T. K. Gaylord and M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE73(5), 894–937 (1985).
[CrossRef]

1981 (1)

1977 (1)

T. Tamir and S. T. Peng, “Analysis and Design of Grating Couplers,” Appl. Phys. (Berl.)14(3), 235–254 (1977).
[CrossRef]

1975 (1)

S. T. Peng, T. Tamir, and H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microw. Theory Tech.23(1), 123–133 (1975).
[CrossRef]

Asakura, T.

Avrutsky, I. A.

Ayre, M.

F. Van Laere, G. Roelkens, M. Ayre, J. Schrauwen, D. Taillaert, D. Van Thourhout, T. F. Krauss, and R. Baets, “Compact and highly efficient grating couplers between optical fiber and nanophotonic Waveguides,” J. Lightwave Technol.25(1), 151–156 (2007).
[CrossRef]

D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys.45(8A), 6071–6077 (2006).
[CrossRef]

Baehr-Jones, T.

M. Hochberg and T. Baehr-Jones, “Towards fabless silicon photonics,” Nat. Photonics4(8), 492–494 (2010).
[CrossRef]

Baets, R.

Bertoni, H. L.

S. T. Peng, T. Tamir, and H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microw. Theory Tech.23(1), 123–133 (1975).
[CrossRef]

Bienstman, P.

D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys.45(8A), 6071–6077 (2006).
[CrossRef]

Bogaerts, W.

D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys.45(8A), 6071–6077 (2006).
[CrossRef]

Brazas, J. C.

Buhl, L. L.

C. R. Doerr, L. Chen, Y. Chen, and L. L. Buhl, “Wide bandwidth silicon nitride grating coupler,” IEEE Photon. Technol. Lett.22(19), 1461–1463 (2010).
[CrossRef]

Chen, L.

C. R. Doerr, L. Chen, Y. Chen, and L. L. Buhl, “Wide bandwidth silicon nitride grating coupler,” IEEE Photon. Technol. Lett.22(19), 1461–1463 (2010).
[CrossRef]

Chen, X.

X. Chen, K. Xu, Z. Cheng, C. K. Y. Fung, and H. K. Tsang, “Wideband subwavelength gratings for coupling between silicon-on-insulator waveguides and optical fibers,” Opt. Lett.37(17), 3483–3485 (2012).
[CrossRef] [PubMed]

X. Chen, C. Li, C. K. Y. Fung, S. M. G. Lo, and H. K. Tsang, “Apodized waveguide grating couplers for efficient coupling to optical fibers,” IEEE Photon. Technol. Lett.22(15), 1156–1158 (2010).
[CrossRef]

Chen, Y.

C. R. Doerr, L. Chen, Y. Chen, and L. L. Buhl, “Wide bandwidth silicon nitride grating coupler,” IEEE Photon. Technol. Lett.22(19), 1461–1463 (2010).
[CrossRef]

Cheng, Z.

Doerr, C. R.

C. R. Doerr, L. Chen, Y. Chen, and L. L. Buhl, “Wide bandwidth silicon nitride grating coupler,” IEEE Photon. Technol. Lett.22(19), 1461–1463 (2010).
[CrossRef]

Fung, C. K. Y.

X. Chen, K. Xu, Z. Cheng, C. K. Y. Fung, and H. K. Tsang, “Wideband subwavelength gratings for coupling between silicon-on-insulator waveguides and optical fibers,” Opt. Lett.37(17), 3483–3485 (2012).
[CrossRef] [PubMed]

X. Chen, C. Li, C. K. Y. Fung, S. M. G. Lo, and H. K. Tsang, “Apodized waveguide grating couplers for efficient coupling to optical fibers,” IEEE Photon. Technol. Lett.22(15), 1156–1158 (2010).
[CrossRef]

Gaylord, T. K.

T. K. Gaylord and M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE73(5), 894–937 (1985).
[CrossRef]

Hochberg, M.

M. Hochberg and T. Baehr-Jones, “Towards fabless silicon photonics,” Nat. Photonics4(8), 492–494 (2010).
[CrossRef]

Krauss, T. F.

Li, C.

