Open Access
Add to BibSonomy
Abstract
The integrated optical delay line plays a crucial role in microwave photonic chips. Continuous tunability is a growing trend in filtering and beamforming techniques of microwave photonics. Based on the silicon platform, we present and experimentally demonstrate an integrated continuously optical tunable delay line (OTDL) chip, which contains a 4-bit optical switched delay line (OSDL) and a thermally tunable delay line based on grating-assisted Contradirectional coupler (CDC). The OSDL can achieve stepwise optical delays, while the CDC is introduced to improve delay tuning resolution within one step delay of the OSDL. The combination of the two modules can realize tuning delays from 0 to 160 ps. Additionally, it is easy to increase the maximum delay by cascading more optical switches. The experimental results demonstrate that the proposed OTDL shows outstanding performance and good expansibility.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Integrated optical delay line (ODL) is a key component of integrated photonic chips [1–3], which has great applications in microwave photonic signal processing systems, such as miniature and large-bandwidth microwave photonic filters [4,5], beamformers of phased array radar [6], and linear Frequency-Modulated pulse signal generators [7].
In recent years, there are various schemes to realize Optical tunable delay lines (OTDLs), such as Optical switched delay lines (OSDLs) [8–15], Microring resonators (MRRs) [13–16], Microdisk resonators (MDRs) [17], Waveguide Bragg gratings (WBGs) [18–31], Subwavelength gratings (SWGs) [32,33], Arrayed waveguide gratings (AWGs) [34,35], Photonic crystal waveguides (PhCWs) [36], topological photonics structures [37]. OSDLs are constructed by cascading optical switches and optical delay waveguides with different lengths. They have advantages of large bandwidth, low in-band delay fluctuations, and relatively large tolerance for fabrication errors. Moreover, OSDLs could be simply controlled using thermal electrodes on silicon-on-insulator (SOI) or Si3N4 platforms. However, general OSDLs cannot achieve continuous delay tuning. The tuning resolution is limited by the minimum delay step. In order to achieve continuous tuning, several works have been proposed by combining one of the continuous delay line with the switch-based delay line, such as MRRs [13,14], asymmetric Mach-Zehnder interferometer (MZI) [12], and gratings [25,26]. The MRRs and MZI tune continuous delays in a fixed wavelength within a small range, and the gratings are adopted to change the slope of dispersion curves. The common structures were assisted by MRRs. MRRs operating at the resonant wavelengths could achieve a wide range of delay tuning by the slow light effect at the resonance peak. However, the large delay introduces the high loss and may lead to nonlinear effects. On the other hand, MRRs operating at anti-resonant wavelengths allow for delay tuning between 0 and the round-trip time of MRRs, while also providing a larger Radio Frequency bandwidth. Increasing the number of MRRs in both types can enhance the maximum delay and bandwidth. Nevertheless, adjusting the resonance wavelength and coupling coefficient simultaneously in multiple tuning units poses challenges in controlling electrode states and minimize crosstalk. In PhCWs, the strong optical confinement and slow light effects can reduce the footprint and achieve a large group delay. However, the PhCWs suffer from high propagation loss, which hinders the real application. There are two approaches for WBGs to realize optical delays: One is to slow down the group velocity of light by inserting a phase-delay structure [24]. It is simple and easy to implement, although the accuracy of group delay is low; the other approach is to adopt chirped Bragg gratings so that the different wavelengths of light are reflected at different positions to achieve group delay. Chirped WBGs with narrow bandwidth and large dispersion have been demonstrated based on SOI platforms [27]. With the advantage of low loss on Si3N4 platforms, delays on the scale of nanosecond level can be achieved [19,22]. For chirped gratings, continuously tunable delays could be achieved by shifting the reflected signal position through thermally and electrically tuning, or switching the wavelength of the laser source. However, a Y-branching or a 1 × 2 MMI usually has to be introduced to conventional waveguide Bragg gratings [22,23] for experiments and applications. The additional loss of 6 dB will increase unexpected delay fluctuations. Therefore, researchers prefer to focus on grating-assisted contradirectional couplers (CDCs) for separating the incident and reflected ports, thereby avoiding additional losses. The tunability of the reflected central wavelength of CDCs has been demonstrated on SOI platforms [29]. Delay lines based on CDCs can be thermally tuned with the driving voltage to achieve the tunable delay [30]. Furthermore, multiple CDCs can also be used to construct a multi-channel delay unit. Due to the same difference of dispersion coefficient between adjacent CDC channels, continuously tunable delay of single-channel can be achieved by switching the wavelength of the laser source, as well as the delay intervals between adjacent channels can be tuned continuously [31]. However, CDCs with long grating-assisted result in delays with large fluctuations hindering their application, because of the fabricating precision.
