The effect of the free carrier effect is more significant in the mid-infrared band when compared with the 1310 band and 1550 band. In this paper, we propose a cascaded Mach-Zehnder interference (MZI) structure to improve the extinction ratio (ER) of the modulator in the mid-infrared band. The cascaded compensation method is to add the next-stage equal-arm MZI device to the two phase shifters of the major MZI. The output light intensity of the two phase shifters can be maintained at the same level by adjusting the output loss of both the equal-arm MZI. With the cascaded compensation method, the simulated ER of the optical modulator is increased from 36 dB to 55 dB under −4 Vbias while the device still maintains a low insertion loss (IL) of 12.5 dB. Through the cascaded compensation method, the modulation depth of the modulator at −2 V, −4 V, −6 V, and −8 V are 58 dB, 53 dB, 57 dB, and 59 dB, respectively. Meanwhile, the dynamic ER is 9.2 dB at a data rate of 40 Gbps, which is 4.5 dB higher than that of the original one.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
The silicon-based devices in optical fiber communication have greatly attracted interest in near-infrared (NIR) wavelength from 1.3 to 1.6 µm in the past decade. However, to meet the growing demand for transmission capacity, it is necessary to extend the available wavelength toward the mid-infrared (MIR) spectrum ranging from 2 to 25 µm. MIR region is expected to be used for thermal imaging, absorption spectra of biology and free-space communication [1,2]. In the past few years, low-loss silicon MIR waveguides have been demonstrated on the silicon-on-insulator (SOI) platform for the wavelength ranging from 2-8 µm [3−6]. Meanwhile, several MIR passive and active devices have also been demonstrated, including the multimode interferometers (MMI) [7,8], grating couplers [7,9], Arrayed Waveguide Grating (AWG) , fiber amplifier  and lasers [12−16], which makes MIR communication become possible.
To achieve the integration of MIR devices for high-speed communication and applications with compatible CMOS processes. Many designs [17,18] in MIR are derived from the device development for the near-infrared band. However, to our knowledge, the research on silicon-based MIR modulators is not much enough. Many related contents [19,20] regarding to the optimization of the ER have been reported in 1550 band. The main optimization approach is to reduce the absorption loss of carriers by changing the structure of the doped region. Although such reports have greatly improved the extinction ratio of the modulator, it also brings huge challenges to the CMOS process. Meanwhile, as our best knowledge, current researches on silicon-based electro-optic modulators in the mid-infrared band, have no report for improving the extinction ratio.
In 2012, IBM  demonstrated a silicon-based modulator operating at 2165 nm using PIN carrier structure. The device can reach a bit rate of 3 Gbit/s with a pre-emphasis drive signal. While the ER of the modulator is about 23 dB, which is insufficient compared to the performance of NIR modulator. Cao  designed a high-speed silicon modulator for the 2 µm wavelength band. Although their research shows that it is possible for the modulator to work in both 1550 nm and 1950 nm wavelength bands, the insertion loss and ER of the device still need to be further optimized. Through improving the ER of the modulator, problems such as bit error rate can be effectively prevented. At the same time, compared with the group-IV-material-based modulators, although the silicon modulator has the characteristics of CMOS process compatibility and low cost, its modulation performance is still far from adequate .
This suggests that although the original modulator using plasma-dispersion-effect in the NIR has convincing properties with CMOS compatibility , there are still many issues that affect its application in MIR band. The Soref’s  research on the plasma dispersion effect suggests that the effect in MIR is more significant than that in NIR band. In that case, the The injection of carriers will cause a higher loss of the device in MIR band. Especially for MZI structure, a greatly quantitative difference in the carrier concentration of the two phase shifters will occur when different voltages are applied to the two phase shifters. This will lead to the output light intensity of the two arms unbalanced when the two arms interfere at the output end, resulting in a relatively low extinction ratio.
