## Continuously tunable slow-light device consisting of heater-controlled silicon microring array |

Optics Express, Vol. 19, Issue 14, pp. 13557-13564 (2011)

http://dx.doi.org/10.1364/OE.19.013557

Acrobat PDF (1364 KB)

### Abstract

We experimentally demonstrate a tunable slow-light device consisting of all-pass Si microrings. A compact device of 0.014 mm^{2} footprint is fabricated by using CMOS-compatible process, and its center wavelength, bandwidth and delay are continuously tuned by integrated heaters. The tuning range is 300 ps at fixed wavelengths with a 1 nm bandwidth. Eye opening of 40 Gbps non-return-to-zero signals is observed at up to a 150 ps delay and a 4 bit buffering capacity is confirmed, which corresponds to a spatial buffering density of 0.29 kbit/mm^{2}.

© 2011 OSA

## 1. Introduction

1. R. S. Tucker, P.-C. Ku, and C. Chang-Hasnain, “Slow-light optical buffers - capabilities and fundamental limitations,” J. Lightwave Technol. **23**(12), 4046–4066 (2005). [CrossRef]

2. T. Baba, “Slow light in photonic crystals,” Nat. Photonics **2**(8), 465–473 (2008). [CrossRef]

3. T. Baba, T. Kawaaski, H. Sasaki, J. Adachi, and D. Mori, “Large delay-bandwidth product and tuning of slow light pulse in photonic crystal coupled waveguide,” Opt. Express **16**(12), 9245–9253 (2008). [CrossRef] [PubMed]

4. J. Adachi, N. Ishikura, H. Sasaki, and T. Baba, “Wide range tuning of slow light pulse in SOI photonic crystal coupled waveguide via folded chirping,” IEEE J. Sel. Top. Quantum Electron. **16**(1), 192–199 (2010). [CrossRef]

5. J. Yang, N. K. Fontaine, Z. Pan, A. O. Karalar, S. S. Djordjevic, C. Yang, W. Chen, S. Chu, B. E. Little, and S. J. B. Yoo, “Continuously tunable, wavelength-selective buffering in optical packet switching network,” IEEE Photon. Technol. Lett. **20**(12), 1030–1032 (2008). [CrossRef]

7. J. Cardenas, M. A. Foster, N. Sherwood-Droz, C. B. Poitras, H. L. R. Lira, B. Zhang, A. L. Gaeta, J. B. Khurgin, P. Morton, and M. Lipson, “Wide-bandwidth continuously tunable optical delay line using silicon microring resonators,” Opt. Express **18**(25), 26525–26534 (2010). [CrossRef] [PubMed]

8. A. Melloni, F. Morichetti, C. Ferrari, and M. Martinelli, “Continuously tunable 1 byte delay in coupled-resonator optical waveguides,” Opt. Lett. **33**(20), 2389–2391 (2008). [CrossRef] [PubMed]

9. A. Melloni, A. Canciamilla, C. Ferrari, F. Morichetti, L. O'Faolain, T. F. Krauss, R. De La Rue, A. Samarelli, and M. Sorel, “Tunable delay lines in silicon photonics: coupled resonators and photonic crystals, a comparison,” IEEE Photon. J. **2**(2), 181–194 (2010). [CrossRef]

10. Q. Li, F. Liu, Z. Zhang, M. Qiu, and Y. Su, “System performances of on-chip silicon microring delay line for RZ, CSRZ, RZ-DB and RZ-AMI signals,” J. Lightwave Technol. **26**(23), 3744–3751 (2008). [CrossRef]

11. F. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics **1**(1), 65–71 (2007). [CrossRef]

7. J. Cardenas, M. A. Foster, N. Sherwood-Droz, C. B. Poitras, H. L. R. Lira, B. Zhang, A. L. Gaeta, J. B. Khurgin, P. Morton, and M. Lipson, “Wide-bandwidth continuously tunable optical delay line using silicon microring resonators,” Opt. Express **18**(25), 26525–26534 (2010). [CrossRef] [PubMed]

