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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 9 — May. 5, 2014
  • pp: 10550–10558
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Integrated silicon modulator based on microring array assisted MZI

Xiangdong Li, Xue Feng, Kaiyu Cui, Fang Liu, and Yidong Huang  »View Author Affiliations


Optics Express, Vol. 22, Issue 9, pp. 10550-10558 (2014)
http://dx.doi.org/10.1364/OE.22.010550


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Abstract

A silicon modulator with microring array assisted MZI is experimentally demonstrated on silicon-on-insulator wafer through CMOS-compatible process. The footprint of the whole modulator is about 600 μm2. With forward-biased current-driven p-n junction, the 3-dB modulation bandwidth is ~2GHz. Furthermore, the impact of ambient temperature is minified with the help of MZI. Within temperature range of 10 – 70 °C, the maximum divergence of modulation curve is less than ~3 dB.

© 2014 Optical Society of America

1. Introduction

Optical interconnection is considered as a promising solution for future high-performance multi-core processors with the attractive prospect of integration with complementary metal-oxide-semiconductor (CMOS) electronics on the same silicon substrate. Silicon optical modulator is a major workhorse in such an optical interconnect system. Till now, the reported silicon modulators are dominantly based on two approaches of the Mach-Zehnder interferometer (MZI) and resonant cavity [1

1. G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010). [CrossRef]

, 2

2. D. Marris-Morini, L. Vivien, G. Rasigade, J.-M. Fedeli, E. Cassan, X. Le Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, and S. Laval, “Recent progress in high-speed silicon-based optical modulators,” Proc. IEEE 97(7), 1199–1215 (2009). [CrossRef]

]. For modulators based on resonant cavity, e.g. microring or disk, the narrow operating spectrum (typically ~0.1 nm) and temperature sensitivity are the main limitations due to the resonant nature [3

3. Q. F. Xu, S. Manipatruni, B. Schmidt, J. Shakya, and M. Lipson, “12.5 Gbit/s carrier-injection-based silicon micro-ring silicon modulators,” Opt. Express 15(2), 430–436 (2007). [CrossRef] [PubMed]

5

5. M. R. Watts, W. A. Zortman, D. C. Trotter, R. W. Young, and A. L. Lentine, “Vertical junction silicon microdisk modulators and switches,” Opt. Express 19(22), 21989–22003 (2011). [CrossRef] [PubMed]

]. On the other side, the temperature stability of a MZI modulator is very outstanding due to the symmetrical structure, while the device footprint is relatively large (103 – 105 μm2) [6

6. D. J. Thomson, F. Y. Gardes, J. M. Fedeli, S. Zlatanovic, Y. F. Hu, B. P. P. Kuo, E. Myslivets, N. Alic, S. Radic, G. Z. Mashanovich, and G. T. Reed, “50-Gb/s silicon optical modulator,” IEEE Photon. Technol. Lett. 24(4), 234–236 (2012). [CrossRef]

8

8. T. Y. Liow, K. W. Ang, Q. Fang, J. F. Song, Y. Z. Xiong, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Silicon modulators and germanium photodetectors on SOI: monolithic integration, compatibility, and performance optimization,” IEEE J. Sel. Top. Quantum Electron. 16(1), 307–315 (2010). [CrossRef]

]. One way to overcome it is to introduce slow-light structures so that the phase-shifter efficiency can be increased to achieve shorter device length [9

9. H. C. Nguyen, Y. Sakai, M. Shinkawa, N. Ishikura, and T. Baba, “10 Gb/s operation of photonic crystal silicon optical modulators,” Opt. Express 19(14), 13000–13007 (2011). [CrossRef] [PubMed]

, 10

10. A. M. Gutierrez, A. Brimont, G. Rasigade, M. Ziebell, D. Marris-Morini, J. M. Fédéli, L. Vivien, J. Marti, and P. Sanchis, “Ring-assisted Mach–Zehnder interferometer silicon modulator for enhanced performance,” J. Lightwave Technol. 30(1), 9–14 (2012). [CrossRef]

