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Abstract
The significant frequency drift of integrated microwave photonic filters (IMPFs) is caused by relatively independent frequency fluctuations of the optical carrier and the photonic integrated filter, which imposes a rigid limitation on the practical application. In this paper, a novel method is proposed for suppressing the frequency drift of IMPFs. The scheme is implemented by utilizing an on-chip high-Q microring resonator as a frequency monitoring unit to track the instantaneous frequency drifts caused by the optical carrier drift and the temperature fluctuations of the photonic integrated chip. And the same frequency tuning is simultaneously applied on the photonic integrated filter to suppress the frequency drift of IMPFs based on the differential scheme. As a proof of concept, the proposed IMPF scheme is demonstrated on the Si3N4 platform, and the frequency drift is measured to be tens of MHz in one hour. Compared with conventional IMPF schemes, the frequency drift is significantly suppressed by 86.3% without using complex laser frequency stabilization and temperature control systems.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Microwave photonic filters (MPFs) have been attracting significant attention as the potential substitute for traditional radio-frequency (RF) filters, especially for large-range analog signal processing [1,2]. Owning to the abundant processing bandwidth in optical domain and the broadband tunability of optical filters [3], MPF becomes a promising technology in modern wireless communication [4] and broadband radar systems [5,6]. In recent years, the concept of integrated microwave photonic filter (IMPF) is rising up with the vigorous development of the photonic integration technology, and brings obvious improvements on system size, performance reliability and costs [7]. Especially, by leveraging of photonic integrated filters (PIFs) [8], several recent studies have achieved considerable progress in improving integration [9], filter resolution [10,11] and programmable signal processing [12,13]. However, it still needs to be further researched to find an effective solution to suppress the IMPF frequency drift, which is caused by the optical carrier (OC) drift and temperature fluctuations of the photonic integrated chip (PIC). And it is worth noting that this frequency drift is usually large due to the general principle of IMPFs, which relies on upconverting RF signals to optical frequencies and processing them by PIFs in optical regime [7]. On the one hand, the OC frequency is disturbed by many noise sources, such as fluctuations of injection current and temperature. Thus it is challenging to stabilize the laser frequency drift to few MHz level, especially in long term [14]. On the other hand, PIFs are sensitive to environmental perturbations, particularly temperature fluctuations [15]. For example, even for a Si3N4-based PIF with a relatively low temperature shift coefficient of about 16 pm/K [16], the frequency drift can be still up to 200 MHz when the temperature of PIC is stabilized to a resolution of 0.1 K in long term.
Although the implementation of active frequency stabilization schemes, such as wavelength modulation spectroscopy [17,18] and similar Pound-Drever-Hall (PDH) technique [19,20], can make high-resolution stabilization of laser frequency possible, it is still hard to keep good performance when the system is scaled down to the chip level [21–23]. Additionally, utilizing a high-resolution temperature control system to reduce the frequency drift of PIFs will further increase costs and complexity. Therefore, stabilizing the frequencies of the OC and the PIF separately to achieve an IMPF with low frequency drift is difficult to simultaneously satisfy performance, costs and integration, which weakens primary advantages of IMPFs.
In this paper, we propose a novel and universally applicable scheme for suppressing the frequency drift of IMPFs. By utilizing a high-Q microring resonator (MRR) as a frequency monitoring unit (FMU) to track the instantaneous frequency drift caused by the OC and the PIC temperature fluctuations, the PIF is simultaneously tuned to follow this frequency variation. Thus the IMPF frequency drift can be suppressed based on the differential scheme. We demonstrate the proposed IMPF scheme on the Si3N4 platform, and the frequency drift is measured to be tens of MHz in one hour without complex laser frequency stabilization schemes and temperature control systems. Compared with conventional IMPFs, the frequency drift is obviously suppressed by 86.3%. On the basis of our previous work presented in MWP2019, we optimize the theoretical model to further eliminate the mutual crosstalk between two MRRs and experimentally characterize the dynamic performance of the servo-loop and tuning characteristics. Moreover, the causes of residual frequency drifts of the proposed IMPF are analyzed in detail.
