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Abstract
A rational number harmonic mode-locked dual-loop optoelectronic oscillator (RHML-DL-OEO) is proposed and experimentally demonstrated. In the proposed system, an external radio frequency (RF) signal and a feedback oscillating microwave signal drive two arms of a dual-drive Mach–Zehnder modulator (DMZM). Mode locking is realized by frequency detuning. The larger effective free spectrum range (FSR) and higher side-mode suppression result from the Vernier effect effectively suppress supermode noise and intermodulation distortions (IMDs). Experimental results demonstrate that the microwave frequency comb (MFC) signals with repetition frequencies of 901.8 kHz, 2.3046 MHz and 5.3106 MHz are generated by 9th-, 23rd- and 53rd-order rational number harmonic mode-locking, respectively. Compared with the rational number harmonic mode-locked optoelectronic oscillator based on single-loop structure, the supermode noise suppression ratios of the scheme we propose are improved by 30.5 dB, 27.6 dB and 20.3 dB, respectively. Furthermore, the performance of single sideband (SSB) phase noise is also investigated.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Microwave frequency combs (MFCs) with rich frequency components, wide frequency range and high-precision comb spacing, play an important role in many fields, such as radar, sensing, multi-carrier communications, signal processing and electronic warfare systems [1–4]. Traditionally, mainstream MFC signals are generated by electronic techniques, which inevitably suffer from poor frequency tunability due to the well-known electronic bottlenecks [5,6]. In order to overcome the deficiencies of traditional electrical methods, lots of photonics-assisted MFCs generation technologies have been proposed, which have the advantages of high frequency, wide frequency range, and low phase noise [7–9]. Unfortunately, the MFCs produced by these methods have non-adjustable comb spacing and poor power spectrum flatness. Although it is possible to achieve excellent phase noise performance through external continuous-wave optical injection [10] or feed-forward [11], these skills make the system structure more complicated and the manufacturing cost higher. Therefore, it remains a challenging problem that how to generate MFC signals with tunable comb interval, wide frequency range, small power fluctuations and low phase noise while minimizing the cost and the complexity of the system.
Optoelectronic oscillators (OEOs) are microwave signal sources that convert optical signals to microwave signals and accomplish oscillation of microwave signals in the optoelectronic hybrid ring cavity [12,13]. Over the last decade, OEOs have shown good performance in single radio frequency (RF) signal generation with an ultra-low phase noise in a broad frequency range [14–19]. As an alternative, the active mode-locking OEO (AML-OEO) [20,21] can be implemented to develop MFCs by transferring the active mode-locking technology [22–24] to OEO. AML-OEO opens new avenues for MFC signals generation, benefiting from the external mode-locking module, the comb spacing of the MFCs can be flexibly changed by the frequency of the injection RF signal. Traditionally, MFCs with large comb spacing can be achieved by high harmonic mode locking [21]. Nevertheless, this kind of method requires the injected RF signal with high frequency, leading to place a greater demand on clamping module bandwidth. Recently, a rational harmonic mode locking OEO (RHML-OEO) has been reported, where high harmonic mode locking is accomplished by frequency detuning [25]. It can alleviate the bandwidth requirement of mode-locked modules, however, the supermode noise and intermodulation distortions (IMDs) associated with rational harmonic mode-locking degrade the performance of the MFC signals [26] and is not conducive to its application in the field of multi-carrier communications [27]. Moreover, all of the schemes mentioned above inject an external RF signal by inserting an additional optical intensity modulator or electrical coupler. These methods not only introduce an additional energy loss, but also increase the complexity and cost of the system architecture.
In this paper, we propose a rational number harmonic mode-locked dual-loop optoelectronic oscillator (RHML-DL-OEO) based on a dual-drive Mach-Zehnder modulator (DMZM), and experimentally verify the supermode noise and IMDs suppression capability of the proposed scheme. The DMZM can realize the feedback of the oscillation signal and the injection of the external RF signal at the same time, reducing link power loss caused by the additional optical intensity modulator or RF coupler, improving the energy conversion efficiency and reducing the structural complexity. By setting the external RF signal drive frequency to $N/M$ times the free spectrum range (FSR), where $N$ and $M$ are integers and relatively prime, the OEO can operate in a stable multimode oscillation state and output MFCs with comb spacing of $N$ times the FSR. The larger effective FSR and higher side-mode rejection brought by the dual-loop structure effectively suppress the unwanted weak modes. Consequently, the supermode noise generated by these unwanted modes can be greatly reduced, thus further suppress the IMDs caused by the beat frequency from low-order harmonics of the injected RF signal with supermode noise. In the experiment, the feasibility of the rational number harmonic mode-locking theory was authenticated. The microwave frequency combs with repetition frequencies of 901.8 kHz, 2.3046 MHz and 5.3106 MHz were produced by 9th-, 23rd- and 53rd-order rational number harmonic mode-locking, respectively. Compared with the RHML-OEO based on the single-loop structure, the supermode noise suppression ratios of the proposed approach are improved by 30.5 dB, 27.6 dB and 20.3 dB, respectively. In addition, a performance comparison of single sideband (SSB) phase noise is performed.