]. Besides photonic crystal waveguide (PCW), which is a typical one of these structures [9

9. H. C. Nguyen, Y. Sakai, M. Shinkawa, N. Ishikura, and T. Baba, “10 Gb/s operation of photonic crystal silicon optical modulators,” Opt. Express 19(14), 13000–13007 (2011). [CrossRef] [PubMed]

], microring array could also act as a slow-light structure [11

11. X. J. Zhang, X. Feng, D. K. Zhang, and Y. D. Huang, “Compact temperature-insensitive modulator based on a silicon microring assistant Mach Zehnder interferometer,” Chin. Phys. B 21, 124203 (2012).

, 12

12. F. Shinobu, N. Ishikura, Y. Arita, T. Tamanuki, and T. Baba, “Continuously tunable slow-light device consisting of heater-controlled silicon microring array,” Opt. Express 19(14), 13557–13564 (2011). [CrossRef] [PubMed]

]. Actually, there have been several reports about the enhanced performance of modulators by introducing more than one ring [13

13. S. Akiyama, T. Kurahashi, T. Baba, N. Hatori, T. Usuki, and T. Yamamoto, “1-Vpp 10-Gb/s operation of slow-light silicon Mach-Zehnder modulator in wavelength range of 1 nm,” in IEEE International Conference on Group IV Photonics, (Beijing, China, 2010), pp. 45–47. [CrossRef]

17

17. Y. Hu, X. Xiao, H. Xu, X. Li, K. Xiong, Z. Li, T. Chu, Y. Yu, and J. Yu, “High-speed silicon modulator based on cascaded microring resonators,” Opt. Express 20(14), 15079–15085 (2012). [CrossRef] [PubMed]

]. Therefore, ring array assisted MZI silicon modulator may open up a new and practical approach for integrated silicon modulator.

In this paper, we experimentally demonstrate a microring array assisted MZI modulator with CMOS-compatible fabrication processes. Three microrings operating at over-coupled state are coupled with each arm of MZI. The device footprint is about 600 μm2. Based on forward-biased current-driven p-n junction, the modulation efficiency is rather high while voltage length product is estimated as low as VπL < 6.63 × 10−3 V·cm at room temperature (20 °C). The temperature stability is also tested and it possesses good temperature insensitivity within 10 to 70 °C with maximum divergence of < 3 dB. Finally, the 3-dB bandwidth of measured frequency response is about 2 GHz. A square wave signal, whose rising edge is about 1 ns and peak voltage is 350 mV, is also modulated.

2. Design and fabrication

The proposed modulator is fabricated by the photonics prototyping service of the Institute of Microelectronics (IME) in Singapore. The silicon-on-insulator (SOI) wafer with a 220-nm-thick top silicon layer and a 2-μm-thick buried oxide layer is used. The pattern of the modulator is defined with a 248 nm deep UV lithography. All the waveguides are etched with inductively coupled plasma reactive ion etch (ICP-RIE). All waveguides are silicon rib waveguides with width of 450 nm, height of 220 nm, and a slab layer with thickness of 60 nm. The arm length of MZI is designed as L = 30 μm and the diameters of three rings are D = 9.98 μm, 10 μm and 10.02 μm, respectively. The distance between the two microrings is 3 μm. Each microring with one arm incorporates a p-n junction, consisting of moderately-doped p and n, as well as highly-doped p+ and n+ regions. The doping level is in the range of 1017 cm−3 and the detailed concentration distribution of p-n junction could be found in [8

8. T. Y. Liow, K. W. Ang, Q. Fang, J. F. Song, Y. Z. Xiong, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Silicon modulators and germanium photodetectors on SOI: monolithic integration, compatibility, and performance optimization,” IEEE J. Sel. Top. Quantum Electron. 16(1), 307–315 (2010). [CrossRef]