7. J. Cardenas, M. A. Foster, N. Sherwood-Droz, C. B. Poitras, H. L. R. Lira, B. Zhang, A. L. Gaeta, J. B. Khurgin, P. Morton, and M. Lipson, “Wide-bandwidth continuously tunable optical delay line using silicon microring resonators,” Opt. Express **18**(25), 26525–26534 (2010). [CrossRef] [PubMed]

**18**(25), 26525–26534 (2010). [CrossRef] [PubMed]

## 2. Theory

*T*(λ) is expressed as [12]where

*T*

_{0}is the single pass transmittance at the directional coupling,

*A*is the single round trip loss in the ring defined as

*A*≡

*e*

^{−αℓ}(

*A*~1 in many cases), α is the average loss coefficient in the ring including waveguide loss, bend loss, and the scattering loss at the directional coupling, ℓ is the orbital length of the ring, and

*n*

_{eq}is the modal equivalent index of the waveguide. Then the full width at half maximum of the resonance, Δλ

_{0}, is derived aswhere

*n*

_{g}is the group index of the waveguide. At the resonant wavelength λ

_{0}, the loss

*L*

_{0}and delay Δ

*t*

_{0}occur due to round trips in the ring. Expressions for them in Refs. [12,13

13. H. P. Uranus and H. J. W. M. Hoekstra, “Modeling of loss-induced superluminal and negative group velocity in two-port ring-resonator circuits,” J. Lightwave Technol. **25**(9), 2376–2384 (2007). [CrossRef]

_{0}decreases while

*L*

_{0}and Δ

*t*

_{0}increase when

*T*

_{0}approaches unity. For any slow light device, the delay-bandwidth product

*DBP*≡ Δ

*t*Δ

*f*constrains the buffering capacity [1

1. R. S. Tucker, P.-C. Ku, and C. Chang-Hasnain, “Slow-light optical buffers - capabilities and fundamental limitations,” J. Lightwave Technol. **23**(12), 4046–4066 (2005). [CrossRef]

2. T. Baba, “Slow light in photonic crystals,” Nat. Photonics **2**(8), 465–473 (2008). [CrossRef]

_{0}. The time-bandwidth product of the pulses increases to 0.693 after they pass through the ring having the same bandwidth as the pulse's. Then, the buffering capacity

*M*[bit] is give by η

*DBP*/0.693

*=*1.44

*ηDBP*, where

*η*is the spectral efficiency defined as the ratio of the pulse bandwidth to the ring bandwidth. From these equations,Note that

*DBP*and

*M*are independent of the ring size because a larger ring gives a longer delay and a narrowed bandwidth. From Eqs. (3) and (4), the buffering loss is given byThe pitch

*p*in Fig. 1(b) can be regarded as the longitudinal length of the device. Then,

*p*and the device footprint

*S*

_{0}of the single ring model are approximated aswhere δ is a correction factor expressing a modified shape of the ring from the circular one (e.g. racetrack) and the space between the rings. The effective group index

*n*

_{geff}of the device is give byThe normalized delay-bandwidth product

*n*

_{geff}(Δλ

_{0}/λ

_{0}) [2

2. T. Baba, “Slow light in photonic crystals,” Nat. Photonics **2**(8), 465–473 (2008). [CrossRef]

*FOM*of slow light, and

*FOM*leads the spatial buffering density such that Equations (6) and (8) indicate that a smaller ℓ directly contributes to reducing the footprint, as well as enhancing

*FOM*and the buffering density. (This is not the case for photonic crystal devices;

*FOM*is independent of the device length while

*DBP*and

*M*increase with the length.) For the microring, ℓ can be reduced by employing a high-index-contrast waveguide. This is the reason that we employ Si wire waveguides in this study rather than other low-index-contrast waveguides. Equations (3) and (5) also imply that the loss could be reduced by a small ℓ. However, it is not straightforward because high-index-contrast waveguides usually have a larger α due to the stronger light scattering from the disordering in fabricated devices.