2. Principle
The principles of conventional IMPF schemes based on the photonic filter unit (PFU) [7] can be summarized as follows. RF signal is modulated to the OC and the first-order sideband is filtered by a PFU, which can be an optical band pass filter or notch filter. Then, the corresponding filtered sideband is down converted to recover the processed RF signal by coherent detection with the OC. The transmission response of IMPF is basically decided by characteristics of the employed PFU. And the center frequency of IMPF is equal to the frequency spacing between the OC and the PFU. Assuming the initial frequency of the OC and the PFU are fOC and fPFU, respectively, thus the center frequency of IMPF can be expressed as
where ΔfOC(t) and ΔfPFU(t) are instantaneous frequency drifts caused by the OC and temperature fluctuations of the PIC. In this case, the frequency fluctuations of the OC and the PFU are both reflected in the IMPF frequency drift, which hinders the practical application of conventional IMPFs.In the proposed IMPF scheme, a high-Q MRR is employed as a frequency monitoring unit (FMU) on the same PIC. And a real-time frequency tuning (denoted as fT(t)) is applied on the FMU to capture the instantaneous frequency drifts caused by the OC and the PIC. Assume the same frequency tuning fT(t) is also applied on the PFU simultaneously, then the IMPF frequency drift caused by the OC and the PIC can be significantly suppressed together based on the differential scheme. The schematic diagram is illustrated in Fig. 1 and the detailed principle is discussed below.
Fig. 1. Schematic diagram of the proposed IMPF scheme based on the carrier tracking servo-loop (LD, laser diode; EOM, Electro-Optic Modulator; OBPF, optical band pass filter; PFU, photonic filter unit; FMU, frequency monitoring unit; MRR, micro ring resonator; PD, photodetector; BPD, balanced photodetector; LIA, lock-in amplifier; MCU, microcontroller unit). Schematic optical spectra of the proposed IMPF scheme at several key parts are shown, the modulation sidebands are omitted.
Because the FMU and the PFU are adjacent on the PIC, sometimes there exists obvious mutual crosstalk between them considering that the tuning method is based on the thermo-optic effect in our experiment. Thus the total frequency tunings applied on the FMU and the PFU in consideration of mutual crosstalk should be expressed as
By keeping the high-Q MRR resonance locked to the OC automatically, the center frequency of the FMU is actively tuned to achieve carrier tracking in real time:
where fFMU is the initial center frequency of the FMU and ΔfFMU(t) is its instantaneous frequency drift caused by temperature fluctuations of the PIC. fFMU(t) is the needed frequency tuning applied on the FMU for carrier tracking and contains the information about ΔfOC(t) and ΔfFMU(t). Because the same frequency tuning is applied on the PFU simultaneously, the Eq. (1) can be rewritten by substituting Eqs. (2) and (3) as3. Experimental setup and calibration
Figure 2 shows the experimental structure of the proposed IMPF scheme. A continuous-wave light as the OC is equally split into two branches by employing a 50:50 optical splitter. The OC in the lower branch is modulated by the RF signal at a phase modulator and then sent into a Si3N4 PIC. The main functional components on the PIC are cascaded MRRs coupled to a bus waveguide. One MRR serves as the PFU while the other MRR serves as the high-Q FMU for carrier tracking. Finally, the output of the PFU and the OC in the upper branch are combined through a 50:50 optical coupler, then a balanced photodetector (BPD) is applied to recover the filtered RF signal.
Fig. 2. Experimental setup of the proposed IMPF scheme (LD, laser diode; PM, phase modulator; PC, polarization controller; PFU, photonic filter unit; FMU, frequency monitoring unit; BPD, balanced photodetector; PD, photodetector; LIA, lock-in amplifier; MCU, microcontroller unit; ADC, analog-to-digital converter; DAC, digital-to-analog converter; EVNA, electric vector network analyzer; TEC, thermoelectric cooler).
Compared to conventional IMPF schemes, the proposed scheme includes a MRR-based carrier tracking servo-loop to track the instantaneous frequency drift caused by the OC and temperature fluctuations of the PIC, as shown in Fig. 1 and Fig. 2. Carrier tracking is an important technique to achieve the proposed IMPF scheme. The employed approach for tracking the instantaneous frequency drift of the OC refers to the idea of widely-used active frequency stabilization schemes [19,20]. However, different from conventional active frequency stabilization techniques, which lock the laser frequency to a desired resonance of an optical bulk etalon, an on-chip high-Q MRR is adopted as the FMU in our proposed scheme and actively tuned to achieve carrier tracking. Moreover, compared with those methods based on passive power monitoring, the employed approach is help to weaken the influence of the amplitude noise of the OC.
Initially, the MRR resonance is slightly wavelength modulated by a predetermined single frequency with a modulation depth less than the 3-dB bandwidth. This can be implemented by applying a square-wave modulated frequency tuning on the MRR. Thus when the MRR resonance is basically aligned with the OC, the output optical intensity filtered by the MRR is also modulated. Then the photocurrent with the same modulation frequency is generated after photodetection and fed into a lock-in amplifier (LIA) module to detect the weak signal. The demodulated signal is further transformed into error signal in the microcontroller unit (MCU), which reflects the needed “correction” tuning for the MRR resonance to keep tracking the OC. In this way, MCU can automatically lock the FMU to the OC by applying well-established feedback control algorithms [25] and thus a closed servo-loop is formed.