To avoid the large fluctuations of delay caused by long grating-assisted CDCs. In this paper, we proposed a continuously tunable OTDL consisting of an OSDL and a grating-assisted CDC. The OSDL achieves a wide range of delay with a step of 10 ps. The tunable delay range of the designed CDC is wider than 10 ps, thereby ensuring a wide tuning range and high tuning resolution. For the improvement of integration, the proposed OTDL was fabricated on the SOI platform, and the dispersion curve could be shifted to tune delay because of the large thermal conductivity of Si. In order to reduce the transmission loss, low-loss multimode optical delay spiral waveguides were adopted. The grating-assisted CDC assures a low insertion loss and transmission loss. The proposed OTDL could achieve continuous tuning with a wide range of delay and has characteristics of small size and low loss.
2. Principle and design
2.1 Principle and design of CDC delay line
Figure 1 shows the scheme of the proposed integrated grating-assisted CDC for delay tuning. It consists of two striped waveguides with different widths. The reason for the difference in the widths of the two waveguides is to separate the incident and reflective light in the contra-directional couplers, which can avoid deterioration of the laser performance. The width of the wide waveguide is w1, and the two ports of the widths of the narrow waveguide are w2 and w3, which determines the chirp coefficient. Because linear variation of the effective index is more robust than varying the grating period [18,28] and fabricating tolerance is larger, the effective index chirping is adopted here by linearly varying the waveguide width on one side of the CDC. The grating period of Λ is a constant with a duty cycle of 50%. The grating number, N, determines the grating length L = N × Λ. The size of the grating teeth, D, determines the perturbation introduced by the grating. The gap between the two waveguides effects the coupling efficiency of the optical field. For tuning the delay in a single wavelength, a heater is set on the top of the entire CDC.
As shown in Fig. 1(b), two spiral loss lines are designed at the end of the two waveguides to further reduce unwanted reflection. The central wavelength of the Bragg gratings follows the Bragg Eq. (1)
Here, the central wavelength ${\lambda _c}$ is determined by effective index ${n_{eff}}$ and grating period $\mathrm{\Lambda }$. When Λ is fixed, the varying range of ${n_{eff}}$ determines the bandwidth of the transmission spectrum, and the group delay depends on the length of the grating. The following parameters were adopted: w1 = 528 nm, w2 = 470 nm, w3 = 490 nm, wgap = 300 nm, Λ = 320 nm, D = 104 nm, N = 1680, and the total length of the grating LG = N×Λ= 537.6 µm. According to the simulated mode of silicon waveguide for the transverse electric (TE) polarization using Lumerical MODE Solutions, the calculated group refractive indices are ng (220 nm × 480 nm) = 4.273 and ng (220 nm × 580 nm) = 4.12 at the wavelength of 1550 nm, the estimated delay group delay $\tau $ followed by Eq. (2):
where $\overline {{\textrm{n}_g}} $ is the average of group refractive indices of two waveguides, ${L_G}\; $ is the length of the grating and c is the light speed.As shown in Fig. 2(a), a transmission spectrum with a bandwidth of 9 nm approximately is obtained by using the 2.5D time domain finite difference (FDTD) method. From the simulated light power distributions at wavelengths of 1550 nm and 1554 nm, the signals of different wavelengths are reflected at different positions of the CDC. The total delay within the transmission spectrum can approach 15 ps, and the analysis considers that the fluctuation in the group delay spectrum calculated by simulation would be larger than the experimental result. The reason is that the effective refractive index difference calculated by 2.5D FDTD is larger than that in 3D FDTD. Although the former saves simulation time, the latter is closer to reality. In addition, periodic perturbations would be transformed from rectangular to trapezoidal, due to proximity effects during fabricating and further reduce the coupling intensity of grating.
Fig. 2. 2.5D FDTD simulated (a) transmission spectrum and group delay, (b) beam propagation of 1550 nm and (c) beam propagation of 1554 nm.
