Open Access
Add to BibSonomy
Abstract
On-chip optical delay lines (ODLs) based on chirped waveguide Bragg gratings (CWBG) have attracted much attention in recent years. Although CWBGs are well developed, the CWBG which have large group delay (GD), large delay-bandwidth product and low loss while is circulator-free have little been investigated so far. In this work, we propose and experimentally demonstrate such a CWBG-based ODL. This device is fabricated on a low-loss 800-nm-height silicon nitride platform, combining 20.11-cm long index-chirped multi-mode spiral waveguide antisymmetric Bragg gratings with a directional coupler. The bandwidth of this circulator-free ODL is 23 nm. The total GD is 2864 ps and the delay-bandwidth product is 65.87 ns·nm, which both are the largest values achieved by on-chip CWBG reported to our knowledge. Its loss is 1.57 dB/ns and the total insertion loss of the device is 6 dB at the central wavelength near 1550 nm. This integrated CWBG can be explored in practical applications including microwave photonics, temporal optics, and optical communication.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
Corrections
4 April 2024: A typographical correction was made to the author affiliations.
1. Introduction
On-chip optical delay line (ODL) is one of the most important components in integrated optical system [1]. It has been widely used in microwave photonics [2–4], optical communication [5], optical coherence tomography [6], etc. In general, two main methods are adopted to realize optical delays [7]. One common method is that light pulses propagate different optical paths of different lengths so that time delays can be produced. Although this method is straightforward and simple, the delay cannot be changed continuously because of the discontinuous variation of optical paths and thus limited tunable resolution [8,9]. The other method is slowing down light group velocity, including optical microring resonators (MRRs) [10], photonic crystal waveguides (PhCWs) [11] and chirped waveguide Bragg gratings (CWBG) [12], which can lead to continuous delay tuning. Among them, MRRs have advantages of compact and simple structures, however, they have limited bandwidths. There is a trade-off between the bandwidth and maximum delay. To realize a large delay with a relatively large bandwidth, cascaded MRRs have been proposed, such as coupled resonator optical waveguides (CROWs) [13] and side-coupled integrated spaced sequences of resonators (SCISSORs) [14]. For PhCWs, the strong slow light effects make time delays and large bandwidth with small footprints realized. Nevertheless, MRRs and PhCWs suffer from high propagation loss, which prevent their applications in systems. Compared with both of them, CWBG has advantages of low loss while maintaining large wide operating band [15]. Besides, compact size can be realized by cascaded or spiral scheme [16,17]. Tunable delay lines can be achieved by the p-n junctions [18] or thermal-optical effects [19]. Therefore, the ODLs based on CWBG have been developed rapidly.
As we know, integrated Bragg gratings are formed by modulating the effective refractive index in the waveguide. Several main structures of CWBG have been proposed including slab-modulated sidewall gratings, height-modulated gratings, cladding-modulated gratings, and sidewall-modulated gratings. Among them, sidewall-modulated gratings are most widely used because of its handiness in the design and fabrication. The chirp can be induced by varying grating period [20] or varying grating width [21]. The wavelength-dependent group delay (GD) is produced as a result of different reflected positions of different wavelengths along the CWBG longitudinal direction.
Nowadays, although the group delay of more than 1 ns with the loss of less than 2 dB/ns based on the CWBG has been realized, larger GD (> 2 ns), lower loss and larger delay-bandwidth product are still desired. Large GD comes from long CWBG but the maximum delay is usually limited by waveguide loss. If the propagation loss is high, it might be hard to be widely applied as a result of large insertion loss. Hence, compared to silicon-on-insulator (SOI) based strip waveguides which have typical waveguide losses of 1 to 2 dB/cm [22,23], silicon nitride (Si3N4) based waveguides offer an attractive compromise between index contrast, low propagation losses and fabrication using standard CMOS technology [24]. The current largest GD of 1440 ps based on CWBG is realized in 90-nm thick Si3N4 with a propagation loss of 1.87 dB/ns [25]. However, an optical circulator is also required to separate the reflection signal from the input one for conventional CWBG where the input and output light are at the same port. Currently, the on-chip circulator is still a challenge and complicated while the solution of Y-branch will induce extra insertion loss (more than 6 dB) [26]. To solve this problem, one promising method is to combine multi-mode gratings with a directional coupler (DC) to separate the reflection [27,28]. The fundamental transverse electric (TE0) mode in reflection band can be transferred from the input waveguide to the output waveguide with low insertion loss using two mode conversions in the gratings and DC. The band splitter based on Si3N4 multimode Bragg gratings [29] and antisymmetric CWBG in SOI waveguides [30] have been demonstrated, respectively, however, none studies have combined antisymmetric CWBG and directional coupler with Si3N4 waveguide to realize compact circular-free CWBG with large group delay and low loss.