Considering that the carrier tracking technique and the feedback control depend on the precise frequency tuning of the FMU and the PFU, we make a series of precise measurements on the fabricated PIC to characterize the frequency tuning for the necessary calibration in the control algorithm.
The PIC employed in our experiment consists of cascaded MRRs with the same design parameters, one is used as the PFU (denoted as Ring1) while the other one serves as the FMU (denoted as Ring2), respectively. The device is fabricated on a Si3N4 PIC utilizing TriPleX double-strip Si3N4 waveguide platform, which features a low loss about 0.1 dB/cm [26]. And Cr-Au metal heaters are fabricated to achieve frequency tuning utilizing thermo-optic effect. The MRR radius is 125 um, the coupling gap of MRR is designed to be 1.5 um, and the spacing between centers of two MRRs is designed to be 750 um, as shown in Fig. 3(a). The micrograph of the fabricated device is shown in Fig. 3(b). Next, we obtain transmission spectra of MRRs using optical vector analyzer (OVA) with a high resolution of 0.16 pm, as shown in Fig. 3(c). By applying Lorentz fitting to spectra of MRRs, we observe that resonances of MRRs are 0.826 GHz (Ring1) and 0.931 GHz (Ring2) wide, corresponding to Q-values of 2.35e5 and 2.08e5.
Fig. 3. (a) Schematic representation of the PIC consisting of cascaded MRRs (MRR radius = 125 um, MRR coupling gap = 1.5 um, the spacing between two MRR centers = 750 um). Inset is the cross section of the waveguide. (b) The micrograph of the fabricated PIC. (c) Transmission spectra of two MRRs.
We make a series of precise measurements on tuning MRRs to characterize the thermo-optic effect quantitatively. First, we measure resonance frequency shifts of two MRRs under different temperatures controlled by a thermoelectric cooler (TEC), as shown in Fig. 4(a). By applying linear fitting on experimental results, we observe a significant linear relationship between the resonance frequency shift and the temperature, with a coefficient of 1.874 ± 0.006 GHz/K for Ring1 and 1.884 ± 0.010 GHz/K for Ring2. Hence, their frequency drifts caused by temperature fluctuations of the PIC are basically the same. Next, by tuning the voltage applied on the micro heater with or without the TEC, we continue to measure the resonance frequency shift and apply linear fitting. As is shown in Fig. 4(b), the heating power (the resistance of designed micro heater is measured about 140 Ω) of the micro heater also holds a good linear relationship with the frequency tuning. The tuning factor of Ring1 is estimated to achieve an unprecedented precision of 0.3132 ± 0.002 GHz/mW with the TEC or 0.3196 ± 0.004 GHz/mW without the TEC, while the tuning factor of Ring2 is estimated to be 0.3152 ± 0.003 GHz/mW with the TEC or 0.3226 ± 0.004 GHz/mW without the TEC. Therefore, adjusting the heating power applied on the micro heater is an applicable solution to precisely tune the MRR resonance based on the thermo-optic effect. In our following experiment, we use a digital-to-analog converter (DAC) with a resolution of 0.5 mV (0.0357 mW under a bias voltage of 5 V) to control the heating voltage (power), corresponding to a frequency tuning resolution of 11.2 MHz, which is relatively acceptable.
Fig. 4. (a) Normalized frequency shifts of two MRRs under different temperatures. (b) Normalized frequency shifts of two MRRs under different heating power with/without TEC.
4. Experimental results and discussion
4.1 Carrier tracking results
Figure 2 includes the experimental representation of the carrier tracking feedback loop utilizing the fabricated Si3N4 PIC. The system consists of a Si3N4 PIC, a PD, a LIA, two 16-bit DACs, a 16-bit analog-to-digital converter (ADC) (the resolution is 0.15 mV) and a MCU. The voltage generated by DACs is slightly modulated by a single frequency in few 100 Hz regime (V(t) = V0 + Vm · cos(2πft), f∼500Hz, V0 > Vm), and the modulation depth of the MRR resonance is fixed about 500 MHz (the modulation voltage Vm corresponds to about 20 mV), corresponding to about half of the MRR 3-dB bandwidth. The generated voltage is applied on the FMU and the PFU simultaneously to modulate the MRR resonance of the FMU. Then the modulated photocurrent generated by the PD is transferred into the LIA for detection combined with the reference signal which has the same modulation frequency. Next, the demodulated signal is acquired by the ADC and sent into the MCU for processing. The MCU then automatically adjusts the DC voltage V0 (the modulation depth should be fixed by slightly changing the modulation amplitude Vm based on V0) to achieve carrier tracking based on the error signal, and thus the FMU will keep locked to the OC in real time. An improved Proportion-Integral-Differential (PID) algorithm is employed in our feedback control system to realize the accurate and fast tracking.