]. On top of waveguides, a SiO2 cladding layer is deposited. Then, an electrode is formed and contacted with p-type and n-type doping region through etched windows on the cladding layer as shown in Fig. 1(b). The electrode contacted with p-n junction is 50 nm/0.75 μm/25 nm TaN/Al/TaN and the electrode on the cladding layer is 2 μm/25 nm Al/TaN. The widths of electrode contacted with P-type doping region and N-type doping region are 7 μm and 4 μm, respectively. Additionally, an inverse taper is adopted at the end of input and output waveguide to effectively couple with fibers in the measurement. According to the SEM photo, the device footprint of the whole modulator is about 600 μm2.

According to our simulation [11

11. X. J. Zhang, X. Feng, D. K. Zhang, and Y. D. Huang, “Compact temperature-insensitive modulator based on a silicon microring assistant Mach Zehnder interferometer,” Chin. Phys. B 21, 124203 (2012).

], this arrangement is enough for stable operation with the temperature span of 130 °C and the gap distance between the arm and the corresponding microring should be 0 – 30 nm to ensure that all microrings operate at much over-coupled state while attenuation coefficient of fabricated Si waveguide is ~2 dB/cm. However, after doping, the waveguide loss would increase due to carrier absorption so that the gap distance should be narrower than 28 nm [11

11. X. J. Zhang, X. Feng, D. K. Zhang, and Y. D. Huang, “Compact temperature-insensitive modulator based on a silicon microring assistant Mach Zehnder interferometer,” Chin. Phys. B 21, 124203 (2012).

] and thus it is set as 20 nm in lithography mask. Actually, such narrow gap cannot be fabricated with existing lithography technology. As shown in the SEM photograph after etching (Fig. 1(c)), the rings conglutinate the arm of MZI. In order to evaluate the impact of such conglutination, some simulations have been carried out with finite difference time domain (FDTD) method and the results are shown in Fig. 2
Fig. 2 (a) The transmission spectrum without (solid) and with (dashed) conglutination at 1548 – 1552nm; the transmission and phase shift spectrum without (b) and with (c) conglutination at the resonant wavelength. Here, only one microring with D = 10 μm and gap distance of 20 nm is calculated with FDTD method.
. Here, only one microring with D = 10 μm and gap distance of 20 nm is concerned with and without conglutination according to the SEM photograph. Figure 2(a) is the calculated transmission spectrum around 1550 nm, which is the concerned operating wavelength of our modulator. It could be found that the conglutination would increase the insertion loss (< 3 dB) while the spectrum is still very flat. In order to reveal the operating state of microring, the spectra of transmission and phase shift around the resonant wavelength are also calculated. Figure 2(b) and 2(c) are the results with and without conglutination, respectively. Comparing them, it could be found that the resonant wavelength (closest to 1550 nm) is varies from 1535.3 nm to 1538.5 nm due to conglutination, but the phase shift around resonance is also slowly varied so that both the two rings are working at over-coupled state. These simulation results indicate that there is little influence on operating state of microring with conglutination while the insertion loss would increase (< 3 dB@1550 nm).

The prepared device samples are characterized with a setup as Fig. 1(d), including a tunable laser source (TLS), a polarization controller (PC, Agilent 11896A) and a power meter (PM, Agilent 81624A). The output power of TLS is set as a constant value of 0.5 mW (–3 dBm). Single-mode lensed optical fibers, mounted on a computer-controlled alignment stage, are used to couple light in and out. A temperature controller with a precision current source (ILX Lightwave LDX-3412) is employed to set the ambient temperature with the range of 10 – 70 °C. In the experiment, the time interval between different temperatures is more than ten minutes, and each value is repeatedly measured with a thermometer to ensure thermal equivalence. A direct current (DC) source (Agilent B2901A) is used to measure the I-V curve and the results are shown in Fig. 1(e). The turn-on voltage is about 0.9 V and the resistance is 70 – 80 Ω. To obtain modulation characteristics, the microwave signal is generated from a function generator (FG) or a 40-G vector network analyzer (VNA, Agilent Technologies E8363B), combined with a suitable DC signal through a bias tee. Additionally, a high-frequency ground-signal-ground (GSG) probe (Cascade Microtech FF23H ACP50-AW-GSG-150) is used to connect with the electrodes. The output light is detected by a photo detector (PD, U2T XPDV2120R), and corresponding waveform and microwave signal response spectrum are measured by an oscilloscope (Agilent infiniium 54833A) and VNA, respectively.

