## Bidirectional grating coupler based optical modulator for low-loss Integration and low-cost fiber packaging |

Optics Express, Vol. 21, Issue 12, pp. 14202-14214 (2013)

http://dx.doi.org/10.1364/OE.21.014202

Acrobat PDF (3470 KB)

### Abstract

We proposed and demonstrated a novel optical modulator based on a bidirectional grating coupler designed for perfectly vertical fiber coupling. The grating functions as the fiber coupler and 3-dB splitter. To observe the interference, an arm difference of 30μm is introduced. As a result of the high coupling efficiency and near perfect split ratio of the grating coupler, this device exhibits a low on-chip insertion loss of 5.4dB (coupling loss included) and high on-off extinction ratio more than 20dB. The modulation efficiency is estimated to be within 3-3.84V•cm. In order to investigate the fiber misalignment tolerance of this modulator, misalignment influence of the static characteristics is analyzed. 10Gb/s Data transmission experiments of this device are performed with different fiber launch positions. The energy efficiency is estimated to be 8.1pJ/bit.

© 2013 OSA

## 1. Introduction

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. A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature **427**(6975), 615–618 (2004). [CrossRef] [PubMed]

3. Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature **435**(7040), 325–327 (2005). [CrossRef] [PubMed]

3. Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature **435**(7040), 325–327 (2005). [CrossRef] [PubMed]

4. L. Zhou and A. W. Poon, “Silicon electro-optic modulators using p-i-n diodes embedded 10-micron-diameter microdisk resonators,” Opt. Express **14**(15), 6851–6857 (2006). [CrossRef] [PubMed]

5. R. Soref and B. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. **23**(1), 123–129 (1987). [CrossRef]

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

6. L. Liao, A. Liu, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, and M. Paniccia, “40 Gbit/s silicon optical modulator for high speed applications,” Electron. Lett. **43**(22), 1196–1197 (2007). [CrossRef]

9. H. Xu, X. Xiao, X. Li, Y. Hu, Z. Li, T. Chu, Y. Yu, and J. Yu, “High speed silicon Mach-Zehnder modulator based on interleaved PN junctions,” Opt. Express **20**(14), 15093–15099 (2012). [CrossRef] [PubMed]

10. G. Rasigade, D. Marris-Morini, L. Vivien, and E. Cassan, “Performance Evolutions of Carrier Depletion Silicon Optical Modulators: From p-n to p-i-p-i-n Diodes,” IEEE J. Sel. Top. Quantum Electron. **16**(1), 179–184 (2010). [CrossRef]

11. H. Yu, M. Pantouvaki, J. Van Campenhout, D. Korn, K. Komorowska, P. Dumon, Y. Li, P. Verheyen, P. Absil, L. Alloatti, D. Hillerkuss, J. Leuthold, R. Baets, and W. Bogaerts, “Performance tradeoff between lateral and interdigitated doping patterns for high speed carrier-depletion based silicon modulators,” Opt. Express **20**(12), 12926–12938 (2012). [CrossRef] [PubMed]

13. X. Tu, T. Y. Liow, J. Song, M. Yu, and G. Q. Lo, “Fabrication of low loss and high speed silicon optical modulator using doping compensation method,” Opt. Express **19**(19), 18029–18035 (2011). [CrossRef] [PubMed]

14. Y. Hui and W. Bogaerts, “An Equivalent Circuit Model of the Traveling Wave Electrode for Carrier-Depletion-Based Silicon Optical Modulators,” J. Lightwave Technol. **30**(11), 1602–1609 (2012). [CrossRef]

15. J. Ding, H. Chen, L. Yang, L. Zhang, R. Ji, Y. Tian, W. Zhu, Y. Lu, P. Zhou, and R. Min, “Low-voltage, high-extinction-ratio, Mach-Zehnder silicon optical modulator for CMOS-compatible integration,” Opt. Express **20**(3), 3209–3218 (2012). [CrossRef] [PubMed]

## 2. Device structure and principle

## 3. Design and realization

26. X. Chen, C. Li, and H. K. Tsang, “Etched waveguide grating variable 1×2 splitter/combiner and waveguide coupler,” IEEE Photon. Technol. Lett. **21**(5), 268–270 (2009). [CrossRef]

