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Abstract
On-chip switchable optical true-time delay lines (OTTDLs) feature a large group delay tuning range but suffer from a discrete tuning step. OTTDLs with a large delay tuning range and a continuous tuning capability are highly desired. In this paper, we propose and experimentally demonstrate a silicon-based broadband continuously tunable OTTDL comprising a 7-bit delay line and a switch-based continuously tunable delay line. The group delay of the entire OTTDL can be continuously tuned from 0 to 1020.16 ps. A delay error within -1.27 ps to 1.75 ps, and a delay fluctuation of less than 2.69 ps in the frequency range of 2∼25 GHz are obtained. We analyze the causes of the delay fluctuation and its influence on beamforming. Moreover, we also propose a simplified non-invasive calibration method that can significantly reduce the complexity of the delay state calibration and can be easily extended to delay lines with more stages of optical switches. The high performance of our OTTDL chip and the calibration method drive practical applications of integrated OTTDLs.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
As one of the most important components in photonic integrated circuits (PICs), integrated optical true-time delay lines (OTTDLs) have broad applications in optical signal processing such as optical beamforming networks (OBFNs) [1–13], microwave photonic filters [14–16], and optical computing [17,18], due to their compact size, low cost, and wide bandwidth. Several structures, including Mach-Zehnder interferometers (MZIs) [19–23], micro-ring resonators (MRRs) [24–28], and waveguide Bragg gratings [29,30], have been adopted to realize OTTDLs. However, integrated OTTDLs possessing a low loss, a large continuous delay tuning, a high tuning accuracy, a wide optical bandwidth, low delay fluctuations, a low power consumption, and a fast delay adjustment have not been demonstrated, which limits their practical applications.
MZI-based OTTDLs are composed of cascaded 2×2 MZI optical switches and optical waveguides of various lengths. By adjusting the MZI switches to the cross- or the bar-states, we can digitally tune the time delay with a large delay tuning range and a broad optical bandwidth. They are insensitive to surrounding temperature variations and the delay state control is simple and easy to extend. However, the time delay of switch-based delay lines can only be tuned with a fixed delay tuning step, which depends on the differential time delay of the first stage. Although a micro-heater can be integrated into the delay waveguides to continuously tune the time delay, the tuning range is limited to 3.15 ps when a fairly high power of 0.42 W is applied [31], due to its low thermal-tuning efficiency of the waveguide group index. Recently, switch-based continuously tunable OTTDLs (SBCT-OTTDLs) have been realized [32–36]. It is identical to that of the first stage of the aforementioned switch-based OTTDL, but the MZIs in the SBCT-OTTDL function as tunable couplers, of which the power coupling ratio, Κ, can be tuned from 0 to 1. In this way, when the SBCT-OTTDL is working at the constructive interference point, the time delay can be continuously changed from 0 to the maximum by tuning the coupling ratio of the MZIs from 0 to 1. Although the SBCT-OTTDL is simple, there is a trade-off between the delay tuning range and the delay bandwidth. A maximum delay tuning range of 125 ps with a bandwidth of 4.45 GHz has been demonstrated using this method [32].
MRR-based OTTDLs have been widely studied. MRR-based OTTDLs feature continuous tunability and a compact footprint, but they suffer from high thermal sensitivity and a narrow delay bandwidth due to the slow-light effect of the on-resonant MRRs. Although cascaded MRRs can be used to expand the delay tuning range and the delay bandwidth, much more complicated control schemes are required to tune each MRR and the in-band delay ripples are hard to suppress. To solve this issue, MRRs working at anti-resonances have been proposed and a low delay fluctuation and a large bandwidth have been achieved [10,13,23]. However, the time delay of one single MRR can only be tuned from 0 to Δτ, where Δτ represents the round-trip delay of this MRR. Cascaded MRRs with exponentially increased round-trip delays can break the delay-bandwidth product limitation of MRR-based OTTDLs. The MZI-based tunable couplers in the MRRs are only digitally tuned to 0 or 1, working like the switch-based OTTDLs. Therefore, a large delay tuning range with a flat delay response can be realized with the digitally tuned MRR OTTDLs. By combining both the anti-resonant MRR and the digitally tuned MRRs, a continuous delay tuning from 0 to 560 ps over a microwave bandwidth of 8 GHz has been demonstrated on the Triplex platform [10]. However, the in-band delay fluctuation is 7.6 ps, as the delay ripples of the MRRs are more sensitive to the extinction ratio (ER) of the tunable couplers. Recently, a combined structure incorporating a 5-bit switch-based OTTDL and a single anti-resonant MRR has been proposed [37]. The time delay can be continuously tuned from 0 to 395.5 ps with a maximum delay fluctuation of less than 4 ps in an 8-GHz microwave bandwidth.