X. Chen, C. Li, C. K. Y. Fung, S. M. G. Lo, and H. K. Tsang, “Apodized waveguide grating couplers for efficient coupling to optical fibers,” IEEE Photon. Technol. Lett.22(15), 1156–1158 (2010).
[CrossRef]

Li, L.

Liow, T. Y.

Lo, S. M. G.

X. Chen, C. Li, C. K. Y. Fung, S. M. G. Lo, and H. K. Tsang, “Apodized waveguide grating couplers for efficient coupling to optical fibers,” IEEE Photon. Technol. Lett.22(15), 1156–1158 (2010).
[CrossRef]

Luan, F.

Miyanaga, S.

Moharam, M. G.

T. K. Gaylord and M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE73(5), 894–937 (1985).
[CrossRef]

Parriaux, O.

Peng, S. T.

T. Tamir and S. T. Peng, “Analysis and Design of Grating Couplers,” Appl. Phys. (Berl.)14(3), 235–254 (1977).
[CrossRef]

S. T. Peng, T. Tamir, and H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microw. Theory Tech.23(1), 123–133 (1975).
[CrossRef]

Roelkens, G.

Schrauwen, J.

Shum, P.

Svakhin, A. S.

Sychugov, V. A.

Taillaert, D.

F. Van Laere, G. Roelkens, M. Ayre, J. Schrauwen, D. Taillaert, D. Van Thourhout, T. F. Krauss, and R. Baets, “Compact and highly efficient grating couplers between optical fiber and nanophotonic Waveguides,” J. Lightwave Technol.25(1), 151–156 (2007).
[CrossRef]

D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys.45(8A), 6071–6077 (2006).
[CrossRef]

Tamir, T.

T. Tamir and S. T. Peng, “Analysis and Design of Grating Couplers,” Appl. Phys. (Berl.)14(3), 235–254 (1977).
[CrossRef]

S. T. Peng, T. Tamir, and H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microw. Theory Tech.23(1), 123–133 (1975).
[CrossRef]

Tsang, H. K.

X. Chen, K. Xu, Z. Cheng, C. K. Y. Fung, and H. K. Tsang, “Wideband subwavelength gratings for coupling between silicon-on-insulator waveguides and optical fibers,” Opt. Lett.37(17), 3483–3485 (2012).
[CrossRef] [PubMed]

X. Chen, C. Li, C. K. Y. Fung, S. M. G. Lo, and H. K. Tsang, “Apodized waveguide grating couplers for efficient coupling to optical fibers,” IEEE Photon. Technol. Lett.22(15), 1156–1158 (2010).
[CrossRef]

Van Laere, F.

F. Van Laere, G. Roelkens, M. Ayre, J. Schrauwen, D. Taillaert, D. Van Thourhout, T. F. Krauss, and R. Baets, “Compact and highly efficient grating couplers between optical fiber and nanophotonic Waveguides,” J. Lightwave Technol.25(1), 151–156 (2007).
[CrossRef]

D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys.45(8A), 6071–6077 (2006).
[CrossRef]

Van Thourhout, D.

Xiao, Z.

Xu, K.

Zhang, J.

Appl. Opt. (2)

Appl. Phys. (Berl.) (1)

T. Tamir and S. T. Peng, “Analysis and Design of Grating Couplers,” Appl. Phys. (Berl.)14(3), 235–254 (1977).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

X. Chen, C. Li, C. K. Y. Fung, S. M. G. Lo, and H. K. Tsang, “Apodized waveguide grating couplers for efficient coupling to optical fibers,” IEEE Photon. Technol. Lett.22(15), 1156–1158 (2010).
[CrossRef]

C. R. Doerr, L. Chen, Y. Chen, and L. L. Buhl, “Wide bandwidth silicon nitride grating coupler,” IEEE Photon. Technol. Lett.22(19), 1461–1463 (2010).
[CrossRef]

IEEE Trans. Microw. Theory Tech. (1)

S. T. Peng, T. Tamir, and H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microw. Theory Tech.23(1), 123–133 (1975).
[CrossRef]

J. Lightwave Technol. (1)

Jpn. J. Appl. Phys. (1)

D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys.45(8A), 6071–6077 (2006).
[CrossRef]

Nat. Photonics (1)

M. Hochberg and T. Baehr-Jones, “Towards fabless silicon photonics,” Nat. Photonics4(8), 492–494 (2010).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Proc. IEEE (1)

T. K. Gaylord and M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE73(5), 894–937 (1985).
[CrossRef]

Other (2)

R. G. Hunsperger, Integrated Optics: Theory and Technology (Springer, 2008).

T. Tamir, “Beam and waveguide couplers,” in Integrated Optics (Springer, 1975).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

(a) Grating coupler model for fiber to waveguide excitation and wavevector diagram (Wave expansion with wavevector from vector Floquet Condition [10]); (b) dispersion diagram.