2.2 Principle and design of entire delay line
Figure 3(a) illustrates the cross-sectional diagram of the waveguide. The thickness of the core layer is 220 nm and TE0 mode can transmit in a waveguide with the width of 500 nm. But from the electric field distribution in Fig. 3(b), the partial power of the electric field exists at the boundary between the core and the cladding on both sides. As the sidewall roughness is unavoidable during the manufacturing process, as in Fig. 2(c), we set the width w as 1200 nm to decrease the transmission loss introduced by sidewall roughness [23].
Fig. 3. (a) Cross-sectional structure of the Si waveguide with a TiW heater on top. Simulated the electronic field distribution for the fundamental TE mode (b) 220 nm × 500 nm and (c) 220 nm × 1200 nm.
Owing to the estimated group delay of the CDC is 15 ps, the delay step of the 4-bit OSDL is designed to be 10 ps to achieve continuous tunability after fabricating. According to waveguide cross-sectional simulation using Lumerical MODE Solutions, the calculated group refractive index ng (220 nm × 1200 nm) is 3.78 at a wavelength of 1550 nm. Then we can set the lengths of the four delay waveguides by Eq. (3):
Here, $\Delta {L_n}({n = 1,2,3,4} )$ is the length of the nth delay waveguide of the 4-bit OSDL. According to the delay step of 10 ps, the lengths of the four optical delay waveguides in the 4-bit OSDL were calculated by Eq. (3), which is given in Table 1. The delay range is from 0 to 150 ps.
Table 1. The lengths of the four delay waveguides
Figure 4(a) shows the schematic diagram of the proposed OTDL, which is constructed by cascading a 4-bit OSDL with a single tunable grating-assisted CDC delay line. The total delay can be expressed as:
where ${t_{4 - bit}}\; $, ${t_{CDC}}$ are the delay times introduced by the 4-bit OSDL, and the tunable grating-assisted CDC, respectively. As the continuously tunable ${t_{CDC}}$ is longer than the delay step of 4-bit OSDL, a wide coarse-tuning range and a small fine-tuning range can be achieved by ${t_{4 - bit}}\; $ and ${t_{CDC}}$, respectively. Then, a wide range of continuously OTDL can be realized.Fig. 4. Schematic diagram of (a) the proposed OTDL; (b) optical switch consisting of two MMIs; (c) spiral delay line; (d) adiabatic taper; (e) test port for optical switch calibration.
Figure 4(b) shows the optical switch used in the OTDL, which consists of two 2 × 2 MMIs and a thermally phase shifter. The reason of choosing the MMI structure is the large fabricating tolerance. In Fig. 4(c), the width of the spiral delay waveguides is set as 1200 nm and the bending radius is set to be 40 µm, which can reduce the transmission loss of TE0 mode. To avoid coupling between waveguides, the interval between adjacent waveguide centers is taken as 8 µm. Figure 4(d) illustrates the adiabatic taper can maintain the TE0 mode for connecting the optical switch and the spiral waveguide to avoid stimulating higher-order modes. To calibrate the driving voltages of all five thermo-optic switches, we added four test ports based on a directional coupler structure near the reference waveguides as shown in Fig. 4(e). A coupling length of 12 µm and a coupling gap size of 400 nm were chosen to download about 1%(-20 dB) optical power for monitoring.
3. Experimental result
3.1 Fabrication
The OTDL chip was fabricated on an 8.78 mm × 8.78 mm SOI wafer from ANT (Canada), which consists of a 220 nm Si layer and a 2 µm SiO2 buried layer, as illustrated in Fig. 3(a). Firstly, the pattern of waveguides was defined by electron beam lithography technology. Then, the fully-etched structures were created using inductively coupled plasma – Reactive Ion Etching process, and a 2.2 µm SiO2 layer was deposited by plasma enhanced chemical vapor deposition. Finally, the heater was formed by depositing a 300 nm TiW/Al layer of low-resistance and a 200 nm TiW layer of high-resistance on the SiO2 layer.