Moreover, fast and non-invasive delay state calibration with a precise delay adjustment is essential for system applications. Previously, off-chip optical power monitoring assisted with directional couplers (DCs) or variable optical attenuators (VOAs) has been demonstrated for delay state calibration [37,40]. These two methods are easy to implement, but they introduce extra insertion loss and the control scheme is complicated. A non-invasive calibration method was then proposed and demonstrated [38,39]. By sweeping the applied voltages on each MZI switch and measuring the standard deviation of the target spectrum at the output port, the OTTDL can be successfully calibrated without any additional calibration-assisted devices. Although the voltages corresponding to the bar- and the cross-states of MZI switches can be obtained in a non-invasive way, it is hard to distinguish the exact bar- or cross-state of each MZI switch, and the time delay measurement is imposed to help differentiate the states, which increases the calibration complexity.
In this paper, we propose and experimentally demonstrate a continuously tunable silicon OTTDL composed of a 7-bit switch-based OTTDL and an SBCT-OTTDL. The time delay can be continuously tuned from 0 to 1020.16 ps within a frequency range of 2∼25 GHz for the entire OTTDL. Benefiting from the wide ridge delay waveguide, we achieved a low delay loss of 3.79 dB/ns and a low delay error within -1.27 ps to 1.75 ps for the entire OTTDL. Besides, the OTTDL has a delay fluctuation of less than 2.69 ps within a 23 GHz bandwidth. The causes for the delay fluctuation and its influence on microwave beamforming are theoretically analyzed and numerically simulated. A simplified non-invasive calibration method along with an automatic calibration technique is proposed to calibrate the delay states of OTTDL. There is no need to measure the time delay, which significantly simplifies the calibration process. The overall high performance of the proposed OTTDLs and the easy calibration method promote the practical applications of integrated OTTDLs.
2. Device structures and the working principle
Figure 1(a) shows the schematics of our entire continuously tunable OTTDL. As our delay line is composed of two types of OTTDLs, we will discuss separately the design and the working principle in the following sections.
Fig. 1. (a) Schematics of the continuously tunable OTTDL. (b) Schematics of the first two stages of the 7-bit OTTDL. (c), (d) Cross-sections of (c) the 2-µm-wide ridge waveguide and (d) the VOA. (e) Simulated waveguide group index deviation of a 500-nm channel waveguide and a 2-µm ridge waveguide with waveguide width variation.
2.1 7-bit OTTDL
The schematic structure of the 7-bit OTTDL is shown in the left panel of Fig. 1(a). Each MZI switch comprises two 2×2 multimode interferometers (MMIs) and two 300-µm-long channel waveguide arms. The two arms are integrated with TiN microheaters for phase-shifting and the waveguides are widened from 0.5 µm to 2 µm to reduce the transmission loss and the fabrication-induced random phase error. MZI switches in the 7-bit OTTDL work at either the bar- or the cross-state so that the optical signals can be routed completely to either the delay or the reference path. Two p-i-n-diode-based VOAs are integrated after the two output ports of each MZI switch and can be used to suppress the crosstalk. Figure 1(d) illustrates the cross-section of the VOA. The highly doped P++ and N++ regions are 0.8 µm away from the edge of the ridge waveguide to reduce the absorption loss from the doping. Each VOA is followed by either a segment of the delay waveguide or a reference waveguide. Figures 1(b) and 1(c) show the schematics of the first two stages of the 7-bit OTTDL and the delay waveguide cross-section, respectively. Euler bends and 2-µm-wide ridge waveguides are utilized to reduce the bending and transmission losses. The bending radius of the Euler bends varies continuously and the corresponding effective bending radius is about 5 µm, which results in a lower bending loss than a conventional arc-bend with the same radius. The Euler bend is based on a channel waveguide with a width of 0.5 µm, which is transitioned to a 2-µm-wide ridge waveguide by a linear taper with a length of 50 µm. According to the simulation, the transition loss is less than 0.01 dB and the crosstalk to higher order modes is below -33 dB, which ensures the fundamental mode operation of the 7-bit OTTDL.