_{eff}is the effective index of the grating region. According to this basic principle, we can estimate the grating period fit for vertical coupling. Then a series of calculations were carried out to find the optimal grating period (Λ), etch depth (d), filling factor (FF = W/Λ, where W is the un-etched top silicon segment length in a period) and grating coupler length (number of periods) respectively using the two-dimensional (2-D) FDTD method. Finally, we obtained the optimal design with a grating period of 580nm, etch depth of 70nm, filling factor of 47% and 22 periods. As a design reference [27

27. D. Taillaert, P. Bienstman, and R. Baets, “Compact efficient broadband grating coupler for silicon-on-insulator waveguides,” Opt. Lett. **29**(23), 2749–2751 (2004). [CrossRef] [PubMed]

*+ x*direction with different fiber launch positions (LP). As shown in Fig. 2(c), when the fiber is placed at the grating center, the split ratio is 0.5 which agrees well with our predictions. When the fiber moves towards the

*+ x*direction, the split ratio will increase drastically except at the wavelength range around 1547nm. We noted that the split ratio at 1547nm is quite close to 0.5 and remain unchanged even if the fiber has a displacement of 3μm. This phenomenon is caused by the strong second order reflection at the resonant wavelength. At the wavelength regions which are far from resonance, the second order reflection is relatively weak. Therefore, the split ratio there is quite stable and increase progressively with the fiber LP increasing. To explain this, it is more convenient to discuss this problem in the perspective of output coupling. Under a one-dimensional approximation, the diffracted field for each port and the fiber mode profile can be expressed as follows [28]: Where,

*D*is the directionality of the grating structure,

*L*is the grating coupling length,

_{d}*L*is the lateral length of the grating,

*w*is the waist radius of the fiber mode,

_{0}*μ*is the launch center position of the fiber. Given the input-output equivalence of this bidirectional coupler, the power coupling efficiency of two arms can be given by the overlap integral of the diffracted field profile with respect to both ports and the fiber mode profile respectively. The coupling efficiency of two ports can be expressed by [27

27. D. Taillaert, P. Bienstman, and R. Baets, “Compact efficient broadband grating coupler for silicon-on-insulator waveguides,” Opt. Lett. **29**(23), 2749–2751 (2004). [CrossRef] [PubMed]

*A*represents the normalization of the Gaussian beam and

*d*represents the one-dimensional diameter of the fiber facet. After a series of calculations, we found that Eqs. (5) and (6) can be further simplified to: The expressions imply the dependent relationship between the coupling efficiency of two ports and the fiber launch positions, If we define

*R(μ)*as the ratio between the power splitting to

*+ x*direction and the power splitting to

*–x*direction, then it can be expressed as follows:This means the function values at the fiber position of 0, 1μm, 2μm, 3μm will be a geometric series with a common ratio of

*exp(2/L*. By curve fitting the simulated diffracted electric field, we obtained that the grating coupling length

_{d})*L*is about 8.46μm giving a common ratio of 1.267. However, according to the simulated results in Fig. 2(c), the function values of

_{d}*R(μ)*at LP = 0, 1, 2, 3μm are 1, 1.597, 2.012, 2.508, which gives a ratio of 1.597, 1.259, 1.246 respectively. These results show a little disagreement with the common ratio predicted by Eq. (9). This can be possibly attributed to the position dependent second order reflection which is not taken into account in our discussions. Although such a relationship isn’t quite accurate, it still implies that a larger grating coupling length can make the grating more misalignment tolerant as a 3-dB splitter. On the other hand, a larger coupling length means a decrease of the total coupling efficiency.

*α*(inversely proportional to the coupling length

*L*) can be varied by changing the filling factor (FF) of the grating [23

_{d}23. 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]

27. D. Taillaert, P. Bienstman, and R. Baets, “Compact efficient broadband grating coupler for silicon-on-insulator waveguides,” Opt. Lett. **29**(23), 2749–2751 (2004). [CrossRef] [PubMed]

23. 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]

