Two novel waveguide gratings for optical phased array transmitters are investigated. By offsetting the grating structures along the waveguide on the upper and lower surfaces of the silicon nitride (Si3N4) waveguide, the dual-level chain and dual-level fishbone structures can achieve 95% of unidirectional radiation with a single Si3N4 layer by design. With apodized perturbation along the gratings, both structures can achieve uniform radiation without compromising the unidirectional radiation performance. In experiment, both demonstrate ∼ 80-90% unidirectionality. With further analysis, it is found that the dual-level fishbone structure is more feasible and robust to process variations in uniform radiation.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Thanks to the advancement of semiconductor technology, in integrated beam steering technology, the use of photonic integrated circuits can achieve high-speed scanning of the narrow beams. At present, there have been many proposals realizing the beam steering with integrated photonic circuits, including optical micromechanical systems (MEMS) [1,2], two-dimensional plane mirror systems , and integrated optical phased arrays [4–12]. In N×N optical phased arrays, a large transmitting aperture is required to achieve small beam divergence for long range applications, which is not easy to achieve [5,9]. We can easily enlarge the aperture in the order of millimeters or even centimeters by using waveguide grating arrays for OPA transmitter or receiver. However, in order to obtain a larger grating aperture, shallow grating etch with weak perturbation is necessary. But the shallow etch scheme makes the grating almost completely symmetrical in the vertical direction, which results in the waveguide grating's upward and downward radiant power being equal. In addition, the SOI structure is similar to a Fabry-Perot cavity so that the downward radiation is reflected multiple times in the silicon substrate and the silicon dioxide cladding structure. This forms a series of diffraction fringes in the far field. Influenced by the destructive interference from the downward radiant power, the transmitted or received power of the optical phased array decreases by up to 5.2 dB at locations of maximum destructive interference , resulting in a series of blind spots in the far-field scanning.
Furthermore, many optical phased arrays reported so far use gratings with uniform perturbation. Although a large-size emission aperture can be achieved by shallow etching, the exponential decay of radiated intensity along waveguide cannot be avoided. As a result, the effective aperture of the waveguide grating is smaller than the actual aperture, which leads to an increase in beam divergence. Consequently, the system performance of the periodic grating is rather limited.
Meanwhile, there have been few studies on the directionality of waveguide gratings. For fiber grating couplers, deep etching, high grating teeth [14,15] and misaligned dual-layer structure [16–19] are used to break the vertical symmetry, thereby to achieve the unidirectional radiation. For waveguide grating transmitters, we need a sufficiently large aperture, which requires extremely small perturbation, so deep etch and high grating teeth are not suitable. In addition, the waveguide arrays can be placed on a metal mirror to achieve unidirectional radiation of the grating , but such process is more difficult to implement, and it is also difficult to suppress the Fabry–Pérot (F-P) resonant effect.
Dual-layer misaligned Si3N4 waveguide structure can realize the unidirectional radiation and large aperture . However, the thin gap as low as 100 nm between the two layers waveguides requires complicated process steps (e.g., multiple chemical mechanical polishing), which may lead to lower yield and high fabrication cost than expectation. Considering that the dual-layer design of the waveguide cannot be implemented on the top single-crystal silicon, in this work we propose to use Si3N4 as the waveguide material. Compared with silicon, the Si3N4 waveguide index contrast is smaller, so it is easy to reduce the waveguide losses caused by sidewall roughness scattering and also to have a sufficiently small perturbation in waveguide grating. Meanwhile, Si3N4 waveguide can withstand higher light power intensity and it is more tolerant to fabrication-induced variation .
In this work, we present a waveguide grating transmitter structure that with dual-layer grating misalignment designed on single Si3N4 layer. By design, this structure can achieve more than 95% unidirectional radiation and uniform radiation with a large aperture. In the subsequent experiments, the two designed 3 mm long waveguide grating arrays are implemented. Both exhibit a unidirectionality of about 80% to 90%. Moreover, the more uniform radiation generated by apodized perturbation strength along the grating is demonstrated being able to achieve a larger effective aperture, comparing with that of the periodic grating.