To reduce the delay error, the differential group delay between the upper and the lower arms is designed to depend only on the length difference of the 2-µm-wide ridge waveguides. The delay error originating from the group index deviation due to fabrication-induced waveguide width variation can be minimized, which improves the accuracy of the time delay. The delay error here is defined as the difference between the measured and the designed time delay. Figure 1(e) shows the calculated group index deviation with the waveguide width. The numerical simulation results show that with the width deviates by ${\pm} 25\,\textrm{nm }$from the desired one, the group index variation is only ∼0.008 for the 2-µm-wide ridge waveguides, which is one-fifth of that for the 500-nm-wide channel waveguide. Thus, for a total delay of 1 ns, the delay error can be reduced from 10.16 ps to 2.14 ps for the wide-ridge waveguide design. As shown in Fig. 1(b), only the length differences of straight 2-µm-wide ridge waveguides are utilized to realize the time delay, which further reduces the delay error. The length difference between the delay waveguide and the reference waveguide after the nth stage of the switch is $\varDelta {L_n}$, which is designed as:
where c, $\varDelta t$ and ${n_g}$ denote the speed of light in the vacuum, the delay tuning step, and the group index of the 2-µm-wide ridge waveguides, respectively. In our work, the delay tuning step is $\varDelta t = \textrm{7}\textrm{.97}$ ps.In addition to the delay error, the in-band delay fluctuation is detrimental to broadband applications. The delay fluctuation describes the difference between the maximum and minimum time delay in the operating bandwidth. As the MZI switches in the 7-bit OTTDL are connected by different lengths of waveguides in between, the OTTDL can be regarded as the cascaded asymmetric MZI interferometers. The limited ERs of non-ideal switches result in undesired interference between the delay path and leakage path, which deteriorates the signal-to-noise (SNR) ratio of the delayed signal [40] and leads to delay fluctuations with wavelength.
To investigate the effect of the switch ERs on the delay fluctuation, we numerically simulated the microwave responses of the 7-bit OTTDL under various ERs and obtained the relationship between the delay fluctuation and the ER with and without VOAs. All switches have identical ERs, and a 10-dB optical attenuation is assumed when each VOA is turned on. In the simulation model, the optical carrier is first intensity-modulated by a modulator driven by a radio frequency (RF) signal, and two sidebands are generated in the optical domain. The modulated signal is then delayed by the OTTDL and finally recovered to the RF signal after the beating of the carrier and the sidebands in the photodetector. After the photodetection, the time-domain RF complex photocurrent ${I_{RF}}(t )$ can be expressed as the conjugate multiplication of the received optical electric field ${E_o}(t )$:
while the recovered frequency-domain RF complex photocurrent ${I_{RF}}({j\omega } )$ can be derived from Fourier transformation as: where ${E_o}({j\omega } )$ is the received frequency-domain complex optical electric field, $\omega $ is the angular frequency of the RF signal, and $\mathrm{\ast }$ between ${E_o}({j\omega } )$ and $E_o^\ast ({ - j\omega } )$ denotes the convolution operation. The microwave time delay can then be expressed as: where $\phi $ represents the phase shift of the RF signal. Figure 2 shows the numerically simulated relationship between the maximum delay fluctuation and the switch ERs in the 25 GHz bandwidth. As shown from the simulation, the delay fluctuation reduces with the ER. When there are no VOAs, the delay fluctuation is much larger. To suppress the delay fluctuation below 1 ps, the ER should exceed 35 dB. In contrast, the required ER is reduced to ∼25 dB with the assistance of VOAs. In our design, we use the 2×2 MMIs as the 3-dB couplers. The simulated power nonuniformity of the two ports of the MMI is less than 0.1 dB within a wavelength range of 60 nm, which guarantees an ER of ∼30 dB of the MZI switch. To further lower the delay fluctuation, we can turn on the VOAs to suppress the leaked optical wave.Fig. 2. (a) Simulated group delay fluctuation of the 7-bit OTTDL under various switch ERs with and without VOAs. (b) Enlarged view of the simulated group delay fluctuation with the ER in the range of 25 dB to 40 dB.