*N*rings having the same λ

_{0}(Fig. 1(b)),

*T*(λ) is given by multiplying Eq. (1)

*N*times. Here, the second term in Eq. (1) is much smaller than unity in many cases. Therefore,

*T*(λ) is approximated asUnder this condition, the total loss

*L*, delay Δ

*t*,

*DBP*and footprint

*S*simply become

*N*times larger, maintaining almost the same Δλ

_{0}. On the other hand, when rings have different λ

_{0}due to the localized index change (Fig. 1(c)), the second term of Eq. (1) is replaced by the sum of all rings’ when the same approximation as for Eq. (9) is used, i.e.In this case, Δλ of the envelope spectrum becomes larger than Δλ

_{0}, and

*L*and Δ

*t*are reduced. Their minimum values will be the same as those for the single ring model when the spectra are completely split.

## 3. Fabrication

*n*

_{g}is calculated by using finite element method to be 4.2 at λ = 1.53 μm. The bus waveguide is terminated at input and output ends by inverse-taper-type fiber coupler, where the tip width of the Si inverse taper is 0.18 μm and the end waveguides are silica rectangular channels of (4 μm)

^{2}cross-section. The coupling loss from lensed single mode fiber of 3 μm spot diameter to the bus waveguide is ~3.5 dB on each side (this loss can be reduced to 0.4 dB if the tip width is narrowed to 80 nm [14

14. T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, S. Uchiyama, and S. Itabashi, “Low-loss Si wire waveguides and their application to thermooptic switches,” Jpn. J. Appl. Phys. **45**(No. 8B), 6658–6662 (2006). [CrossRef]

*n*

_{g}and ℓ to be 11.9 nm at λ = 1.53 μm. When the gap between the waveguide and ring,

*g*, is 0.23 μm,

*T*

_{0}is calculated to be 0.65 by using three-dimensional finite-difference time-domain simulation. The scattering loss at the coupling is also calculated to be 0.4%. Considering this value and an average waveguide loss of 4 dB/cm, α is estimated to be 1.84 cm

^{−1}, which ensures the above assumptions that

*A*~1 and the second term in Eq. (1) is much smaller than unity. Substituting these values into Eqs. (2)–(4) gives Δλ

_{0}= 0.84 nm,

*L*= 0.35

*N*[dB], Δ

*t*= 6.1

*N*[ps] and

*DBP*= 0.64

*N*. Provided that the total insertion loss including the fiber coupling must be less than 30 dB so that the loss can be recovered by standard optical amplifier,

*N*is set at 50, for which we calculate

*L*= 17.4 dB, Δ

*t*= 305 ps and

*DBP*= 32.

*p*(1 + δ)

*N*is 1060 μm, and the total footprint

*S*=

*S*

_{0}

*N*only counting rings and the bus waveguide is as small as 0.014 mm

^{2}. From these values, Eqs. (4), (5), (7), (8) predict

*M*= 46

*η*[bits],

*L*

_{0}/

*M*= 0.38/

*η*[dB/bit],

*n*

_{geff}= 95,

*FOM*= 0.051, and

*M*/

*S*= 3.2

*η*[kbit/mm

^{2}].

## 4. Measurement

*g*. The spectral dip and delay peak are very simple and smooth, which may be difficult to obtain in CROW. Such a dip and peak were observed periodically with a free spectral range of 11.9 nm at λ ~1.53 μm. It completely agrees with the aforementioned calculated value, which assures that other calculated values are also correct. The delay and loss at the resonance increase with increasing

*g*. At

*g*= 0.23 μm, the experimentally measured values are Δλ = 1.0 nm,

*L*= 18 dB, Δ

*t*= 300 ps,

*DBP*= 36,

*n*

_{geff}= 85 and

*FOM*= 0.056, all of which are in good agreement with theoretical values. This

*FOM*is 4 − 5 fold smaller than typical values of 0.2 − 0.3 for photonic crystal devices. It is a reasonable result because the phase shift at the resonance of rings is smaller than that of photonic crystals under the slow light condition.