2. Si3N4 dual-layer waveguide grating
The proposed Si3N4 dual-layer waveguide grating structure is shown in Fig. 1(a) and (b). The grating structure is comprised of the same grating teeth in both the upper and lower layers. We can consider it as a grating with a double-toothed composite structure. The offset between the upper and lower gratings can break the vertical symmetry of the waveguide grating, thus achieving unidirectional radiation. In our work, the misalignment of the upper and lower gratings is adjusted to yield the best unidirectionality, and the optical path of a single period of the grating should be consistent. The relationship between the parameters is described below:
Where Lf and Lp are the length of the unetched portion and the etched portion respectively, Lo is the offset distance between the upper and lower gratings along the waveguide (x-axis), and C is a pending constant, which can be set to the center wavelength of the operating band.
Here, the ratio of the upward radiation power to the total longitudinal radiation power is defined as the directivity (i.e., D = Pup / (Pup+Pdown)). Through 3D-FDTD simulation, the offset distances of the dual-layer grating are varied and analyzed, as shown in Fig. 2(a). We can find that when the offset Lo=175 nm, a unidirectionality of 0.95 is achieved. In FDTD simulation, we recorded a video of the transmission of the input power in the grating and intercepted a certain moment in the transmission, as shown in Fig. 2(b), (c). In addition, Fig. 2(a) and (b) only show the intensity profile at a certain moment, not the diffraction direction. Visualization 1 is a single-level grating, and Visualization 2 is a dual-level grating with Lo=175 nm. For more details about the radiation process of unidirectional and bidirectional gratings, see Visualization 1 and Visualization 2. It is found that ordinary single-layer gratings radiate upward and downward power rather equally, while the optimized dual-layer waveguide grating radiate power only upward.
The theoretical model of dual-layer gratings has also been discussed in previous studies . As shown in Fig. 3, the phase difference between the two gratings can be decomposed into a vertical phase difference φv and a lateral phase difference φl, so that the phase difference between the power radiated upward φup =φv-φl, and the downward one is φdown=φv+φl. Through the destructive interference of the downward radiation and the constructive interference of the upward radiation, the unidirectional radiation of the waveguide grating emitter can be realized. In the structure shown above, assuming that the power exits from the center of the side wall of the grating teeth, the vertical and lateral phase differences can be expressed as4(a), (b). Figure 4(a) illustrates the unidirectionality of dual-layer waveguide gratings with different waveguide thicknesses and offset distance. It can be seen that when the waveguide thickness is greater than 280 nm, higher unidirectionality can be obtained. In Fig. 4(b), we simulate the offset Lo corresponding to the maximum radiated upward power and the minimum radiated downward power by FDTD, and compare it with the calculation result of expression (2), which are quite consistent.
Although the periodic uniform perturbation of Si3N4 grating can easily achieve a millimeter-sized aperture, the radiant power will extenuate exponentially along the waveguide, which makes the effective aperture of the waveguide grating smaller than the actual aperture, causing the beam divergence to increase. Variable waveguide grating perturbation is used to achieve uniform radiation, such as varying the duty cycle , and by varying the bone width of fish bone structure [13,20]. For the dual-level structure shown above, we need to find a parameter that can engineer the radiation coefficient without affecting the unidirectionality. In the following two sections, we will show such structures.