Figure 5(a) shows the microscope image of the fabricated chip with the area of the major part of OTDL about 6.5 × 0.65 mm2. The electrical wire bonding is shown in Fig. 5(b) and the SEM image of the CDC is shown in Fig. 5(c). Two grating-assisted CDCs with identical parameters were fabricated on the left side of the chip. One is the reference and the other one is connected to the 4-bit OSDL, which contains five optical switches. The fabricated chip was packaged by SJTU-Pinghu Institute of Intelligent Optoelectronics (China). The left side of the chip was aligned with a fiber array with a 127 µm interval. The wire bonding for connecting the TiW/AI layer is shown in Fig. 5(b). And Fig. 5(c) shows the SEM image of the CDC, where the periodic grating teeth can be obviously seen.
Fig. 5. Optical microscope image of (a) the fabricated chip and (b) electrical wire bonding. (c) SEM image of the CDC.
3.2 Experimental arrangement
The experiment setup for delay measurement is illustrated in Fig. 6. An optical carrier is generated by a tunable laser source (TLS, Santac WSL-710) with TE mode. A polarization-maintaining fiber is used to connect the TLS and the optical delay meter (ODM, NEWKWY ODM-M100), which contains an intensity modulator and a photodetector. A 12 GHz radio frequency signal from the vector network analyzer (VNA, Agilent-N5242A) is injected into the ODM, and the optical carrier is modulated with double sideband operation. The modulated optical signal entered ODL after the polarization controller with TE polarization state, and finally transmitted back to the ODM. The VNA receives the electrical signal from the ODM, then the delay can be calculated by computer. In order to minimize the effect of thermal crosstalk introduced by multiple heaters, a thermo-electric cooler (TEC, Arroyo instrument) was adopted to maintain the chip temperature around 21 °C.
Fig. 6. Experiment setup for the delay measurement. TLS: Tunable laser source, PC: Polarization controller, ODM: Optical delay meter, VNA: Vector network analyzer, TEC: Thermo-Electric cooler, ODL: Optical delay line
3.3 Characterization of the CDC
The measured group delays as well as the transmission spectrum of the CDC are shown in Fig. 7(a). The total insertion loss of the packaged chip is about 6.4 dB, the 3-dB bandwidth is about 8.7 nm with a fitted slope of 2.25 ps/nm. Obviously, the spectrum has great power flatness in the passband, while there is an unavoidable delay fluctuation due to the strong grating perturbation.
Fig. 7. Measured transmission spectra and group delays of the reference CDC at different loaded voltages of (a) 0 V; (b) 4 V; (c) 8 V; (d) 12 V.
Figure 7 demonstrated transmission spectra and group delays at different loaded voltages of 0 V, 4 V, 8 V and 12 V. From Fig. 8(a), a redshift of 4.8 nm occurred in both the spectral responses and the group delays curve with loaded voltage of 12 V with the maximum electric power of 221 mW. The fitted slopes of the group delays are 2.25 ps/nm (0 V), 2.13 ps/nm (4 V), 2.26 ps/nm (8 V) and 2.25 ps/nm (12 V), respectively. The fitted slopes have a tiny difference. It appears that the resistance of the TiW heater is not uniformly distributed above the CDC, resulting in uneven thermal tuning efficiency in different parts of the CDC.
Fig. 8. The reference CDC at different loaded voltage. (a) Measured transmission spectra. (b) Fitted slopes of group delays.
According to the experimental results shown in Fig. 8(b), if the average slope of the group delay is assumed to be 2.21 ps/nm, the variation of delay can reach 10.608 ps with a spectral shift of 4.8 nm, which could achieve a continuous tuning range of 10 ps. The selected wavelengths of the laser must fall within the range between the orange lines, so the working bandwidth is about 3.5 nm (1551.7 nm to 1555.2 nm) with a maximum voltage of 12 V. CDCs in Ref. [31] can realize delay tuning by changing the wavelength of the optical carrier. However, this tuning approach relies on a laser source with tunable wavelength capability. In most cases, the laser source has a fixed wavelength without tunability. Therefore, the following experiments can tune the delay by shifting the dispersion curve. Due to the large thermal conductivity of Si, the laser source does not need to tune its wavelength, which is more suitable for the application.
3.4 Characterization of the entire delay line
From Fig. 8, it is obvious that thermal tuning causes a red shift of the transmission spectrum and the group delay curve. When the wavelength of the TLS is fixed, a certain delay state of the OSDL can be selected by setting driving voltages of the five optical switches. A continuously tunable range of delay more than 10 ps can be achieved by thermal tuning of the grating. In addition, it is required that the wavelength is within the passband of the grating at different load voltages. In order to exactly choose the delay path of the OSDL, we firstly set the wavelength of TLS as 1552.7 nm to calibrate the voltages of five optical switches, and this wavelength is on the left side of the overlapping region in Fig. 8(b). It is just a 4-bit OSDL, and the grating can be set up before the OTDL to play the role of a polarizer. With the measuring voltage interval of 0.01 V, the extinction ratios of the optical switches are more than 28 dB, as shown in Fig. 9.