In this paper, we propose and experimentally demonstrate, for the first time, a compact circulator-free CWBG-based ODL device on Si3N4 platform. The device combines long multi-mode spiral index-chirped waveguide antisymmetric Bragg gratings with a DC. To get long CWBG with a controllable small chirp, the grating is usually designed to have a tapered width with a uniform period. Because the width variation has a three-order of magnitude smaller effect than the period variation in reflection bandwidth [31]. To realize a compact footprint, the Si3N4 spiral tapered CWBG is first demonstrated to our knowledge. Here, we choose 800-nm thick waveguides due to its tight confinement and relatively large effective refractive index [32]. Moreover, compared to thin Si3N4 waveguides (less than 100 nm), index-chirping and compactness are easier to achieve on the thick platform. The simulation and experiment are implemented to verify good performance of the proposed structure. The practical CWBG is 20.11-cm long with a large GD of 2864 ps, a large delay-bandwidth product of 65.87 ns·nm and a low loss of 1.57 dB/ns.
2. Design and simulation
Figure 1(a) is an illustration of the designed structure. It consists of 20.11-cm long multi-mode spiral tapered waveguide antisymmetric Bragg gratings and a DC at the reflection port of gratings. The multi-mode waveguide can support more than two transverse electric (TE) modes. The fundamental and the first higher-order optical modes are used in our design. The working principle of this device is as follows. The input TE0 mode is launched in the edge coupler waveguide and spreads to gratings while the DC does not work. An adiabatic tapered waveguide is placed between the main waveguide of the DC and gratings to avoid excess loss and inter-mode cross talk. When the TE0 mode propagates through the antisymmetric Bragg gratings, it is transformed into the TE1 mode and reflected back to the DC. The TE1 mode is converted back into the TE0 mode in the drop waveguide as it passes the DC again.
Fig. 1. (a) 3D diagram of the device (top oxide not shown). Insets show the electric field distributions of the TE0 and TE1 modes. (b) Partial schematic of antisymmetric Bragg gratings.
The structure of the antisymmetric Bragg gratings is depicted in Fig. 1(b). N and Λ represent the number and period of gratings, respectively. Δw represents the corrugation depth of gratings. The index-chirp is introduced by changing linearly the width w of Bragg gratings from w1 to w2 along the length. The widths w1 and w2 of two ports are set as 1.8 and 2.2 µm, respectively. The long Bragg gratings are wrapped into compact layout through Archimedean spiral. A terminator is added at the transmission end of gratings to dissipate the transmission light to free space because only the reflected light within bandwidth is desired. The interval distance G between adjacent waveguides is set as 10 µm to avoid crosstalk. The minimum radius R0 is set as 600 µm to guarantee the performance of Bragg gratings on the curved waveguide close to that on the straight one and the outermost radius reaches 1000 µm.
According to the coupling coefficient ${\kappa _{ij}}$ between two given modes,
The dispersion curve of a 2-µm wide waveguide is calculated to fix the grating period as shown in Fig. 2(a). The intersect of the black and orange lines indicates that when the grating period is selected as 435 nm, λB turns out to be around 1550 nm. Figure 2(b) shows that the effective refractive indices neff increase along the propagation route normalized to the total length of CWBG with the decreasing curvature radius. The average neff of TE0 and TE1 modes changes from 1.767 to 1.792 and the variation range determines the bandwidth of gratings. It can be seen that the variation curve is not linear, which will cause nonlinear GD due to the nonlinear distribution of the reflected position of every wavelength along the length and the changing optical path difference between wavelengths.
Fig. 2. Effective refractive indices variation of the TE0 and TE1 modes as a function of (a) wavelength and (b) position and curvature radius along the propagation route in CWBG. Orange dashed line denotes the relationship between the effective refractive index and Bragg wavelength.
