## Series-coupled silicon racetrack resonators and the Vernier effect: theory and measurement |

Optics Express, Vol. 18, Issue 24, pp. 25151-25157 (2010)

http://dx.doi.org/10.1364/OE.18.025151

Acrobat PDF (1127 KB)

### Abstract

Silicon-on-insulator racetrack resonators can be used as multiplexers in wavelength division multiplexing applications. The free spectral range should be comparable to the span of the C-band so that a maximum number of channels can be multiplexed. However, the free spectral range is inversely proportional to the length of the resonator and, therefore, bending losses can become non-negligible. A viable alternative to increase the free spectral range is to use the Vernier effect. In this work, we present the theory of series-coupled racetrack resonators exhibiting the Vernier effect. We demonstrate the experimental performance of the device using silicon-on-insulator strip waveguides. The extended free spectral range is 36 nm and the interstitial peak suppression is from 9 dB to 17 dB.

© 2010 Optical Society of America

## 1. Introduction

1. L. Zhang, Y. Li, M. Song, J. Yang, R. Beausoleil, and A. Willner, “Silicon microring-based signal modulation for chip-scale optical interconnection,” Appl. Phys. A **95**, 1089–1100 (2009). [CrossRef]

2. F. Xia, M. Rooks, L. Sekaric, and Y. Vlasov, “Ultra-compact high order ring resonator filters using submicron silicon photonic wires for on-chip optical interconnects,” Opt. Express **15**, 11934–11941 (2007). [CrossRef] [PubMed]

^{st}order, thermally tunable, two channel multiplexer based on SOI racetrack resonators was fabricated [3

3. P. Dong, W. Qian, H. Liang, R. Shafiiha, N. Feng, D. Feng, X. Zheng, A. V. Krishnamoorthy, and M. Asghari, “Low power and compact reconfigurable multiplexing devices based on silicon microring resonators,” Opt. Express **18**, 9852–9858 (2010). [CrossRef] [PubMed]

3. P. Dong, W. Qian, H. Liang, R. Shafiiha, N. Feng, D. Feng, X. Zheng, A. V. Krishnamoorthy, and M. Asghari, “Low power and compact reconfigurable multiplexing devices based on silicon microring resonators,” Opt. Express **18**, 9852–9858 (2010). [CrossRef] [PubMed]

2. F. Xia, M. Rooks, L. Sekaric, and Y. Vlasov, “Ultra-compact high order ring resonator filters using submicron silicon photonic wires for on-chip optical interconnects,” Opt. Express **15**, 11934–11941 (2007). [CrossRef] [PubMed]

4. M. S. Dahlem, C. W. Holzwarth, A. Khilo, F. X. Kartner, H. I. Smith, and E. P. Ippen, “Eleven-channel second-order silicon microring-resonator filterbank with tunable channel spacing,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (CD) (Optical Society of America, 2010), paper CMS5.

^{nd}order [4

4. M. S. Dahlem, C. W. Holzwarth, A. Khilo, F. X. Kartner, H. I. Smith, and E. P. Ippen, “Eleven-channel second-order silicon microring-resonator filterbank with tunable channel spacing,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (CD) (Optical Society of America, 2010), paper CMS5.

^{th}order [5], and 5

^{th}order [2

2. F. Xia, M. Rooks, L. Sekaric, and Y. Vlasov, “Ultra-compact high order ring resonator filters using submicron silicon photonic wires for on-chip optical interconnects,” Opt. Express **15**, 11934–11941 (2007). [CrossRef] [PubMed]

6. B. Timotijevic, G. Mashanovich, A. Michaeli, O. Cohen, V. M. N. Passaro, J. Crnjanski, and G. T. Reed, “Tailoring the spectral response of add/drop single and multiple resonators in silicon-on-insulator,” Chin. Opt. Lett. **7**, 291–295 (2009). [CrossRef]

6. B. Timotijevic, G. Mashanovich, A. Michaeli, O. Cohen, V. M. N. Passaro, J. Crnjanski, and G. T. Reed, “Tailoring the spectral response of add/drop single and multiple resonators in silicon-on-insulator,” Chin. Opt. Lett. **7**, 291–295 (2009). [CrossRef]