*+ x*direction) with different FF when the fiber has a 1μm misalignment. It is worth noting that the wavelength dependent curve of the split ratio is symmetric around the resonant wavelength of 1543nm when FF = 0.5. This can be explained that both the coupling and the reflection are symmetrical respect to the resonant wavelength in this condition. As the FF changes from 0.5, the wavelength dependent relationship begins to run out of symmetry. Thus, there is some disagreement between what this simulation shows and our discussion predicts at some period of wavelength. However, for a grating coupler, the splitting performance at the wavelength range of strongest coupling is what we are most concerned about, which is shown in the inset picture of Fig. 3(b). It is clear that the curves at this wavelength range is more flat, which means a stable value of split ratio. As the FF increases from 0.2 to 0.4, the split ratio increases significantly due to the decreasing coupling length. Because the grating coupling length remains unchanged when FF increases from 0.4 to 0.5, the split ratio of FF = 0.5 almost overlapped with that of FF = 0.4. From the above discussions, we know there is a compromise between the coupling efficiency and the misalignment tolerance of the splitting behavior for this bidirectional grating. A possible method to reach a trade-off is tailoring the coupling length by chirping the gratings while not breaking the symmetry of this device. Such a work is left for future discussion.

^{17}cm

^{−3}, and the N-type doping concentration is about 5 × 10

^{17}cm

^{−3}. In order to achieve an efficient overlap between P doped region and the strongest optical mode, the PN junction is designed to be located 50nm right off waveguide center which means the P doped region is 300nm wide in waveguide. The P + and N + regions are doped to a concentration of 10

^{20}cm

^{−3}to minimize the contact resistivity. To avoid the optical loss caused by heavy doping, the P + and N + doped regions are located 1μm away from the ridge side.

## 4. Measurement and discussion

*S*is the split ratio of the

*+ x*direction,

*ΔΦ*is the phase difference between two arms, the first part in Eq. (11) represents the phase difference caused by the waveguide arm length difference, and the second part is due to fiber misalignment.

*N*and

_{effw}*N*are the effective index of the single mode waveguide arm and the grating respectively,

_{effg}*ΔL*is the length difference between two single mode waveguide arms.

*Δx*is the fiber displacement along the

*x*direction. At the dip wavelengths,

*ΔΦ*should fit:Therefore, the dip wavelengths can be expressed by:When the fiber is launched at the grating center (LP = 0), the grating functions as a 3-dB splitter, which means

*S*= 0.5. According to Eq. (10), the output intensity should reach a maximum value of

*I*and a minimum value of 0 at the constructive point and destructive point respectively. Therefore, when the fiber shifts away from grating center, the IL has a small increase and the notch depth decreases. If the fiber moves towards the

_{in}*+ x*direction (more close to the longer arms as shown in the inset of Fig. 5(a)), the second part of

*ΔΦ*should be negative. According to Eq. (13), the dip wavelengths will shift to the smaller wavelengths, which means a blue shift of the spectrum will occur. On the contrary, a fiber move towards the

*–x*direction will cause a spectrum red shift. With the calculated waveguide group index of 3.9, the designed free spectral range (FSR) can be obtained by the following equation:However, if taking into account the influence of the fiber displacement, Eq. (14) should be modified to:Where,

*λ*is the vacuum wavelength of 1.55μm,

_{0}*λ*and

_{1}*λ*are the two dip wavelengths closest to

_{2}*λ*,

_{0}*N*is the group index of the single mode waveguide,

_{gw}*N*is the group index of the grating region. The calculated result from Eq. (14) is about 20nm. The measured results show that the FSR is 19.2nm, 19.7nm and 20.1nm at fiber launch positions of −1μm, 0, 1μm respectively. This changing trend coincides well with what Eq. (15) implies. Figure 5(b) shows how the fiber position affects the IL and notch depth of the transmission spectrum. The IL increase is no more than 1dB within the ± 3μm range off center. Although the misalignment of fiber in the

_{gg}*x*direction will deteriorate the extinction ratio, a notch depth decrease of no more than 4dB within the ± 1μm is still acceptable for the modulator application.

_{1}is considered to be not suitable for working. However, when considering the possible misalignment of fiber, the unsuitable wavelength range will be enlarged. We noted that the wavelength dependent curves for different fiber LPs differ from each other significantly in the wavelength range Δλ

_{2}. This means the modulator performance at this wavelength range could be very sensitive to the fiber perturbation in testing or the fiber misalignment in packaging. It is also worth noting the dependent curves at LP = 0 and LP = −1μm and the dependent curves at LP = 0 and LP = 1μm almost overlapped at the two side bands out of the range Δλ

_{2}respectively. This implies this modulator performance can be maintained for at least one side band within a ± 1μm misalignment range. Furthermore, this wavelength dependent relationship could be eliminated by using a balance-armed modulator.