Fig. 9. The normalized transmissions with driving voltages. (a) Measured optical power of the test port at the fourth optical switch and (b) measured optical power of the output port after the fifth optical switch.
After calibrating, we applied different voltage combinations to generate a total 24 = 16 different delay states, as shown in Fig. 10. At 1552.7 nm wavelength, the total insertion loss of the shortest path in the optical delay line is about 15 dB, which is larger than the conventional OSDLs. After the experimental analysis, we found that the chip has dilatation effect due to the dry process during the packaging, resulting in the ports below the chip and the fiber array not being fully aligned. There is a reference waveguide below the optical delay line and its insertion loss is larger than the reference CDC. As can be seen from Fig. 5(a), the output ports of the OSDL + CDC structure are located below the chip, leading to a larger insertion loss. The power difference between the shortest path and the longest path is 2.24 dB. The estimated transmission loss of the OSDL is only about 0.016 dB/ps, which benefits from the low-loss multimode waveguides. After applying the voltages, the delay tuning in the range of 10 ps can guarantee a constant optical power, thanks to the low insertion loss and the flat transmission spectrum of the CDC. Based on the estimation from Fig. 8, the voltage range between 0 V and 12 V can achieve a continuous tuning in a range of 10 ps, then the OTDL can realize a continuous tuning with the maximum delay of 160 ps.
When the wavelength of TLS is set to 1552.7 nm, delays in each state with four loaded voltages are shown in Fig. 11 (a). According to the delay measurements in the shortest and longest paths, the maximum delay is calculated to be 160.73 ps. Within each delay state n Δτ (n = 0, 1, 2, 3, …15), a tuning range of 10 ps can be obtained by applying the load voltage, and the continuous tuning step depends on the minimum resolution of the applied voltage.
Similarly, at the 1554.8 nm wavelength of TLS (near the right side of the bandwidth in Fig. 8(b)) was chosen, and the experiment was repeated. The measured delays are shown in Fig. 11(b). Compared with the measured delays at the 1552.7 nm wavelength, a 10 ps delay tuning range was also achieved in each delay state, and the entire OTDL realized continuous tuning with a maximum delay of 161.68 ps. Considering the grating is a resonant structure and the heating efficiency of the various parts of the CDC is not strictly uniform, the loaded voltage ranges for 10 ps delay tuning are not exactly same in different wavelengths. Since the delay fluctuation is unavoidable, it is possible to use algorithmic fine-tuning to obtain a relatively accurate load voltage. With the maturity of the fabrication, introducing an appropriate apodized function could reduce delay fluctuations and decrease the difficulty of designing the algorithms.
Table 2 gives a comparison of various continuously tunable delay lines with OSDL. As can be seen, there are three structures combine with OSDL to achieve continuous tunable delay. Due to the maximum delay is mainly determined by OSDL, a longer delay needs the larger footprint. On the same platform, the delay loss of the proposed chip is comparable with Ref. [13], and the bandwidth of is larger. Thermal tuning is also popular because its simplicity and convenience. By properly combining the driving voltages of the five thermo-optic switches in the 4-bit OSDL and adjusting the loaded voltage on the CDC, it is demonstrated that the proposed OTDL can be continuously tuned in the range of 0-160 ps with tiny variation of optical power.
Table 2. Comparison of various continuously tunable delay lines with OSDL
4. Conclusion
In summary, based on the 220 nm-SOI platform, we designed and fabricated an integrated continuously OTDL. The OSDL provides large-range coarse tuning of the delay by thermos-optic switches, while the grating-assisted CDC gives fine tuning by the heater. The measured results demonstrated that the CDC can be driven by 0-12 V to achieve a 10 ps tuning range wider than the delay step of the 4-bit OSDL, realizing continuous tuning in a delay range of 0-160 ps. Owing to the 1200 nm low-loss multimode spiral waveguides, the transmission loss is about 0.016 dB/ps. Meanwhile, low insertion loss and constant optical power in each delay path can be obtained due to the separated input and output ports of the grating-assisted CDC. In addition, a larger delay of the OTDL can be exponentially increased by cascading more optical switches, and the delay bandwidth and fine-tuning range can be expanded by changing the chirp coefficient and length of the grating-assisted CDC. With the maturity of the fabrication, the delay fluctuations will be further reduced, and the linearity can be improved by introducing a reasonable apodized function, which will enhance the precision of microwave signal generation and measurement. The continuously tunable OTDL with excellent performance and good expandability has great potential for microwave photonic chips, especially in microwave photonic filters and beamforming of phased array radar.
