Open Access
Add to BibSonomy
Abstract
It is essential to bias a thin-film lithium-niobate Mach-Zehnder electro-optic (EO) modulator at the desired operation condition to ensure optimal performance of the modulator. While thermo-optic (TO) control can solve the problem of bias drift, it consumes significant electric power. In this paper, we propose a technique to largely reduce bias power consumption by combining passive bias and TO bias. In our design, waveguide sections with different widths are introduced in the two arms of the MZ modulator to produce a desired phase difference of π/2 rad (the desired operation condition), and local heating with electrode heaters placed on the waveguides is employed to provide compensation for any phase drift caused by fabrication errors and other effects. As the TO control only serves to compensate for small errors, the electric power required is low and the response is fast. To demonstrate our technique experimentally, we fabricate several modulators of the same design on the same chip. Our experimental modulators can operate up to ∼40 GHz with a half-wave voltage of ∼2.0 V over a wide optical bandwidth, and the performances are insensitive to ambient temperature variations. The TO bias powers required range from 1 mW to 15 mW, and the thermal rise and fall times are 47 µs and 14 µs, respectively. Our technique can facilitate the development of practical high-speed EO modulators on the lithium-niobate-on-insulator platform.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Thin-film lithium-niobate (LN) electro-optic (EO) modulators based on the structure of the Mach-Zehnder interferometer (MZI) could find important applications in the next generation of fiber communication systems. In recent years, many exciting developments in such modulators have appeared [1–12]. In particular, high-speed EO modulators that can be directly driven by CMOS circuits have been demonstrated [5]. Effective fiber-waveguide coupling has also been achieved with various kinds of edge couplers, such as bilayer edge couplers without [13] and with [14,15] cladding waveguides and step edge couplers [16]. To further push the voltage-bandwidth limit for efficient ultra-high frequency modulation, micro-structured EO electrodes have been proposed [11]. Regardless of these developments, bias drift is currently considered to be a serious problem that hampers practical applications of thin-film LN modulators [2,17]. In this paper, we propose and demonstrate an effective technique to bias a thin-film LN modulator.
To properly operate a thin-film LN modulator, the modulator must be biased at the desired operation condition to provide a fixed, desired phase difference between the two arms of the MZI. A drift in the bias point can degrade the performance of the modulator. Conventional LN modulators employ EO bias, where a direct-current (DC) voltage is applied across the modulation electrodes to set the operating point. However, the applied DC electric field can slowly polarize the charge carriers in LN, which leads to a slowly varying counteracting field and causes a drift in the bias condition. This effect, known as dielectric relaxation, is the dominant effect that causes bias drift in an EO-biased LN modulator [17]. Careful preparation of the LN/metal surface or annealing the waveguide in nitrogen could mitigate the DC bias drift [18]. There are also other effects that contribute to bias drift, such as the thermo-optic (TO) effect, the pyroelectric effect, and the photoelastic effect. To avoid dielectric relaxation, TO bias has been recently proposed to replace EO bias [19]. TO bias relies on local heating of a waveguide with applied electric power to change the phase of the propagating wave. Over the last two years or so, a number of TO-tuned thin-film LN devices have been reported, which include EO modulators [15,19], micro-ring resonators [20], and asymmetric MZIs [21,22]. The major drawback of TO bias or tuning is the need for electric power consumption. As the TO coefficient of LN is low, the power consumption is high (∼100 mW for a π-phase shift [15,19]). By employing heaters with air trenches, the TO tuning efficiency can be increased by 10 to 20 times, but the response time increases from tens of microseconds to milliseconds because of reduced heat coupling to the environment [20], which is unacceptable for the applications that require fast locking and tracking responses. In addition, incorporation of air trenches increases the fabrication complexity and weakens the physical strength of the device. It is important to devise a bias solution that can provide both low power consumption and fast response.