To suppress spectral side-lobes and GD ripples caused by sudden change of neff near the input port of gratings, different apodization profiles have been investigated [33]. Among them, the positive hyperbolic tangent profile has overall superior performance, as it provides highly linearized GD characteristics with minimum reduction in linear dispersion compared with the unapodized case. Therefore, a modified apodization function of hyperbolic tangent is applied. It imposes a profile on the corrugation depth of gratings. The profile is
To investigate the spectral response and GD of the proposed CWBG, a simulation is implemented using transfer-matrix method (TMM) on the basis of parameters obtained above. It can be seen from Fig. 3 that GD ripples are obviously reduced and the sidelobe suppression ratio (SLSR) is promoted through the apodization compared with the unapodized one. However, the bandwidth and GD are also reduced. Figure 3 (b) indicates that the reflection spectrum with a bandwidth of 23.3 nm and a high sidelobe suppression ratio of more than 20 dB can be achieved. The central wavelength is around 1550 nm. A total GD of 2920 ps can be realized. It can be seen that due to the nonlinear variation of neff, the GD curve is not linear, which agrees with the theoretical prediction. Hence, the slope increases from 88 to 161 ps/nm as the wavelength increases. In addition, GD ripples are within ±25 ps. It is obtained by subtracting the GD data from its fitting data. The proportion of ripple amplitude in the total GD is less than 1%. In contrast, for unapodized gratings, the proportion is higher than 5% under the same condition. The apodization function of the modulation coefficient α = 2, α = 4 and α = 5 are also explored, respectively. These four apodized CWBGs have similar performances. Here, α = 3 is selected.
Fig. 3. Simulated reflection spectrum and group delay (a) without apodization and (b) with apodization. Black dashed line denotes the fitting result.
After propagating through the antisymmetric Bragg gratings, the incident TE0 mode is transformed into the TE1 mode and reflected back to the DC. Figure 4(a) shows the schematic of the DC. It consists of a main waveguide and a drop waveguide. The drop waveguide is composed of two curved parts with a radius of 200 µm and one straight part parallel to the main waveguide. When the phase-matching condition is satisfied, the TE1 mode in the main waveguide can be converted back into the TE0 mode in the drop waveguide with high efficiency. Figure 4(b) shows the calculated effective refractive indices of TE0 and TE1 modes under different widths. w3 and w4 are the selected widths. The simulation of beam propagation and conversion efficiency (CE) is performed using 3D-FDTD. In the simulation, the widths w3 and w4 are set as 2.3 and 1 µm, respectively. The gap wg is set as 300 nm and the length LDC of the straight part of the drop waveguide is set as 25 µm. The simulated light power distribution at the wavelength of 1550 nm is shown Fig. 4(c). The TE1 mode launched in the main waveguide at the right side can be converted efficiently into the TE0 mode in the drop waveguide at the left side. The calculated CE between the TE1 and TE0 modes is higher than −1.8 dB in a bandwidth of 40 nm as shown in Fig. 4(d). Besides, the coupling between TE0 modes in the main and drop waveguides of the DC is also simulated and the CE is as low as around −41 dB at 1550 nm. It indicates that the TE0 mode is almost unaffected when light passes the main waveguide of the DC.
Fig. 4. (a) Schematic of the DC. (b) Effective refractive indices of the TE0 and TE1 modes as a function of the waveguide width. The black dotted line represents the selected widths when phase-matching condition is satisfied. (c) Simulated beam propagation in the DC. (d) Simulated conversion efficiency from the TE1 to TE0 modes.
3. Experiment and results
The device is manufactured on an 800-nm thick Si3N4 platform with a 4.4-µm buried oxide layer and a 3.3-µm top cladding oxide layer by LIGENTEC. It has a footprint of only ∼2 × 2 mm2. The experimental setup and microscope image of the fabricated device are displayed in Fig. 5. The light source is a homemade nonlinear polarization rotation passive mode-locked laser (MLL) with a large bandwidth of more than 100 nm. The polarization controller (PC) is used to adjust the polarization of the input light. The light is coupled into the chip via a tapered fiber and an edge coupler. The edge coupling loss is 4 dB per facet. The spectral response of the device is characterized by an optical spectrum analyzer (OSA) and its resolution is set as 0.1 nm. To obtain the accurate CE of the DC, 20 identical DCs are cascaded for testing. Its transmission spectrum is also recorded by the OSA. The measured spectral results are all normalized to the transmission of a 1-µm wide reference waveguide on the same chip. The GD is then measured by an optical vector network analyzer (OVNA) and its resolution is 16.67 pm.