2. Principle
Figure 1 shows the schematic of the proposed RHML-DL-OEO. A continuous-wave (CW) light from a laser diode (LD) enters an electro-optical dual-drive Mach-Zehnder modulator (DMZM), which is biased at the quadrature point. In the DMZM, the CW light is intensity modulated by the feedback oscillating microwave signal centered at ${f_0}$. After passing through a polarization-beam splitter (PBS), the intensity-modulated optical signal is split into two branches whose power ratio is controlled by a polarization controller (PC). Then, the optical signal in each branch propagates through two different lengths of single-mode fibers (SMFs), respectively. The polarization-beam combiner (PBC) is employed to combine the two optical signals, and the combined optical signal is sent into the photodetector (PD) to accomplish photoelectric conversion. Subsequently, two broadband electrical amplifiers (EAs) with tunable gain are used to compensate for the power loss in the cavity. Oscillating microwave signals are selected by the electrical bandpass filter (EBF) with center frequency at ${f_0}$. Finally, the microwave signals are separated by an electrical splitter, where one port is applied to output the generated MFC signals and the other port is sent back to the RF port 2 of the DMZM to close the OEO loop.
Fig. 1. Schematic diagram of the proposed RHML-DL-OEO. LD: laser diode; DMZM: dual-drive Mach-Zehnder modulator; PC: polarization controller; PBS: polarization beam splitter; SMF: single-mode fiber; PBC: polarization beam combiner; PD: photodetector; EA: electrical amplifier; EBF: electrical bandpass filter; ES: electrical splitter; SG: signal generator; ESA: electrical spectrum analyzer.
In order to realize RHML, an external RF modulation signal at ${f_m}$ is injected into the OEO cavity through the RF port 1 of the DMZM, which intensity modulates the microwave signal. After intensity modulation, the output RF signal can be expressed as
Fig. 2. Frequency-domain representations of (a) $N$th-order RHML-OEO and (b) Vernier effect. IMDs: intermodulation distortions.
In order to suppress supermode noise and IMDs, a polarization multiplexing dual-loop OEO is introduced. The mode-locking principle is similar to the RAML-OEO [25], with the key difference being the addition of equivalent FSR and the side-mode suppression resulting from the dual-loop structure. As shown in Fig. 2(b), the effective FSR can be derived from the following equation
where ${f_{FSRi}} = 1/{\tau _i} = c/n{L_i}$ $(i = 1$ or $2)$ is the FSR of a single-loop OEO with a length of ${L_i}$, ${f_{FSR3}}$ is the lowest common multiple of ${f_{FSR1}}$ and ${f_{FSR2}}$, and ${N_1}$ and ${N_2}$ are the smallest integers satisfying Eq. (2). Due to the unequal gain induced by the vernier effect, only the common modes of the two loops can obtain sufficient gain to oscillate, other modes will be suppressed in the early stages of oscillation, as shown in Fig. 2(b). As a result, the supermode noises and IMDs can be greatly reduced by Vernier effect.3. Experimental results
A proof-of-concept experiment is carried out to demonstrate the proposed RHML-DL-OEO. In the experiment, a CW light with the center wavelength of 1550 nm and a power of 13.5 dBm is created by a laser diode (Emcore, TTX1995). A dual-drive electro-optical MZM (Fujitsu, FTM7937EZ) biased at its quadrature point is utilized to feed the oscillating microwave signal back to the optical link. The intensity-modulated optical signal is separated by a polarized beam splitter and fed into two different lengths of single-mode fibers, where the power ratio of the two optical signals is controlled by a polarization controller as 1:1. After passing through a polarization beam combiner, the combined optical signal is detected by a photodetector (Discovery, DSC40S). Two electrical amplifiers (Muitilink, MTC5515) with tunable gain are used to compensate for the power loss in the OEO cavity, while the net cavity gain can be fine-tuned to obtain a stable rational number of harmonic mode-locking states [21]. In addition, an electrical bandpass filter with a center frequency of 5.5 GHz and a 3-dB bandwidth of 2 GHz is used to select the oscillating modes in the OEO cavity. The oscillating microwave signal is separated by an electrical splitter, of which one port is monitored by an electrical signal analyzer (ESA) (Keysight, N9020A), and the other port is connected to the RF port 2 of the DMZM. In order to obtain the rational number harmonic mode-locking, the external RF signal from a signal generator (Siglent, SDG1025) is injected into the RF port 1 of the DMZM, where the signal frequency is set to be $M/N$ times of the FSR.