6. B. Timotijevic, G. Mashanovich, A. Michaeli, O. Cohen, V. M. N. Passaro, J. Crnjanski, and G. T. Reed, “Tailoring the spectral response of add/drop single and multiple resonators in silicon-on-insulator,” Chin. Opt. Lett. **7**, 291–295 (2009). [CrossRef]

## 2. Theory

*X*=

_{i}*exp*(−

*αL*/2 +

_{i}*iφ*),

_{i}*t*= (1 –

_{i}*κ*)

_{i}^{1/2},

*φ*= (2

_{i}*πn*)/

_{g}L_{i}*λ*,

*α*[/m] is the total loss coefficient,

*L*

_{1}[m] and

*L*

_{2}[m] are the total lengths of the first and second racetrack resonator, respectively,

*λ*is the wavelength,

*n*is the group index,

_{g}*κ*

_{1}and

*κ*

_{3}are the symmetric (real) point power coupling factors to the bus waveguides, and

*κ*

_{2}is the (real) point inter-ring power coupling factor.

*n*is given by [11] where

_{g}*n*is the effective index and T is temperature.

_{eff}*n*is

_{eff}*λ*and T dependent since the refractive indices of Si and SiO

_{2}are functions of

*λ*and T.

*n*can be calculated using a mode solver and the λ and T dependency of the refractive indices can be modeled using experimental data [12

_{eff}12. N. Rouger, L. Chrostowski, and R. Vafaei, “Temperature Effects on Silicon-on-Insulator (SOI) Racetrack Resonators: A Coupled Analytic and 2-D Finite Difference Approach,” J. Lightwave Technol. **28**, 1380–1391 (2010). [CrossRef]

14. C. Z. Tan and J. Arndt, “Temperature dependence of refractive index of glassy SiO2 in the infrared wavelength range,” J. Phys. Chem. Solids **61**, 1315–1320 (2000). [CrossRef]

*m*

_{1}and

*m*

_{2}are chosen to be 9 and 7, respectively. To remove the occurrence of the twin peaks,

*m*

_{2}should be equal to

*m*

_{1}-1 (assuming

*m*

_{1}>

*m*

_{2}). The optimized device shown in Fig. 2(a) has an interstitial peak suppression greater than 41.8 dB which is sufficient for WDM applications. Figure 2(b) shows that the optimized device does not have any main resonance peak splitting. If we increase

*m*

_{1}(and

*m*

_{2}), the interstitial peak suppression decreases. Thus,

*m*

_{1}needs to be small enough to give adequate interstitial peak suppression. The choice of

*L*

_{1}and

*L*

_{2}determines the extended FSR. The power coupling factors need to be optimized to obtain high main resonance intensity, minimal main resonance splitting, and large interstitial peak suppression [15

15. O. Schwelb, “The nature of spurious mode suppression in extended FSR microring multiplexers,” Opt. Commun. **271**, 424–429 (2007). [CrossRef]

## 3. Experimental results

*μ*m long tapers (to ensure single mode propagation for the TE-polarization) are used [17

17. W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert, B. Luyssaert, J. V. Campenhout, P. Bienstman, and D. V. Thourhout, “Nanophotonic Waveguides in Silicon-on-Insulator Fabricated With CMOS Technology,” J. Lightwave Technol. **23**, 401 (2005). [CrossRef]

*μ*m. These waveguide dimensions typically result in about 20 dB/cm propagation loss [18

18. P. Dumon, W. Bogaerts, V. Wiaux, J. Wouters, S. Beckx, J. Van Campenhout, D. Taillaert, B. Luyssaert, P. Bienstman, D. Van Thourhout, and R. Baets, “Low-Loss SOI Photonic Wires and Ring Resonators Fabricated With Deep UV Lithography,” IEEE Photon. Technol. Lett. **16**, 1328–1330 (2004). [CrossRef]

*m*

_{2}= 4 and

*m*

_{1}= 5 (ratio equal to 0.8), which turns out to be the same values as given in [16]. The straight sections of the racetrack resonator,

*L*, are 15

_{c}*μ*m. The radii (defined from the centers of the waveguides),

*R*

_{1}and

*R*

_{2}, of the half-circle sections of the racetrack resonators are 6.545

*μ*m and 4.225

*μ*m, respectively. A small straight section of 50 nm is added to the middle of each half-circle of the racetrack resonator. This straight section was inserted so that several devices with different total resonator lengths (different straight section length) could be fabricated while the power coupling factors remained the same. However, this straight section can increase the scattering losses. The ratio of

*L*

_{2}to

*L*

_{1}is 0.7953. The gap distances for the inter-ring coupling region and the two coupling regions to the bus waveguides are approximately 410 nm and 230 nm, respectively. Figure 3 shows scanning-electron micrographs (SEMs) of the fabricated device.