3. Measurements and results

Furthermore, the microwave frequency response is also measured at the wavelength of 1550 nm. The DC bias is set as 1.1 V and the signal power is from –10 to 16 dBm, which is limited by the VNA. Figure 5(a)
Fig. 5 (a) Normalized microwave frequency response of the modulator; (b) the bandwidths under different signal powers; (c) the modulated square wave signal.
is the measured results with the signal power of 12 dBm. The 3-dB bandwidth is about 2 GHz. Such modulation bandwidth could sustain transmission data rate higher than 1 Gb/s with non-return-to-zero signal and if pre-emphasis of driving signal is employed, higher data rate could be achieved [9

9. H. C. Nguyen, Y. Sakai, M. Shinkawa, N. Ishikura, and T. Baba, “10 Gb/s operation of photonic crystal silicon optical modulators,” Opt. Express 19(14), 13000–13007 (2011). [CrossRef] [PubMed]

]. Figure 5(b) shows the bandwidths under different signal powers. It could be found that higher signal power is better, which is similar to an over-coupled ring modulator as in [19

19. L. Zhang, Y. C. Li, J. Y. Yang, M. P. Song, R. G. Beausoleil, and A. E. Willner, “Silicon-based microring resonator modulators for intensity modulation,” IEEE J. Sel. Top. Quantum Electron. 16(1), 149–158 (2010). [CrossRef]

]. In addition, a square wave signal with rising edge of 200 ps and peak voltage of 350 mV is modulated. The driving signal (black and dashed) and detected signal (blue and real) are shown in Fig. 5(c). Limited by the bandwidth of the oscilloscope, the rising edges of the driving signal and detected signal are ~1 ns. It should be mentioned that due to the forward-biased p-n junction, the modulation bandwidth is lower than those reported in recent years. A straightforward way to improve it is to employ other carrier injection structures, e.g. depletion of a horizontal p-n junction and reverse-biased p–n junction [1

1. G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010). [CrossRef]

]. It should be mentioned that employing high speed p-n junction may increase the half wave voltage Vπ and leads to the deterioration of the overall modulation efficiency.

Finally, the modulation curves are measured with varied temperatures from 10 to 70 °C at the wavelength of 1550 nm. The normalized results are shown in Fig. 6
Fig. 6 Modulation curves at different temperature.
. For the modulation curve, the maximum divergence is about 3 dB within the range of 0 to 2 V. Such variation is nearly equal to that without driving voltage (Fig. 3(a)). Thus, we believe that it is mainly due to the asymmetrical ring arrays and could be further reduced with improving fabrication technology. Such experimental results indicate that our proposed modulator possesses good temperature stability within 10 to 70 °C. It should be mentioned that the measurements only carried out within such range are limited by temperature controller.

4. Conclusions

In this paper, a silicon modulator is experimentally demonstrated on SOI wafer through CMOS-compatible fabrication processes. Due to the symmetrical structure of MZI, the maximum divergence of modulation curves is only 3 dB within the temperature range of 10 – 70 °C. Meanwhile, with the help of over-coupled microring array, the arm length of MZI is only 30 μm and consequently the corresponding voltage length product is as low as VπL < 6.63 × 10−3 V·cm. The measured 3 dB modulation bandwidth is ~2 GHz.