In this paper, we design and simulate a cascaded MZI structure to improve the ER during modulation. The entire modulator structure consists of two stages. These two phase shifters of the major stage are connected to a next-stage MZI structure. To reduce the optical transmission loss of the phase shifter caused by carriers while keeping the modulation efficiency at a high level, doping compensation method is utilized on the phase shifters [26−28]. Since the difference in loss between two phase shifters of the major stage are caused by the different carrier concentrations and unequal waveguide length. The role of the next-stage MZI is compensating for the loss to the same level. It will match the light intensity of the two arms when they interfere at the output end. Compared with original MZI modulators, the ER of the cascaded modulator has been increased from 36 dB to 55 dB. Meanwhile, the dynamic ER is 9.2 dB at a data rate of 40 Gbps, which is 4.5 dB higher than that of the original one. This shows that MZI can significantly improve the modulation depth and extinction ratio of the device after utilizing the cascaded compensation method. This structure can truly improve the application of silicon modulators in the future.
2. Principle and device design
2.1 Principle analysis
Since carrier dispersion and carrier absorption exist at the same time when the phase shifter is under phase modulation, changes in intensity are inevitable for silicon-based MZI devices based on the plasma dispersion effect. This accompanying intensity change will produce different light field attenuation between the two arms, which makes the modulation depth at the output of the interferometer decrease when they combine. At the same time, carrier absorption will cause additional absorption loss when the device working. Figure 1(a) shows the structure of an original MZI modulator. Assuming that a polarized light with an amplitude of A is divided into two beams with equal power. Beams respectively transmitted through two parallel straight waveguides and one of the straight waveguides is a phase shift arm. The two beams can be approximately expressed as follows before they combined:
Equations (4) and (5) suggest that the plasma dispersion effect is much stronger in 2 µm than that in both 1310 and 1550 nm, which will lead to a further increase of $\Delta \delta$, resulting in a decrease in the ER of the device. To solve this problem, we have designed a device structure that can balance the loss of the two arms of the modulator, so that $\Delta \delta$ can be greatly reduced.
2.2 Structure design
The device can be divided into two parts. First part consists of two equal-armed MZI, which are connected to the phase shifter of the second part. The structure of the device is shown in Fig. 1(b). 1st-1 and 1st-2 are designed with an equal-length phase shifter. This will make the output light intensity spectrum a fixed value rather than a periodic one. When the 2nd part is under high-speed modulation, 1st-1 and 1st-2 will apply corresponding compensation voltages to keep the total loss of the two phase shifters of the 2nd at the same level. Furtherly, to reduce the loss of the device, the length of 1st-1 and 1st-2 should be as small as possible. The compensated doping method [26−29] utilized in this structure can reduce the loss caused by the PN junction. Although the PIN structure of the 1st can better reduce the added insert loss of the device, we still choose the reverse compensation doped PN junction structure for the first stage under the trade-off. This is because the same structure of the first stage and the second stage can make it easier for us to demonstrate the effects of the device. At the same time, the same structure also facilitates operability, reduces the difficulty of subsequent processes, and avoids unnecessary errors. The schematic diagram and doping profile of all the phase shifter are shown in Fig. 2.
The SOI wafer has a 220 nm top silicon layer with a 2 µm buried oxide (BOX) layer. The height of the rib is 130 nm while the width is 600 nm. The device adopts a reverse PN junction without offset. The doping concentrations for n, p, n+, p+ are 5e17 cm−3, 5e17 cm−3, 1e20 cm−3 and 1e20 cm−3, the i region is back doped to form an intrinsic region. For the 2nd part, the length of the phase shifter is 2.5 mm and the lower arm is 120 µm longer than the upper one. In design process, two important dimension parameters should be optimized to improve the efficiency of the device. The first one is the distance from the intrinsic region to the center of the waveguide (Wp) and the second one is the length of the phase shifter of the 1st-1 and 1st-2.