Fig. 2
Fig. 2

Fiber Gaussian beam model and schematic grating coupler structure in coordination system.

Fig. 3
Fig. 3

Grating field decay and the bandwidth calculation by Eq. (2) and Eq. (11): (a) and (b) for C-I; (c) and (d) for C-II; (e) and (f) for C-III; (g) and (h) for C-IV.

Fig. 4
Fig. 4

(a) The analytic bandwidth calculation based on Eq. (2) and Eq. (11) for different fiber x-axis position d; (b) Comparison of the bandwidth calculation by FDTD simulation and analytic results. Inset: spectral response obtained by FDTD simulation.

Fig. 5
Fig. 5

(a) The analytic bandwidth calculation based on Eq. (2) and Eq. (11) for different fiber waist w0; (b) Comparison of the bandwidth calculation by FDTD simulation and analytic results. Inset: spectral response obtained by FDTD simulation.

Fig. 6
Fig. 6

The illustration of “effective interaction area” and its alteration as fibers beam waist and position changes.

Fig. 7
Fig. 7

(a) The analytic bandwidth calculation based on Eq. (2) and Eq. (11) for relatively large fiber position d;(b)The analytic bandwidth calculation for different field amplitude decay rate α

Fig. 8
Fig. 8

(a) The model of output coupling from waveguide to fiber coupling; (b) The typical intensity profile of the output radiation waves

Tables (1)

Tables Icon

Table 1 Grating parameters and bandwidth calculation by FDTD and formula

Equations (18)

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

Δβ= β w β 1 x = 2π λ n w ( 2π λ n 0 sin θ i + 2π Λ 0 )
Δβ=± 2π λ 0 | Δλ || 1 Λ 0 d n w (λ) dλ | λ= λ 0 |
s 0 (x)= E 0 e (x+d) 2 / w 0 2
{ s(x)= E 0 e (x+d) 2 / w 1 2 w 1 [ w 0 +htan(ψ)]/cos( θ i )
w 1 [ w 0 +h NA n 0 cos(ψ) ]/cos( θ i )
η=C | a(0) | 2
da(x) dx =(α+iΔβ)a(x)+cs(x)
η= C | Lg 0 e (α+iΔβ)x e (x+d) 2 / w 1 2 dx | 2
{ η= 1 4 C ' π w 1 2 e 1 2 (4αd+ α 2 w 1 2 Δ β 2 w 1 2 ) C erf C erf = | Erf[ d w 1 + 1 2 (α+Δβi) w 1 ]+Erf[ d+ L g w 1 + 1 2 (α+Δβi) w 1 ] | 2
η 0 = η η| Δβ=0 = e 1 2 Δ β 2 w 1 2 C erf C erf | Δβ=0
{ Δ λ 1dB = 1 | 1 Λ 0 d n w ( λ 0 ) dλ | C 1dB C 1dB = λ 0 2π w 1 ln10 5 +2ln C erf C erf | Δβ=0
Δ λ 1dB = 1 | 1 Λ 0 d n w ( λ 0 ) dλ | n 0 cos( θ i ) λ 0 2π[ w 0 n 0 +hNA/cos(ψ)] ln10 5 +2ln C erf C erf | Δβ=0
NA= n 0 sinψ λ 0 /π w 0
β q = β w +qK
β 1 x = β w 2π Λ 0
n 0 sin θ r (λ)= n w λ Λ 0
Δ λ 1dB = n 0 cos( θ 0 ) | 1 Λ 0 d n w ( λ 0 ) dλ | η 1dB
η 1dB = λ 0 2π[ w 0 n 0 +hNA/cos(ψ)] In10 5 +2In C erf C erf | Δβ=0

Metrics