Acknowledgments

This work was supported by the National Basic Research Program of China (No. 2011CBA00608, 2011CBA00303, 2011CB301803, and 2010CB327405), the National Natural Science Foundation of China (Grant No. 61307068, 61036010, 61036011, and 61321004). The authors would like to thank Dr. Wei Zhang, Mr. D. K. Zhang, Mr. Y. Z. Li, and Mr. Q. Zhao for valuable discussions and helpful comments. The authors also thank the Institute of Microelectronics, Singapore for device fabrication.

References and links

1.

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010). [CrossRef]

2.

D. Marris-Morini, L. Vivien, G. Rasigade, J.-M. Fedeli, E. Cassan, X. Le Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, and S. Laval, “Recent progress in high-speed silicon-based optical modulators,” Proc. IEEE 97(7), 1199–1215 (2009). [CrossRef]

3.

Q. F. Xu, S. Manipatruni, B. Schmidt, J. Shakya, and M. Lipson, “12.5 Gbit/s carrier-injection-based silicon micro-ring silicon modulators,” Opt. Express 15(2), 430–436 (2007). [CrossRef] [PubMed]

4.

L. Chen, K. Preston, S. Manipatruni, and M. Lipson, “Integrated GHz silicon photonic interconnect with micrometer-scale modulators and detectors,” Opt. Express 17(17), 15248–15256 (2009). [CrossRef] [PubMed]

5.

M. R. Watts, W. A. Zortman, D. C. Trotter, R. W. Young, and A. L. Lentine, “Vertical junction silicon microdisk modulators and switches,” Opt. Express 19(22), 21989–22003 (2011). [CrossRef] [PubMed]

6.

D. J. Thomson, F. Y. Gardes, J. M. Fedeli, S. Zlatanovic, Y. F. Hu, B. P. P. Kuo, E. Myslivets, N. Alic, S. Radic, G. Z. Mashanovich, and G. T. Reed, “50-Gb/s silicon optical modulator,” IEEE Photon. Technol. Lett. 24(4), 234–236 (2012). [CrossRef]

7.

P. Dong, L. Chen, and Y. K. Chen, “High-speed low-voltage single-drive push-pull silicon Mach-Zehnder modulators,” Opt. Express 20(6), 6163–6169 (2012). [CrossRef] [PubMed]

8.

T. Y. Liow, K. W. Ang, Q. Fang, J. F. Song, Y. Z. Xiong, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Silicon modulators and germanium photodetectors on SOI: monolithic integration, compatibility, and performance optimization,” IEEE J. Sel. Top. Quantum Electron. 16(1), 307–315 (2010). [CrossRef]

9.

H. C. Nguyen, Y. Sakai, M. Shinkawa, N. Ishikura, and T. Baba, “10 Gb/s operation of photonic crystal silicon optical modulators,” Opt. Express 19(14), 13000–13007 (2011). [CrossRef] [PubMed]

10.

A. M. Gutierrez, A. Brimont, G. Rasigade, M. Ziebell, D. Marris-Morini, J. M. Fédéli, L. Vivien, J. Marti, and P. Sanchis, “Ring-assisted Mach–Zehnder interferometer silicon modulator for enhanced performance,” J. Lightwave Technol. 30(1), 9–14 (2012). [CrossRef]

11.

X. J. Zhang, X. Feng, D. K. Zhang, and Y. D. Huang, “Compact temperature-insensitive modulator based on a silicon microring assistant Mach Zehnder interferometer,” Chin. Phys. B 21, 124203 (2012).

12.

F. Shinobu, N. Ishikura, Y. Arita, T. Tamanuki, and T. Baba, “Continuously tunable slow-light device consisting of heater-controlled silicon microring array,” Opt. Express 19(14), 13557–13564 (2011). [CrossRef] [PubMed]

13.

S. Akiyama, T. Kurahashi, T. Baba, N. Hatori, T. Usuki, and T. Yamamoto, “1-Vpp 10-Gb/s operation of slow-light silicon Mach-Zehnder modulator in wavelength range of 1 nm,” in IEEE International Conference on Group IV Photonics, (Beijing, China, 2010), pp. 45–47. [CrossRef]

14.