To maintain the efficiency of the phase shifter while keeping the absorption loss of the PN junction at a relatively low level, an optimizing Wp should be discussed. The simulated phase shift and absorption loss of the compensated doping silicon waveguide with different Wp are shown in Fig. 3(a) and (b). For a reversed PN junction, the phase shift and absorption loss coming from the overlap between optical mode distribution and the depletion region on the cross section of the phase shifter. Simulated results from Fig. 3(a) show that the absorption loss is reduced from 4.2 dB/cm under no compensation case to 3.3 dB/cm with Wp = 100 nm compensated at 0 V. While under reversed voltage, the depletion layer become wider due to the reversed bias. The compensation method does not reduce the loss significantly, but there is still a reduction to some extends. The shift efficiency under 2.5 mm length phase shifter is shown in Fig. 3(b). With the applied voltage increased, the optimized Wp with the peak value of phase shift has increased from 0 nm to 120 µm. This suggests that the optimal Wp value increases as the applied voltage increases. An optimized modulation efficiency can be got at about Wp = 100 nm. To obtain relatively high modulation efficiency while reducing loss, we choose 100 nm for Wp in this article. The phase shifter efficiency Vπ•Lπ and optical loss under different Vbias are shown in Fig. 3(c). Although most of the research on MZI devices is to obtain a high phase change to obtain a higher extinction ratio of the device. The purpose of this article is to improve the extinction ratio of the device through the compensation method. The use of this method enables a small phase change to obtain a very large extinction ratio of the device, so a high phase change is not the focus of this article.
The length of the phase shifter in the 1st-1 and 1st-2 is the second major parameter that affects the efficiency of the modulator. Although we use doping compensation to reduce the absorption loss in the waveguide while ensuring the shifting efficiency, the length of the phase shifter in the 1st-1 and 1st-2 still needs to be considered. Since the 1st part is added to the modulator, a longer length will increase the insert loss of the total device, while a shorter length will lead a higher voltage for the 1st part to balance the light intensity of the 2nd. As shown in Fig. 4(a), when varying the phase shifter length, there is a trade-off between added total insert loss of the total 1st part and compensated efficiency. The total insertion loss of the entire device can be reduced to 8.4dB, but the compensation voltage needs to be 4.6V, when the 2nd applies a modulation voltage of 8V. At the same time, the compensation voltage of the first stage can be reduced by 0.8V, but the total insertion loss of the device will reach 14dB. In this design, to maintain the modulator at a relatively low loss, we choose the length of the arm at 2.5 mm. The added insert loss with 2.5 mm length is 6.7 dB, which is shown in Fig. 4(a). The normalized transmission spectra of the 1st-1 and 1st-2 are the same as shown in Fig. 4(b). Since both 1st parts are designed as a balanced arm, there is no periodic value change in the spectra.
Considering the applications of the modulator, the 1st part should match the dynamic loss of the 2nd part during modulation. We study the $\Delta \delta \cdot L$ of the two arms by 2nd part and the compensated loss which caused by the 1st part under different Vbias.
For $\Delta \delta L$ of the 2nd part, the lower phase shifter is 120 µm longer than the upper one. It will cause additional transmission loss and bending loss for the lower arms, resulting in an original $\Delta \delta L$=0.22 dB of the two arms at 0V. Besides, when the device is under working state, a further increased $\Delta \delta$ will happen since the relative change in carrier concentration between the two arms. Figure 5 shows the change of $\Delta \delta L$ with different voltage applied to the upper arm. As the applied voltage for the upper phase shifter of the 2nd increases, $\Delta \delta L$ increases significantly, which will severely reduce the ER of the device. While for the 1st part, since both arms of the 2nd part are cascaded with an equal-arm MZI structure (1st-1 and 1st-2), it will not affect $\Delta \delta L$ of the 2nd part at 0V. Therefore, only the compensated voltage is applied to the 1st-1 or 1st-2, it will compensate the $\Delta \delta L$ of the 2nd part. The loss that 1st part can compensate with different Vbias is also given in Fig. 5. The phase shifter of the 1st has a similar doping profile with the one of the 2nd part, so the compensated loss can be increased when the applied voltage gets higher.
3. Properties simulation and discuss
To prove the ER of the modulator after cascaded compensation improving significantly compared to the original silicon-based MZI modulator (Fig. 1(a and b)). In this part, a properties simulation for both compensated and original MZI modulators will be given.