2.2 SBCT-OTTDL
The schematic structure of the SBCT-OTTDL is shown on the right side of Fig. 1(a). The optical responses at the bar- and cross-ports can be analyzed by the transfer matrix method. The phase differences between the two waveguide arms of the first and the second MZIs are defined as $\varDelta {\phi _1}\; $ and $\varDelta {\phi _2}$, respectively. Continuous delay adjustment can be realized at the cross-port with $\varDelta {\phi _1}\mathrm{ = (\pi -\ }\varDelta {\phi _2})$, corresponding to ${K_1} = 1 - {K_2}$ where ${K_1}$ and ${K_2}$ are the power coupling coefficients of the two MZIs. With $\varDelta {\phi _1}\textrm{ = }\varDelta {\phi _2}$ and ${K_1} = {K_2}$, a broad delay response can be obtained at the bar-port. Figures 3(a) and 3(b) show the numerically simulated transmission and group delay responses from the cross-port in the optical domain. In the simulation, $\varDelta t$ is set to 7.97 ps, and the propagating loss is neglected. As shown from the simulation, the transmission spectra are identical for K1=a and 1-a (0<a < 1). In contrast, the group delay is complementary for these two power coupling coefficients. The operating wavelength is set at the constructive interference point as indicated by the red dashed line in Figs. 3(a) and 3(b). When ${\textrm{K}_1}$ changes from 0 to 1, the group delay varies from 0 to $\varDelta t$.
Fig. 3. Simulated (a) optical transmission, (b) group delay responses, (c) microwave photonic phase, and (d) group delay responses of the SBCT-OTTDL. The constructive interference wavelength is marked by the red dashed line. (e) Simulated group delay of the SBCT-OTTDL as a function of the arm phase difference in the first MZI.
The microwave responses of the SBCT-OTTDL are then numerically simulated using the same model as in Section 2.1. Here we take the results from the cross-port for example. The numerically simulated phase and time delay responses are shown in Figs. 3(c) and 3(d). The minimum and maximum time delays can be reached with ${K_1} = 1,\,{K_2} = 0$ and ${K_1} = 0,\,{K_2} = 1$, respectively. Due to the interference of the unbalanced MZIs, the group delay is not flat over the whole spectrum with K1≠0, 1. Therefore, we define the 1-ps delay bandwidth, which describes the frequency range with less than 1 ps delay fluctuation, to describe the operating bandwidth of the SBCT-OTTDL. The 1-ps delay bandwidth is around 30 GHz. The group delay ${\tau _{CTD}}$ obtained at the constructive interference point can be derived as a function of ${\varDelta }{\phi _\textrm{1}}$:
2.3 Device fabrication and package
The chip was fabricated on an 8-inch silicon-on-insulator (SOI) wafer with a top silicon layer thickness of 220 nm and a buried oxide (BOX) layer thickness of 3 $\mathrm{\mu}\textrm{m}$ by Advanced Micro Foundry (AMF). All the key elements are designed for the C-band and the transverse-electric (TE) polarization. The chip footprint is 10 mm × 1.13 mm and the microscope image of this fabricated chip is presented in Fig. 4(a). The chip was wire-bonded to a printed circuit board (PCB) and the packaged chip is shown in Fig. 4(b). Fiber arrays were edge-coupled to the input and output ports of the chip and attached to the metal shell by ultra-violet adhesive. Direct current (DC) control voltages were applied to the chip through I-PEX cables connected between the chip and the PCB. A thermo-electric cooler (TEC) along with a thermistor was placed under the chip to monitor and keep the chip temperature stable. This chip was packaged by the SJTU-Pinghu Institute of Intelligent Optoelectronics (SPIOE).
Fig. 4. (a) Microscope image of the fabricated continuously tunable OTTDL. (b) Picture of the packaged chip with the printed circuit board and the mount for thermal control and input/output-fiber array.
3. Experimental results
3.1 Characterizations of key components
We first characterized the performances of the on-chip key elements. The waveguide bending loss is measured to be as low as 0.003 dB/90°, while the loss of 5-µm-bending-radius arc-bends is around 0.013 dB/90°. Figures 5(a) and 5(b) show the measured transmission spectra of the MZI switch in the bar- and cross-states. As the phase responses from the two input ports of the MMI-based 3-dB coupler are slightly different, the optimal voltages for the minimum crosstalk of the cross- (bar-) state MZI are different when light inputs from different input ports. Therefore, we slightly adjusted the applied voltages in the measurement to obtain comparable crosstalk. The optimal voltages are 7.73 V and 3.40 V for the bar1 and cross1 states when light inputs from port 1, and are 7.76 V and 3.21 V for the bar2 and cross2 states when light inputs from port 2. The insertion loss and the crosstalk of the MZI switch are ∼0.52 dB and < -28 dB, respectively. Almost identical performances were obtained for the bar- and cross-states. The resistance of the heater is about 1890 $\mathrm{\Omega}$. The $\mathrm{\pi }$-phase-shift power consumption is ∼23 mW. In addition, we characterized the switching time of the MZI switch. A 150 Hz square-wave electrical signal was applied to the first MZI switch of the 7-bit OTTDL by an arbitrary waveform generator (AWG). The switching time discussed here refers to the time latency between the trigger signal from the AWG and the output signal from the photodetector. The measured waveforms are depicted in Fig. 5(c). The rising time and the falling time are 22 µs and 41 µs, respectively.
