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Abstract
Microwave frequency combs (MFCs) have important applications in communication and sensing owing to their characteristics of large number of comb lines, wide frequency range, and high precision of comb spacing. In many applications, MFCs are required to emit signals with tunable center frequency and variable comb spacing to accommodate different operating frequency bands and accuracies. Here, we demonstrate a tunable MFC by injecting a low-frequency electrical signal into a tunable optoelectronic oscillator (OEO). Tuning of MFC’s center frequency and comb spacing are realized, allowing a frequency tuning range from 1 to 22 GHz and 50 comb lines within a 5 MHz bandwidth obtained in the MFC generator. In addition, the introduction of the silicon nitride micro-disk resonator (Si3N4-MDR) in the system paves the way for the integration of MFC generator.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Optical frequency combs (OFCs) have already got extensive use in atomic clocks, optical communications and other fields [1–2]. Similarly, Microwave frequency combs (MFCs) can provide multiple microwave signals with equally frequency spacing within a certain bandwidth, which plays an essential role in Doppler radar and high-precision sensing, etc. [3–4]. In traditional electrical systems, MFCs are generated based on nonlinear effects of electronic devices [5–6]. However, the frequency tunability, high-frequency (HF) and wide bandwidth are limited by electronic bottlenecks. Currently, MFCs based on optical schemes have attracted increasing attention to break the electronic bottlenecks. In Ref. [7], MFC was generated based on the nonlinear effect of semiconductor laser under the condition of negative photoelectric feedback, 9 comb lines were achieved within 3 GHz bandwidth. In Ref. [8], MFC was achieved by optical pulse injection locking of a master-slave laser (MSL) system. Comb spacings of 900 MHz and 1.2 GHz were obtained within 20 GHz bandwidth by pulse injection at different frequencies. However, the above-mentioned MFCs based on the nonlinear effects of the lasers typically have a relatively large frequency spacing among the comb lines, resulting in a small number of comb lines within a certain bandwidth. This is mainly due to the short cavity length and large mode spacing of the laser. In order to obtain more comb lines and smaller frequency spacing, OEO with narrower longitudinal mode spacing is introduced to generate MFC. In OEO, the oscillation modes are initially independent oscillations, thus there is no definite phase relationship among them. Due to the gain competition between the oscillation modes, a single-frequency microwave signal can be finally generated. In the actively mode-locked laser, mode locking is achieved with a modulator [9], which modulates the resonator losses in exact synchronism with the resonator round-trips. Likewise, microwave mode-locking means that in an OEO cavity, the fixed phase relationship is achieved between its longitudinal modes. In Ref. [10], active mode locking (AML) technology based on the low-frequency signal source has been introduced into OEO to realize phase locking among the modes, thus breaking the mode competition and then MFC with multi-frequency oscillations were obtained. In OEO, the introduction of long fiber loops makes it possible to generate high-quality, low phase noise radio frequency (RF) signals. Meanwhile, with increasing fiber loop length in OEO’s cavity, the longitudinal mode spacing decreases, which is beneficial to generate more comb lines within a certain bandwidth. In Ref. [10], more than 200 comb lines were obtained within 4 GHz bandwidth, and tunable comb spacing was achieved by introducing the active mode locking (AML) signals with different frequencies. Furthermore, the MFC generation schemes based on actively mode-locked OEO (AML-OEO) were reported in Ref. [11–13]. Among them, different injection methods of mode locking signals, including using electric coupler, modulator bias, and cascaded modulator injection were proposed and analyzed. Then, a theoretical model of the AML-OEO based on the amplitude modulation was presented [14]. And polarization multiplexing was introduced into double loop to suppress the super-mode noise in the generation process of MFC based on AML-OEO [15]. In the above schemes [10–15], electronic filters were employed and the center frequencies of the MFCs were fixed. As far as we known, MFCs with frequency tunability has not been reported yet. It is known that microwave photonic filter (MPF) can be tuned over a very wide frequency range, which can overcome the shortcomings in previously reported schemes. In Ref. [16–17], by combing the electro-optic effect of lithium tantalate (LiTaO3) and the whispering gallery mode resonator (WGMR) with high quality factor, various tunable single-frequency OEOs were realized. However, tunable multi-frequency MFC based on the tunable AML-OEO has not yet been reported.