2.1 Si3N4 dual-level chain
Considering that the unidirectionality of the dual-layered grating depends mainly on the offset and the thickness of the waveguide, as long as we do not change these two parameters, we should not destroy the characteristics of the unidirectional radiation of the dual-layered grating. We change the size of the etched area of the grating structure to obtain a dual-level chain structure, as shown in Fig. 5(a), (b). For the structure shown, we can achieve various perturbation strength by changing its lateral dimension (defined as the width of the etched hole wp) or its longitudinal dimension (defined as the length of the etched hole Lp). During the course of scanning Lp and wp on the unidirectional radiation capability of the waveguide grating, we also need to ensure that the optical paths in a period are equal. The difference is that na and ns are no longer constants, and the effective refractive index can be calculated by eigenmode solver. The effective refractive index in response to the width of the etched hole is shown in Fig. 5(c). Using Eq. (1), in order to ensure that the optical path is consistent within a period, it should satisfy
Here, we also analyze the effects of wp and Lp on the unidirectionality of the waveguide grating. As shown in Fig. 5(d), it can be seen that the change in the width of the etched hole has less effect on the unidirectionality of the waveguide grating. However, the length of the etched hole exhibits a great influence. Because when Lp is too large or too small, the relationship in Eq. (2) doesn’t hold, which means that we need to readjust Lo to achieve the best unidirectional radiation. Instead, we choose wp, which has little effect on unidirectionality, as the parameter to adjust the grating radiation coefficient.
For a waveguide grating emitter with uniform periodic perturbation, the power in the waveguide along the waveguide follows an exponential decay of exp(-αx), where α is the radiation coefficient of the grating, and the starting position of the grating is x=0. The radiation coefficient α depends on the width wp and the length Lp of the etched hole in the waveguide grating. From the above analysis above, we choose to fix Lp = 500 nm and Lo = 175 nm, and adjust wp along the waveguide (x-axis). We can use FDTD simulation to obtain the relationship between the power in the waveguide and the transmission distance. Here I0 is the input power and I(x)/I0 is the normalized power. Taking the logarithm on both sides of the above equation, we get ln(I(x) / I0) = -αx, and then obtain the radiation coefficient α by linear fitting.
In order to increase the effective aperture of the waveguide grating emitter, it is desirable to obtain a waveguide grating that radiates uniformly along the waveguide. The power in the apodized waveguide grating should satisfy the following equation
To achieve uniform radiation, the following differential equation needs to be as follow:
Among them, I(x) is the power in the waveguide grating at x, α(x) is the radiation coefficient at x, the starting position of the grating is defined as x=0, and S(x) is the power radiated by the grating at x. To achieve uniform radiation of the waveguide grating, S(x) needs to be a constant independent of x, as follow:
Then, we can get
According to the expression of α(x), it can be seen that in order to achieve a uniform emission of a large-scale waveguide grating, the radiation coefficient needs to have a sufficiently large range of variation. We use FDTD simulation to calculate the curve of the radiation coefficient and the period with the width of the etched hole, as shown in Fig. 6(a). It shows that by changing the width of the etched holes, we can achieve a wide range of changes in the radiation coefficient. In order to facilitate the subsequent calculations, we use polynomials to fit the curve of the etched hole width with respect to the radiation coefficient, as well as the curve of the period length and the etched hole width, as shown in Fig. 6(b), (c), to obtain the functional relationship as follow:
The unit of the etched hole width wp and period length Lperiod is micron, and the unit of the radiation coefficient α is mm−1. We substitute the expression of α(x) into (8-9), and calculate the structure of the waveguide grating with uniform radiation of one millimeter, as shown in Fig. 6(d). Since the maximum value of the radiation coefficient is limited, it is impossible for us to ensure that all the power is radiated out, and at the same time, to ensure uniform radiation over the entire size. In Fig. 6(d), we can see that in the last part of the grating, because the radiation coefficient has reached the maximum value, we have to use a periodically uniformly etched structure as the end of the grating. Compared with the reported SiN-Si dual-layer structure , due to the larger value range of the radiation coefficient α, our dual-level chain structure described above can obtain a larger area of uniform radiation.
2.2 Si3N4 dual-level fishbone
Fishbone gratings are feasible to achieve sufficiently small perturbations, and have been widely used in OPA waveguide grating transmitters [13,20]. In addition to adjusting the width of the etching holes, we can also adjust the bone width of the fish bone structure to achieve a uniform radiation grating design. The structure of dual-layer fishbone grating is shown in Fig. 7(a), (b). The etch width on both sides of the waveguide is defined as we and the etching length is Lp. Figure 7(c) is the curve of the effective refractive index of each part with the etching width we on both sides of the fishbone-shaped grating. The FDTD simulation is used to calculate the change in radiation unidirectionality of the dual-level fishbone structure with we and Lp, as shown in Fig. 7(d). The analysis here is basically the same as the dual-layer chain structure. Etching changes in the lateral direction(y-axis) will not destroy the unidirectional radiation of the structure.