Fig. 5. (a), (b) Measured transmission spectra of (a) the bar and (b) the cross states of the MZI switch element. (c) Measured temporal response of the MZI switch. The rising/falling times are 22 µs and 41 µs.
3.2 Non-invasive calibration of the OTTDL
We propose a simplified non-invasive calibration method of which there is no need to measure time delay. Figure 6(a) shows the experimental setup. To reduce the delay fluctuation and to reduce the crosstalk of the MZI switches, we need to calibrate the operating voltages of the four states of each MZI switch, except for the first and the last MZIs. As the input and output ports of the 7-bit OTTDL are fixed, these two MZIs only work in two states. As shown in Fig. 6(b), all the operating states of the MZI switches are included in these four delay states. Therefore, only four delay states of the 7-bit OTTDL are needed for the whole calibration, and the rest of the delay states can then be derived from the obtained operating voltages of each MZI switch.
Fig. 6. (a) Experimental setup schematics of the calibration. (b) The 4 chosen delay states of N = 1, 43, 86, and 128 for the simplified non-invasive calibration. (c) Measured power ripple of the transmission spectrum at various iterations of the calibration process for the first delay state. Inset: the optimized voltages of each switch. (d) Measured transmission spectra of the four delay states. (e) Measured power ripples of all delay states in a 2-nm wavelength span. (f) Measured insertion loss of each delay state at 1537 nm.
During the calibration process, all the VOAs were turned off and an automatic calibration process based on a sequential quadratic programming (SQP) algorithm was introduced to seek the exact operating voltages of each switch. A spectrum covering a wavelength span from 1536 nm to 1538 nm was obtained for each iteration. The maximum power ripple, which is defined as the difference between the maximum and the minimum optical transmissions in the spectrum, was monitored and the operating voltages were optimized automatically to minimize this ripple. When all switches are tuned to the corresponding bar- or cross-state, the ripple is anticipated to be minimized [38]. As the initial state of the MZI switch is near the cross-state, and the two arms of the MZI switches can be chosen for the phase-tuning, the operating voltage range of every switch was limited to 0∼5 V for the cross-state and 5∼9 V for the bar-state, so that the bar- or the cross-state can be distinguished by the operating voltages. The operating voltage range was chosen according to the experimental results of a reference MZI switch element. We note that the lower arms of all the MZI switches were chosen for phase-tuning at first. If an obvious interference with a maximum power ripple exceeding 1 dB can still be observed in the spectrum for any of the four delay states after the optimization, voltages would be applied to the upper arm of some of the switches for another round of optimization, until no obvious interference exists and the power ripple is below 1 dB. The free spectral range (FSR) of interference and the applied voltages determine which switch would be changed to the upper arm for phase tuning. We take the first delay state for instance, in which all the switches are normally in the cross-state except for the first one. Therefore, the voltage searching range for the first MZI was 5∼9 V, while the voltages applied to the other MZIs were set in the range from 0 V to 5 V. Figure 6(c) shows the measured power ripple of the transmission spectrum under various iterations for the calibration of the first delay state. The result was obtained after the confirmation of the tuning arm of each MZI switch. After 11 iterations, the power ripple can be controlled within 0.7 dB. The optimized voltages of MZI switches are shown in the inset of Fig. 6(c). If the FSR of interference is around 4 GHz, and the voltage of the sixth MZI switch reaches 0 V after the optimization, then the upper arm of this switch would be tuned to reach the cross-state. This confirmation process is the same for other switches. Two rounds of optimization were implemented before the final one was confirmed, resulting in approximately 30 iterations in total for the three rounds of optimization. The upper arms of switches 1, 3, 4, and 6 were chosen for phase-tuning in our device.
Figure 6(d) shows the measured transmission spectra of the four delay states after calibration. The voltages of each switch for the four delay states are shown in Table 1. The calibrated voltages for the two bar- (cross-) states of each MZI are shown in each row. As can be seen, they are slightly different. Calibration voltages of other delay states can then be derived based on these results. The maximum power consumption is about 186.60 mW. We obtain the power ripple of each delay state and the corresponding insertion loss at 1537 nm, as shown in Figs. 6(e) and 6(f). The insertion loss varies from 8 dB to 13 dB and the unit delay loss is ∼3.79 dB/ns, which indicates that the transmission loss of the 2-µm-wide ridge waveguides is 0.472 dB/cm. The total loss for the 8 switches is about 4.16 dB and the rest of the insertion loss comes from the VOAs and the connecting waveguides. The maximum power ripple for all the delay states is below 1 dB, indicating the correct calibration of all the MZIs.