Y. Li, L. Zhang, M. Song, B. Zhang, J. Y. Yang, R. G. Beausoleil, A. E. Willner, and P. D. Dapkus, “Coupled-ring-resonator-based silicon modulator for enhanced performance,” Opt. Express 16(17), 13342–13348 (2008). [CrossRef] [PubMed]

15.

L. Zhang, M. Song, T. Wu, L. Zou, R. G. Beausoleil, and A. E. Willner, “Embedded ring resonators for microphotonic applications,” Opt. Lett. 33(17), 1978–1980 (2008). [CrossRef] [PubMed]

16.

Q. Xu, “Silicon dual-ring modulator,” Opt. Express 17(23), 20783–20793 (2009). [CrossRef] [PubMed]

17.

Y. Hu, X. Xiao, H. Xu, X. Li, K. Xiong, Z. Li, T. Chu, Y. Yu, and J. Yu, “High-speed silicon modulator based on cascaded microring resonators,” Opt. Express 20(14), 15079–15085 (2012). [CrossRef] [PubMed]

18.

J. E. Heebner, V. Wong, A. Schweinsberg, R. W. Boyd, and D. J. Jackson, “Optical transmission characteristics of fiber ring resonators,” IEEE J. Quantum Electron. 40(6), 726–730 (2004). [CrossRef]

19.

L. Zhang, Y. C. Li, J. Y. Yang, M. P. Song, R. G. Beausoleil, and A. E. Willner, “Silicon-based microring resonator modulators for intensity modulation,” IEEE J. Sel. Top. Quantum Electron. 16(1), 149–158 (2010). [CrossRef]

OCIS Codes
(120.6780) Instrumentation, measurement, and metrology : Temperature
(200.4650) Optics in computing : Optical interconnects
(130.4110) Integrated optics : Modulators
(130.3990) Integrated optics : Micro-optical devices

ToC Category:
Integrated Optics

History
Original Manuscript: February 17, 2014
Revised Manuscript: April 19, 2014
Manuscript Accepted: April 20, 2014
Published: April 24, 2014

Citation
Xiangdong Li, Xue Feng, Kaiyu Cui, Fang Liu, and Yidong Huang, "Integrated silicon modulator based on microring array assisted MZI," Opt. Express 22, 10550-10558 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-9-10550