^{31}-1. The output RF signal with peak to peak value (VPP) of 1.6V is mixed with a DC reverse bias of 0.8V. In order to get an enough high driving voltage swing, the mixed signal is amplified by a microwave amplifier with a typical gain of 12dB and then coupled in to the device through a microwave probe. Then the amplitude of the amplified RF signal is about 6V. In order to lower down the microwave reflection, a standard 50Ω terminal resistance was used to terminate this device. The optical output from the lensed fiber is directly fed to a digital series analyzer (Tektronix DSA 8300) with a 14GHz optical head for eye diagram test. Figure 9 shows the eye diagram measurement results. The eye diagrams with different fiber positions (LP = −1, 0, 1μm) are all given as a comparison. The dynamic extinction ratios are 3.6dB, 5.4dB and 6.1dB respectively. Comparing with the static ERs of 4.8dB, 8dB and 9dB, the dynamic ERs are a bit lower. This can be attributed to the reflection of the electrical wave caused by impedance mismatch, the transmission loss of the CPW electrode and the velocity mismatch between the optical mode and the microwave mode. Although improving the absolute speed is not the focus of this work, the device speed is still a bit lower than we expected. A possible reason is that the symmetrical phase shifter in our device may make the travelling wave electrode ineffective though it cuts the electrode length by half.

29. D. A. B. Miller, “Device requirements for optical interconnects to silicon chips,” Proc. IEEE **97**(7), 1166–1185 (2009). [CrossRef]

15. J. Ding, H. Chen, L. Yang, L. Zhang, R. Ji, Y. Tian, W. Zhu, Y. Lu, P. Zhou, and R. Min, “Low-voltage, high-extinction-ratio, Mach-Zehnder silicon optical modulator for CMOS-compatible integration,” Opt. Express **20**(3), 3209–3218 (2012). [CrossRef] [PubMed]

30. J. Ding, H. Chen, L. Yang, L. Zhang, R. Ji, Y. Tian, W. Zhu, Y. Lu, P. Zhou, R. Min, and M. Yu, “Ultra-low-power carrier-depletion Mach-Zehnder silicon optical modulator,” Opt. Express **20**(7), 7081–7087 (2012). [CrossRef] [PubMed]

## 5. Conclusion

## Acknowledgments

## References and links

1. | G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics |

2. | A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature |

3. | Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature |

4. | L. Zhou and A. W. Poon, “Silicon electro-optic modulators using p-i-n diodes embedded 10-micron-diameter microdisk resonators,” Opt. Express |

5. | R. Soref and B. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. |

6. | L. Liao, A. Liu, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, and M. Paniccia, “40 Gbit/s silicon optical modulator for high speed applications,” Electron. Lett. |

7. | F. Y. Gardes, D. J. Thomson, N. G. Emerson, and G. T. Reed, “40 Gb/s silicon photonics modulator for TE and TM polarisations,” Opt. Express |

8. | D. J. Thomson, F. Y. Gardes, J.-M. Fedeli, S. Zlatanovic, Y. 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. |

9. | H. Xu, X. Xiao, X. Li, Y. Hu, Z. Li, T. Chu, Y. Yu, and J. Yu, “High speed silicon Mach-Zehnder modulator based on interleaved PN junctions,” Opt. Express |

10. | G. Rasigade, D. Marris-Morini, L. Vivien, and E. Cassan, “Performance Evolutions of Carrier Depletion Silicon Optical Modulators: From p-n to p-i-p-i-n Diodes,” IEEE J. Sel. Top. Quantum Electron. |

11. | H. Yu, M. Pantouvaki, J. Van Campenhout, D. Korn, K. Komorowska, P. Dumon, Y. Li, P. Verheyen, P. Absil, L. Alloatti, D. Hillerkuss, J. Leuthold, R. Baets, and W. Bogaerts, “Performance tradeoff between lateral and interdigitated doping patterns for high speed carrier-depletion based silicon modulators,” Opt. Express |

12. | Y. H. Y. Hui, B. W., and D. K. A., “Optimization of ion implantation condition for depletion-type silicon optical modulators,” IEEE J. Quantum Electron. |