19. M. A. Popovic, E. P. Ippen, and F. X. Kartner, “Universally balanced photonic interferometers,” Opt. Lett. **31**, 2713–2715 (2006). [CrossRef] [PubMed]

19. M. A. Popovic, E. P. Ippen, and F. X. Kartner, “Universally balanced photonic interferometers,” Opt. Lett. **31**, 2713–2715 (2006). [CrossRef] [PubMed]

20. A. Fallahkhair, K. S. Li, and T. E. Murphy, “Vector Finite Difference Modesolver for Anisotropic Dielectric Waveguides,” J. Lightwave Technol. **26**, 1423–1431 (2008). [CrossRef]

*κ*

_{1}= 0.3665,

*κ*

_{2}= 0.02485 and

*κ*

_{3}= 0.3665. From these values, we determine the gap distances using supermode analysis to be between 405 nm and 410 nm for the inter-ring coupling region and between 230 nm and 235 nm for the two coupling regions to the bus waveguides, which are very close to the values determined from the SEM images in Fig. 3(a) and Fig. 3(b). The curve-fit takes into account the wavelength dependency of the power coupling factors using the 2D FD mode solver.

^{o}[21] and a trapezoidal waveguide structure will change the effective index as well as the gap distances); (2) the group index is assumed to be wavelength independent; (3) the height of the waveguide is assumed to be 220 nm; (4) the waveguide curvature is neglected for

*n*calculations; and (5) the distance between waveguides is not considered for

_{eff}*n*calculations.

_{eff}*μ*m and 4.225

*μ*m are approximately 1091 and 1157, respectively. The periodic resonance peaks of both racetrack resonators overlap at 1502.44 nm and 1538.24 nm. The difference between these two resonance wavelengths is 35.8 nm, which is close to value of the extended FSR shown in Fig. 4(a).

## 4. Summary

## Acknowledgments

## References and links

1. | L. Zhang, Y. Li, M. Song, J. Yang, R. Beausoleil, and A. Willner, “Silicon microring-based signal modulation for chip-scale optical interconnection,” Appl. Phys. A |

2. | F. Xia, M. Rooks, L. Sekaric, and Y. Vlasov, “Ultra-compact high order ring resonator filters using submicron silicon photonic wires for on-chip optical interconnects,” Opt. Express |

3. | P. Dong, W. Qian, H. Liang, R. Shafiiha, N. Feng, D. Feng, X. Zheng, A. V. Krishnamoorthy, and M. Asghari, “Low power and compact reconfigurable multiplexing devices based on silicon microring resonators,” Opt. Express |

4. | M. S. Dahlem, C. W. Holzwarth, A. Khilo, F. X. Kartner, H. I. Smith, and E. P. Ippen, “Eleven-channel second-order silicon microring-resonator filterbank with tunable channel spacing,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (CD) (Optical Society of America, 2010), paper CMS5. |

5. | M. Popovic, T. Barwicz, M. Dahlem, F. Gan, C. Holzwarth, P. Rakich, H. Smith, E. Ippen, and F. Kartner, “Tunable, fourth-order silicon microring-resonator add-drop filters,” IET Digest |

6. | B. Timotijevic, G. Mashanovich, A. Michaeli, O. Cohen, V. M. N. Passaro, J. Crnjanski, and G. T. Reed, “Tailoring the spectral response of add/drop single and multiple resonators in silicon-on-insulator,” Chin. Opt. Lett. |

7. | L. Jin, M. Li, and J. He, “Experimental investigation of waveguide sensor based on cascaded-microring resonators with Vernier effect,” in 2010 Conference on Lasers and Electro-Optics (CLEO) and Quantum Electronics and Laser Science Conference (QELS), 1–2 (2010). |

8. | P. Koonath, T. Indukuri, and B. Jalali, “3-D integrated Vernier filters in silicon,” in |