Our proposed bias technique is based on combining passive bias and TO bias, where the bias point of the modulator is preset by introducing a small fixed optical path difference between the two arms of the MZI and any changes in the bias point caused by unavoidable fabrication errors [23] or other effects is compensated by TO bias. As TO bias serves to compensate only for the deviation from the ideal bias point, the electric power required should be low, even using heaters without air trenches. As such, both low power consumption and fast response could be achieved. We should note that passive bias has long been used in conventional EO-biased bulk LN modulators for reducing the bias voltage [24]. Recently, passive bias has also been adopted in a thin-film LN modulator [5], where two semicircular waveguides with different lengths are introduced in the MZI to generate a few interference fringes within the desired optical band, so that optimal biasing is available at certain selected wavelengths within the band. However, such a modulator has a limited optical bandwidth, which is incompatible with the current wavelength-division-multiplexing (WDM) systems. As the optical path difference introduced in the MZI is large, the interference fringes and, hence, the optimal operating wavelengths may shift significantly with fabrication errors and the ambient temperature. Moreover, the use of semicircular waveguides increases the optical propagation loss and the footprint of the device. To overcome these drawbacks, in our design, passive bias is achieved by using two sections of straight few-mode waveguides (FMWs) with the same length but slightly different widths in the respective arms of the MZI and TO bias is achieved by placing electrode heaters on these two waveguide sections. The use of FMWs can provide ultra-low dispersion for the fundamental mode, which allows the tolerances on the waveguide parameters to be greatly relaxed and the phase difference between the two arms of the MZI to be precisely set to π/2 rad. Such a minimal imbalance in the MZI can lead to an exceedingly wide optical bandwidth and excellent thermal stability. To verify our ideas, we fabricated four modulators of the same design on an LN-on-insulator (LNOI) wafer chip. Our experimental devices show flat transmission spectra over a wide optical band (1525–1605 nm), which are insensitive to the ambient temperature (10°C – 70°C). The bias electric powers required for our devices range from 1 mW to 15 mW, which reflects the variation of the fabrication errors across the chip. The electric power consumption in our devices is much lower than that required for TO bias alone (e.g., ∼50 mW without air trenches [15]). The thermal rise and fall times are 47 µs and 14 µs, respectively, which are much shorter than those achieved with heaters that incorporate air trenches (∼2 ms) [20]. Our modulators have a half-wave voltage of ∼2.0 V and a 3-dB modulation bandwidth of ∼40 GHz.
2. Modulator structure, principle, and design
The layout of the proposed thin-film LN EO modulator is shown schematically in Fig. 1(a). The modulator is formed on an X-cut LNOI wafer. The structure of the modulator is a slightly unbalanced MZI constructed with two slightly different FMW arms (Arm 1 and Arm 2) connected at the two ends with identical multimode interference (MMI) couplers, which function as equal power splitters. The waveguides in the two arms have the same LN film thickness tLN, the same etch depth t, and the same sidewall angle θ. As shown in Fig. 1(a), the MZI is divided into two sections: a slightly unbalanced bias section and a balanced modulation section. In the bias section, as shown in Fig. 1(b), the widths of the waveguides in the two arms are wp, except for a short section in Arm 2, which is tapered to a slightly wider width of wp + ΔwP over a length of Lp. The linear taper that bridges the two widths has a length of Lt. As shown in Fig. 1(b) and 1(c), heater electrodes with length Lh, width wh, and thickness th are placed on the corresponding waveguides in the bias section to provide TO bias tuning. The thickness of the SiO2 buffer that separates the heater and the waveguide is tb. In the modulation section, as shown in Fig. 1(a) and 1(d), coplanar waveguide (CPW) electrodes with length Le, width we, thickness te, and gap distance Ge are placed along the waveguides in the two arms to provide EO modulation. The waveguides in the modulation section have width w. Although the modulator is designed to operate for the fundamental quasi-TE mode, denoted as the TE00 mode, we employ FMWs to construct the MZI to take advantage of the low-dispersion characteristics of the fundamental mode in such waveguides. The use of FMWs can also ease the fabrication tolerances. To filter out any unwanted high-order modes, two single-mode waveguide (SMW) sections are inserted, respectively, near the input and output ends of the modulator with biconical linear tapers, as shown in Fig. 1(a). We employ slow cosine profiles for all the S-bend waveguides used in the structure to minimize excitation of high-order modes.
Fig. 1. Schematic diagrams showing (a) the top view of the proposed thin-film LN modulator, (b) the top view of the waveguides in the bias section, (c) the cross-sectional view of the bias section, and (d) the cross-sectional view of the modulation section.