To acquire the exact fundamental frequency ${f_{FSR}}$ of the single-loop OEO, which is the free spectral range of the OEO. We first insert a SMF spool of length 2 km into the OEO cavity as a long loop and disconnect the short loop, which is the structure of a single-loop OEO. Figure 3(a) shows the output electrical spectrum of the free-running OEO. As can be seen, the FSR of the free-running OEO is 100.2 kHz. It is noteworthy that due to the uneven gain of the EAs and the unhomogeneous bandpass of the EBF, the gain peak of about 4.74 GHz appears in the microwave signals. So the range of rational number harmonic mode locking of the system achieve in the following step is not broad. If an EBF with more uniform bandpass and an EA with flater gain are employed, the rational number harmonic mode-locking over a larger frequency range will be reached.
Fig. 3. Output electrical spectra of (a)-(b) a free-running OEO , (c)-(d) an OEO under fundamental rational number harmonic mode-locking.
When an external RF signal is injected, and the external RF signal frequency is set to be ${(1/2) \times f_{FSR}}$ = 50.1 kHz, the fundamental rational number harmonic mode-locking OEO is realized (i.e., $N$ = 1, $M$ = 2) as shown in Fig. 3(c) and (d). It is obvious from Fig. 3(d) that a comb-spaced 100.2 kHz and power-flat MFC is generated. It should be noted that there are low-order harmonics of the modulated signal in the generated MFC, which can be reduced by using a Mach-Zehnder interferometer filter [28].
Then, the externally applied RF signal frequency is set to be ${(9/2) \times f_{FSR}}$ = 450.9 kHz to realize 9th-order rational number harmonic mode locking (i.e., $N$ = 9, $M$ = 2). Figure 4(a) and (b) show the spectrums of the MFC generated based on the single-loop structure, where the mode spacing increases to 901.8 kHz. In Fig. 4(b), in addition to the dominant oscillating longitudinal mode and the lower order harmonics of the injected RF signal, there are supermode noise and IMDs located at the idle longitudinal mode frequency, and their presence results in a supermode noise suppression ratio of only 14.2 dB. Figure 4(c) and (d) show the spectrum of the OEO locked by the rational number of harmonic modes based on the dual-loop structure, where the lengths of SMF1 and SMF2 are 2 km and 220 m, respectively. As can be seen in Fig. 4(d), the mode spacing is also 901.8 kHz, but both the supermode noise and IMDs are evidently suppressed. As a result, the supermode noise suppression ratio reaches 44.7 dB, which is an improvement of 30.5 dB compared with the single-loop structure.
Fig. 4. Output electrical spectra of the generated MFCs by a 9th-order rational number harmonic mode-locking OEO based on a (a)-(b): single-loop, and (c)-(d): dual-loop architecture.
Figure 5(a)-(b) and 5(c)-(d) show the spectrums of the 23rd-order rational number harmonic locking OEO based on the single-loop and dual-loop structures achieved when the length of SMF2 is changed to 87 m and the frequency of the externally applied RF signal is set to be ${(23/2) \times f_{FSR}}$ = 1.1523 MHz (i.e. $N$ = 23, $M$ = 2), respectively. Compared with Fig. 4, the mode spacing increases to 2.3046 MHz. Thus, by inserting a shorter SMF into the OEO cavity and varying the frequency of the injected RF signal, higher order rational number harmonic mode-locking can be achieved using the proposed scheme. Comparing Fig. 5(b) with 5(d), the supermode noise and IMDs of the dual-loop structure are evidently suppressed. The supermode noise suppression ratio is improved by 27.6 dB. Accordingly, by varying the length difference of the SMFs inserted in the OEO cavity and the frequency of the externally injected RF signal, the proposed scheme can generate MFC signals with low supermode noise and tunable comb spacing.