9. | T. Chu, N. Fujioka, S. Nakamura, M. Tokushima, and M. Ishizaka, “Compact, low power consumption wavelength tunable laser with silicon photonic-wire waveguide micro-ring resonators,” in 35th European Conference On Optical Communication (ECOC), 1–2 (2009). |

10. | R. Boeck, N. A. F. Jaeger, and L. Chrostowski, “Experimental Demonstration of the Vernier Effect using Series-Coupled Racetrack Resonators,” in 2010 International Conference on Optical MEMS & Nanophotonics (2010). |

11. | D. G. Rabus, |

12. | N. Rouger, L. Chrostowski, and R. Vafaei, “Temperature Effects on Silicon-on-Insulator (SOI) Racetrack Resonators: A Coupled Analytic and 2-D Finite Difference Approach,” J. Lightwave Technol. |

13. | H. H. Li, “Refractive index of silicon and germanium and its wavelength and temperature derivatives,” J. Phys. Chem. Ref. Data |

14. | C. Z. Tan and J. Arndt, “Temperature dependence of refractive index of glassy SiO2 in the infrared wavelength range,” J. Phys. Chem. Solids |

15. | O. Schwelb, “The nature of spurious mode suppression in extended FSR microring multiplexers,” Opt. Commun. |

16. | C. Chaichuay, P. P. Yupapin, and P. Saeung, “The serially coupled multiple ring resonator filters and Vernier effect,” Opt. Appl. |

17. | W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert, B. Luyssaert, J. V. Campenhout, P. Bienstman, and D. V. Thourhout, “Nanophotonic Waveguides in Silicon-on-Insulator Fabricated With CMOS Technology,” J. Lightwave Technol. |

18. | P. Dumon, W. Bogaerts, V. Wiaux, J. Wouters, S. Beckx, J. Van Campenhout, D. Taillaert, B. Luyssaert, P. Bienstman, D. Van Thourhout, and R. Baets, “Low-Loss SOI Photonic Wires and Ring Resonators Fabricated With Deep UV Lithography,” IEEE Photon. Technol. Lett. |

19. | M. A. Popovic, E. P. Ippen, and F. X. Kartner, “Universally balanced photonic interferometers,” Opt. Lett. |

20. | A. Fallahkhair, K. S. Li, and T. E. Murphy, “Vector Finite Difference Modesolver for Anisotropic Dielectric Waveguides,” J. Lightwave Technol. |

21. | P. Dumon, “Ultra-Compact Integrated Optical Filters in Silicon-on-insulator by Means of Wafer-Scale Technology,” PhD Thesis, Universiteit Gent, (2007). |

**OCIS Codes**

(130.0130) Integrated optics : Integrated optics

(230.5750) Optical devices : Resonators

(130.7408) Integrated optics : Wavelength filtering devices

**ToC Category:**

Integrated Optics

**History**

Original Manuscript: August 24, 2010

Revised Manuscript: October 22, 2010

Manuscript Accepted: November 2, 2010

Published: November 17, 2010

**Citation**

Robi Boeck, Nicolas A. Jaeger, Nicolas Rouger, and Lukas Chrostowski, "Series-coupled silicon racetrack resonators and the Vernier effect: theory and measurement," Opt. Express **18**, 25151-25157 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-24-25151