Fig. 5. Experimental setup for the characterization of (a) reflection spectrum and (b) group delay. (c) Microscope image of the fabricated device. MLL, mode-locked laser; PC, polarization controller; OSA, optical spectrum analyzer; OVNA, optical vector network analyzer.
As shown in Fig. 6, the measured reflection spectrum of the proposed ODL device possesses a bandwidth of 23 nm from 1541 to 1564 nm. Its sidelobe suppression ratio is as high as 25 dB and the center wavelength is around 1553 nm. A large GD of 2864 ps is realized. Therefore, the delay-bandwidth product is 65.87 ns·nm. It can be seen that the GD curve is nonlinear and thus its slope is not a constant value, which agrees well with the simulated result. The slope varies from 84 to 158 ps/nm. GD ripples is mainly within ±30 ps and its maximum value takes around 1% proportion in the total GD. Besides, the CE of the DC is higher than −1.8 dB in the range from 1530 to 1570 nm and is −1.5 dB at the wavelength of 1550 nm. The total insertion loss of the device is 6 dB at the central wavelength. The minimum insertion loss is around 3.6 dB at 1545.2 nm and the peak reflectivity of gratings can be evaluated to 0.6. The power at long wavelength is smaller than that at short wavelength because light of long wavelength propagates longer optical path and thus suffers relatively larger loss. A figure of merit to evaluate the ODL performance is the loss per ns delay increment (in dB/ns unit). This value is evaluated to be as low as 1.57 dB/ns according to the slope of the inclined reflection spectrum.
Fig. 6. (a) Measured result of reflection spectrum. (b) Measured result of group delay and (c) a zoom in the span of 4 nm. The black dashed line denotes the fitting result. Inset in (a) is showing the loss of the DC.
The experimental results of the proposed device are in good agreement with the simulated results. The minor difference with respect to the reflection spectrum and GD may come from the fabrication imperfections. The actual refractive index and geometric dimension of the device may be slightly different from the designed values. Besides, the refractive index selection and the parameter accuracy in simulation can also lead to discrepancies.
Furthermore, a linear GD curve can be achieved by optimizing the width profile of the tapered CWBG. The linearly widening profile of the grating width can be replaced with the nonlinearly widening one, which is deduced from the target linear variation curve of the effective index. Thus, it will cause a linear varying effective index along the gratings and the delay difference between different wavelengths is almost a constant value so that the GD will have high linearity. According to the equation GDD = τ/Δλ, where τ denotes the total group delay and Δλ denotes reflection bandwidth, if a larger dispersion is needed, we can make it via increasing τ by further increasing the gratings length or decreasing Δλ by reducing the width difference between two ends of gratings for smaller variation of the effective index. The ripples are related to the strength of the index perturbation and can be further suppressed by decreasing corrugation depths or increasing the width of gratings to weaken the strength of the index perturbation. In addition, the DC can be improved by replacing it with the adiabatic coupler which has large fabrication error tolerance [30].
Table 1 shows a comparison of the on-chip CWBG reported in recent years. It can be seen the longer CWBG with larger GD and lower loss is the general trend. Our proposed CWBG is the longest with the largest GD and delay-bandwidth product, and the lowest loss as reported.
Table 1. Comparison of the device performance with earlier reported CWBG
4. Conclusion
A novel circulator-free CWBG-based ODL is fabricated and experimentally demonstrated. It has a total GD of 2864 ps within the bandwidth of 23 nm based on a 20.11-cm long CWBG on the low-loss 800-nm thick silicon nitride platform and therefore, a delay-bandwidth product of 65.87 ns·nm is realized. The chirp is achieved by widening linearly the width of the Bragg gratings along the length while the grating period keeps the same. GD ripples are effectively suppressed by hyperbolic tangent apodization. Meanwhile, a combination of the asymmetric CWBG in Si3N4 and the DC leads to a low-loss performance. The loss of the ODL is 1.57 dB/ns, and the total insertion loss of the device is 6 dB at the central wavelength around 1550 nm. This integrated device has great potential for diverse applications such as optical communication, microwave photonics, and temporal optics.
Funding
National Key Research and Development Program of China (2019YFB2203102; 2018YFB2201901); National Natural Science Foundation of China (61735006, 61927817, 62075072, 62175078).
