Frequency Stabilization of Wideband-Tunable Low-Phase-Noise Optoelectronic Oscillator Based on Fundamental and Subharmonic RF Injection Locking

Abstract

A frequency stabilization scheme for a wideband-tunable optoelectronic oscillator (OEO) based on fundamental and subharmonic RF injection locking is proposed, achieving a tuning range of 2–22 GHz with low phase noise. The injection-locked performance of the OEO using the fundamental RF signal and its 1/n subharmonic is investigated. The fundamental injection locking achieves a phase noise of <−130 dBc/Hz @ 10 kHz offset across the entire tuning range. An examination of phase noise behavior at different subharmonic orders reveals that fundamental and subharmonic injection locking achieve a five-order-of-magnitude improvement in Allan variance (0.1 s) and approximately 40 dB phase noise reduction at a 10 Hz offset from the carrier. This approach leverages the low-phase-noise advantage of the OEO while benefiting from the high stability of low-frequency external RF sources, enabling multi-frequency point frequency stabilization optimization.

1. Introduction

Optoelectronic oscillators (OEOs) can generate RF signals with high spectral purity and ultra-low phase noise [1] due to the use of high-quality (Q)-factor energy storage media. The phase noise of the RF signals generated by an OEO is independent of the oscillation frequency. This unique characteristic, combined with its exceptional features—including its high operational frequency, wideband tunability, low phase noise, and superior spectral purity—empower the OEO with unparalleled advantages in diverse applications in communication, sensing, ranging, and signal processing [2,3,4,5]. Nevertheless, to maintain low-phase-noise characteristics, an OEO typically needs optical fibers ranging from several kilometers to tens of kilometers. However, long optical fibers are highly susceptible to temperature and stress variations, which can cause mode drifting and hopping in the OEO’s output and degrade its frequency stability. To effectively enhance OEOs’ frequency stability, various technical approaches have been explored, including multi-loop OEO structures [6], high-Q RF photonic filters [7], phase-locked loops [8], parity–time symmetry [9], and injection-locking technology [10], among others. Among these, injection locking stands out as a simple yet effective approach, which usually involves injecting an RF signal into an OEO to lock the free-running oscillation frequency. It is possible to stabilize a high-performance OEO with a low-cost RF synthesizer. When the center frequency of the injected signal is tuned, the output of the OEO can be correspondingly adjusted, thereby achieving a frequency-tuned OEO. In addition to the frequency stability optimization mentioned above, the OEO system based on the injection-locking structure is also helpful for improving the side mode suppression ratio [11,12]. In such injection-locked OEO architectures, however, the microwave filter is usually excluded to allow for frequency tuning. In the absence of the filter, the gain and mode competition arising from the system’s uneven response limit the tuning range, typically by one to several GHz.

In this paper, we propose a wideband-tunable injection-locked OEO structure that utilizes an Yttrium Iron Garnet (YIG) tunable filter and employs fundamental and subharmonic injection using an external tunable RF synthesizer. The OEO is tunable from 2 GHz to 22 GHz, whilst it maintaining a phase noise performance better than −130 dBc/Hz at a 10 kHz offset across the entire operational bandwidth. Injection locking serves as the primary mechanism for achieving frequency stabilization. To characterize the RF frequency stability, Allan variance is used. Injection locking significantly improves the OEO’s Allan variance, demonstrating enhanced frequency stability. The Allan variance of the signal at 0.1 s has been improved by nearly five orders of magnitude, and the phase noise near the carrier frequency has been reduced by approximately 40 dB. Additionally, we investigate the effects of different subharmonic orders and the power of the injected subharmonic signal for 10 GHz RF generation, providing insights into how these factors influence the overall performance of the oscillator. The use of YIG helps maintain an optimal sidemode suppression ratio (SMSR), mode selectivity, and stability. Additionally, the current tuning mechanism of the filter supports fast frequency tuning, enhancing the system’s overall responsiveness. This scheme enables a wideband-tunable OEO with superior frequency stability while preserving the low-cost and simplicity of the injection-locking approach.