The simulated error signal is plotted in Fig. 5(a) as a function of relative frequency offset between the OC and the FMU resonance. We can observe that the normalized error signal reaches the minimum value as the frequency spacing between the OC and the FMU resonance is 275 MHz, about half of the designed modulation depth of 500MHz in simulation. When the OC deviates from this offset locking point due to laser frequency drift, the error signal will increase rapidly. Besides, with the increase of the Q-value of FMU resonance, the error signal becomes more sensitive to the frequency drift of the OC, which means higher tracking accuracy. Therefore, by keeping the error signal always at its minimum value using feedback algorithms, we can lock the FMU resonance to the OC with fixed offset in real time. Based on section 2.1, the IMPF frequency drift can still be suppressed despite of the offset. And a high-Q MRR is necessary to be utilized as the FMU to improve carrier tracking performance.
Fig. 5. (a) Normalized error signal varies with the relative frequency offset between the FMU resonance and the OC under different FMU bandwidths (left). FMU spectrum responses (with different 3-dB bandwidths) employed in simulation are shown (right). (b) Instantaneous DC voltage V0 and normalized error signal vary with monitoring time (Stage 1: 0∼7 min; Stage 2: 7∼24 min; Stage 3: 24∼39 min).
To characterize the performance of this carrier tracking system, we monitor the error signal in the MCU when switching on or off the feedback loop over a period of time, as shown in Fig. 5(b). The whole experiment is composed of three stages. Initially (denoted as t = 0 min), the feedback loop is switched on so that the voltage applied on the micro heater can be adjusted automatically and the MRR resonance of the FMU can track the OC in real time. Next, the servo-loop is cut off at t = 7 min and the MRR resonance stops tracking the OC. Finally, the feedback loop is switched on again at t = 24 min and lasts 15 minutes. The error signal and the DC voltage applied on the micro heater are plotted as a function of time in Fig. 5(b). As can be seen, in the first and third stage, the DC voltage is adjusted instantaneously. The minimal error signal shows that the FMU keeps locked to the OC at the predetermined locking point. This is in contrast to the second stage, where the feedback loop is cut off and the FMU does not follow the OC frequency drift. In that case, the error signal increases significantly, implying that the OC detunes from the locking point. The algorithm supports automatic searching for the OC after restarting the feedback control loop. Once the OC is captured, the MRR resonance will keep locked to it. Therefore, we can conclude that the employed carrier tracking system based on the on-chip high-Q MRR can realize the carrier tracking in a good manner.
4.2 Measurement of the frequency drift of the proposed IMPF scheme
In experiment, we use a vector network analyzer (VNA, Keysight PNA-X Network Analyzer N5242A) to measure the IMPF transmission response, and the spectrum resolution of VNA is 1.32 MHz. The transmission response spectrum of IMPF is shown in Fig. 6(a), we can observe that the measured response spectrum agrees well with the Ring1 transmission response serving as the PFU as shown in Fig. 3(c). Besides, the center frequency is tuned from 3 GHz to 18 GHz by adjusting the initial frequency spacing between the PFU and the FMU, and the 3-dB bandwidth is 0.828 GHz. Next, in order to quantitatively describe the suppression effect on the IMPF frequency drift of the proposed scheme, we record the IMPF center frequency for one hour from the transmission response spectrum under four different conditions. And the normalized frequency drifts of IMPF are plotted as a function of the monitoring time. First, the carrier tracking system and the TEC are both closed, and the whole IMPF system is free running like a conventional IMPF in that case. As shown in Fig. 6(b), the original frequency drift is measured to be about 660 MHz for an hour, which is caused by the OC and temperature fluctuations of the PIC together. Next, we use a high-resolution TEC (the resolution is 0.01 K) to stabilize the temperature of the PIC while the carrier tracking system keeps off. Under this condition, the frequency drift can be suppressed to 287.5 MHz, because the temperature fluctuations of the FMU is basically stabilized by the TEC and most of the frequency drift comes from the instability of the OC. This case can be thought of as a conventional IMPF with an accurate temperature control on the PIC. As a contrast, we repeat the experiment under the same conditions but using the proposed carrier tracking technique to suppress the frequency drift. Measured frequency drifts are shown in Fig. 6(c), and we can observe that the frequency drifts can be reduced accordingly to about 73.7 MHz (with TEC on) and 90.6 MHz (with TEC off). Compared these experimental results shown in Figs. 6(b) and 6(c), we can conclude that the proposed scheme can significantly suppress frequency drifts caused by the OC. Besides, as shown in Fig. 6(c), even the temperature of the PIC is not actively stabilized by the TEC, the proposed IMPF scheme can still maintain a relatively stable center frequency. Therefore, the ability to immune the influence of PIC temperature change on the center frequency of the proposed IMPF scheme can also be proved.