Table 1. Calibration voltages for non-invasive and VOAs-based calibration methods (unit: V)
Calibration using the VOAs was also implemented, where the VOAs were turned on to attenuate the optical power on the undesired path. The same optimization algorithm was used to calibrate the four delay states by maximizing the optical power at the output port. Table 1 lists the calibration voltages of the MZI switches when the VOAs-based method was utilized. Almost identical calibration voltages were obtained for these two methods. The voltage difference between these two methods is less than 0.3 V. For the simplified non-invasive calibration method, there is no need to measure the time delay to verify the bar- and the cross-states of each switch. Furthermore, this method can be readily extended to an OTTDL with more stages, and one can still complete the calibration by measuring only the four delay states, which significantly simplifies the calibration process especially if the OTTDL comprises many stages.
For the SBCT-OTTDL, we utilized the same method to acquire the voltages for the cross- (K = 1) and the bar- (K = 0) states of the two MZIs. According to the numerical simulations shown in Fig. 3(e), we obtain the relationship between the group delay and the phase shift ${\varDelta }{\phi _\textrm{1}}$. Because the phase shift is proportional to the applied electrical power [41], the relationship between ${\varDelta }{\phi _\textrm{1}}$ and the applied voltages can then be expressed as
where V, ${V_{bar}}$, and ${V_{cross}}$ represent the voltage to be applied for phase shift ${\varDelta }{\phi _\textrm{1}}$, the voltages for the bar and the cross states of the MZI, respectively. The required voltage can be calculated by Eq. (6) if $\varDelta {\phi _1}$ is known. In this case, we can obtain the relationship between the desired group delay and the applied voltages. For example, if a time delay ${\tau _0}$ is desired, we only need to find the corresponding phase shift $\varDelta {\phi _0}$ according to the numerical simulations and then find the applied voltage by: providing that $V_{bar} $ is larger than $V_{cross} $. The lower arms of the two MZIs were used for the phase tuning. The calibrated voltages for the bar- and the cross-states of the first MZI are 7.08 V and 2.52 V, and they are 6.92 V and 1.88 V for the second one.3.3 Microwave responses of the integrated OTTDL
After calibration, the phase and group delay responses of the 7-bit OTTDL were characterized. Figure 7(a) depicts the experimental setup schematics for the RF response measurement. The optical signal was generated by a continuous-wave (CW) laser (Agilent 8164A) with 0 dBm optical output power. An electro-optic intensity modulator (iXblue MXAN-LN-20) driven by RF signals from a vector network analyzer (VNA, Anritsu MS46522B) and biased at the quadrature point was used to modulate the optical signal. The modulated signal was then sent into our chip and then amplified by an erbium-doped fiber amplifier (EDFA). The delayed signal was filtered by a bandpass filter with a 3-dB bandwidth of 0.8 nm and finally converted to an electrical signal by a photodetector (PD, Finisar XPDV3120R). The phase and group delay responses were then acquired by the VNA. We controlled all the instruments with a MATLAB program on a computer.
Fig. 7. (a) Experimental setup schematics of the phase and group delay responses measurement. PC: polarization controller; DUT: device under test; EDFA: erbium-doped fiber amplifier; PD: photodetector; VNA: vector network analyzer. (b), (c) Measured (b) phase and (c) group delay responses of all delay states of the 7-bit OTTDL. (d)-(g) Measured group delay fluctuations of all delay states in the frequency range from 2 to 25 GHz when (d) 0, (e) 2, (f) 4, and (g) 6 VOAs were turned on. (h) Measured averaged group delay fluctuations and standard deviations when different numbers of VOAs were switched on. (i) Extracted delay errors of all delay states with 6 VOAs turned on in the frequency range of 2∼25 GHz.