The phase difference Δφ (in rad) between the two waveguides with different widths in the bias section is given by:
where N1 and N2 are the effective indices of the TE00 modes in the waveguides with widths wp and wp + Δwp, respectively, and λ0 is the free-space operating wavelength. Equation (1) assumes that the effective index in the taper is the average of N1 and N2. The desired bias condition (i.e., the quadrature condition) for linear operation of the modulator is Δφ = π/2 + mπ rad with m = 0, 1, 2, $^{\dots}$ . Obviously, to achieve the smallest wavelength dependence for the bias phase and hence the widest optical bandwidth, the bias phase should be set at the smallest value, namely Δφ = π/2 rad (m = 0). Thus, our task is to choose the values for the waveguide parameters to satisfy Δφ = π/2 rad. We employ a commercial mode solver (COMSOL) to calculate the effective indices and the modal losses.In our design, an X-cut LNOI wafer with a 600-nm-thick LN film (tLN = 600 nm), 1-mm-long aluminum (Al) heaters (Lh = 1 mm), and 12-mm-long Al modulation electrodes (Le = 12 mm) are employed. The etch depth t and the sidewall angle θ of the waveguides are 250 nm and 70°, respectively.
We first consider the bias section. The thickness and the width of the heaters are fixed at th = 200 nm and wh = 5.0 µm, respectively. A narrower heater could provide a higher heating efficiency, but would be more susceptible to damages at a high driving electric power. Assuming a waveguide width of wp = 4.0 µm, we calculate the dependence of the absorption loss αh for the TE00 mode induced by the aluminum heater on the SiO2 buffer thickness tb at the wavelength of 1550 nm. The results are shown in Fig. 2(a). As expected, the absorption loss decreases with an increase in the buffer thickness. To keep the total absorption lower than 0.1 dB, we choose a buffer thickness of tb = 600 nm. The dependence of the effective index on the waveguide width wp calculated for different modes at 1550 nm is shown in Fig. 2(b). As shown in Fig. 2(b), the dispersion curves for the modes become flatter and more linear, as the waveguide width increases, which suggests that the bias phase Δφ becomes less sensitive to the waveguide width variation. For our design, we choose wp = 4.0 µm and Δwp = 0.5 µm. The corresponding effective indices of the TE00 modes are 1.9629 and 1.9641, respectively. With the taper length set at Lt = 50 µm, we find from Eq. (1) that the length of the waveguide that has a width of wp + Δwp required for achieving Δφ = π/2 rad at λ0 = 1550 nm is Lp = 275 µm.
Fig. 2. (a) Dependence of the heater-induced absorption loss for the TE00 mode on the buffer thickness tb at 1550 nm. (b) Dependence of the effective index N with the waveguide width wp calculated for different modes at 1550 nm.
Figure 3(a) shows the variation of the bias phase change Δθ (≡ Δφ − π/2) with the wavelength. Over the (S + C + L)-band, the bias phase changes only slightly from 0.024π to −0.023π rad (i.e., a total change of 0.047 π rad) and can be considered to be wavelength-insensitive. This characteristic of our modulator is important for application in WDM systems. Figure 3(b) shows the tolerance of the bias phase on the waveguide width wp (for t = 250 nm). For a ± 10% change in wp (3.60 µm ≤ wp ≤ 4.40 µm), which is within the fabrication tolerance, the bias phase change is within ±0.10π rad. Figure 3(c) shows the tolerance of the bias phase on the etch depth t (for wp = 4.0 µm). For a ± 12% change in t (220 nm ≤ t ≤ 280 nm), the bias phase change is within ±0.02π rad. Our analysis confirms that our design has excellent tolerances against waveguide parameter variations. We also perform an analysis of the temperature sensitivity of the bias phase and find no significant change in the bias phase over the temperature range from 10°C to 70°C. Our design is insensitive to ambient temperature variations. The slight imbalance in the bias section does not cause any significant thermal drift.
Fig. 3. Variations of the bias phase change Δθ (in rad) with (a) the wavelength λ0 over the (S + C + L)-band (1460–1625 nm), (b) the waveguide width wp, and (c) the etch depth t.
We next consider the modulation section. We fix the electrode gap at Ge = 6 µm and calculate the dependence of the absorption loss αe induced by the modulation electrodes for the TE00 mode on the waveguide width w at 1550 nm. As shown in Fig. 4(a), the electrode-induced absorption loss αe increases with the waveguide width w. To keep the absorption loss low, a narrow waveguide should be used. On the other hand, small fluctuations in w due to unavoidable waveguide nonuniformity can give rise to a random bias phase change [23,25] and a wider waveguide should be employed to reduce such a bias phase change [25]. To balance the electrode-induced loss and the random bias phase change, we choose a waveguide width of w = 3.0 µm for our design. The group index Ng of the waveguide with w = 3.0 µm is 2.21. To achieve velocity match between the optical wave and the microwave in the modulation section, the electrode width and thickness required are we = 16.0 µm and te = 1.0 µm. The characteristic impedance Z0 of the CPW electrodes and the effective index Nm of the microwave, calculated with the software ANSYS HFSS, are shown in Fig. 4(b) and the modulation frequency response, calculated with the method proposed in [26], is shown in Fig. 4(c). The 3-dB bandwidth calculated for our modulator is 68 GHz.