In this work, the frequency-tunable MPF based on a Si3N4 micro-disk resonator (MDR) was introduced into the AML-OEO to generate MFCs with tunable center frequencies. By using cascaded modulation and low frequency injection, this scheme locks the cavity modes of the OEO into a fixed phase relationship, which supports the MFC generating. Experiment results show that continuous center frequency tuning range of 1∼22 GHz can be achieved by both the optical carrier wavelength tuning and thermal tuning of the MDR. Moreover, The OEOs with different loop lengths of 34 m, 234 m, 534 m and 1034 m were adopted to explore the number and frequency spacing of comb lines of the generated MFCs. In addition, by adjusting the frequency of the injected signal, mode locking at fundamental frequency and higher harmonics were achieved, where MFCs with different comb spacings can be achieved. As a proof of concept, when OEO’s loop length is 2034 m, mode locking of the 1st, 3rd, and 6th harmonics were realized and MFCs with multiple frequency spacing were obtained.
2. Principle
The scheme of the proposed tunable MFC generator using a Si3N4-MDR-based OEO is shown in Fig. 1. The laser emitted by the tunable laser source (TLS) passes through the Mach-Zehnder modulator (MZM) driven by a low frequency signal, then serve as an optical carrier with periodic power variations, which is then injected into the following OEO loop. At any time point, the variable optical carrier can be regarded as an optical carrier with constant power, which is then injected into the phase modulator (PM) and optical double sideband (ODSB) with π phase difference between the two optical sidebands is obtained at Location C. One optical sideband of the ODSB signal is filtered by the MDR notch filter while the other optical sideband is unaffected, then the two optical sidebands and the optical carrier are amplified by the erbium-doped fiber amplifier (EDFA) and beaten at the photodetector (PD) to complete the well-known phase-intensity conversion and generate the RF signal with frequency fRF. In a word, the TLS, PM, tunable MDR and PD jointly form a frequency-tunable band-pass MPF, whose center frequency fRF is determined by the difference between the center frequency of the MDR notch filter (fMDR) and the laser frequency (fTLS). Then the RF signal is amplified by the two-stage cascaded electric amplifiers and divided into two paths at the electric coupler. One of the signal paths is fed into the PM to form a closed OEO loop, and the other is input into electrical spectrum analyzer (ESA) for detecting. In addition, the polarization controllers PC1, PC2 and PC3 are introduced to adjust the laser’s polarization states to maximize the transmissions of the MZM, PM and MDR. The electric attenuator (ATT) is applied to control the link gain and protect the electrical amplifiers (Amp1 and Amp2). The AML module is composed of the arbitrary waveform generator (AWG) and the MZM as shown in the dashed box in Fig. 1. A sinusoidal signal (fAWG) emitted from the AWG is applied on the quadrature biased MZM and then the modulated optical carrier is entered into the OEO loop to periodically regulating the loss in the OEO cavity. When the regulation frequency (fAWG) is an integer multiple N of the OEO’s longitudinal mode spacing (fFSR), active mode locking can be achieved [10,14]:
Fig. 1. Scheme of the proposed tunable microwave frequency comb generation using a Si3N4-MDR-based OEO. TLS: tunable laser source, PC: polarization controller, AWG: arbitrary waveform generator, MZM: Mach-Zehnder modulator, PM: phase modulator, MDR: micro-disk resonator, SMF: single mode fiber, EDFA: Erbium Doped Fiber Amplifier, PD: photodetector, Amp: amplifier, ATT: attenuator, EC: electronic coupler, ESA: electronic spectrum analyzer.