2. Principle and Experimental Setup

For an injection-locked OEO, its phase noise power spectral density can be expressed as follows [10]:

$$S_{\mathrm{i}\mathrm{n}\mathrm{j}-\mathrm{o}\mathrm{e}\mathrm{o}}\left(\omega \right)=\left|H_{\mathrm{i}\mathrm{n}}\right(j\omega \left){|}^2{S}_{\mathrm{i}\mathrm{n}}\right(\omega )+|H_{\mathrm{o}\mathrm{s}\mathrm{c}}\left(j\omega \right){|}^2{S}_{\mathrm{o}\mathrm{s}\mathrm{c}}\left(\omega \right)$$

(1)

where $S_{\mathrm{i}\mathrm{n}}\left(\omega \right)$ and $S_{\mathrm{o}\mathrm{s}\mathrm{c}}\left(\omega \right)$ represent the phase noise power spectral density of the injected signal and the free-running OEO, respectively. $\left|H_{\mathrm{i}\mathrm{n}}\right(j\omega ){|}^2$ and $\left|H_{\mathrm{o}\mathrm{s}\mathrm{c}}\right(j\omega ){|}^2$ represent the phase noise transfer function of the injected RF signal in the injection-locked OEO and the phase noise transfer function of the free-running OEO in the injection-locked state, respectively, which can be expressed as

$$\begin{gathered} |H_{\mathrm{i}\mathrm{n}}(j\omega ){|}^2={\displaystyle \frac{S_{\mathrm{o}\mathrm{u}\mathrm{t}}\left(\omega \right)}{S_{\mathrm{i}\mathrm{n}}\left(\omega \right)}}={\displaystyle \frac{1}{1+{\left(\omega /\Delta {\omega }_0\right)}^2}} \\ |H_{\mathrm{o}\mathrm{s}\mathrm{c}}(j\omega ){|}^2={\displaystyle \frac{S_{\mathrm{o}\mathrm{u}\mathrm{t}}\left(\omega \right)}{S_{\mathrm{o}\mathrm{s}\mathrm{c}}\left(\omega \right)}}={\displaystyle \frac{1}{1+{\left(\Delta {\omega }_0/\omega \right)}^2}} \end{gathered}$$

(2)

where $\Delta {\omega }_0$ is the injection-locking range [13]:

$$\Delta {\omega }_0={\displaystyle \frac{{\omega }_0}{2Q}}{\displaystyle \frac{U_{in}}{U_{out}}}={\displaystyle \frac{f_{FSR}}{2}}\sqrt{{\displaystyle \frac{P_{in}}{P_{out}}}}$$

(3)

Here, $Q$ represents the quality factor, ${\omega }_0$ represents the oscillation frequency, $U_{in}$ and $U_{out}$ represent the amplitudes of the input signal and the output signal, respectively, and $P_{in}$ and $P_{out}$ represent the powers of the input signal and the output signal, respectively, and $f_{FSR}$ is the loop mode spacing. This shows that the locking range of the injection-locked OEO is determined by the loop mode spacing of the free-running OEO and the voltage ratio of the injected signal to the mode of the free-running OEO, where the loop mode spacing of the OEO is determined by the fiber length.

Figure 1 plots the relationship between $S_{\mathrm{i}\mathrm{n}\mathrm{j}-\mathrm{o}\mathrm{e}\mathrm{o}}$ and $\omega$ using Equation (1). It can be seen that the phase noise of the injection-locked OEO system is determined by the collective contributions from both the free-running OEO and the injected signal. In the vicinity of the carrier frequency ($\omega$ << Δ${\omega }_0$), the phase noise is predominantly influenced by the external injected RF signal. Conversely, in the frequency range far from the carrier (ω >> Δω₀), the phase noise primarily reflects the characteristics of the free-running OEO. By using this approach, the low frequency stability follows that of the external RF source, while the phase noise maintains the OEO’s inherent low-phase noise characteristics. In other words, the injection scheme combines the excellent frequency stability of conventional RF synthesizers with the superior phase noise performance offered by OEO technology.