We use the same method to obtain the relationship between the radiation coefficient of the dual-level fishbone structure and the etching width on both sides of the waveguide grating, as shown in Fig. 8(a). In order to facilitate the design of the device, we fit the curve of we with respect to α, and the curve of Lperiod and we as shown in Fig. 8(b)(c). The fitted function is as follows:
The unit of we and Lperiod is micron, and the unit of α is mm−1. We substitute the expression of α(x) into the Eq. (10) and (11), and calculate the structural parameters of the waveguide grating with uniform radiation of 1 mm, as shown in Fig. 8(d). Due to process limitations, the minimum bone width is set to 200 nm, so the range of we is 0 to 400 nm.
Since 3D-FDTD simulation requires a lot of computer resources, it is difficult to simulate a three-millimeter waveguide grating, so here we simulate two types of waveguide gratings with a length of one millimeter. Figure 9 illustrates the profile of the radiation intensity of two structures along the gratings. Due to the limited perturbation strength, radiant intensity exponentially decays at the ends of both structures, other than that, uniform radiation is maintained.
3. Comparison between the two dual-layer structures in simulation
For waveguide grating transmitter arrays, we use phase shifters to achieve lateral scanning and input lasers of different wavelengths to achieve longitudinal scanning. This requires that our devices have stable operating performance in the entire operating band. Through 3D-FDTD simulation, we find that the unidirectionality of our device is greater than 90% in the operating wavelength range. We design two apodized grating transmitters at the operating center wavelength. When the input wavelength is changed, if the radiation coefficient α of the device will change accordingly, the effective aperture of the waveguide grating will be different, which will reduce the device performance. We use FDTD simulation to calculate the function of the radiation coefficient and the wavelength under different perturbation strength of the two structures, such as Fig. 10(a) and (b). The radiation coefficient α change slightly at different wavelengths. It is proved that the two structures both illustrate good performance at different wavelengths in respect to unidirectional radiation and uniform emission.
In practice, the radiation coefficient α can neither reach infinity nor infinitesimal, because the minimum size of the structure depends on the process, which means that it is difficult to achieve extremely weak radiation coefficient. Considering the limit of the fabrication process, we set the minimum etch width of the device to 150 nm and the minimum etch hole spacing to 200 nm (i.e., the minimum bone width of the fish bone structure is 200 nm). When the structure size is smaller than the minimum size, we use a uniform perturbation instead, and then switch to apodized perturbation, so that the radiant power decays exponentially at the beginning. Figure 11(a) is the structural parameter of the 3 mm long dual-level chain grating. We can see that the waveguide grating is perturbed uniformly in more than half the length, which means that it is difficult to achieve a large-sized uniformly radiating grating. Figure 11(b) demonstrates the structural parameters of the 3 mm device of the dual-level fishbone. It illustrates that dual-level fishbone structure is more feasible to realize a large effective aperture waveguide grating than dual-level chain. Figure 11(c) and (d) show the mode profile at the grating teeth of the two structures in the region IV respectively. The etched area of the former is closer to the center of mode, which leads to a strong interaction with mode. In contrast, the etched area of the latter is far away from the center for reducing the reaction with mode. Thus, the dual-level fishbone structure is more robust to achieve extremely weak perturbations.