11. F. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics **1**(1), 65–71 (2007). [CrossRef]

*t*is controlled in the range of 4 – 300 ps. At Δ

*t*≥ 150 ps, Δ

*t*and the bandwidth are changed continuously while maintaining the peak wavelength. Αt Δ

*t*= 150 ps, a flat top spectrum of 1.3 nm width is obtained. At Δ

*t*< 150 ps, the heating power to the inner heaters increased and the thermal crosstalk became severer. Since the temperature slope was not sufficient under this condition, it was difficult to expand the bandwidth further at the same wavelength. Therefore, we simply blueshifted the peak wavelength by reducing the total power so that Δ

*t*decreases to 4 ps at its minimum.

^{7}−1 pseudo-random bit sequence (PRBS), as shown in Fig. 4 . At Δ

*t*≤ 150 ps, the eye opening is observed with the clear bit pattern, for which we can confirm the tunable buffering capacity of

*M*= 4 bits, the buffering density

*M*/

*S*= 0.29 kbit/mm

^{2}, and the buffering loss

*L*/

*M*= 3.5 dB/bit. At Δ

*t*> 150 ps, the eye closes although the pattern can still be recognized. It might be affected by a dispersion larger than 10 ps/nm. It can be reduced by suppressing the thermal crosstalk and controlling the local temperature minutely. D exhibits a delay of 184 ps = 7.3 bit, which agrees with the result in Fig. 3(b) and is also consistent with the theoretical prediction that

*M*~9 bit and

*M*/

*S*~0.64 kbit/mm

^{2}at the maximum delay when we assume

*η*~0.2 approximated for the PRBS signals against the spectral response without heating in Fig. 3(a).

## 5. Discussion

^{2}, which is much smaller than 0.09 mm

^{2}for a similar device [11

11. F. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics **1**(1), 65–71 (2007). [CrossRef]

^{2}for a Si microring CROW [9

9. A. Melloni, A. Canciamilla, C. Ferrari, F. Morichetti, L. O'Faolain, T. F. Krauss, R. De La Rue, A. Samarelli, and M. Sorel, “Tunable delay lines in silicon photonics: coupled resonators and photonic crystals, a comparison,” IEEE Photon. J. **2**(2), 181–194 (2010). [CrossRef]

**1**(1), 65–71 (2007). [CrossRef]

5. J. Yang, N. K. Fontaine, Z. Pan, A. O. Karalar, S. S. Djordjevic, C. Yang, W. Chen, S. Chu, B. E. Little, and S. J. B. Yoo, “Continuously tunable, wavelength-selective buffering in optical packet switching network,” IEEE Photon. Technol. Lett. **20**(12), 1030–1032 (2008). [CrossRef]

8. A. Melloni, F. Morichetti, C. Ferrari, and M. Martinelli, “Continuously tunable 1 byte delay in coupled-resonator optical waveguides,” Opt. Lett. **33**(20), 2389–2391 (2008). [CrossRef] [PubMed]

^{2}). In a larger array, the fine control of local temperatures will be easier, so the dispersion will be more suppressed. The main issue is the reduction of loss. The buffering loss in this study is 3 – 5 times higher than those of low-index-contrast systems, and the total loss for a 1 ns delay cannot be recovered by optical amplifier. At the very least, the buffering loss will be reduced to a comparable level and the total loss will be acceptable by suppressing the scattering loss at the directional coupling by optimizing the design and by using the state-of-the-art Si photonics technology, which has already achieved a waveguide loss of 2 dB/cm [14

14. T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, S. Uchiyama, and S. Itabashi, “Low-loss Si wire waveguides and their application to thermooptic switches,” Jpn. J. Appl. Phys. **45**(No. 8B), 6658–6662 (2006). [CrossRef]