Figure 2 shows the schematic configuration of the subharmonic RF injection-locked tunable OEO. The system employs a co-packaged module that integrates a DFB laser with a Mach–Zehnder modulator (−3 dB bandwidth of 20 GHz) for optical carrier generation and modulation purposes. The light from the DFB-MZM module is split into two parts by a 5:5 optical coupler (OC) and then converted into an RF signal using a balanced photodetector (BPD, Finisar BPDV2120R, Sunnyvale, CA, USA) after passing through optical fibers of 5 km and 300 m, respectively. The resulting RF signal is then amplified by two electrical amplifiers (EAs, Marki APM-6848PA, Greensboro, NC, USA) with a total gain of 46 dB. After amplification, the signal passes through a DC block and is filtered by a tunable YIG filter (tunable range: 1.8–23 GHz; bandpass width: approximately 55 MHz, tuning rate of 75 MHz/mA). Subsequently, the RF signal is split into two paths by a 9:1 electrical coupler (EC). Ninety percent of the signal serves as the output RF signal of the OEO, while the remaining 10% is further amplified by a third EA (gain: 23 dB) before being modulated onto the MZM in the DFB-MZM module. By adjusting the control current of the YIG filter, its center frequency can be tuned, thereby enabling the tunability of the OEO system’s oscillation frequency. The optical output of the OEO is analyzed using an optical spectrum analyzer (Advantest Q8384, Tokyo, Japan, minimum resolution: 0.01 nm), while the phase noise and Allan variance are measured using a phase noise analyzer (Rohde & Schwarz FSWP50, Munich, Germany, frequency range: 1 MHz to 50 GHz).

Compared to conventional injection-locking structures, the proposed system incorporates a tunable filter to ensure effective injection locking, mitigating the impact of the system’s uneven frequency response. This design helps maintain an optimal SMSR, mode selectivity, and stability. Additionally, the current tuning mechanism of the filter supports fast frequency tuning, enhancing the system’s overall responsiveness. In this structure, the YIG filter is employed for coarse frequency selection, while the injected RF signal enables precise frequency tuning. The RF source, operating at the $1/n$ subharmonic of the OEO’s free-running frequency, allows the OEO to lock onto the n-th harmonic of the injected RF signal, which is generated through the nonlinear frequency response of the optical modulator.

3. Experiments and Results

3.1. Fundamental RF Signal Injection Locking

The baseline performance of the tunable OEO prior to injection locking was first evaluated. Figure 3a,b show the RF spectrum for different spans and Figure 3c shows the phase noise of the 10 GHz output. The RF signal exhibits high spectral purity with a spurious suppression ratio of approximately 75.9 dB. The side mode spacing of $\Delta \nu =660 \mathrm{k}\mathrm{H}\mathrm{z}$ corresponds to a short loop length of 300 m. The phase noise reaches −133.83 dBc/Hz at a 10 kHz offset from the carrier frequency. By adjusting the current of the YIG filter, the free-running OEO can be tuned within the range of 2–22 GHz. Figure 4a presents the RF spectrum of the tunable OEO with a 1 GHz frequency step, while Figure 4b shows the corresponding optical spectra at several selected frequencies. The overlay of single-sideband phase noise curves across the entire tuning range is shown in Figure 4c. Throughout this range, the phase noise at a 10 kHz offset from the carrier frequency remains below −130.02 dBc/Hz.

Despite its superior phase noise performance, the free-running OEO suffers from unsatisfactory low-frequency stability. As indicated by the black dash-dotted line in Figure 5a, it is difficult to identify a clear center frequency of the signal within a measurement span of 1 kHz. The phase noise at a 10 Hz offset, as depicted in Figure 5b, approaches 0 dBc/Hz; however, its reliability is compromised due to frequency drifting, making it difficult to discern accurately.

Subsequently, the OEO was injection-locked by its fundamental frequency, with the injection signal’s phase noise measuring −75.87 dBc/Hz @ 10 Hz offset and −125.55 dBc/Hz @ 10 kHz offset, respectively. Following injection locking, a well-defined and stable RF tone (blue solid line) emerges within the identical measurement range. The phase noise decreases to −43.57 dBc/Hz @ 10 Hz (blue solid line), demonstrating a significant improvement of nearly 40 dB, as illustrated in Figure 5b. At frequencies far from the carrier, the phase noise remains close to that of the free-running OEO (e.g., −133.84 dBc/Hz @10 kHz), better than that of the injected fundamental RF signal. The comparison of Allan variance before and after injection locking is shown in Figure 5c. The Allan variance of the OEO decreases from 3.40 × 10⁻¹⁷ at 0.1 s in the free-running state to 3.99 × 10⁻²² at 0.1 s, representing an improvement of five orders of magnitude.

Next, the phase noise and Allan variance of the OEO under frequency tuning are evaluated. Figure 6 summarizes and compares the phase noise at a 10 kHz offset from the carrier frequency and the Allan variance at 0.1 s for the wideband-tunable OEO in both the free-running and fundamental injection-locking states. The phase noise remains nearly identical to that of the free-running OEO under RF injection, staying below −130 dBc/Hz, while the Allan variance improves by approximately five orders of magnitude across the entire tuning range compared to the free-running state.