In the fabrication process, taking into account feasibility and robustness, we set the minimum etching width of the dual-level chain structure to 150 nm and the maximum etching width to 1um as abovementioned design. For the dual-level fishbone structure, we set the minimum and maximum etching width to 150 nm and 400 nm. Taking dual-level fishbone as an example, we pattern the lower grating on the silica cladding to form 70 nm thick blocks, as shown in Fig. 12(a). Deposit 340 nm Si3N4 on the etched silicon dioxide cladding. Due to the underlying grating, the deposited Si3N4 surface is not flat and requires chemical mechanical polishing (CMP) to obtain a smooth Si3N4 surface as shown in Fig. 12(b). As shown in Fig. 12(c), the upper grating is patterned by 175 nm offset from the lower grating along the waveguide to achieve 70 nm deep etched holes. Then, we lithographically pattern the waveguide to obtain a waveguide grating with a width of 1um, as shown in Fig. 12(d). Finally, we deposit silicon dioxide cladding on the device to obtain a dual-level fishbone structure. The fabrication process of dual-level chain grating structure is similar.
Figure 13(a) is the scanning electron microscope picture (SEM) of dual-level fishbone waveguide grating along the grating direction (x-axis). We find that due to the deviation of the alignment in the photolithography process, both the upper and lower gratings are offset by about 115 nm in the lateral direction (y-axis) relative to the Si3N4 waveguide. Figure 13(a) is the scanning electron microscope picture of the grating along the y-axis. The misalignment between the upper and lower gratings along the grating direction (x-axis) is about 200 nm. According to the aforementioned simulation results, that can also achieve more than 90% unidirectional radiation.
Figure 14(a), (b) are schematic diagrams of power transmission in a straight waveguide and a waveguide grating, respectively. In the case of no loss, the power in the straight waveguide is input from the input port (Pin) and all output from the output port (Pw). For the waveguide grating, the power input from the input port (Pin) will be output from the grating radiation area (Pg) and the waveguide output port (Pgw). The output power from the grating radiation area includes upward radiation power (Pup) and downward radiation power (Pdown). With the same input power, that satisfy Pw= Pgw+ Pup + Pdown. Thus, the unidirectionality of the grating radiation is:
In order to measure the unidirectionality of the dual-level gratings we design, we have designed two chips, one with a straight waveguide array as the output port and the another with a gratings array as the output port (namely, one is a straight waveguide array and the another is a waveguide gratings array). Except for that, the two chips are exactly the same, and we test the two chips with the same input power. The setup shown in Fig. 15(a) is used to measure the power output from the end of the waveguides, and the corresponding schematic is shown in Fig. 15(b). The setup shown in Fig. 15(c) is used to measure the power output from gratings, and the corresponding schematic is shown in Fig. 15(d). The laser passes through the polarization controller and is coupled into the chip. For the straight waveguide array chip, we utilize the setup shown in Fig. 15(a) to measure power output by the end of waveguides (Pw=2.64 mW). For the waveguide gratings array chip, we first use the setup shown in Fig. 15(a) to measure the power output from the end of waveguides (Pgw=0.19 mW), and then use the setup shown in Fig. 15(c) to measure the upward radiated power of dual-level fishbone grating (Pup=2.22 mW). Since the photodetector is integrated in the system, we can utilize probes and ammeter to achieve the same fiber-chip coupling in two setups. According to Eq. (12), the radiation unidirectionality of dual-level fishbone is 90.6%. Using the same measurement method, the unidirectionality of the dual-level chain is 87.7%.
In the above experiment, considering the imperfect fiber-chip coupling, part of the power that is not coupled into the waveguide may propagate along the cladding or substrate. Therefore, the Pw and Pgw measured by the power meter in the setups may both contain some imperfectly coupled power. But this will not have an impact on our experimental results, because with the same input power, (Pw – Pgw) in Eq. (12) has excluded this impact.