Fig. 5. Output electrical spectra of the generated MFCs by a 23rd-order rational number harmonic mode-locking OEO based on a (a)-(b): single-loop, and (c)-(d): dual-loop architecture.
To further validate the principle, the frequency of the externally injected RF signal is set to be ${(53/3) \times f_{FSR}}$ = 1.7702 MHz (i.e. $N$ = 53, $M$ = 3)and the length of SMF2 is changed to 38 m. Figure 6(a)-(b) and 6(c)-(d) show the output electrical spectra of the 53rd-order RHML-OEO based on the single-loop and dual-loop structures, respectively. Similar to 9rd- and 23rd-order RHML, the supermode noise and IMDs will be well suppressed by inserting a polarised dual-loop structure. The supermode noise suppression ratio is improved by 20.3 dB, as shown in Figs. 6(b) and 6(d). Nonetheless, as $M = 2$ changes to $M = 3$, the frequency of the injected external RF signal will be reduced from ${(53/2) \times f_{FSR}}$ = 2.6553 MHz to ${(53/3) \times f_{FSR}}$ = 1.7702 MHz. Thus, high-order RHML-OEO can be obtained even with low-frequency modulated signals by increasing the value of $M$. This is important for its application in radar and communication systems because it frees up the bandwidth requirements of mode-locked modules and greatly reduces the difficulty and cost of system manufacturing.
Fig. 6. Output electrical spectra of the generated MFCs by a 53rd-order rational number harmonic mode-locking OEO based on a (a)-(b): single-loop, and (c)-(d): dual-loop architecture.
Figure 7 shows the comparison of the single sideband (SSB) phase noise of MFC signals generated by rational number harmonic mode-locked OEOs of different orders based on single-loop and dual-loop structures at about 4.74 GHz. It can be seen from Fig. 7(a)-(c) that the microwave signals generated by different-order rational harmonic mode-locked OEOs have similar phase noise, which is about −98 dBc/Hz at 10 kHz frequency offset. However, by introducing the dual-loop structure, better side-mode suppression can be provided at different orders, so the supermode noise and IMDs will be obviously suppressed, and the phase noise performance under large frequency offset can be improved. It is worth noting that the jumps above 1 MHz frequency offset in Fig. 7(b) and (c) are due to the coarse frequency resolution and small pattern frequency separation of the phase noise analysis module. Besides, since the phase noise is related to the time jitter of the MFC, the lower the phase noise, the smaller the time jitter. The phase noise performance can be further improved by increasing the length of SMF1, thereby improving the accuracy of radar detection [21].
Fig. 7. Comparison of single-sideband phase noise profiles of microwave signals generated by (a) 9th-order, (b) 23rd-order, and (c) 53rd-order rational number harmonic mode-locked OEO at about 4.74 GHz based on single-loop and double-loop structures.
Finally, it should be pointed out again that by employing a Mach-Zehnder interferometer filter [28] to the proposed OEO, the low-order harmonics injected into the RF signal can be suppressed, bring about the higher supermode noise suppression ratio. Furthermore, frequency-reconfigurable RHML-DL-OEO can be achieved by replacing the electronic bandpass filter with a tunable electronic bandpass filter [29], or utilizing stimulated Brillouin scattering for frequency tuning [30].
4. Conclusion
In summary, we propose and experimentally demonstrate a RHML-DL-OEO based on a DMZM, which can generate large-comb-spaced MFCs using low-frequency modulated signals. By using two OEO loops of different lengths to extend the equivalent FSR, the supermode noise and IMDs are suppressed, and the phase noise performance of the MFC signals is improved. In the experiment, the 9th-orde, 23rd- and 53rd-order RHML are realized. Compared with the RHML-OEO based on single-loop, the supermode noise suppression ratios are improved by 30.5 dB, 27.6 dB and 20.3 dB, respectively. MFCs of different orders have similar phase noise, which is about −98 dBc/Hz at 10 kHz frequency offset. Besides the high supermode noise suppression ratio and low phase noise, the main benefits of the proposed scheme include low structural complexity, low cost, and adjustable comb spacing. The proposed system can be widely used in radar and communication fields.
Funding
Open Fund of IPOC (BUPT) (IPOC2021A06); Science and Technology Program of Guangzhou (2019050001, 202201010340); Natural Science Foundation of Guangdong Province (2021A1515012652); National Natural Science Foundation of China (61774062, 61875057, 62175070).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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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