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### References

- L. Zhang, Y. Li, M. Song, J. Yang, R. Beausoleil, and A. Willner, "Silicon microring-based signal modulation for chip-scale optical interconnection," Appl. Phys. A 95, 1089-1100 (2009). [CrossRef]
- F. Xia, M. Rooks, L. Sekaric, and Y. Vlasov, "Ultra-compact high order ring resonator filters using submicron silicon photonic wires for on-chip optical interconnects," Opt. Express 15, 11934-11941 (2007). [CrossRef] [PubMed]
- P. Dong, W. Qian, H. Liang, R. Shafiiha, N. Feng, D. Feng, X. Zheng, A. V. Krishnamoorthy, and M. Asghari, "Low power and compact reconfigurable multiplexing devices based on silicon microring resonators," Opt. Express 18, 9852-9858 (2010). [CrossRef] [PubMed]
- M. S. Dahlem, C. W. Holzwarth, A. Khilo, F. X. Kartner, H. I. Smith, and E. P. Ippen, "Eleven-channel second-order silicon microring-resonator filterbank with tunable channel spacing," in Conference on Lasers and Electro-Optics, OSA Technical Digest (CD) (Optical Society of America, 2010), paper CMS5.
- M. Popovic, T. Barwicz, M. Dahlem, F. Gan, C. Holzwarth, P. Rakich, H. Smith, E. Ippen, and F. Kartner, "Tunable, fourth-order silicon microring-resonator add-drop filters," IET Digest 123, (2007).
- B. Timotijevic, G. Mashanovich, A. Michaeli, O. Cohen, V. M. N. Passaro, J. Crnjanski, and G. T. Reed, "Tailoring the spectral response of add/drop single and multiple resonators in silicon-on-insulator," Chin. Opt. Lett. 7, 291-295 (2009). [CrossRef]
- L. Jin, M. Li, and J. He, "Experimental investigation of waveguide sensor based on cascaded-microring resonators with Vernier effect," in 2010 Conference on Lasers and Electro-Optics (CLEO) and Quantum Electronics and Laser Science Conference (QELS), 1-2 (2010).
- P. Koonath, T. Indukuri, and B. Jalali, "3-D integrated Vernier filters in silicon," in Integrated Photonics Research and Applications/Nanophotonics, Technical Digest (CD) (Optical Society of America, 2006), paper IMG1.
- T. Chu, N. Fujioka, S. Nakamura, M. Tokushima, and M. Ishizaka, "Compact, low power consumption wavelength tunable laser with silicon photonic-wire waveguide micro-ring resonators," in 35th European Conference On Optical Communication (ECOC), 1-2 (2009).
- R. Boeck, N. A. F. Jaeger, and L. Chrostowski, "Experimental Demonstration of the Vernier Effect using Series-Coupled Racetrack Resonators," in 2010 International Conference on Optical MEMS & Nanophotonics (2010).
- D. G. Rabus, Integrated Ring Resonators: The Compendium, 1st ed. (Springer, 2007).
- N. Rouger, L. Chrostowski, and R. Vafaei, "Temperature Effects on Silicon-on-Insulator (SOI) Racetrack Resonators: A Coupled Analytic and 2-D Finite Difference Approach," J. Lightwave Technol. 28, 1380-1391 (2010). [CrossRef]
- H. H. Li, "Refractive index of silicon and germanium and its wavelength and temperature derivatives," J. Phys. Chem. Ref. Data 9, 561 (1980). [CrossRef]
- C. Z. Tan, and J. Arndt, "Temperature dependence of refractive index of glassy SiO2 in the infrared wavelength range," J. Phys. Chem. Solids 61, 1315-1320 (2000). [CrossRef]
- O. Schwelb, "The nature of spurious mode suppression in extended FSR microring multiplexers," Opt. Commun. 271, 424-429 (2007). [CrossRef]
- C. Chaichuay, P. P. Yupapin, and P. Saeung, "The serially coupled multiple ring resonator filters and Vernier effect," Opt. Appl. XXXIX, (2009).
- W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert, B. Luyssaert, J. V. Campenhout, P. Bienstman, and D. V. Thourhout, "Nanophotonic Waveguides in Silicon-on-Insulator Fabricated With CMOS Technology," J. Lightwave Technol. 23, 401 (2005). [CrossRef]
- P. Dumon, W. Bogaerts, V. Wiaux, J. Wouters, S. Beckx, J. Van Campenhout, D. Taillaert, B. Luyssaert, P. Bienstman, D. Van Thourhout, and R. Baets, "Low-Loss SOI Photonic Wires and Ring Resonators Fabricated With Deep UV Lithography," IEEE Photon. Technol. Lett. 16, 1328-1330 (2004). [CrossRef]
- M. A. Popovic, E. P. Ippen, and F. X. Kartner, "Universally balanced photonic interferometers," Opt. Lett. 31, 2713-2715 (2006). [CrossRef] [PubMed]
- A. Fallahkhair, K. S. Li, and T. E. Murphy, "Vector Finite Difference Modesolver for Anisotropic Dielectric Waveguides," J. Lightwave Technol. 26, 1423-1431 (2008). [CrossRef]
- P. Dumon, "Ultra-Compact Integrated Optical Filters in Silicon-on-insulator by Means of Wafer-Scale Technology," PhD Thesis, Universiteit Gent, (2007).

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