15. J. Cardenas, C. B. Poitras, J. T. Robinson, K. Preston, L. Chen, and M. Lipson, “Low loss etchless silicon photonic waveguides,” Opt. Express **17**(6), 4752–4757 (2009). [CrossRef] [PubMed]

## Acknowledgments

## References and links

1. | R. S. Tucker, P.-C. Ku, and C. Chang-Hasnain, “Slow-light optical buffers - capabilities and fundamental limitations,” J. Lightwave Technol. |

2. | T. Baba, “Slow light in photonic crystals,” Nat. Photonics |

3. | T. Baba, T. Kawaaski, H. Sasaki, J. Adachi, and D. Mori, “Large delay-bandwidth product and tuning of slow light pulse in photonic crystal coupled waveguide,” Opt. Express |

4. | J. Adachi, N. Ishikura, H. Sasaki, and T. Baba, “Wide range tuning of slow light pulse in SOI photonic crystal coupled waveguide via folded chirping,” IEEE J. Sel. Top. Quantum Electron. |

5. | J. Yang, N. K. Fontaine, Z. Pan, A. O. Karalar, S. S. Djordjevic, C. Yang, W. Chen, S. Chu, B. E. Little, and S. J. B. Yoo, “Continuously tunable, wavelength-selective buffering in optical packet switching network,” IEEE Photon. Technol. Lett. |

6. | W. M. J. Green, H. F. Hamann, L. Sekaric, M. J. Rooks, and Y. A. Vlasov, “Ultra-compact reconfigurable silicon optical devices using micron-scale localized thermal heating,” Tech. Dig. Opt. Fiber Commun. Conf., OtuM3 (2007). |

7. | J. Cardenas, M. A. Foster, N. Sherwood-Droz, C. B. Poitras, H. L. R. Lira, B. Zhang, A. L. Gaeta, J. B. Khurgin, P. Morton, and M. Lipson, “Wide-bandwidth continuously tunable optical delay line using silicon microring resonators,” Opt. Express |

8. | A. Melloni, F. Morichetti, C. Ferrari, and M. Martinelli, “Continuously tunable 1 byte delay in coupled-resonator optical waveguides,” Opt. Lett. |

9. | A. Melloni, A. Canciamilla, C. Ferrari, F. Morichetti, L. O'Faolain, T. F. Krauss, R. De La Rue, A. Samarelli, and M. Sorel, “Tunable delay lines in silicon photonics: coupled resonators and photonic crystals, a comparison,” IEEE Photon. J. |

10. | Q. Li, F. Liu, Z. Zhang, M. Qiu, and Y. Su, “System performances of on-chip silicon microring delay line for RZ, CSRZ, RZ-DB and RZ-AMI signals,” J. Lightwave Technol. |

11. | F. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics |

12. | K. Okamoto, |

13. | H. P. Uranus and H. J. W. M. Hoekstra, “Modeling of loss-induced superluminal and negative group velocity in two-port ring-resonator circuits,” J. Lightwave Technol. |

14. | T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, S. Uchiyama, and S. Itabashi, “Low-loss Si wire waveguides and their application to thermooptic switches,” Jpn. J. Appl. Phys. |

15. | J. Cardenas, C. B. Poitras, J. T. Robinson, K. Preston, L. Chen, and M. Lipson, “Low loss etchless silicon photonic waveguides,” Opt. Express |

**OCIS Codes**

(230.3120) Optical devices : Integrated optics devices

(230.5750) Optical devices : Resonators

**ToC Category:**

Optical Devices

**History**

Original Manuscript: April 20, 2011

Revised Manuscript: June 10, 2011

Manuscript Accepted: June 17, 2011

Published: June 29, 2011

**Citation**

Fumihiro Shinobu, Norihiro Ishikura, Yoshiki Arita, Takemasa Tamanuki, and Toshihiko Baba, "Continuously tunable slow-light device consisting of heater-controlled silicon microring array," Opt. Express **19**, 13557-13564 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-14-13557