Fig. 4. (a) Dependence of the electrode-induced absorption loss αe for the TE00 mode on the waveguide width w in the modulation section of the MZI at 1550 nm. (b) Calculated characteristic impedance Z0 of the modulation electrodes and the effective index Nm of the microwave. (c) Calculated modulation frequency response of the modulator.
3. Modulator fabrication and characterization
The proposed device was fabricated with our in-house microfabrication facilities. A 180-nm-thick chromium (Cr) was first deposited on a commercial X-cut LNOI wafer. The waveguide pattern was defined on the Cr film by the standard lithography and wet etching processes. The waveguides were then formed by the proton-exchange assisted dry etching method [27]. The measured etch depth was 244 nm, which is close to the design value (250 nm). The residual Cr film was next removed with a dechroming solution and a ∼600-nm-thick SiO2 buffer layer was deposited on the chip. The SiO2 layer in the modulation section was then removed with a buffered oxide etchant (BOE) and two ∼200-nm-thick Al heaters were formed in the bias section by the thermal evaporation and lift-off processes. Subsequently, ∼1.0-µm-thick Al CPW electrodes were formed in the modulation section by the thermal evaporation and lift-off processes. Finally, both input and output facets of the sample were polished. As a routine screening process, we inspected the fabricated sample carefully with a microscope to make sure that the modulators to be tested contained no visible defects, such as cracks and bulges. A photograph of the chip is shown in Fig. 5(a). There are four modulators of the same design on the chip, which are labelled as S1, S2, S3, and S4, respectively. A microscopic image of the two waveguides in the bias section of the MZI in one of the modulators (prior to heater deposition) is shown in Fig. 5(b). The widths of the waveguides match the design values.
Fig. 5. (a) Photograph of our fabricated chip showing four modulators and (b) microscopic image of the two waveguides in the bias section of the MZI in one of the modulators.
We first characterized the transmission spectra and the thermal stability of the fabricated modulators by placing the chip on a thermoelectric cooling (TEC) chip. Light from an amplified spontaneous emission (ASE) source (1525–1605 nm) was launched into the modulator under test with a lensed single-mode fiber. The polarization state of light was controlled with an inline fiber polarizer and a polarization controller (PC). The output light from the modulator was collected with another lensed fiber and monitored with an optical spectrum analyzer (OSA) (Anristu, MS97740A). The transmission spectra of S2 measured for the TE polarization over the temperature range from 10°C to 70°C are shown in Fig. 6, where the reference is the direct fiber-to-fiber transmission spectrum. The transmission spectra of the modulator measured at different temperatures closely follow the reference spectrum, which indicates a wide optical bandwidth and excellent thermal stability. The wavelength range was limited by the light source available. The actual optical bandwidth of the modulator should be much wider than the (C + L)-band shown in Fig. 6. The results in Fig. 6 show no interference fringes, which indicates that the bias phase is insensitive to the wavelength and the temperature, i.e., the device can offer temperature-insensitive operation over a wide optical bandwidth. A comparison of the relative amplitudes of the modulator spectra and the reference spectrum indicates that the insertion loss (IL) of the modulator is ∼15 dB, which is mainly contributed by the fiber-waveguide butt-coupling losses at the two ends. It should be possible to significantly reduce the insertion loss by incorporating edge couplers [13–16] in our design. The other three modulators show similar characteristics.
Fig. 6. Transmission spectra of the modulator S2 measured at different temperatures from 10°C to 70°C, where the reference is the direct fiber-to-fiber transmission spectrum.