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References

  1. G. T. Reed, G. Mashanovich, F. Y. Gardes, D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010). [CrossRef]
  2. D. Marris-Morini, L. Vivien, G. Rasigade, J.-M. Fedeli, E. Cassan, X. Le Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, S. Laval, “Recent progress in high-speed silicon-based optical modulators,” Proc. IEEE 97(7), 1199–1215 (2009). [CrossRef]
  3. Q. F. Xu, S. Manipatruni, B. Schmidt, J. Shakya, M. Lipson, “12.5 Gbit/s carrier-injection-based silicon micro-ring silicon modulators,” Opt. Express 15(2), 430–436 (2007). [CrossRef] [PubMed]
  4. L. Chen, K. Preston, S. Manipatruni, M. Lipson, “Integrated GHz silicon photonic interconnect with micrometer-scale modulators and detectors,” Opt. Express 17(17), 15248–15256 (2009). [CrossRef] [PubMed]
  5. M. R. Watts, W. A. Zortman, D. C. Trotter, R. W. Young, A. L. Lentine, “Vertical junction silicon microdisk modulators and switches,” Opt. Express 19(22), 21989–22003 (2011). [CrossRef] [PubMed]
  6. D. J. Thomson, F. Y. Gardes, J. M. Fedeli, S. Zlatanovic, Y. F. Hu, B. P. P. Kuo, E. Myslivets, N. Alic, S. Radic, G. Z. Mashanovich, G. T. Reed, “50-Gb/s silicon optical modulator,” IEEE Photon. Technol. Lett. 24(4), 234–236 (2012). [CrossRef]
  7. P. Dong, L. Chen, Y. K. Chen, “High-speed low-voltage single-drive push-pull silicon Mach-Zehnder modulators,” Opt. Express 20(6), 6163–6169 (2012). [CrossRef] [PubMed]
  8. T. Y. Liow, K. W. Ang, Q. Fang, J. F. Song, Y. Z. Xiong, M. B. Yu, G. Q. Lo, D. L. Kwong, “Silicon modulators and germanium photodetectors on SOI: monolithic integration, compatibility, and performance optimization,” IEEE J. Sel. Top. Quantum Electron. 16(1), 307–315 (2010). [CrossRef]
  9. H. C. Nguyen, Y. Sakai, M. Shinkawa, N. Ishikura, T. Baba, “10 Gb/s operation of photonic crystal silicon optical modulators,” Opt. Express 19(14), 13000–13007 (2011). [CrossRef] [PubMed]
  10. A. M. Gutierrez, A. Brimont, G. Rasigade, M. Ziebell, D. Marris-Morini, J. M. Fédéli, L. Vivien, J. Marti, P. Sanchis, “Ring-assisted Mach–Zehnder interferometer silicon modulator for enhanced performance,” J. Lightwave Technol. 30(1), 9–14 (2012). [CrossRef]
  11. X. J. Zhang, X. Feng, D. K. Zhang, Y. D. Huang, “Compact temperature-insensitive modulator based on a silicon microring assistant Mach Zehnder interferometer,” Chin. Phys. B 21, 124203 (2012).
  12. F. Shinobu, N. Ishikura, Y. Arita, T. Tamanuki, T. Baba, “Continuously tunable slow-light device consisting of heater-controlled silicon microring array,” Opt. Express 19(14), 13557–13564 (2011). [CrossRef] [PubMed]
  13. S. Akiyama, T. Kurahashi, T. Baba, N. Hatori, T. Usuki, T. Yamamoto, “1-Vpp 10-Gb/s operation of slow-light silicon Mach-Zehnder modulator in wavelength range of 1 nm,” in IEEE International Conference on Group IV Photonics, (Beijing, China, 2010), pp. 45–47. [CrossRef]
  14. Y. Li, L. Zhang, M. Song, B. Zhang, J. Y. Yang, R. G. Beausoleil, A. E. Willner, P. D. Dapkus, “Coupled-ring-resonator-based silicon modulator for enhanced performance,” Opt. Express 16(17), 13342–13348 (2008). [CrossRef] [PubMed]
  15. L. Zhang, M. Song, T. Wu, L. Zou, R. G. Beausoleil, A. E. Willner, “Embedded ring resonators for microphotonic applications,” Opt. Lett. 33(17), 1978–1980 (2008). [CrossRef] [PubMed]
  16. Q. Xu, “Silicon dual-ring modulator,” Opt. Express 17(23), 20783–20793 (2009). [CrossRef] [PubMed]
  17. Y. Hu, X. Xiao, H. Xu, X. Li, K. Xiong, Z. Li, T. Chu, Y. Yu, J. Yu, “High-speed silicon modulator based on cascaded microring resonators,” Opt. Express 20(14), 15079–15085 (2012). [CrossRef] [PubMed]
  18. J. E. Heebner, V. Wong, A. Schweinsberg, R. W. Boyd, D. J. Jackson, “Optical transmission characteristics of fiber ring resonators,” IEEE J. Quantum Electron. 40(6), 726–730 (2004). [CrossRef]
  19. L. Zhang, Y. C. Li, J. Y. Yang, M. P. Song, R. G. Beausoleil, A. E. Willner, “Silicon-based microring resonator modulators for intensity modulation,” IEEE J. Sel. Top. Quantum Electron. 16(1), 149–158 (2010). [CrossRef]

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