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### References

- R. S. Tucker, P.-C. Ku, and C. Chang-Hasnain, “Slow-light optical buffers - capabilities and fundamental limitations,” J. Lightwave Technol. 23(12), 4046–4066 (2005). [CrossRef]
- T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2(8), 465–473 (2008). [CrossRef]
- T. Baba, T. Kawaaski, H. Sasaki, J. Adachi, and D. Mori, “Large delay-bandwidth product and tuning of slow light pulse in photonic crystal coupled waveguide,” Opt. Express 16(12), 9245–9253 (2008). [CrossRef] [PubMed]
- J. Adachi, N. Ishikura, H. Sasaki, and T. Baba, “Wide range tuning of slow light pulse in SOI photonic crystal coupled waveguide via folded chirping,” IEEE J. Sel. Top. Quantum Electron. 16(1), 192–199 (2010). [CrossRef]
- J. Yang, N. K. Fontaine, Z. Pan, A. O. Karalar, S. S. Djordjevic, C. Yang, W. Chen, S. Chu, B. E. Little, and S. J. B. Yoo, “Continuously tunable, wavelength-selective buffering in optical packet switching network,” IEEE Photon. Technol. Lett. 20(12), 1030–1032 (2008). [CrossRef]
- W. M. J. Green, H. F. Hamann, L. Sekaric, M. J. Rooks, and Y. A. Vlasov, “Ultra-compact reconfigurable silicon optical devices using micron-scale localized thermal heating,” Tech. Dig. Opt. Fiber Commun. Conf., OtuM3 (2007).
- J. Cardenas, M. A. Foster, N. Sherwood-Droz, C. B. Poitras, H. L. R. Lira, B. Zhang, A. L. Gaeta, J. B. Khurgin, P. Morton, and M. Lipson, “Wide-bandwidth continuously tunable optical delay line using silicon microring resonators,” Opt. Express 18(25), 26525–26534 (2010). [CrossRef] [PubMed]
- A. Melloni, F. Morichetti, C. Ferrari, and M. Martinelli, “Continuously tunable 1 byte delay in coupled-resonator optical waveguides,” Opt. Lett. 33(20), 2389–2391 (2008). [CrossRef] [PubMed]
- A. Melloni, A. Canciamilla, C. Ferrari, F. Morichetti, L. O'Faolain, T. F. Krauss, R. De La Rue, A. Samarelli, and M. Sorel, “Tunable delay lines in silicon photonics: coupled resonators and photonic crystals, a comparison,” IEEE Photon. J. 2(2), 181–194 (2010). [CrossRef]
- Q. Li, F. Liu, Z. Zhang, M. Qiu, and Y. Su, “System performances of on-chip silicon microring delay line for RZ, CSRZ, RZ-DB and RZ-AMI signals,” J. Lightwave Technol. 26(23), 3744–3751 (2008). [CrossRef]
- F. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1(1), 65–71 (2007). [CrossRef]
- K. Okamoto, Fundamentals of Optical Waveguides, 2nd ed. (Academic Press, 2000).
- H. P. Uranus and H. J. W. M. Hoekstra, “Modeling of loss-induced superluminal and negative group velocity in two-port ring-resonator circuits,” J. Lightwave Technol. 25(9), 2376–2384 (2007). [CrossRef]
- T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, S. Uchiyama, and S. Itabashi, “Low-loss Si wire waveguides and their application to thermooptic switches,” Jpn. J. Appl. Phys. 45(No. 8B), 6658–6662 (2006). [CrossRef]
- J. Cardenas, C. B. Poitras, J. T. Robinson, K. Preston, L. Chen, and M. Lipson, “Low loss etchless silicon photonic waveguides,” Opt. Express 17(6), 4752–4757 (2009). [CrossRef] [PubMed]

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