3. Experimental results and discussion
The experiment setup was constructed as shown Fig. 1 to generate the tunable MFC. A tunable laser (CoBriteMX) was sent into the MDR notch filter after the MZM (Eospace, DC∼10 GHz) and the PM (Eospace, DC∼20 GHz). By properly adjusting the polarization states of PC1, PC2 and PC3 (Thorlabs, 3-Paddle), maximum outputs from the MZM, the PM and the MDR were achieved, respectively. The PD (Finisar, XPDV3120R) with responsivity of 0.6 A/W and 3 dB bandwidth of 70 GHz was used to convert the modulated optical carrier to RF signal. The electronic variable attenuator (RBS-69-26.5-7) was used to control the loop gain and protect the components. The gains of two cascaded amplifiers (MWLA-1966, 20 kHz∼20 GHz) are both 30 dB. The 3dB EC (RS2W04260-S, 0.4∼ 26.5 GHz) was used to divide the amplified RF signal into two paths, one was injected into the PM to close the OEO loop, and the other was sent to the ESA (Keysight, N9040B) for testing. The silicon nitride MDR with radius of 100 µm and coupling gap of 1.05 µm was fabricated by TriPleX technology, as shown in Fig. 2(a) and Fig. 2(b) [18]. By using the lightwave measurement system (Agilent 8164A, resolution∼1pm), the transmission spectrum of the MDR notch filter was measured and shown in Fig. 2(c). The insertion loss of the MDR chip is about 5 dB, and the notch dip with maximum extinction ratio (ER) of about 18 dB in the black dot box was chosen to achieve the PM-IM conversion process. Since the MPF’s frequency is determined by the frequency difference between the optical carrier and the notch frequency of the MDR, two kinds of methods were used to achieve MPF’s frequency tuning, then the frequency tuning of the proposed MFC. One method of frequency tuning is adjusting the optical carrier’s wavelength, which is set at the red side of the chosen notch wavelength as the blue arrows in Fig. 2(c). The other method is thermally tuning the MDR to achieve the frequency tuning, the optical carrier wavelength is fixed at the blue side of the selected notch wavelength, as shown the green arrows in Fig. 2(c). The optical response of dip in the black box of the MDR is measured by the optical vector network analysis (OVNA) method based on optical single-sideband (OSSB) modulation. The measured linewidth of the MDR is about 300 MHz, and the corresponding Q value can reach 6.5×105 as shown in Fig. 2(c). The RF response of the MPF was measured by using the vector network analyzer (VNA, Keysight N5242A) at the gain probing point shown in Fig. 1. The measured S21 is shown in Fig. 2(d), where the center frequency of the MPF is about 10.3 GHz, the 3dB bandwidth is about 300 MHz, and the out-of-band rejection ratio reaches 19 dB. Additionally, an EDFA (NAKU, EDFA-BA-GF-15) was inserted into the microwave photonic link to compensate the link losses.
Fig. 2. (a) Full view of the packaged Si3N4 chip (b) Detailed view of the Si3N4 MDR. (c) Transmission spectrum of the Si3N4-MDR. (d) The RF response of the MPF based on the Si3N4-MDR.
After closing the OEO loop, we shut off the AWG (Agilent, 33512B) to make the OEO operating in free oscillation mode and the measured RF spectrum is shown in Fig. 3(a). There is a main oscillation mode at the center frequency of about 10.3 GHz, which is prone to mode hopping due to mode competition. Meanwhile, the mode spacing of OEO is about 5.89 MHz, which is consistent with that obtained using Eq. (1). Then the AWG was turned on and output a 5.89 MHz sinusoidal signal, which was applied on the MZM to achieve the AML-OEO. By properly adjusting the signal power of the AWG, stable MFC signal was obtained as shown in Fig. 3(b), where 11 comb lines were generated within ±10 dB power variations. Furthermore, different OEO loop lengths of 234 m, 534 m and 1034 m have also been verified by experiments and 21, 35, and 41 comb lines within ±10 dB power variations were obtained as shown in Fig. 3(d), Fig. 3(f) and Fig. 3(h), respectively. At the PD (Optilab, 0∼40 GHz), the OSSB signals convert into the RF signal. The recovered RF signal was amplified through two cascaded electronic amplifiers (MWLA-1966, 20 kHz∼20 GHz), and an electronic variable attenuator (RBS-69-26.5-7) was introduced to protect the link components. Finally, the amplified RF signal passed through a 3 dB electric coupler (RS2W04260-S, 0.4∼ 26.5 GHz) and divided into two parts, where one part was sent back to the PM to close the OEO loop, and the other part was fed into the ESA (Keysight, N9040B) for measuring the RF spectrum and the phase noise.