All the Allan variance measurements in this article were constrained to a maximum duration of 0.1 s due to the measurement limitations of the FSWP. To evaluate long-term frequency stability beyond this constraint, the output frequency drift of the OEO was characterized by recording its peak position over a 5 min period using the spectrum analyzer’s MaxHold function, as shown in Figure 7. The resulting spectrum demonstrates a stable peak frequency and almost no frequency drift is observed within 5 min, which confirms the OEO system’s long-term stability.

The influence of the injection power on the performance of the OEO is also investigated. Figure 8a,c depict the relationship between the phase noise and the Allan variance of the injection-locked OEO under different injection power levels. As the injection power increases from −24 dBm to 15 dBm, the phase noise @ 10 Hz decreases from −36.06 dBc/Hz to −58.40 dBc/Hz, showing a minimum 36 dB improvement compared to that of the free-running OEO. The phase noise far from the carrier frequency gradually converges to that of the free-running OEO. Figure 8b summarizes variation in the phase noise at a 10 Hz and 10 kHz offset from the carrier frequency with the injected RF signal power. Similarly, the improvement in Allan variance also increases with higher injection power, particularly for time intervals longer than 1 μs. Notably, for a time interval of 0.1 s, a minimum improvement of four orders of magnitude has been achieved, even with very weak injection. Figure 8d summarizes the variation in the Allan variance at 0.1 s under different injection powers. Investigations of the 15 GHz and 20 GHz cases also demonstrate similar performance.

Finally, the minimum RF power required for the fundamental injection locking of the OEO was experimentally investigated. Measurements were taken at 2, 5, 10, 15, and 20 GHz, as shown in Figure 9a. Across the entire tuning range of the OEO, the minimum power required for fundamental injection locking gradually rises from −50 dBm @ 2 GHz to −18 dBm @ 20 GHz due to degradation of the system response as frequency increases. Figure 9b,c show the phase noise and Allan variance of the OEO system in the minimum-RF-power injection-locking state, respectively. Notably, across the entire tuning range, the phase noise of the OEO system remains the same as that in the free-running state, while the Allan variance is significantly improved, consistent with the earlier experimental findings.

3.2. Subharmonic RF Signal Injection Locking

Fundamental injection locking is effective in reducing close-to-carrier phase noise and improving the Allan variance of the OEO. To further reduce system costs associated with the wideband synthesizer, a subharmonic injection-locking scheme is explored. This approach allows a synthesizer operating at the $1/n$ fundamental frequency of the OEO to achieve the desired frequency tuning range. For the OEO system, the n-th harmonic of the injected RF signal can be directly obtained from the Mach-Zehnder modulator, using its inherent nonlinear response. Based on the previous investigation, which demonstrated that the minimum injection power for fundamental injection locking can be reduced to −20 dBm, it is feasible to obtain the n-th harmonic of the subharmonic injection signal with sufficient power to effectively lock the OEO.

The subharmonic injection-locking range can be expressed as [14]:

$$\Delta {\omega }_{{\displaystyle \frac{1}{n}}}={\displaystyle \frac{{\omega }_0}{2Q}}{\displaystyle \frac{U_{in}}{U_{out}}}={\displaystyle \frac{{\omega }_0}{2Q}}\sqrt{{\displaystyle \frac{P_{in}}{P_{out}}}}$$

(4)

The locking range is also related to the Q factor and the injection power of the injected signal.

The OEO was first investigated using the $1/2$, $1/3$, $1/4$, and $1/5$ subharmonics of 10 GHz, each with a power of −7 dBm. Figure 10 presents the phase noise and Allan variance of the signal generated by the OEO under different subharmonic injection-locking conditions. As shown in Figure 10a, regardless of the injected subharmonic frequency, the phase noise at a 10 Hz offset from the carrier frequency is reduced by approximately 40 dB, and the phase noise curves of the subharmonic injection-locked OEO system remain highly consistent within a 1 kHz offset from the carrier frequency. Beyond 1 kHz, however, the phase noise of the OEO system increases after subharmonic injection locking. As $n$. increases, the phase noise curve at frequencies farther from the carrier also rises.