Figures 7(b) and 7(c) show the measured normalized phase and group delay responses of all the 128 delay states in the 25 GHz frequency range. All the delay responses were normalized to the shortest path. We characterized the delay fluctuation of each delay state. In the experiment, various groups of the VOAs were turned on to suppress the crosstalk of the MZI switches. Figures 7(d) to 7(g) show the measured delay fluctuations within the RF frequency range of 2∼25 GHz for all the delay states with 0, 2, 4, and 6 groups of the VOAs turned on, respectively. Every individual point represents the measured delay fluctuation of one delay state. The delay fluctuation is below 4.5 ps without VOAs, which is slightly smaller than the simulated one of ∼5.3 ps under 28-dB ER. This is possibly because the ERs of MZIs in our chip are not the same, and some of the MZIs have an ER of larger than 28 dB. A smaller delay fluctuation can be observed when more VOAs are switched on. The delay fluctuation of below 1.56 ps was obtained in the frequency range of 2∼25 GHz when 6 groups of VOAs were introduced. The average power consumption of each VOA was approximately 75 mW. The average group delay fluctuation and its standard deviation are shown in Fig. 7(h). As can be seen, the group delay fluctuation can be significantly reduced when the ERs of switches are increased, which matches well with the simulation. Figure 7(i) shows the extracted delay errors in the frequency range of 2∼25 GHz for the 128 delay states with 6 VOAs turned on. We set the RF frequency step identical to that of the group delay responses shown in Fig. 7(c). Thanks to the 2-µm-wide ridge waveguide and the identical structure design of the delay and reference arms, the delay error is within -0.96 ∼ 0.86 ps for all the 128 delay states.
To characterize the RF response of the SBCT-OTTDL, the 7-bit OTTDL was first tuned to zero delay. Then, the desired group delay of the SBCT-OTTDL ranging from 0 to $\varDelta t$ with a step of 0.2 ps was tested. The operating wavelength of the CW laser was 1537.3 nm, which was at the constructive interference point. Figures 8(a) to 8(c) show the measured RF transmission, phase, and group delay responses, respectively. The transmission spectra covering an entire FSR cannot be acquired as the FSR of this SBCT-OTTDL is ∼125 GHz, which is far beyond the RF frequency range of our VNA. We measured the RF transmission and delay responses in the range of 0 to 25 GHz. Figures 8(d) and 8(e) show the measured delay error and delay fluctuation. The measured group delay with respect to the phase tuning of the first MZI is shown in Fig. 8(f). The delay error is extracted within the frequency range from 2 GHz to 25 GHz with an RF frequency step of 1 GHz. The group delay can be continuously tuned from 0 to around 7.97 ps with a delay error within -0.31 ps to 0.89 ps. In addition, the group delay fluctuation below 1.13 ps can be obtained in the RF frequency range of 2∼25 GHz. We note that the measured bandwidth is narrower than the 1-ps delay bandwidth in simulation, which we attribute to the thermal variations in the experiment. Although a TEC was placed under the chip to control the temperature, the operating wavelength deviated slightly from the desired one, leading to a narrower 1-ps delay bandwidth.
Fig. 8. (a)-(c) Measured normalized microwave (a) transmission, (b) phase, and (c) group delay responses of the SBCT-OTTDL. (d) Measured delay errors within the frequency range from 2 GHz to 25 GHz. (e) Measured group delay at various phase shifts.
3.4 Effects of the delay fluctuation on an OBFN
To further demonstrate the significance of the low in-band delay fluctuation, the emitting beam patterns using the 7-bit OTTDLs were calculated with the simulated phase responses under various ERs of the MZI switches. 16 linear-spaced antenna elements were utilized and a uniform amplitude of each antenna element was assumed. The frequency of the microwave signal ranges from 5 GHz to 25 GHz, and the pitch of antenna elements was set to a half wavelength of the 25-GHz RF signal, which leads to a narrower beam width at higher frequencies. The group delay increment between adjacent antenna elements is set to be the minimum delay tuning step of our 7-bit OTTDL, resulting in an ideal beam angle of ${\theta _{idl}} = \arcsin ({c{\varDelta }t/d} )\sim 23.5^\circ $, where $d = {\lambda _{RF}}/2$ is the pitch of antenna elements, ${\lambda _{RF}}$ is the wavelength of the 25-GHz RF signal. Figure 9(a) shows the calculated emitting beam patterns upon a 40 dB ER of each switch. Figure 9(b) depicts the calculated beam angles under 15-dB and 40-dB ER of each switch at various RF frequencies. A beam angle deviation can be observed under various RF frequencies when the ERs of the switches are only 15 dB. Figure 9(c) shows the simulated beam angle error with respect to the ER of the MZI switches. The beam angle error describes the maximum difference between the simulated beam angle under various RF frequencies and the desired one under various ERs. The beam angle error is the maximum at 15 dB ER, while it reduces until the ER reaches 32 dB. It demonstrates that the delay fluctuation affects the direction of the emitting beam, and a minimum beam angle deviation can be obtained with the ER exceeding 32 dB.