3.1 Fringe spectrum
For silicon-based electro-optic modulators with MZI structure, the static extinction ratio of the device is an important parameter when making the device, which can reflect many issues on the material characteristics, processing technology, Optical structure, electrical structure and voltage loading. At the same time, it is the basis for measuring the transient characteristics of optical modulators.
To show the modulation effect of the cascaded MZI intuitively, single-drive simulation tests are used for DC static simulation. When the same voltage is applied to the upper arm and the lower arm of 2nd part, the change of $\Delta \delta$ will be different due to the initial unbalance of the waveguide length and bending loss of them. To fully verify the feasibility of the device, we respectively give the test results of compensation when the same voltage is applied to the upper arm and the lower arm.
The applied voltage on the upper arm of the 2nd part and the compensated voltage for 1st-1 and 1st-2 is shown in Table 1. Due to the 120 µm arm length difference, the loss of the lower arm is greater than that of the upper arm when no voltage is applied. At this time, applying a reverse bias to the upper arm will make the depletion layer in the center of the upper arm waveguide larger, which will further reduce the loss of the upper arm, resulting in a further increase in $\Delta \delta$. To reduce $\Delta \delta$, we need to apply a bias voltage to 1st-1 to compensate for the loss of the upper arm. After compensating for the loss of the upper arm, the loss of the upper arm will be increased to the same as that of the lower arm, which makes the two arms interfere at the output end to obtain a large modulation depth. Since the upper arm has less loss than the lower arm from the beginning, there is no need to compensate for the loss of the lower arm. Hence, there is no need to apply a reverse voltage to 1st-2. When −2 V, −4 V, −4 V and −8 V are applied to the upper arm of 2rd respectively, the required compensation voltages for 1st are shown in Table 1. The spectrums under −2V, −4V, −6V and −8V applied to the upper arm for both original modulator and compensated one are shown in Fig. 6(a), (b), (c) and (d).
Compared with the original modulator, the compensated one has an added insert loss of about 6.5 dB, which is caused by the structure of the 1st part. While the total loss of the compensated modulator is about 12.5 dB, which mainly comes from the bending waveguide, absorption loss of the PN junction and the Y splitter. Compared with the original one, the spectrum of the compensated modulator has a relative blue shift, which is mainly caused by the 1st part. When the 1st is under work to compensate for the 2nd part, a certain phase shifter will occur at the output of the 1st part. However, this blue shift is only about 1nm, and the generation of blue shift will increase the change of phase, resulting in an increasing ER of the device to some extent. More importantly, the modulation depth of the compensated one has a significant improvement. Figure 6 clearly shows that the modulation depth of the original one is no more than 30 dB. Besides, as the applied voltage increases, the modulation depth will further decrease. However, when the compensation is applied, the modulation depth can be maintained at 60 dB under different modulation voltages. At the same time, since the compensated voltage can be adjusted, it is possible to maintain the modulation depth of about 60 dB under variable modulation voltages.
Similarly, when a single-drive voltage is applied to the lower arm of the 2nd, the modulation depth of the modulator can also be optimized by adjusting the 1st compensation voltage. Figure 7(a), (b), (c) and (d) show the spectrums of both the original modulator and the compensated one under −2 V, −4 V, −6 V and −8 V applied to the lower arm.
Also, the needed voltage for 1st-1 and 1st-2 is shown in Table 2. As mentioned above, the initial loss of the lower arm at 0V is greater than that of the upper arm at the beginning. In that case, when the modulation voltage is applied to the lower arm, the loss of it will be smaller, which makes the $\Delta \delta$ of the two arms gradually decrease. However, when the loss induced by modulation voltage is greater than the initial loss difference between the two arms, the loss of the upper arm begins to be greater than that of the lower arm, which makes $\Delta \delta$ increases again. In this case, we need to adjust the voltage of 1st-1 or 1st-2 according to the different $\Delta \delta L$. In Table 2, when the loss of the lower arm is less than that of the upper arm, $\Delta \delta L$ is represented by a negative number. Figure 7 shows a similar result to Fig. 6. The modulator depth of the original modulation depth is about 35 dB. Since the $\Delta \delta L$ of 2V is very little, it makes the modulation depth of the original modulator reach 55 dB. When applying modulation voltage to the 2nd, the spectrum will have a red shift. However, the effect of the 1st part will also lead to a blue shift, resulting in a spectrum overlap of the original modulator and the compensated one under a modulation voltage of −6V and −8V.