In order to further prove the unidirectionality of the grating radiation, we measured the loss of each part of the chip to understand the power transmission in the chip. The loss in the chip includes: (1) The loss of the fiber-to-chip coupling is 1.45 dB. (2) The insertion loss of a single Y-Branch is 0.36 dB. There are seven levels of Y-Branch in the system, and the total insertion loss is 2.52 dB. (3) The thermo-optic coefficient of Si is five times that of SiN, thus the power consumption of the Si modulator is lower. We use the SiN-Si dual-layer transition structure [24,25] to make a phase shifter on a silicon waveguide. Our SiN-Si-SiN insertion loss is 0.39 dB. (4) The insertion loss of the straight waveguide of silicon is 1.78 dB/cm, and that of Si3N4 is 0.25 dB/cm. The length of the silicon waveguide in the chip is 0.2 cm, and the length of the Si3N4 waveguide is 1.4 cm, so the total straight waveguide insertion loss is 0.71 dB. (5) In order to facilitate fiber-to-chip coupling and packaging, we also integrated a photodetector in the chip, and its loss is 1.27 dB. (6) For waveguide gratings, when light is radiated from the waveguide to the free space, power loss occurs in the silica-air interface due to reflection. We measured its loss to be about 0.96 dB. (7) Due to the limitation of layout size, part of the power cannot be radiated from the grating, but output from the waveguide (Pgw), resulting in a loss of 0.36 dB for dual-level fishbone structure, and 1.02 dB for dual-level chain structure. Then, we can get the insertion loss of the system.
For dual-level fishbone grating, the insertion loss of the system is 7.66 dB. When the input power is Pin=12.09 dBm, the power radiate upward is Pup=3.46 dBm. Therefore, its directionality is 0.97 dB (80.0%). For dual-level chain grating, the system insertion loss is 8.32 dB. With the same input power, its upward radiation power Pup=2.75 dBm, so the directionality is 1.04 dB (79.1%).
The unidirectionality measured in the experiment is lower than the simulation result, because the unidirectionality is defined as D = Pup / (Pup+Pdown) in the simulation process. But in addition to upward radiation and downward radiation, there is also a part of weaker lateral radiation Pside. Therefore, the rigorous Eq. (11) should be:
In the actual experiment, it is difficult to measure the power of the lateral radiation. Considering that the low ratio of its power to the total power, we can ignore this item in the measurement process, so the unidirectionality measured in the experiment is lower than the simulation.
Due to experimental errors, the unidirectionality of the grating radiation of the two measurement methods differs by about 10%. The unidirectionality of dual-level fishbone and dual-level chain can reach about 80%∼90%, and there is no obvious difference between the two.
The images of the near field of the abovementioned apodized dual-level chain grating and apodized dual-level fishbone grating are shown respectively in Fig. 16(a) and (b). For comparison, a near-field image of a dual-level fishbone grating with constant perturbation of we = 250 nm is shown in Fig. 16(c). Due to the microscope without antireflection coating, the reflection in the test equipment results in the oblique fringes in the picture. The emission intensity along the gratings with both apodized grating and periodic gratings are shown in Fig. 16(d). As expected, although the gratings’ lengths are the same, the effective aperture of the apodized fishbone is larger than that of periodic grating. And the limited perturbation strength causes the exponential decay of radiation intensity at end of both apodized chain and apodized fishbone structure.
According to the aforementioned process error, the upper and lower gratings both have a 115 nm offset in the lateral direction relative to the Si3N4 waveguide, so the profile of the radiation intensity is different from the design. The etched hole of the chain structure is shifted from the center of the waveguide to the edge, the perturbation becomes weak, and the radiation intensity also decreases. The width wp of the hole etched in the front part of the grating is only 150 nm. Such fine holes close to the center of the waveguide are extremely sensitive to fabrication variations, so deviation of 115 nm causes the radiation intensity significantly decreases. As the width of the etched holes along the grating (a-axis) becomes large, and the influence of the offset on the emissivity gradually weaken, causing the emission intensity of the rear part of the grating to be much higher. The Fishbone structure is etched on both sides of the waveguide for weak interaction with the mode, that make it robust to the lateral offset. Consequently, the emission intensity decreases slightly along the grating (x-axis). The emission intensity of periodic fishbone grating decays exponentially along the x-axis.