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. L. Zhou, X. Wang, L. Lu, and J. Chen, “Integrated optical delay lines: a review and perspective [Invited],” Chin. Opt. Lett. 16(10), 101301 (2018). [CrossRef]
2. C. Zhu, L. Lu, W. Shan, W. Xu, G. Zhou, L. Zhou, and J. Chen, “Silicon integrated microwave photonic beamformer,” Optica 7(9), 1162–1170 (2020). [CrossRef]
3. W. Zhang and J. Yao, “Photonic generation of linearly chirped microwave waveforms using a silicon-based on-chip spectral shaper incorporating two linearly chirped waveguide Bragg gratings,” J. Lightwave Technol. 33(24), 5047–5054 (2015). [CrossRef]
4. R. L. Moreira, J. Garcia, W. Li, J. Bauters, J. S. Barton, M. J. R. Heck, J. E. Bowers, and D. J. Blumenthal, “Integrated ultra-low-loss 4-bit tunable delay for broadband phased array antenna applications,” IEEE Photonics Technol. Lett. 25(12), 1165–1168 (2013). [CrossRef]
5. H. Lee, T. Chen, J. Li, O. Painter, and K. J. Vahala, “Ultra-low-loss optical delay line on a silicon chip,” Nat. Commun. 3(1), 867 (2012). [CrossRef]
6. X. Ji, X. Yao, Y. Gan, A. Mohanty, and M. Lipson, “On-chip tunable photonic delay line,” APL Photonics 4(9), 090803 (2019). [CrossRef]
7. X. Wang, L. Zhou, R. Li, J. Xie, L. Lu, K. Wu, and J. Chen, “Continuously tunable ultra-thin silicon waveguide optical delay line,” Optica 4(5), 507–515 (2017). [CrossRef]
8. S. Hong, L. Zhang, Y. Wang, M. Zhang, Y. Xie, and D. Dai, “Ultralow-loss compact silicon photonic waveguide spirals and delay lines,” Photonics Res. 10(1), 1–7 (2022). [CrossRef]
9. W. Ke, Y. Lin, M. He, M. Xu, J. Zhang, Z. Lin, S. Yu, and X. Cai, “Digitally tunable optical delay line based on thin-film lithium niobate featuring high switching speed and low optical loss,” Photonics Res. 10(11), 2575–2583 (2022). [CrossRef]
10. J. Xie, L. Zhou, Z. Zou, J. Wang, X. Li, and J. Chen, “Continuously tunable reflective-type optical delay lines using microring resonators,” Opt. Express 22(1), 817–823 (2014). [CrossRef]
11. R. Hayakawa, N. Ishikura, H. C. Nguyen, and T. Baba, “High-speed delay tuning of slow light in pin-diode-incorporated photonic crystal waveguide,” Opt. Lett. 38(15), 2680–2682 (2013). [CrossRef]
12. I. Giuntoni, D. Stolarek, D. I. Kroushkov, J. Bruns, L. Zimmermann, B. Tillack, and K. Petermann, “Continuously tunable delay line based on SOI tapered Bragg gratings,” Opt. Express 20(10), 11241–11246 (2012). [CrossRef]
13. F. Morichetti, C. Ferrari, A. Canciamilla, and A. Melloni, “The first decade of coupled resonator optical waveguides: bringing slow light to applications,” Laser Photonics Rev. 6(1), 74–96 (2012). [CrossRef]
14. C. Xiang, M. L. Davenport, J. B. Khurgin, P. A. Morton, and J. E. Bowers, “Low-loss continuously tunable optical true time delay based on Si3N4 ring resonators,” IEEE J. Sel. Top. Quantum Electron. 24(4), 5900109 (2017). [CrossRef]
15. W. Shi, V. Veerasubramanian, D. Patel, and D. V. Plant, “Tunable nanophotonic delay lines using linearly chirped contradirectional couplers with uniform Bragg gratings,” Opt. Lett. 39(3), 701–703 (2014). [CrossRef]
16. L. Jiang and Z. R. Huang, “Integrated cascaded bragg gratings for on-chip optical delay lines,” IEEE Photonics Technol. Lett. 30(5), 499–502 (2018). [CrossRef]
17. Z. Chen, J. Flueckiger, X. Wang, F. Zhang, H. Yun, Z. Lu, M. Caverley, Y. Wang, N. A. F. Jaeger, and L. Chrostowski, “Spiral Bragg grating waveguides for TM mode silicon photonics,” Opt. Express 23(19), 25295–25307 (2015). [CrossRef]
18. S. Khan, M. A. Baghban, and S. Fathpour, “Electronically tunable silicon photonic delay lines,” Opt. Express 19(12), 11780–11785 (2011). [CrossRef]
19. S. Liu, J. He, and D. Dai, “Tunable Dispersion Compensator Based on Taper Bragg Gratings with Heating-Engineering,” in Asia Communications and Photonics Conference2021, paper W2G.5.