As confirmed by the results in Fig. 6, the bias phase is insensitive to the wavelength. Therefore, it is sufficient to measure the bias phases of our modulators at a single wavelength. For this purpose, TE-polarized light at the wavelength 1550 nm generated from a tunable laser was launched into the modulator under test with a lensed fiber. A 100-kHz triangular electrical signal from a signal generator (Aim-TTi, TG5011A) was applied to the CPW electrodes of the modulator. The output light was collected with another lensed fiber and then detected with a photodetector (PD) (New Focus, Model 1811). The output electrical signal from the PD was analyzed with an oscilloscope (Tektronix, TDS 3054C). The characteristics measured for the four modulators are shown in Fig. 7(a). All the four modulators have a similar half-wave voltage (Vπ) of ∼2.0 V and a similar extinction ratio (ER) of ∼15 dB. We can see from Fig. 7(a) that the modulator S4 is biased almost exactly at the quadrature point, while the modulators S2 and S3 have a small bias phase deviation of ∼π/12 rad. The modulator S1 has the largest bias phase deviation of ∼π/5 rad, which is still considerably smaller than π/2 rad. These results prove the effectiveness of our passive bias method. The small differences in the bias points among the four modulators represent the uncertainties in the control of the waveguide parameters in our fabrication process. In addition, the EO response of the modulator S4 was also measured with a light-wave component analyzer (Keysight, N4373E) and the result is shown in Fig. 7(b). For this modulator, there was no need to apply TO bias tuning for small-signal measurements. As shown in Fig. 7(b), the 3-dB modulation bandwidth of this modulator is slightly larger than 40 GHz. The modulation bandwidth is limited by the microwave propagation loss, the velocity mismatch between the optical wave and the microwave, and the impedance mismatch [26]. The microwave propagation loss can be reduced by using micro-structured electrodes [11], while the velocity mismatch and the impedance mismatch can be reduced by further optimizing the electrode parameters, especially the thickness of the electrodes. There is much room to further increase the modulation bandwidth of the modulator.
Fig. 7. (a) Normalized transmission as a function of the driving voltage measured for the four modulators at 1550 nm and (b) EO modulation response measured for the modulator S4 at 1550 nm.
Although the bias phase is insensitive to the wavelength, the half-wave voltage decreases with the wavelength. With the small wavelength dependences of the material dispersion and the EO coefficient ignored, the half-wave voltage varies by ∼6% across the (C + L)-band. Thanks to the low optical group-index dispersion in our design, there is no significant change in the modulation bandwidth across the (C + L)-band.
We finally measured the TO bias powers of the four modulators and their thermal response times at the wavelength 1550 nm. A 1-kHz triangular electrical signal was applied to the heater on Arm 2 of the MZI. The electric power applied to the heater can be calculated with the voltage of the triangular electrical signal and the measured resistance of the heater (∼95 Ω). The output light was detected with a PD and the output electrical signal from the PD was recorded with an oscilloscope. The normalized transmission as a function of the electric power applied to the heater measured for the four modulators is shown in Fig. 8(a). The TO bias powers required for the modulators S1, S2, S3, and S4 are 15 mW, 8 mW, 8 mW, and 1 mW, respectively, which are much lower than that required with TO bias alone (e.g., ∼50 mW [15]). A 1-kHz square-wave electrical signal was applied to the heater to investigate the thermal response. The bandwidth of the PD is 125 MHz, corresponding to a response time of ∼8 ns, which is fast enough for the measurement. The measured thermal response of the modulator S4 is shown in Fig. 8(b). The rise and the fall time are 47 µs and 14 µs, respectively, which are ∼50 times shorter than those obtained by using heaters with air trenches (∼2 ms) [19].
Fig. 8. (a) Normalized transmission as a function of the heating power measured for the four modulators at 1550 nm and (b) thermal response times measured for the modulator S4 at 1550 nm.
4. Conclusions
We have designed and demonstrated thin-film LN EO modulators with combined passive bias and TO bias. Our design features the use of FMWs to form the MZI and the introduction of two short sections of waveguides with the same length but slightly different widths in the two arms of the MZI to achieve precise passive bias. Our passive bias method can offer a wide optical bandwidth, large fabrication tolerances, and excellent thermal stability. As TO bias serves only to compensate for the deviation from the ideal bias condition caused by fabrication errors, the TO power required is low and the response time is short. Our experimental modulators fabricated on the same LNOI wafer chip fully confirm the expected performances. The transmission spectra of the modulators are flat over the (C + L)-band and beyond and insensitive to the ambient temperature (10°C – 70°C). The TO bias powers of the modulators range from 1 mW to 15 mW, which are much lower than that reported for using TO bias alone. The thermal rise and fall times of our modulators are 47 µs and 14 µs, respectively. In addition, our modulators have a low half-wave voltage of ∼2.0 V (or Vπ·L ≅ 2.4 V·cm) and an EO modulation bandwidth slightly larger than 40 GHz. Our modulators achieve not only excellent EO modulation performance but also low TO bias power consumption and fast TO tuning response.