Fig. 3. RF spectra of the output signals with different loop lengths (a) (c) (e) (g) under free oscillations, (b) (d) (f) (h) under fundamental mode locking.
Besides, by tuning the frequency of the AML signal from the AWG to integer multiple of the mode spacing of the OEO loop, harmonic mode locking of the OEO was also achieved and experimentally verified. At this time, only those oscillation modes with integer multiple of N can be activated while the other modes will be suppressed. In the experiment, a single mode fiber with length 2034 m was used in the OEO loop, which induces a mode spacing of 100.5 kHz. Figure 4(b)–(d) show the RF spectra of the generated MFC signals, which were obtained by injecting the AML signals of 100.5 kHz, 302.5 kHz, and 600.1 kHz, respectively. When the fundamental frequency is locked, there are 50 comb lines with low power fluctuations in 5 MHz bandwidth as shown in Fig. 4(b). When considering the 3rd and 6th harmonic mode locking cases, only 5 comb lines within ±10 dB power variations were generated because of the super-mode noise and mode competition.
Fig. 4. RF spectra of the output signals with OEO’s loop length of about 2 km. (a) under free oscillation. (b) under fundamental mode locking. (c) under 3rd harmonic mode locking. (d) under 6th harmonic mode locking.
Finally, the frequency tunability of the generated MFC signals were achieved by adjusting the optical carrier wavelength and thermal tuning the MDR notch filter. The center frequency of the MFC can be tuned in the range of 2∼22 GHz through carrier wavelength tuning, as shown in Fig. 5.
As an alternative, by thermal tuning the MDR notch filter, MFC with frequency tuning range of 1∼22 GHz was also achieved (Fig. 6(a)). Figure 6(c)–(e) show the spectra responses of the MFC signals at the center frequencies of 1 GHz, 11 GHz and 21.1 GHz, respectively. Figure 6(b) shows that the driving power consumption of the MDR linearly increases when the MFC’s frequency increases, and the tuning efficiency is about 0.8 GHz/mW. The reason for less comb lines in the high and low frequency bands in Fig. 5 and Fig. 6(a) may attribute to the variation of the PM’s half-wave voltages, the un-flat gain of the electric amplifiers and different insertion losses of the RF devices at different frequencies.
Fig. 6. (a) Frequency tunability of the MFC based on thermal tuning the Si3N4 MDR, (b) Power consumption for thermal tuning of Si3N4 MDR (Resistance = 130 Ω), (c)-(e) The spectra of the MFC signals at the center frequencies of 1 GHz, 11 GHz and 21.1 GHz
The center frequency tuning speed of the proposed MFCs are determined by the wavelength tuning speed of the TLS, the thermo-optic tuning speed of the MDR, and the OEO’s oscillation stabilization time. Among them, the OEO oscillation stabilization time of about 10 µs exists in both tuning methods. For the optical carrier tuning method, the tuning speed of the proposed MFC is determined by the laser tuning speed, which is about 12 s [19] for the used commercial laser. While for the optical filter tuning method, the tuning speed of the proposed MFC is determined by the thermo-optic tuning speed of the MDR, which is about 1 ms limited by the 8 µm thick buffer layer separating the micro-heater from the MDR. Nevertheless, the tuning speed of the proposed MFC can be improved by adopting faster TLS or tunable MDR with thinner buffer layer under the condition that the tuning time is less than 10 µs, which is the OEO’s oscillation stabilization time.