20. Y. Sun, D. Wang, C. Deng, M. Lu, L. Huang, G. Hu, B. Yun, R. Zhang, M. Li, J. Dong, A. Wang, and Y. Cui, “Large Group Delay in Silicon-on-Insulator Chirped Spiral Bragg Grating Waveguide,” IEEE Photonics J. 13(5), 1–5 (2021). [CrossRef]
21. X. Wang, Y. Zhao, Y. Ding, S. Xiao, and J. Dong, “Tunable optical delay line based on integrated grating-assisted contradirectional couplers,” Photonics Res. 6(9), 880–886 (2018). [CrossRef]
22. R. Baets, A. Z. Subramanian, S. Clemmen, B. Kuyken, P. Bienstman, N. Le Thomas, G. Roelkens, D. Van Thourhout, P. Helin, and S. Severi, “Silicon Photonics: silicon nitride versus silicon-on-insulator,” in Optical Fiber Communication Conference 2016, paper Th3J.1.
23. Y. Su, Y. Zhang, C. Qiu, X. Guo, and L. Sun, “Silicon photonic platform for passive waveguide devices: materials, fabrication, and applications,” Adv. Mater. Technol. 5(8), 1901153 (2020). [CrossRef]
24. M. H. P. Pfeiffer, C. Herkommer, J. Liu, T. Morais, M. Zervas, M. Geiselmann, and T. J. Kippenberg, “Photonic damascene process for low-loss, high-confinement silicon nitride waveguides,” IEEE J. Sel. Top. Quantum Electron. 24(4), 1–11 (2018). [CrossRef]
25. Z. Du, C. Xiang, T. Fu, M. Chen, and H. Chen, “Silicon nitride chirped spiral Bragg grating with large group delay,” APL Photonics 5(10), 101302 (2020). [CrossRef]
26. M. Burla, X. Wang, M. Li, L. Chrostowski, and J. Azaña, “Wideband dynamic microwave frequency identification system using a low-power ultracompact silicon photonic chip,” Nat. Commun. 7(1), 13004 (2016). [CrossRef]
27. H. Qiu, J. Jiang, T. Hu, P. Yu, J. Yang, X. Jiang, and H. Yu, “Silicon Add-Drop Filter Based on Multimode Bragg Sidewall Gratings and Adiabatic Couplers,” J. Lightwave Technol. 35(9), 1705–1709 (2017). [CrossRef]
28. Q. Liu, D. Zeng, C. Mei, H. Li, Q. Huang, and X. Zhang, “Integrated photonic devices enabled by silicon traveling wave-like Fabry–Perot resonators,” Opt. Express 30(6), 9450–9462 (2022). [CrossRef]
29. J. Cauchon, J. St-Yves, F. Menard, and W. Shi, “Silicon Nitride Band Splitter Based on Multimode Bragg Gratings,” in Optical Fiber Communication Conference2021, paper F2B.5.
30. R. Xiao, Y. Shi, J. Li, P. Dai, C. Ma, M. Chen, Y. Zhao, and X. Chen, “Integrated Bragg grating filter with reflection light dropped via two mode conversions,” J. Lightwave Technol. 37(9), 1946–1953 (2019). [CrossRef]
31. F. Zhang, J. Dong, Y. Zhu, X. Gao, and X. Zhang, “Integrated Optical True Time Delay Network Based on Grating-Assisted Contradirectional Couplers for Phased Array Antennas,” IEEE J. Sel. Top. Quantum Electron. 26(5), 1–7 (2020). [CrossRef]
32. J. Liu, G. Huang, R. N. Wang, J. He, A. S. Raja, T. Liu, N. J. Engelsen, and T. J. Kippenberg, “High-yield, wafer-scale fabrication of ultralow-loss, dispersion-engineered silicon nitride photonic circuits,” Nat. Commun. 12(1), 2236 (2021). [CrossRef]
33. K. Ennser, M. N. Zervas, and R. I. Laming, “Optimization of apodized linearly chirped fiber gratings for optical communications,” IEEE J. Quantum Electron. 34(5), 770–778 (1998). [CrossRef]