Comparing with periodic grating, apodized grating has a significant improvement in the uniformity of radiation intensity along the grating. In addition, comparing with the dual-level chain structure, the dual-level fishbone structure is more robust to fabrication variations. For the same lateral etching deviation, the emission intensity of the fishbone structure along the grating can maintain better uniformity.
We have demonstrated the design and experiment of two innovative dual-level waveguide gratings. The two structures both achieve 95% unidirectional radiation by design, and about 80∼90% in experiment, by offsetting grating structures along the waveguide on the upper and lower surfaces of the silicon nitride waveguide. In addition, with apodized perturbation strength along the gratings, both structures can achieve uniform radiation, thus obtain large effective aperture without destroying the unidirectionality. However, the radiation coefficient of dual-level chain grating is extremely sensitive to variations introduced by fabrication, which leads to a significant difference in the emission intensity profile from the design. In contrast, the dual-level fishbone grating is feasible and robust to process variations, so it is more reliable to achieve a larger effective aperture generated by uniform emission intensity profile. Unidirectional radiation suppresses the extinction ratio due to reflections in the silicon substrate, and increase the utilization of power in optical phased arrays. 3 mm long waveguide grating arrays with uniform emission intensity profile can provide larger effective aperture, comparing with one with an exponentially decaying emission profile. Unidirectional gratings with a large effective aperture provide small beam divergence and high receiving efficiency for long range applications.
National Key Research and Development Program of China (2016YFE0200700); National Natural Science Foundation of China (61627820, 61934003, 62090054); Jilin Scientific and Technological Development Program (20200501007GX); Program for Jilin University Science and Technology Innovative Research Team (JLUSTIRT) (2021TD-39).
The authors declare that there are no conflicts of interest related to this article.
Data underlying the results presented in this paper are not publicly available at this time but maybe obtained from the authors upon reasonable request.
1. Y. Wang, G. Zhou, X. Zhang, K. Yu, and M. C. Wu, “160×160 MEMS-Based 2-D Optical Phased Array,” in conference on lasers and electro optics, 2018).
2. T. Chan, M. Megens, B. Yoo, J. Wyras, C. J. Changhasnain, M. C. Wu, and D. A. Horsley, “Optical beamsteering using an 8 × 8 MEMS phased array with closed-loop interferometric phase control,” Opt. Express 21(3), 2807–2815 (2013). [CrossRef]
3. J. J. Lopez, S. Skirlo, D. Kharas, J. Sloan, J. S. Herd, P. W. Juodawlkis, M. Soljacic, and C. Soraceagaskar, “Planar-lens Enabled Beam Steering for Chip-scale LIDAR,” in conference on lasers and electro optics, 2018).
4. A. Yaacobi, J. Sun, M. Moresco, G. Leake, D. D. Coolbaugh, and M. R. Watts, “Integrated phased array for wide-angle beam steering,” Opt. Lett. 39(15), 4575–4578 (2014). [CrossRef]
5. J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493(7431), 195–199 (2013). [CrossRef]
6. D. Kwong, A. Hosseini, Y. Zhang, and R. T. Chen, “1 × 12 Unequally spaced waveguide array for actively tuned optical phased array on a silicon nanomembrane,” Appl. Phys. Lett. 99(5), 051104 (2011). [CrossRef]
