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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 5 — Mar. 11, 2013
  • pp: 5688–5700
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Bandwidth analysis of waveguide grating coupler

Zhe Xiao, Tsung-Yang Liow, Jing Zhang, Ping Shum, and Feng Luan  »View Author Affiliations


Optics Express, Vol. 21, Issue 5, pp. 5688-5700 (2013)
http://dx.doi.org/10.1364/OE.21.005688


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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

Silicon photonic devices are promising for various optical processing on a dense integrated photonic chip fabricated by CMOS compatible technology [1

1. M. Hochberg and T. Baehr-Jones, “Towards fabless silicon photonics,” Nat. Photonics 4(8), 492–494 (2010). [CrossRef]

]. Diffraction grating couplers provide a practical and effective means of light coupling between fiber and chip. They are easier to package in a monolithic system and capable of multi-port applications. Efficiency and bandwidth are two critical specifications of planar waveguide grating couplers. While many novel techniques, such as adding bottom reflection mirror [2

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

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]

], apodized grating strength [4

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]

] and polysilicon overlay [5

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]

], were proposed to increase the coupling efficiency, only a few attempts have been reported to increase the coupling bandwidth. C. R. Doerr et.al first made an approximate calculation of the bandwidth of grating couplers by relating the efficiency drop in the coupling spectrum to the wavelength-dependent diffraction angles [6

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]

]. This approach overestimates the coupling bandwidth, as the grating dispersion effects have been neglected. Based on the same understanding, X. Chen et.al gave a supplemental discussion with the grating dispersion effects being considered [7

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]

]. We gave a different explanation on the bandwidth issue, attributing the coupling bandwidth to the mismatch of effective indices between the diffracted beam and the actual grating structure around the resonance wavelength [8

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]

], which more directly reveals the intrinsic bandwidth mechanism of grating couplers. However, all these aforementioned studies are only based on simple estimations rather than rigorous derivation. Especially, the 1 dB bandwidth coefficient introduced as a constant in these bandwidth approximations has no proper physics explanation, which is too rough that important details are ignored. In this paper, we derive the rigorous bandwidth formula for planar waveguide grating couplers based on the rigorous grating theory [9

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

]. We find that the 1 dB coefficient is not a constant value but a function of both fiber parameters such as beam waist and position and the grating parameters such as the field decay rate of the grating coupler etc. We investigate in detail the effect of each of these parameters on the bandwidth behavior. A complete analysis is presented based on the rigorous bandwidth formula, which offers new insights on grating bandwidth and also provides practical guidelines for grating design and fiber operation for wideband fiber-to-chip excitation. In the later discussion, the content is arranged as follows: In section 2, we start from the fiber-to-chip input coupling to derive the rigorous bandwidth formula. As a verification of the formula, the analytic results are compared with the FDTD simulation and reported experimental results for several grating couplers of different structures; in section 3, the effect of individual parameter on bandwidth performance is separately investigated, and an intuitive physics explanation is then given based on the results; owing to reciprocality of fiber-to-chip grating coupling system, the bandwidth formula is also adapt for the chip-to-fiber output coupling, in section 4, we will discuss and explain the rigorous bandwidth formula for the output coupling case. Finally, as a summary, several useful guidelines are presented for grating design and fiber operation.

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

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

In this section, we investigate the effect of individual parameter on bandwidth performance of planar waveguide grating couplers. We take grating coupler C-I as an example for this part discussion. Likewise, both the analytic results and FDTD calculation results are given as a comparison. In Eq. (11), the grating pitch and dispersion relationship are determined by the grating materials and structure, which are fixed after the grating design. Here, we focus on discussion of the parameters in C1dB including the fiber x-axis position d, fiber beam size w0 and amplitude decay factor α. Let us first examine the dependency of coupling bandwidth on the fiber position. Figure 4 (a)
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.
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.

Then, we investigate the effect of fiber beam waist w0 on the coupling bandwidth. In the same way, the analytic results are illustrated in Fig. 5(a)
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.
. 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.

Finally, we investigate the relationship between the bandwidth and the field amplitude decay rate α. The value of α mainly depends on the gating materials and structure parameters such as etching depth etc. However, α is not easy to be solely adjusted because other parameters in Eq. (11) such as grating pitch and dispersion will also changes correspondingly when the gating structure changes. Here, we just simply consider the monotonicity of the bandwidth versus the field amplitude decay rate α by assuming other parameters remain unchanged. In Fig. 7(b), we change the field amplitude decay rate α with value of 0.05, 0.15 and 0.25 to calculate the 1 dB bandwidth. We can see that the bandwidth monotonically increases with the increase of α.

4. Bandwidth for waveguide to fiber excitation

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

Acknowledgments

This work was supported in part by the Nanyang Technological University (NTU) under Grant NTU-SUG-M4080142 MOE RG24/10 and in part by the Institute of Microelectronics, Agency for Science, Technology and Research (A*STAR) Science and Engineering Research Council under Grant 1021290052.

References and links

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]

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. IEEE 73(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]

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

  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]

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