13. | X. Tu, T. Y. Liow, J. Song, M. Yu, and G. Q. Lo, “Fabrication of low loss and high speed silicon optical modulator using doping compensation method,” Opt. Express |

14. | Y. Hui and W. Bogaerts, “An Equivalent Circuit Model of the Traveling Wave Electrode for Carrier-Depletion-Based Silicon Optical Modulators,” J. Lightwave Technol. |

15. | J. Ding, H. Chen, L. Yang, L. Zhang, R. Ji, Y. Tian, W. Zhu, Y. Lu, P. Zhou, and R. Min, “Low-voltage, high-extinction-ratio, Mach-Zehnder silicon optical modulator for CMOS-compatible integration,” Opt. Express |

16. | A. W. Fang, H. Park, O. Cohen, R. Jones, M. J. Paniccia, and J. E. Bowers, “Electrically pumped hybrid AlGaInAs-silicon evanescent laser,” Opt. Express |

17. | S. Tanaka, S. H. Jeong, S. Sekiguchi, T. Kurahashi, Y. Tanaka, and K. Morito, “High-output-power, single-wavelength silicon hybrid laser using precise flip-chip bonding technology,” Opt. Express |

18. | S. Messaoudene, S. Keyvaninia, C. Jany, F. Poingt, F. Lelarge, G. De Valicourt, G. Roelkens, D. Van Thourhout, F. Lelarge, J. Fedeli, and G. Duan, “Low-Threshold Heterogeneously Integrated InP/SOI Lasers With a Double Adiabatic Taper Coupler,” IEEE Photon. Technol. Lett. |

19. | M. Pu, L. Liu, H. Ou, K. Yvind, and J. M. Hvam, “Ultra-low-loss inverted taper coupler for silicon-on-insulator ridge waveguide,” Opt. Commun. |

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21. | G. Roelkens, D. Vermeulen, S. Selvaraja, R. Halir, W. Bogaerts, and D. Van Thourhout, “Grating-Based Optical Fiber Interfaces for Silicon-on-Insulator Photonic Integrated Circuits,” IEEE J. Sel. Top. Quantum Electron. |

22. | D. Vermeulen, S. Selvaraja, P. Verheyen, G. Lepage, W. Bogaerts, P. Absil, D. Van Thourhout, and G. Roelkens, “High-efficiency fiber-to-chip grating couplers realized using an advanced CMOS-compatible silicon-on-insulator platform,” Opt. Express |

23. | 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. |

24. | A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. De Dobbelaere, “A grating-coupler-Enabled CMOS Photonics Platform,” IEEE J. Sel. Top. Quantum Electron. |

25. | A. Mekis, S. Abdalla, P. M. De Dobbelaere, D. Foltz, S. Gloeckner, S. Hovey, S. Jackson, Y. Liang, M. Mack, G. Masini, R. Novais, M. Peterson, T. Pinguet, S. Sahni, J. Schramm, M. Sharp, D. Song, B. P. Welch, K. Yokoyama, and S. Yu, “Scaling CMOS photonics transceivers beyond 100 Gb/s,” Proc. SPIE |

26. | X. Chen, C. Li, and H. K. Tsang, “Etched waveguide grating variable 1×2 splitter/combiner and waveguide coupler,” IEEE Photon. Technol. Lett. |

27. | D. Taillaert, P. Bienstman, and R. Baets, “Compact efficient broadband grating coupler for silicon-on-insulator waveguides,” Opt. Lett. |

28. | G. Roelkens, J. Schrauwen, D. Van Thourhout, and R. Baets, “High Efficiency Fiber-to-Waveguide Grating Couplers in Silicon-on-Insulator Waveguide Structures,” in |

29. | D. A. B. Miller, “Device requirements for optical interconnects to silicon chips,” Proc. IEEE |

30. | J. Ding, H. Chen, L. Yang, L. Zhang, R. Ji, Y. Tian, W. Zhu, Y. Lu, P. Zhou, R. Min, and M. Yu, “Ultra-low-power carrier-depletion Mach-Zehnder silicon optical modulator,” Opt. Express |