Finally, the spectrums of the original modulator and the compensated modulator are shown in Fig. 8(a) and (b). Figure 8 clearly shows that the compensated modulator has an ER of about 55 dB, which is 20 dB higher than that of an original one. It fully suggests that the compensated modulator has a significant optimization in the ER.
3.2 AC properties result
We built TWE models and calculated the 3dB electro-optical response bandwidth of two modulators under different voltages by the combination of HFSS software and Lumerical software. For the modulator of cascade compensation type, the TWE is only loaded on the modulator of the 2nd, and the applied voltage of the 1st is a static voltage. In that case, As shown in Fig. 9, compared with the original modulator, the compensated one has a little difference in bandwidth. For the compensated modulator, the function of the 1st part is only to compensate for the static loss of the 2nd part, which does not participate in modulation and affect the bandwidth of the device.
The eye diagrams in Fig. 10(a) and (b) illustrate the modulation performance of both the original modulator and the compensated modulator at 40 Gbps while injecting a continuous wave (CW) input signal at a wavelength of 2005 nm. Both modulators were driven in a single-drive configuration with a signal of −1 V with Vpp = 4 V. For the compensated modulator, a −2.85 V is applied to 1st-1 for compensation. By comparing the photonics detector transmission at voltages corresponding to the “1” and “0” levels. The PRBS signal is used to generate the eye, which is a data pattern of 2e8-1. The dynamic ERs for the original modulator and compensated modulator are 4.7 dB and 9.2 dB. It suggests that the compensated modulator can also maintain a larger dynamic ER than the original one under high-speed modulation.
In this paper we demonstrate a silicon-based optical modulator working at 2 µm using cascade compensation method. With the method of cascaded compensation, the device has a modulation ER of 55 dB, a modulation depth of about 57 dB and a dynamic ER of 9.2 dB. Compared with the original MZI structure, the compensated MZI structure has higher modulation efficiency and ER. At the same time, the compensated MZI structure have little impact on the bandwidth. This modulator provides a solution for future MIR band communications.
National Natural Science Foundation of China (No. 61764008); National Key Research and Development Program of China (Grant No. 2018YFB2200500).
The authors declare no conflicts of interest.
No data were generated or analyzed in the presented research.
1. R. Soref, “Mid-infrared photonics in silicon and germanium,” Nat. Photonics 4(8), 495–497 (2010). [CrossRef]
2. Y. Zou, S. Chakravarty, C. J. Chung, X. C. Xu, and R. T. Chen, “Mid-infrared silicon photonic waveguides and devices Invited,” Photonics Res. 6(4), 254–276 (2018). [CrossRef]
3. N. Hattasan, B. Kuyken, F. Leo, E. M. P. Ryckeboer, D. Vermeulen, and G. Roelkens, “High-Efficiency SOI Fiber-to-Chip Grating Couplers and Low-Loss Waveguides for the Short-Wave Infrared,” IEEE Photonics Technol. Lett. 24(17), 1536–1538 (2012). [CrossRef]