Another advantage of OEO-based MFC generators is that the OEO’s long cavity delay is conducive to generate high-quality microwave signals with low-phase noises. In the experiment, when the fiber length is increased to 2 km, the measured phase noise is about -80 dBc/Hz at 10 kHz frequency offset from 10.3 GHz carrier frequency under free oscillation (Fig. 7(a)). As a comparison, the phase noise obtained by using an electrical filter instead of a microwave photonic filter under the same conditions is about -130 dBc/Hz at 10 kHz offset frequency under free oscillation. The RF responses of the electrical filter with the microwave photonic filter is shown in Fig. 7(b). As can be seen, the bandwidth of the electric filter (MPF) is about 100 MHz and the out-of-band rejection (OBR) ratio is about 80 dB. Furthermore, the spectral shape is symmetric and good. However, it’s filtering frequency is fixed, which cannot support the frequency tuning of the proposed AMO-OEO. However, for the used MPF based on the MDR, the measured bandwidth and OBR are 300 MHz and 19 dB, respectively. And the spectral shape is asymmetric. So, the bandwidth, OBR and spectral shape of the used MPF are not as good as the electrical filter, which cause the deterioration of the phase noise. However, the MPF’s frequency can be widely tuned to achieve frequency tunable AMO-OEO, which cannot be realized by the electric filter. By comparing the electric filter and the MPF, the deterioration of phase noise is mainly blamed on the OEO’s cavity mode competitions within the MPF’s passband, which can be improved by using feedback control and optimizing the MPF’s shape factor [20].
Fig. 7. (a) Comparison of OEO’s phase noise based on electrical filter and MPF under free oscillation (loop length =2 km), (b) Comparison of electrical filter and microwave photonic filter
For comparison between the free oscillation and mode-locking schemes, we additionally measured the phase noises of the proposed AML-OEO at different delay lengths and different carrier frequencies as shown in Fig. 8. The phase noise of -60 dBc/Hz, -90 dBc/Hz and -110 dBc /Hz at 10 kHz frequency offset from 10 GHz carrier frequency were obtained with loop lengths of 34 m, 1034 m and 2034 m, respectively. As the loop delay increases, the phase noise of AML-OEO decreases gradually. In addition, when loop length is 2034 m, the phase noises of -110 dBc/Hz, -110 dBc/Hz and -90 dBc /Hz at 10 kHz frequency offset from 1 GHz, 10 GHz and 20 GHz carrier frequencies were obtained, respectively. The increasing phase noise at 20 GHz carrier frequency is blamed on the deterioration of the RF device performances and the increasing noise floor of the ESA at high frequencies.
Fig. 8. (a) AML-OEO phase noise spectrum with different lengths, (b) AML-OEO phase noise at different frequency points of 2 km fiber
To further characterize the short-term stability of the proposed AML-OEO, we measured the frequency drift of a mode within one minute as shown in Fig. 9(a). The results show that the frequency drift of one mode is less than 20 kHz during one minute and no mode hopping is observed. The long-term stability of AML-OEO is related to the drift of MPF, and we measured the MPF jitter within one hour as shown in Fig. 9(b). The results show that the frequency drift of the MPF is about ±250 MHz within one hour, which is close to the wavelength stability of the TLS. And the measured power jitter is less than ±0.4 dB. So, the jitter of the MPF mainly comes from the wavelength and power instabilities of the TLS. In addition, the wavelength shifting of the MDR due to the temperature variation will also affect the frequency stability of the proposed AML-OEO. In future, following methods can be adopt to improve the stability of the proposed AML-OEO. The resonant wavelength of the MDR can be stabilized by using a feedback control loop based on a threshold detection method. And the wavelength of the TLS can be stabilized by locking the laser to an optical resonator by Pound-Drever-Hall (PDH) technology [21].
Fig. 9. (a) Short-term stability of the AML-OEO within one minute, (b) RF response stability of the MPF within one hour.
4. Conclusion
A tunable MFC generator using a Si3N4-MDR-based AML-OEO is proposed. The center frequency tunability of the MFC is achieved by changing the oscillation frequency of the tunable OEO. The numbers of comb lines and the comb spacing were investigated by changing the loop delay of the OEO. In addition, the higher-order harmonic mode locking and the phase noise of the generating signals of the AML-OEO were also investigated. The experiment results show that the frequency tuning of the MFC in the range of 1∼22 GHz can be achieved and 50 comb lines with low power fluctuations in 5 MHz bandwidth can be obtained.
Funding
National Key Research and Development Program of China (2018YFB2201800); National Natural Science Foundation of China (62171118); National Natural Science Foundation of China (62105061).
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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