Funding
National Natural Science Foundation of China (62075027, U20A20165); Key R & D Program of Sichuan Province (2020YFSY0003); Key Technology R&D Program of Shenzhen (JSGG20210802154413040); Fundamental Research Funds for the Central Universities (ZYGX2019J050, ZYGX2020ZB015); Research Grants Council, University Grants Committee (RGC, UGC), Hong Kong (CityU 11212621).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. G. Poberaj, H. Hu, W. Sohler, and P. Günter, “Lithium niobate on insulator (LNOI) for micro-photonic devices,” Laser Photonics Rev. 6(4), 488–503 (2012). [CrossRef]
2. D. Zhu, L. B. Shao, M. J. Yu, R. Cheng, B. Desiatov, C. J. Xin, Y. W. Hu, J. Holzgrafe, S. Ghosh, A. Shams-Ansari, E. Puma, N. Sinclair, C. Reimer, M. Zhang, and M. Lončar, “Integrated photonics on thin-film lithium niobate,” Adv. Opt. Photonics 13(2), 242–352 (2021). [CrossRef]
3. A. J. Mercante, P. Yao, S. Y. Shi, G. Schneider, J. Murakowski, and D. W. Prather, “110 GHz CMOS compatible thin film LiNbO3 modulator on silicon,” Opt. Express 24(14), 15590–15595 (2016). [CrossRef]
4. A. Rao, A. Patil, P. Rabiei, A. Honardoost, R. DeSalvo, A. Paolella, and S. Fathpour, “High performance and linear thin-film niobate Mach-Zehnder modulators on silicon up to 50 GHz,” Opt. Lett. 41(24), 5700–5703 (2016). [CrossRef]
5. C. Wang, M. Zhang, X. Chen, M. Bertrand, A. Shams-Ansari, S. Chandrasekhar, P. Winzer, and M. Lončar, “Integrated lithium niobate electro-optic modulators operating at CMOS-compatible voltages,” Nature 562(7725), 101–104 (2018). [CrossRef]
6. C. Wang, M. Zhang, B. Stern, M. Lipson, and M. Lončar, “Nanophotonic lithium niobate electro-optic modulators,” Opt. Express 26(2), 1547–1555 (2018). [CrossRef]
7. T. H. Ren, M. Zhang, C. Wang, L. B. Shao, C. Reimer, Y. Zhong, O. King, R. Esman, T. Cullen, and M. Lončar, “An integrated low-voltage broadband lithium niobate phase modulator,” IEEE Photonics Technol. Lett. 31(11), 889–892 (2019). [CrossRef]
8. M. B. He, M. Y. Xu, Y. X. Ren, J. Jian, Z. L. Ruan, Y. S. Xu, S. Q. Gao, S. H. Sun, X. Q. Wen, L. D. Zhou, L. Liu, C. J. Guo, H. Chen, S. Y. Yu, L. Liu, and X. L. Cai, “High-performance hybrid silicon and lithium niobate Mach-Zehnder modulators for 100 Gbit s-1 and beyond,” Nat. Photonics 13(5), 359–364 (2019). [CrossRef]
9. M. X. Li, J. W. Ling, Y. He, U. A. Javid, S. X. Xue, and Q. Lin, “Lithium niobate photonic-crystal electro-optic modulator,” Nat. Commun. 11(1), 4123 (2020). [CrossRef]
10. K. Luke, P. Kharel, C. Reimer, L. Y. He, M. Lončar, and M. Zhang, “Wafer-scale low-loss lithium niobate photonic integrated circuits,” Opt. Express 28(17), 24452–24458 (2020). [CrossRef]
11. P. Kharel, C. Reimer, K. Luke, L. Y. He, and M. Zhang, “Breaking voltage-bandwidth limits in integrated lithium niobate modulators using micro-structured electrodes,” Optica 8(3), 357–363 (2021). [CrossRef]
12. M. Y. Xu, Y. T. Zhu, F. Pittalà, J. Tang, M. B. He, W. C. Ng, J. Y. Wang, Z. L. Ruan, X. F. Tang, M. Kuschnerov, L. Liu, S. Y. Yu, B. F. Zheng, and X. L. Cai, “Dual-polarization thin-film lithium niobate in-phase quadrature modulators for terabit-per-second transmission,” Optica 9(1), 61–62 (2022). [CrossRef]