7. D. N. Hutchison, S. Jie, J. K. Doylend, R. Kumar, and H. Rong, “High-resolution aliasing-free optical beam steering,” Optica 3(8), 887 (2016). [CrossRef]
8. J. K. Doylend, M. J. R. Heck, J. Bovington, J. Peters, M. L. Davenport, L. A. Coldren, and J. E. Bowers, “Hybrid III/V silicon photonic source with integrated 1D free-space beam steering,” Opt. Lett. 37(20), 4257–4259 (2012). [CrossRef]
9. F. Ashtiani and F. Aflatouni, “N × N optical phased array with 2N phase shifters,” Opt. Express 27(19), 27183–27190 (2019). [CrossRef]
10. L.-X. Zhang, Y.-Z. Li, M. Tao, Y.-B. Wang, Y. Hou, B.-S. Chen, Y.-X. Li, L. Qin, F.-L. Gao, X.-S. Luo, G.-Q. Lo, and J.-F. Song, “Large-Scale Integrated Multi-Lines Optical Phased Array Chip,” IEEE Photonics J. 12(4), 1–8 (2020). [CrossRef]
11. D. Zhuang, L. Zhagn, X. Han, Y. Li, Y. Li, X. Liu, F. Gao, and J. Song, “Omnidirectional beam steering using aperiodic optical phased array with high error margin,” Opt. Express 26(15), 19154–19170 (2018). [CrossRef]
12. T. Komljenovic, R. Helkey, L. A. Coldren, and J. E. Bowers, “Sparse aperiodic arrays for optical beam forming and LIDAR,” Opt. Express 25(3), 2511–2528 (2017). [CrossRef]
13. M. Raval, C. V. Poulton, and M. R. Watts, “Unidirectional waveguide grating antennas with uniform emission for optical phased arrays,” Opt. Lett. 42(13), 2563–2566 (2017). [CrossRef]
14. D. Vermeulen, S. K. 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 18(17), 18278–18283 (2010). [CrossRef]
15. G. Roelkens, D. Van Thourhout, and R. Baets, “High efficiency Silicon-on-Insulator grating coupler based on a poly-Silicon overlay,” Opt. Express 14(24), 11622–11630 (2006). [CrossRef]
16. W. D. Sacher, Y. Huang, L. Ding, B. Taylor, H. Jayatilleka, G. Lo, and J. K. S. Poon, “Wide bandwidth and high coupling efficiency Si 3 N 4 -on-SOI dual-level grating coupler,” Opt. Express 22(9), 10938–10947 (2014). [CrossRef]
17. E. W. Ong, M. F. Nicholas, and D. C. Douglas, “SiNx bilayer grating coupler for photonic systems,” in OSA Continuum, (2018).
18. C. R. Doerr, L. Chen, Y. K. Chen, and L. L. Buhl, “Wide Bandwidth Silicon Nitride Grating Coupler,” IEEE Photonics Technol. Lett. 22(19), 1461–1463 (2010). [CrossRef]
19. M. Dai, L. Ma, Y. Xu, M. Lu, X. Liu, and Y. Chen, “Highly efficient and perfectly vertical chip-to-fiber dual-layer grating coupler,” Opt. Express 23(2), 1691–1698 (2015). [CrossRef]
20. W. Xie, J. Huang, T. Komljenovic, L. A. Coldren, and J. E. Bowers, “Diffraction limited centimeter scale radiator: metasurface grating antenna for phased array LiDAR,” arXiv: Applied Physics (2018).
21. D. T. H. Tan, K. Ikeda, P. C. Sun, and Y. Fainman, “Group velocity dispersion and self phase modulation in silicon nitride waveguides,” Appl. Phys. Lett. 96(6), 061101 (2010). [CrossRef]
22. M. Fan, M. A. Popovic, and F. X. Kartner, “High Directivity, Vertical Fiber-to-Chip Coupler with Anisotropically Radiating Grating Teeth,” in conference on lasers and electro optics, 2007), 1–2.
23. M. Zadka, Y. Chang, A. Mohanty, C. T. Phare, S. P. Roberts, and M. Lipson, “On-chip platform for a phased array with minimal beam divergence and wide field-of-view,” Opt. Express 26(3), 2528–2534 (2018). [CrossRef]
24. P. Wang, G. Luo, Y. Xu, Y. Li, and J. Pan, “Design and Fabrication of SiN-Si Dual-layer Optical Phased Array Chip,” Photonics Res. 8(6), 912–919 (2020). [CrossRef]
25. Y. Huang, J. Song, X. Luo, T. Y. Liow, and G. Q. Lo, “CMOS compatible monolithic multi-layer Si3N4-on-SOI platform for low-loss high performance silicon photonics dense integration,” Opt. Express 22(18), 21859–21865 (2014). [CrossRef]