Figure 10b summarizes the phase noise at a 10 kHz offset from the carrier frequency under different injection orders. The phase noise gradually deteriorates, increasing from −133.83 dBc/Hz in the free-running state to −131.49 dBc/Hz @ 5 GHz injection, −129.77 dBc/Hz @ 3.3 GHz injection, −123.43 dBc/Hz @ 2.5 GHz injection, and −113.87 dBc/Hz @ 2 GHz injection, respectively. This degradation occurs because, as $n$ increases, the subharmonic signal becomes weaker under the same modulation depth. The practical subharmonic order depends on the extent to which the phase noise degrades to outperform that of the fundamental RF signal. For the 10 GHz case, our RF synthesizer can generate a signal with a phase noise of −125.55 dBc/Hz at 10 GHz. Based on this, the effective subharmonic order is determined to be 3, corresponding to a phase noise of −129.77 dBc/Hz at 3.3 GHz. For an RF synthesizer with poorer phase noise performance, the usable subharmonic order can be further increased if the goal is to obtain an RF signal with better phase noise characteristics than the synthesizer itself.

Figure 10c illustrates the Allan variance of the OEO within the 0.1 s measurement range before and after subharmonic injection locking. In the free-running state, the Allan variance of the OEO system at 0.1 s is 3.4 × 10⁻¹⁷. After subharmonic injection, the Allan variance for all cases at 0.1 s decreases to approximately 5 × 10⁻²², representing a reduction of nearly five orders of magnitude, similar to the improvement achieved with fundamental injection locking.

Next, the influence of subharmonic power on phase noise and Allan variance is investigated using $1/3$ subharmonic injection. As shown in Figure 11a, when the power of the injected subharmonic signal increases from −7 dBm to 10 dBm, the phase noise at a 10 Hz offset from the carrier frequency improves from −42.05 dBc/Hz @ −7 dBm to −59.63 dBc/Hz @ 10 dBm, achieving a maximum reduction of approximately 40 dB compared to the free-running case. At a 10 kHz offset from the carrier frequency, the phase noise remains relatively stable, ranging from −126.68 dBc/Hz to −129.77 dBc/Hz, which represents a 5~7 dB decrease compared to that of the fundamental injection locking. Figure 11b summarizes the phase noise at 10 Hz and 10 kHz offsets for different injection power levels.

Figure 11c,d illustrate the influence of subharmonic power on the Allan variance. As the injection power increases, the Allan variance at 0.1 s improves from 5.87 × 10⁻²² at −7 dBm to 1.65 × 10⁻²³ at 10 dBm, demonstrating a dependence on subharmonic injection power. However, for all injection power levels, the Allan variance can be optimized to five orders of magnitude.

The minimum RF power required to lock the OEO at different subharmonic orders is investigated. We define the critical injection-locking state as the point where the Allan variance of the injected OEO becomes comparable to that of the free-running OEO. The results are presented in Figure 12. For a specific frequency, when injecting $1/n$ subharmonics of different frequencies, the minimum RF power required for the OEO to reach the locked state increases as $n$ increases. Additionally, when $n$ is constant, the minimum RF power required for locking rises as the free-running frequency of the OEO increases. This trend is consistent with that observed in the fundamental injection-locked OEO system.

4. Conclusions

This paper presents a wideband-tunable, low-phase-noise OEO based on fundamental and subharmonic injection locking. The injection-locked OEO enables a 2–22 GHz wideband-tunable RF signal output, featuring high spectral purity, a high spurious suppression ratio, and low phase noise. Phase noise levels below −130.02 dBc/Hz at a 10 kHz offset have been demonstrated across the full frequency tuning range for the fundamental injection-locking configuration. The close-in phase noise of the OEO-generated RF signal is reduced by approximately 40 dB at a 10 Hz offset from the carrier frequency, while the maintaining low-phase-noise characteristics of the OEO at frequencies several kHz from the carrier. The Allan variance improves by about five orders of magnitude at a 0.1 s. Subharmonic injection locking is also demonstrated for 10 GHz RF generation, with phase noise performance degrading from −131.49 dBc/Hz to −113.87 dBc/Hz at a 10 kHz offset as the subharmonic order (n) increases from 2 to 5. The influence of injection power on the system performance is also examined.

This scheme facilitates the easy implementation of frequency stabilization for high-performance OEOs. Depending on specific requirements, either the fundamental or subharmonic injection schemes can be employed to achieve high-performance or cost-effective RF generation. Furthermore, this work offers a technical reference for optimizing the stability performance of high-performance wideband-tunable opto-generated RF sources.