Fig. 6. (a) Measured transmission response of IMPF (the center frequency is tuned from 3 GHz to 18 GHz and the 3-dB bandwidth is 0.828 GHz). (b) Normalized IMPF frequency drift varies with monitoring time when the carrier tracking technique is not used (with TEC on or off). (c) Normalized IMPF frequency drift varies with monitoring time when the carrier tracking technique is used (with TEC on or off).
The residual frequency drifts of the proposed IMPF scheme observed in experiment can be classified into three categories as follows. First, the limited resolution of employed electronic components, especially DACs, restricts the frequency tuning accuracy of the FMU and the PFU during carrier tracking and feedback tuning, then causes errors in suppressing the frequency drifts. In our experiment, a resolution of 0.5 mV for DAC corresponds to a tuning resolution of about 11.2 MHz. This can be improved by employing higher-resolution DACs or increasing the heater resistance. Second, the carrier tracking technique can only capture laser frequency drift with a relatively slow speed, which is limited by the thermo-optic modulation frequency (500 Hz). Therefore, those faster short-term laser frequency drifts cannot be tracked in real time and thus the frequency drifts caused by the OC cannot be suppressed completely. From Fig. 6(c), we can observe that the long-term frequency drift is obviously better than the short-term frequency drift. This can be further improved by optimizing the design of micro heaters [27] or employing other tuning methods, such as utilizing piezo-optical effect [28]. Third, due to fabrication errors, the waveguide geometry of the FMU and the PFU cannot be exactly the same (ΔfFMU(t) ≠ ΔfPFU(t)), which means that the frequency drift caused by the PIC temperature change cannot be eliminated completely based on the differential scheme. As is shown in Fig. 4(a), the temperature shift coefficients of two MRRs are slightly different. Thus, the residual relative frequency drift between two MRRs caused by the PIC temperature change is reflected in the frequency drifts of the proposed IMPF scheme.
For the employed Si3N4 platform, the thermal bistability [29] is also a noise source, which means that the light injected into the MRR may be absorbed by the waveguide and causes a local temperature rise. In the steady state (FMU is locked to the OC), because FMU can track the OC instantaneously, the light injected into the waveguide doesn’t have significant changes, which means the compensation error cannot be large. However, due to the different power injected into two MRRs, the wavelength shifts of two MRRs may be different and the center frequency of IMPF (decided by the frequency spacing of two MRRs) will slightly change on the basis of the initial state.
The ultimate precision of carrier tracking technique is mainly decided by the Q-value of MRR utilized as the FMU, as shown in Fig. 5(a). If the Q-value increases, the resolution of carrier tracking can be further improved. Therefore, in the next study, our main work will focus on improving the Q-value of FMU.
5. Conclusion
We propose a novel scheme for suppressing the frequency drift of IMPFs in this paper. By utilizing an on-chip high-Q MRR as the FMU to track the instantaneous frequency drifts caused by the OC and temperature fluctuations of the PIC, and tuning PFU to follow this frequency variation, the IMPF frequency drift can be rejected based on the differential scheme. We demonstrate the proposed scheme based on a Si3N4 PIC and quantitatively characterize the suppression effect on the IMPF frequency drift by measuring the transmission response spectrum for one hour. Benefiting from the ability to immune the frequency drifts caused by the OC and the PIC, the proposed IMPF scheme shows a low frequency drift of tens of MHz in one hour without using complex laser frequency stabilization and temperature control systems. Compared with conventional IMPFs, the frequency drift can be significantly suppressed by 86.3%. The simple but effective solution to overcome the IMPF frequency drift will make IMPF more applicable and robust in practical scenarios.
Funding
Ministry of Science and Technology of the People's Republic of China (2018YFB2201802); National Natural Science Foundation of China (61771285).
Acknowledgments
The authors thank LioniX International B. V. for offering the TriPleX waveguide technique.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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