Funding
National Natural Science Foundation of China (62075038).
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. J. Yao and J. Capmany, Microwave photonics, Science China Information Sciences, 65 (2022).
2. D. Marpaung, J. Yao, and J. Capmany, “Integrated microwave photonics,” Nat. Photonics 13(2), 80–90 (2019). [CrossRef]
3. H. Lee, T. Chen, J. Li, et al., “Ultra-low-loss optical delay line on a silicon chip,” Nat. Commun. 3, 867 (2012). [CrossRef]
4. Z. Gong, B. He, W. Ji, et al., “LNOI waveguide grating based true time delay line for tunable bandpass microwave photonic filter,” Opt. Quantum Electron. 52(10), 427 (2020). [CrossRef]
5. W. Shan, L. Lu, X. Wang, et al., “Broadband continuously tunable microwave photonic delay line based on cascaded silicon microrings,” Opt. Express 29(3), 3375 (2021). [CrossRef]
6. C. Zhu, L. Lu, W. Shan, et al., “Silicon integrated microwave photonic beamformer,” Optica 7(9), 1162 (2020). [CrossRef]
7. D. Wang, Y. Sun, C. Deng, et al., “Simultaneous Generation of Two Negatively Correlated Linearly Frequency-Modulated Pulses Based on an Integrated Anti-Reflection Spectral Shaper,” ACS Photonics 10(5), 1275–1285 (2023). [CrossRef]
8. P. Zheng, X. Xu, D. Lin, et al., “A wideband 1× 4 optical beam-forming chip based on switchable optical delay lines for Ka-band phased array,” Opt. Commun. 488, 126842 (2021). [CrossRef]
9. W. Ke, Y. Lin, M. He, et al., “Digitally tunable optical delay line based on thin-film lithium niobate featuring high switching speed and low optical loss,” Photonics Res. 10, 2575 (2022). [CrossRef]
10. J. Xie, L. Zhou, Z. Li, et al., “Seven-bit reconfigurable optical true time delay line based on silicon integration,” Opt. Express 22(19), 22707 (2014). [CrossRef]
11. S. Hong, L. Zhang, Y. Wang, et al., “Ultralow-loss compact silicon photonic waveguide spirals and delay lines,” Photonics Res. 10, 1 (2022). [CrossRef]
12. S. Shi, D. Lin, H. Niu, et al., “Compact optical beamforming chip using broadband continuously tunable delay lines,” J Lightwave Technol. (2023).