**OCIS Codes**

(050.0050) Diffraction and gratings : Diffraction and gratings

(220.0220) Optical design and fabrication : Optical design and fabrication

(230.1360) Optical devices : Beam splitters

(250.5300) Optoelectronics : Photonic integrated circuits

(250.7360) Optoelectronics : Waveguide modulators

**ToC Category:**

Diffraction and Gratings

**History**

Original Manuscript: April 15, 2013

Revised Manuscript: May 27, 2013

Manuscript Accepted: May 27, 2013

Published: June 7, 2013

**Citation**

Zanyun Zhang, Beiju Huang, Zan Zhang, Chuantong Cheng, and Hongda Chen, "Bidirectional grating coupler based optical modulator for low-loss Integration and low-cost fiber packaging," Opt. Express **21**, 14202-14214 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-12-14202

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### References

- G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics4(8), 518–526 (2010). [CrossRef]
- A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature427(6975), 615–618 (2004). [CrossRef] [PubMed]
- Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature435(7040), 325–327 (2005). [CrossRef] [PubMed]
- L. Zhou and A. W. Poon, “Silicon electro-optic modulators using p-i-n diodes embedded 10-micron-diameter microdisk resonators,” Opt. Express14(15), 6851–6857 (2006). [CrossRef] [PubMed]
- R. Soref and B. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron.23(1), 123–129 (1987). [CrossRef]
- L. Liao, A. Liu, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, and M. Paniccia, “40 Gbit/s silicon optical modulator for high speed applications,” Electron. Lett.43(22), 1196–1197 (2007). [CrossRef]
- F. Y. Gardes, D. J. Thomson, N. G. Emerson, and G. T. Reed, “40 Gb/s silicon photonics modulator for TE and TM polarisations,” Opt. Express19(12), 11804–11814 (2011). [CrossRef] [PubMed]
- D. J. Thomson, F. Y. Gardes, J.-M. Fedeli, S. Zlatanovic, Y. 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]
- H. Xu, X. Xiao, X. Li, Y. Hu, Z. Li, T. Chu, Y. Yu, and J. Yu, “High speed silicon Mach-Zehnder modulator based on interleaved PN junctions,” Opt. Express20(14), 15093–15099 (2012). [CrossRef] [PubMed]
- G. Rasigade, D. Marris-Morini, L. Vivien, and E. Cassan, “Performance Evolutions of Carrier Depletion Silicon Optical Modulators: From p-n to p-i-p-i-n Diodes,” IEEE J. Sel. Top. Quantum Electron.16(1), 179–184 (2010). [CrossRef]
- H. Yu, M. Pantouvaki, J. Van Campenhout, D. Korn, K. Komorowska, P. Dumon, Y. Li, P. Verheyen, P. Absil, L. Alloatti, D. Hillerkuss, J. Leuthold, R. Baets, and W. Bogaerts, “Performance tradeoff between lateral and interdigitated doping patterns for high speed carrier-depletion based silicon modulators,” Opt. Express20(12), 12926–12938 (2012). [CrossRef] [PubMed]
- Y. H. Y. Hui, B. W., and D. K. A., “Optimization of ion implantation condition for depletion-type silicon optical modulators,” IEEE J. Quantum Electron.46(12), 1763–1768 (2010).
- X. Tu, T. Y. Liow, J. Song, M. Yu, and G. Q. Lo, “Fabrication of low loss and high speed silicon optical modulator using doping compensation method,” Opt. Express19(19), 18029–18035 (2011). [CrossRef] [PubMed]
- Y. Hui and W. Bogaerts, “An Equivalent Circuit Model of the Traveling Wave Electrode for Carrier-Depletion-Based Silicon Optical Modulators,” J. Lightwave Technol.30(11), 1602–1609 (2012). [CrossRef]
- J. Ding, H. Chen, L. Yang, L. Zhang, R. Ji, Y. Tian, W. Zhu, Y. Lu, P. Zhou, and R. Min, “Low-voltage, high-extinction-ratio, Mach-Zehnder silicon optical modulator for CMOS-compatible integration,” Opt. Express20(3), 3209–3218 (2012). [CrossRef] [PubMed]
- A. W. Fang, H. Park, O. Cohen, R. Jones, M. J. Paniccia, and J. E. Bowers, “Electrically pumped hybrid AlGaInAs-silicon evanescent laser,” Opt. Express14(20), 9203–9210 (2006). [CrossRef] [PubMed]
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