## Bandwidth analysis of waveguide grating coupler |

Optics Express, Vol. 21, Issue 5, pp. 5688-5700 (2013)

http://dx.doi.org/10.1364/OE.21.005688

Acrobat PDF (1273 KB)

### 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

## 1. Introduction

1. M. Hochberg and T. Baehr-Jones, “Towards fabless silicon photonics,” Nat. Photonics **4**(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. Express **14**(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]

## 2. Derivation of rigorous bandwidth formula for fiber-to-chip excitation

## 3. Investigation of the effect of individual parameter on bandwidth behavior

*C*

_{1dB}including the fiber x-axis position

*d*, fiber beam size

*w*

_{0}and amplitude decay factor α. Let us first examine the dependency of coupling bandwidth on the fiber position. Figure 4 (a) illustrates the bandwidth calculated by Eqs. (2) and (11) for a group of different fiber position values. It can be seen that the 1 dB bandwidth decreases with increase of fiber position

*d*. The same trend is also achieved by the FDTD results shown in the inset of Fig. 4(b). The comparison of bandwidth calculation by the rigorous equations and simulation results is also illustrated in Fig. 4(b), which indicates a good agreement. The small difference (ceiling to 4 nm) of both bandwidth results comes from the calculation accuracy limitation.

*w*

_{0}on the coupling bandwidth. In the same way, the analytic results are illustrated in Fig. 5(a). It can be observed that the coupling bandwidth will increase when the grating is excited by a fiber beam with smaller waist. The results of FDTD calculation are given in the inset of Fig. 5(b), which verifies the trend. The comparison of 1 dB bandwidth calculated by the rigorous equations and simulation results is given in Fig. 5(b). By comparing the Fig. 4(b) and Fig. 5(b), we observe that to adjust the beam waist is a better choice to broaden the coupling bandwidth because it would not induce great efficiency drop meanwhile increasing the coupling bandwidth. In addition, according to Eq. (13), it is known that the Gaussian beam with smaller beam waist exerts a larger numerical aperture. It means that to increase the incident beam numerical aperture will also broaden the coupling bandwidth.

*λ*

_{1dB}is mainly affected by the parameters of

*C*

_{1dB}in Eq. (11). By examining the mathematic properties of

*C*

_{1dB}, we give a more intuitive explanation for these relationships. We first introduce a definition of “effective interaction area”, that is, the fiber beam effectively covered grating area. In Fig. 6(a), the dash-line labeled area indicates the effective interaction area. In actuality, to alter the fiber beam waist or position is inherently changing the size of effective interaction area and power distribution in the area. Figure 6(b) intuitively illustrates the effective interaction area when fibers beam waist and position changes. It is clear that a larger beam waist or a further distance between the fiber center and the first gating pitch (x = 0) exerts a larger interaction area, which will result in narrower coupling bandwidth according to the aforementioned discussion. The trends can be simply understood that since the wavevector mismatch always exists in the effective interaction area for the wavelengths that deviating theresonance wavelength

*λ*

_{0}, so a longer traveling distance in the area will induce more serious efficiency drop for these wavelengths and therefore narrow down the coupling bandwidth. Moreover, as stated by Eqs. (7) and (8), the reduced field amplitude

*a*(

*x*) in the grating region has a factor of

*α*is the field amplitude decay rate and Δ

*β*i can be also viewed as a decay factor. Since the integral operation needs to be done over the whole effective interaction area, a longer effective interaction area in the propagation direction therefore results in a smaller coupling bandwidth. It is easy to imagine that the size of the effective interaction area will become constant while the distance

*d*from the first gating pitch to fiber center is large enough (larger than

*w*

_{1}). In Fig. 7(a), we show the bandwidth calculation for the case that the fiber is put relatively far away from the grating beginning (

*d*equals to 10, 11, 12 and 20 µm). It can be seen that the 1 dB bandwidth is almost changeless (about 30nm) even though

*d*keep increasing. The results are verified by FDTD simulation as well.

## 4. Bandwidth for waveguide to fiber excitation

## 5. Summary and guidelines for grating coupler design and fiber operation

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]

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]

## Acknowledgments

## References and links

1. | M. Hochberg and T. Baehr-Jones, “Towards fabless silicon photonics,” Nat. Photonics |

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. |

3. | I. A. Avrutsky, A. S. Svakhin, V. A. Sychugov, and O. Parriaux, “High-efficiency single-order waveguide grating coupler,” Opt. Lett. |

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. |

5. | G. Roelkens, D. Van Thourhout, and R. Baets, “High efficiency silicon-on-Insulator grating coupler based on a poly-silicon overlay,” Opt. Express |

6. | C. R. Doerr, L. Chen, Y. Chen, and L. L. Buhl, “Wide bandwidth silicon nitride grating coupler,” IEEE Photon. Technol. Lett. |

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. |

8. | Z. Xiao, F. Luan, T. Y. Liow, J. Zhang, and P. Shum, “Design for broadband high-efficiency grating couplers,” Opt. Lett. |

9. | T. Tamir, “Beam and waveguide couplers,” in |

10. | T. K. Gaylord and M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE |

11. | R. G. Hunsperger, |

12. | J. C. Brazas and L. Li, “Analysis of input-grating couplers having finite lengths,” Appl. Opt. |

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. |

14. | T. Tamir and S. T. Peng, “Analysis and Design of Grating Couplers,” Appl. Phys. (Berl.) |

15. | S. T. Peng, T. Tamir, and H. L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microw. Theory Tech. |

16. | S. Miyanaga and T. Asakura, “Intensity profile of outgoing beams from uniform and linearly tapered grating couplers,” Appl. Opt. |

**OCIS Codes**

(050.1950) Diffraction and gratings : Diffraction gratings

(130.0130) Integrated optics : Integrated optics

**ToC Category:**

Integrated Optics

**History**

Original Manuscript: October 26, 2012

Revised Manuscript: November 14, 2012

Manuscript Accepted: November 20, 2012

Published: March 1, 2013

**Citation**

Zhe Xiao, Tsung-Yang Liow, Jing Zhang, Ping Shum, and Feng Luan, "Bandwidth analysis of waveguide grating coupler," Opt. Express **21**, 5688-5700 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-5-5688

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### References

- M. Hochberg and T. Baehr-Jones, “Towards fabless silicon photonics,” Nat. Photonics4(8), 492–494 (2010). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- T. Tamir, “Beam and waveguide couplers,” in Integrated Optics (Springer, 1975).
- T. K. Gaylord and M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE73(5), 894–937 (1985). [CrossRef]
- R. G. Hunsperger, Integrated Optics: Theory and Technology (Springer, 2008).
- J. C. Brazas and L. Li, “Analysis of input-grating couplers having finite lengths,” Appl. Opt.34(19), 3786–3792 (1995). [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]
- 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]
- 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]

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