4. M. S. Rouifed, C. G. Littlejohns, G. X. Tina, H. Qiu, T. Hu, Z. Zhang, C. Liu, G. T. Reed, and H. Wang, “Low Loss SOI Waveguides and MMIs at the MIR Wavelength of 2 mu m,” IEEE Photonics Technol. Lett. 28(24), 2827–2829 (2016). [CrossRef]
5. S. A. Miller, M. J. Yu, X. C. Ji, A. G. Griffith, J. Cardenas, A. L. Gaeta, and M. Lipson, “Low-loss silicon platform for broadband mid-infrared photonics,” Optica 4(7), 707–712 (2017). [CrossRef]
6. B. W. Dong, X. Guo, C. P. Ho, B. Li, H. Wang, C. Lee, X. S. Luo, and G. Q. Lo, “Silicon-on-Insulator Waveguide Devices for Broadband Mid-Infrared Photonics,” IEEE Photonics J. 9(3), 1–10 (2017). [CrossRef]
7. M. Nedeljkovic, J. S. Penades, C. J. Mitchell, A. Z. Khokhar, S. Stankovic, T. D. Bucio, C. G. Littlejohns, F. Y. Gardes, and G. Z. Mashanovich, “Surface-Grating-Coupled Low-Loss Ge-on-Si Rib Waveguides and Multimode Interferometers,” IEEE Photonics Technol. Lett. 27(10), 1040–1043 (2015). [CrossRef]
8. Y. Wei, G. Li, Y. Hao, Y. Li, J. Yang, M. Wang, and X. Jiang, “Long-wave infrared 1 ( 2 MMI based on air-gap beneath silicon rib waveguides,” Opt. Express 19(17), 15803–15809 (2011). [CrossRef]
9. C. Alonso-Ramos, M. Nedeljkovic, D. Benedikovic, J. S. Penades, C. G. Littlejohns, A. Z. Khokhar, D. Perez-Galacho, L. Vivien, P. Cheben, and G. Z. Mashanovich, “Germanium-on-silicon mid-infrared grating couplers with low-reflectivity inverse taper excitation,” Opt. Lett. 41(18), 4324–4327 (2016). [CrossRef]
10. A. Malik, M. Muneeb, S. Pathak, Y. Shimura, J. Van Campenhout, R. Loo, and G. Roelkens, “Germanium-on-Silicon Mid-Infrared Arrayed Waveguide Grating Multiplexers,” IEEE Photonics Technol. Lett. 25(18), 1805–1808 (2013). [CrossRef]
11. Z. Li, A. M. Heidt, J. M. O. Daniel, Y. Jung, S. U. Alam, and D. J. Richardson, “Thulium-doped fiber amplifier for optical communications at 2 mu m,” Opt. Express 21(8), 9289–9297 (2013). [CrossRef]
12. Z. Zhang, D. Y. Shen, A. J. Boyland, J. K. Sahu, W. A. Clarkson, and M. Ibsen, “High-power Tm-doped fiber distributed-feedback laser at 1943nm,” Opt. Lett. 33(18), 2059–2061 (2008). [CrossRef]
13. W. Q. Yang, B. Zhang, J. Hou, R. Xiao, R. Song, and Z. J. Liu, “Gain-switched and mode-locked Tm/Ho-codoped 2 mu m fiber laser for mid-IR supercontinuum generation in a Tm-doped fiber amplifier,” Laser Phys. Lett. 10(4), 045106 (2013). [CrossRef]
14. S. Liu, K. Xu, Q. Song, Z. Cheng, and H. K. Tsang, “Design of Mid-Infrared Electro-Optic Modulators Based on Aluminum Nitride Waveguides,” J. Lightwave Technol. 34(16), 3837–3842 (2016). [CrossRef]
15. S. J. Park, A. Zakar, V. L. Zerova, D. Chekulaev, L. T. Canham, and A. Kaplan, “All-optical modulation in Mid-Wavelength Infrared using porous Si membranes,” Sci. Rep. 6(1), 8 (2016). [CrossRef]
16. M. Razeghi, Q. Y. Lu, N. Bandyopadhyay, W. Zhou, D. Heydari, Y. Bai, and S. Slivken, “Quantum cascade lasers: from tool to product,” Opt. Express 23(7), 8462–8475 (2015). [CrossRef]