13. L. Y. He, M. Zhang, A. Shams-Ansari, R. R. Zhu, C. Wang, and M. Lončar, “Low-loss fiber-to-chip interface for lithium photonic integrated circuits,” Opt. Lett. 44(9), 2314–2317 (2019). [CrossRef]
14. C. R. Hu, A. Pan, T. A. Li, X. H. Wang, Y. H. Liu, S. Q. Tao, C. Zeng, and J. S. Xia, “High-efficient coupler for thin-film lithium niobate waveguide devices,” Opt. Express 29(4), 5397–5406 (2021). [CrossRef]
15. P. Ying, H. Y. Tan, J. W. Zhang, M. B. He, M. Y. Xu, X. Y. Liu, R. Y. Ge, Y. T. Zhu, C. Liu, and X. L. Cai, “Low-loss edge-coupling thin-film lithium niobate modulator with an efficient phase shifter,” Opt. Lett. 46(6), 1478–1481 (2021). [CrossRef]
16. M. K. Wang, J. H. Li, H. Yao, Y. J. Long, F. Zhang, and K. X. Chen, “A cost-effective edge coupler with high polarization selectivity for thin film lithium niobate modulators,” J. Lightwave Technol. 40(4), 1105–1111 (2022). [CrossRef]
17. J. P. Salvestrini, L. Guilbert, M. Fontana, M. Abarkan, and S. Gille, “Analysis and control of the DC drift in LiNbO3-based Mach-Zenhder modulators,” J. Lightwave Technol. 29(10), 1522–1534 (2011). [CrossRef]
18. E. Puma, R. Cheng, J. Holzgrafe, A. Shams-Ansari, R. Shanlar, and M. Lončar, “Mitigating anomalous sub-megahertz frequency response of electro-optic phase modulators in X-cut lithium niobate on insulator,” in 2022 Conference on Lasers and Electro-Optics (CLEO), Paper SF2O.1.
19. M. Y. Xu, M. B. He, H. G. Zhang, J. Jian, Y. Pan, X. Y. Liu, L. F. Chen, X. Y. Meng, H. Chen, Z. H. Li, S. Y. Yu, and X. L. Cai, “High-performance coherent optical modulators based on thin film lithium niobate platform,” Nat. Commun. 11(1), 3911 (2020). [CrossRef]
20. X. Y. Liu, P. Ying, X. M. Zhong, J. Xu, Y. Han, S. Y. Yu, and X. L. Cai, “Highly efficient thermo-optic tunable microring resonator based on an LNOI platform,” Opt. Lett. 45(22), 6318–6321 (2020). [CrossRef]
21. G. Y. Chen, H. L. Lin, J. D. Ng, and A. J. Danner, “Integrated thermally tuned mach-zehnder interferometer in Z-cut lithium niobate thin film,” IEEE Photonics Technol. Lett. 33(13), 664–667 (2021). [CrossRef]
22. G. Y. Chen, H. L. Lin, and A. J. Danner, “Highly efficient thermal tuning interferometer in lithium niobate thin film using air bridge,” IEEE Photonics J. 13(3), 1–9 (2021). [CrossRef]
23. S. K. Selvaraja, W. Bogaerts, P. Dumon, D. V. Thourhout, and R. Bates, “Subnanometer linewidth uniformity in silicon nanophotonic waveguide devices using CMOS fabrication technology,” IEEE J. Sel. Top. Quantum Electron. 16(1), 316–324 (2010). [CrossRef]
24. E. L. Wooten, K. M. Kissa, A. Y. Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6(1), 69–82 (2000). [CrossRef]
25. L. J. Song, H. Li, and D. X. Dai, “Mach-Zehnder silicon-photonic switch with low random errors,” Opt. Lett. 46(1), 78–81 (2021). [CrossRef]
26. A. Honardoost, R. Safian, A. Rao, and S. Fathpour, “High-speed modeling of ultracompact electrooptic modualtors,” J. Lightwave Technol. 36(24), 5893–5902 (2018). [CrossRef]
27. X. P. Li, K. X. Chen, and Z. F. Hu, “Low-loss bent channel waveguides in lithium niobate thin film by proton exchange and dry etching,” Opt. Mater. 8(5), 1322–1327 (2018). [CrossRef]