Fig. 9. (a) Calculated emitting beam patterns upon a switch ER of 40 dB for the 7-bit OTTDL. (b) Simulated beam angles upon various RF frequencies and two ERs of the switch. (c) Simulated maximum beam angle error at various ERs of the switch. (d) Calculated emitting beam patterns with the measured phase responses of the 7-bit OTTDL and the SBCT-OTTDL. (e) Simulated maximum beam angle error with the measured phase at various RF frequencies.
Besides, to demonstrate our continuously tunable OTTDL has a broad operation band, we further calculate the emitting beam patterns using the measured phase responses shown in Fig. 7(b) and 8(b). Figure 9(d) shows the emitting beam patterns at various RF frequencies. The group delay increment between adjacent antenna elements is set to 8.37 ps, which is a combination of the minimum delay tuning step of the 7-bit OTTDL and another 0.4 ps provided by the SBCT-OTTDL. The ideal beam angle is ∼24.73°. As depicted in Fig. 9(e), the maximum beam angle error is below 0.06°, which verifies the broadband operation of our entire continuously tunable OTTDL.
4. Discussion
We compare our work with the state-of-the-art on-chip continuously tunable OTTDLs, which are shown in Table 2. The continuous tunability of most of these works is realized by micro-ring resonators (MRRs). Although the chip in [23] exhibits the largest delay tuning range, it suffers from a large delay loss of around 10 dB/ns. The work in [37] features a small in-band delay fluctuation, but the bandwidth is relatively small. In addition, the power consumption of the chip is large. In our work, by combining the 7-bit OTTDL with the SBCT-OTTDL, we realize a continuously tunable time delay ranging from 0 to 1020.16 ps. The delay error of the 7-bit OTTDL and the SBCT-OTTDL is within -0.96 ∼ 0.86 ps and -0.31 ps ∼ 0.89 ps, respectively, leading to a delay error of -1.27 ∼ 1.75 ps for the entire OTTDL. The delay fluctuation in the bandwidth of 2 to 25 GHz is as low as 2.69 ps, which is the lowest among all these works. A unit delay loss of 3.79 dB/ns is achieved, which is comparable with or even better than the OTTDLs based on the Si3N4 platform [6,10,37].
Table 2. Performance comparison of integrated continuously tunable OTTDLs
We can further improve the performance of our OTTDL. Although the differential group delay is designed to depend only on the length difference of the straight 2-µm-wide ridge waveguides to reduce the delay error, the random width deviation and thickness variation of the waveguides lead to inevitable delay errors. Since the delay errors are related to the length of the waveguides in the delay line, we can reduce the delay errors by using more compact design. For example, the transitions between the channel waveguides and the ridge waveguides can be removed, and a wide Euler ridge bending waveguides can be adopted to connect the ridge delay waveguides to reduce the waveguide length, and also the transition and the bending losses. In addition, by improving the ERs of the MZI switches, we can remove the VOAs to further reduce the insertion loss and the power consumption. Active devices, including on-chip modulators and photodetectors, can be integrated with our device to realize a fully integrated OTTDL [3].
5. Conclusion
We have experimentally demonstrated a high-performance continuously tunable OTTDL comprising a 7-bit switch-based OTTDL and an SBCT-OTTDL on the SOI platform. The entire OTTDL exhibits a large delay tuning range of 0∼1020.16 ps, a small delay error of -1.27 ∼ 1.75 ps, and a small delay fluctuation of below 2.69 ps over the frequency range from 2 to 25 GHz. The causes of the delay fluctuation and its influence on beamforming are analyzed. Our OTTDL has a low unit delay loss of about 3.8 dB/ns. A simplified non-invasive calibration method, which can be readily extended to OTTDLs with more stages, was proposed and utilized to fast calibrate our OTTDL. The power consumption of the delay line is below 630.6 mW, which can be further reduced by removing VOAs from the chip provided that the ERs of the MZI switches exceed 32 dB. The successful demonstration of our device shows great promise for various broadband optical signal processing applications, including microwave photonic beamforming.
Funding
National Natural Science Foundation of China (62075128, 62090052, 62135010); National Key Research and Development Program of China (2018YFB2201702).
Acknowledgments
The authors thank Advanced Micro Foundry (AMF) for chip fabrication.
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.
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