17. L. Zhang, H. Y. Zhao, H. Y. Wang, S. Z. Shao, W. J. Tian, J. F. Ding, X. Fu, and L. Yang, “Cascading Second-Order Microring Resonators for a Box-Like Filter Response,” J. Lightwave Technol. 35(24), 5347–5360 (2017). [CrossRef]
18. L. C. Zheng, S. Z. Shao, J. F. Ding, L. Zhang, X. Fu, and L. Yang, “Intrinsic chirp analysis of a single dual-drive silicon PAM-4 optical modulator,” Opt. Express 26(24), 32014–32025 (2018). [CrossRef]
19. D. J. Thomson, F. Y. Gardes, Y. Hu, G. Mashanovich, M. Fournier, P. Grosse, J. M. Fedeli, and G. T. Reed, “High contrast 40Gbit/s optical modulation in silicon,” Opt. Express 19(12), 11507–11516 (2011). [CrossRef]
20. 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 Photonics Technol. Lett. 24(4), 234–236 (2012). [CrossRef]
21. M. A. Van Camp, S. Assefa, D. M. Gill, T. Barwicz, S. M. Shank, P. M. Rice, T. Topuria, and W. M. J. Green, “Demonstration of electrooptic modulation at 2165 nm using a silicon Mach-Zehnder interferometer,” Opt. Express 20(27), 28009–28016 (2012). [CrossRef]
22. W. Cao, D. Hagan, D. J. Thomson, M. Nedeljkovic, C. G. Littlejohns, A. Knights, S. U. Alam, J. J. Wang, F. Gardes, W. W. Zhang, S. H. Liu, K. Li, M. S. Rouifed, G. Xin, W. J. Wang, H. Wang, G. T. Reed, and G. Z. Mashanovich, “High-speed silicon modulators for the 2 mu m wavelength band,” Optica 5(9), 1055–1062 (2018). [CrossRef]
23. M. U. Sadiq, H. Y. Zhang, J. O’Callaghan, B. Roycroft, N. Kavanagh, K. Thomas, A. Gocalinska, Y. Chen, T. Bradley, J. R. Hayes, Z. H. Li, S. U. Alam, F. Poletti, M. N. Petrovich, D. J. Richardson, E. Pelucchi, P. O’Brien, F. H. Peters, F. Gunning, and B. Corbett, “40 Gb/s WDM Transmission Over 1.15-km HC-PBGF Using an InP-Based Mach-Zehnder Modulator at 2 mu m,” J. Lightwave Technol. 34(8), 1706–1711 (2016). [CrossRef]
24. G. T. Reed, G. Z. Mashanovich, F. Y. Gardes, M. Nedeljkovic, Y. F. Hu, D. J. Thomson, K. Li, P. R. Wilson, S. W. Chen, and S. S. Hsu, “Recent breakthroughs in carrier depletion based silicon optical modulators,” Nanophotonics 3(4-5), 229–245 (2014). [CrossRef]
25. M. Nedeljkovic, R. Soref, and G. Z. Mashanovich, “Free-Carrier Electrorefraction and Electroabsorption Modulation Predictions for Silicon Over the 1-14-mu m Infrared Wavelength Range,” IEEE Photonics J. 3(6), 1171–1180 (2011). [CrossRef]
26. X. G. Tu, T. Y. Liow, J. F. Song, M. B. 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]
27. X. G. Tu, T. Y. Liow, J. F. Song, X. S. Luo, Q. Fang, M. B. Yu, and G. Q. Lo, “50-Gb/s silicon optical modulator with traveling-wave electrodes,” Opt. Express 21(10), 12776–12782 (2013). [CrossRef]
28. Y. Yang, Q. Fang, M. B. Yu, X. G. Tu, R. Rusli, and G. Q. Lo, “High-efficiency Si optical modulator using Cu travelling-wave electrode,” Opt. Express 22(24), 29978–29985 (2014). [CrossRef]
29. H. Hu, X. Zhang, M. Gu, Y. Liu, L. Jia, S. Feng, Q. Fang, and H. Chen, “Low-loss silicon optical modulator using doping compensation method at 2 µm wavelength band,” Proc. SPIE 11780, 117800C (2021). [CrossRef]