13. X. Wang, L. Zhou, R. Li, et al., “Continuously tunable ultra-thin silicon waveguide optical delay line,” Optica 4(5), 507 (2017). [CrossRef]
14. D. Lin, S. Shi, W. Cheng, et al., “A High Performance Silicon Nitride Optical Delay Line With Good Expansibility,” J. Lightwave Technol. 41(1), 209–217 (2023). [CrossRef]
15. D. Lin, X. Xu, P. Zheng, et al., “A Tunable Optical Delay Line Based on Cascaded Silicon Nitride Microrings for Ka-Band Beamforming,” IEEE Photonics J. 11(5), 1–10 (2019). [CrossRef]
16. T. Xu, S. Zheng, Y. Qiu, et al., “Tunable slow and fast light in a silicon-on-insulator Fano resonator,” Opt. Lett. 48(2), 335 (2023). [CrossRef]
17. Y. Xu, W. Zhang, and B. Wang, “Ultra-Fast Tunable Optical Delay Line Based on Cascaded Silicon Microdisk Resonators,” IEEE Photonics J. 15(6), 1–6 (2023). [CrossRef]
18. I. Giuntoni, D. Stolarek, D. I. Kroushkov, et al., “Continuously tunable delay line based on SOI tapered Bragg gratings,” Opt. Express 20(10), 11241–11246 (2012). [CrossRef]
19. Y. Li, L. Xu, D. Wang, et al., “Large group delay and low loss optical delay line based on chirped waveguide Bragg gratings,” Opt. Express 31(3), 4630 (2023). [CrossRef]
20. M. Burla, L. R. Cortes, M. Li, et al., “On-chip programmable ultra-wideband microwave photonic phase shifter and true time delay unit,” Opt. Lett. 39(21), 6181–6184 (2014). [CrossRef]
21. J. Ding, X. Zou, F. Zou, et al., “Thermal tuning of chirped SOI sidewall grating for tunable wavelength, delay, and bandwidth,” Optoelectron Lett. 17(4), 205–208 (2021). [CrossRef]
22. Z. Du, C. Xiang, T. Fu, et al., “Silicon nitride chirped spiral Bragg grating with large group delay,” APL Photonics 5(10), 101302 (2020). [CrossRef]
23. Y. Sun, D. Wang, C. Deng, et al., “Large Group Delay in Silicon-on-Insulator Chirped Spiral Bragg Grating Waveguide,” IEEE Photonics J. 13(5), 1–5 (2021). [CrossRef]
24. 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]
25. S. Liu, D. Liu, Z. Yu, et al., “Digitally tunable dispersion controller using chirped multimode waveguide gratings,” Optica 10(3), 316 (2023). [CrossRef]
26. S. Liu, R. Ma, Z. Yu, et al., “On-chip digitally tunable positive/negative dispersion controller using bidirectional chirped multimode waveguide gratings,” Adv. Photonics 5(06), 066005 (2023). [CrossRef]
27. B. Stern, H. Chen, K. Kim, et al., “Large Dispersion Silicon Bragg Grating for Full-Field 40-GBd QPSK Phase Retrieval Receiver,” J. Lightwave Technol. 40(22), 7358–7363 (2022). [CrossRef]
28. W. Shi, V. Veerasubramanian, D. Patel, et al., “Tunable nanophotonic delay lines using linearly chirped contradirectional couplers with uniform Bragg gratings,” Opt. Lett. 39(3), 701–703 (2014). [CrossRef]
29. J. St-Yves, H. Bahrami, P. Jean, et al., “Widely bandwidth-tunable silicon filter with an unlimited free-spectral range,” Opt. Lett. 40(23), 5471–5474 (2015). [CrossRef]
30. X. Wang, Y. Zhao, Y. Ding, et al., “Tunable optical delay line based on integrated grating-assisted contradirectional couplers,” Photonics Res. 6, 880 (2018). [CrossRef]
31. F. Zhang, J. Dong, Y. Zhu, et al., “Integrated Optical True Time Delay Network Based on Grating-Assisted Contradirectional Couplers for Phased Array Antennas,” IEEE J. Select. Topics Quantum Electron. 26(5), 1–7 (2020). [CrossRef]
32. H. Sun, Y. Wang, and L. R. Chen, “Integrated Discretely Tunable Optical Delay Line Based on Step-Chirped Subwavelength Grating Waveguide Bragg Gratings,” J. Lightwave Technol. 38(19), 5551–5560 (2020). [CrossRef]
33. Y. Wang, H. Sun, M. Khalil, et al., “On-chip optical true time delay lines based on subwavelength grating waveguides,” Opt. Lett. 46(6), 1405 (2021). [CrossRef]
34. X. Wang, L. Zhou, L. Lu, et al., “Integrated Optical Delay Line Based on a Loopback Arrayed Waveguide Grating for Radio-frequency Filtering,” IEEE Photonics J. 12(6), 1–12 (2020). [CrossRef]
35. G. Hu, Y. Cui, Y. Yang, et al., “Optical Beamformer Based on Diffraction Order Multiplexing (DOM) of an Arrayed Waveguide Grating,” J. Lightwave Technol. 37(13), 2898–2904 (2019). [CrossRef]
36. J. Sancho, J. Bourderionnet, J. Lloret, et al., “Integrable microwave filter based on a photonic crystal delay line,” Nat. Commun. 3(1), 1075 (2012). [CrossRef]
37. S. Wu, W. Mo, F. Jin, et al., “Optical delay lines in topological microring resonator array,” J. Opt. 25(1), 015801 (2023). [CrossRef]
