Advanced radar and communication systems demand radio frequency (RF) sources with an expansive tuning range and minimal phase noise to meet diverse application requirements [1–4]. Furthermore, the escalating needs for heightened information security in data transmission [5], anti-jamming capabilities in military deployments, and increased data capacity in mobile and satellite communications [6] have fueled a surge in demand for frequency-hopping (FH) systems. Traditional electronic oscillators, however, exhibit limited bandwidths, and the phase noise of the frequency synthesis systems based on these oscillators rapidly decreases during the frequency multiplication process before phase-locking. Moreover, due to the inherent electronic bottleneck and limited frequency bandwidth of electronic devices, it is very challenging for electronics-based FH systems to achieve bandwidths of over several gigahertz at close to real-time hopping speeds.

Microwave photonics [7–9] is a critical link between RF and photonic signal processing, presenting a solution to electronic bottlenecks by offering attributes such as high bandwidth, instantaneous responsiveness, flexibility, and reconfigurability. Recent advancements in microwave photonics have emerged as promising solutions for broadband, low-phase-noise, and agile frequency sources. An exemplary technology is the optoelectronic oscillator (OEO) [10–14], a hybrid microwave and photonic system uniquely capable of generating frequency-independent, low-phase-noise microwave signals. At present, state-of-the-art X band OEO has a record low phase noise (−163dBc/Hz at 6 kHz offset) by a 16 km feedback loop [15]. Utilizing broadband optoelectronic devices, the OEO can synthesize low-phase-noise signals across a broad frequency range. Microwave photonic filter (MPF)-based OEO [16–19] and dissipative microwave photonic soliton OEO [20] have demonstrated the generation of FH signals with sub-microsecond switching times.

However, the long fiber loop required for a high-Q OEO also leads to spurious modes (spurs), which are spaced too narrowly to be filtered by standard electronic devices. While dual- or multi-ring OEO configurations [21,22] offer a solution, their practical implementation introduces complexity, resulting from constraints in frequency tunability or the necessity of regulating loop length during the tuning process. Recently, there has been a notable development in the form of tunable OEOs utilizing PT symmetry [23–32] for mode selection, thereby mitigating the reliance on fixed and ultra-narrow RF filters. However, this design usually uses two interlinked yet physically isolated loops, resulting in heightened system complexity and reduced stability. To extend the tuning bandwidth, several approaches centered around tunable microwave bandpass filters [33,34] or MPFs have been used to attain broadband tuning. However, due to the typically wide passband of these filters, the extension of the fiber loop is constrained, thereby limiting the potential for further phase noise reduction. Fortunately, the utilization of coupled optoelectronic oscillators (COEOs) [35–38] is viable, incorporating active fiber ring cavities as an alternative to long fibers. This configuration enhances mode selection while upholding exceptional phase noise performance [39].

In this work, by introducing a noise-canceled harmonic mode-locked laser, we report a frequency-hopping coupled optoelectronic oscillator (FH-COEO) with ultralow phase noise, broadband tuning range, and high robustness. This achievement is realized through the integration of an yttrium-iron garnet (YIG) filter within the RF feedback loop and the implementation of the quiet point (QP)-operated cascaded optical amplifier (COA). In a Kerr-microcomb-based oscillator, a QP refers to a biased detuning that minimizes the comb repetition rate noise [40,41]. Here, the specific detuning is replaced by the bias current of the SOA for QP operation. The resulting output signal of the oscillator spans from 2 to 18 GHz, exhibiting typical phase noise below −135dBc/Hz at a 10 kHz offset from the carrier frequency and side-mode suppression ratios (SMSRs) exceeding 85 dB. Random frequency hopping within a specific frequency range is demonstrated, achieving a resolution of 1.25 MHz and a hopping speed of approximately 3.5 GHz/ms, constrained only by the tuning speed of the filter. Beyond the study of the FH-COEO, a convenient way to operate the oscillator at the QP while disciplining it to an external reference is demonstrated. The fractional frequency stability (Allan deviation) of the output signal is reduced to 6.1×10−12 at an averaging time of 1 s.

The schematic of the proposed COEO is depicted in Fig. 1(a). The oscillator is a typical configuration consisting of a fiber ring laser and an RF feedback loop. In the fiber ring loop, the intensity jitter of pulses (thereby supermode noise) is reduced through the COA configuration, and the identification of a QP operation is attained by setting the near-transparent state of the semiconductor optical amplifier (SOA) within the COA, thereby contributing to the minimization of repetition frequency noise. Subsequently, the signals are amplified, filtered in the RF feedback loop, and then fed back into the fiber loop through the modulator to achieve active harmonic mode-locking. The oscillator is robust due to the inherent large locking bandwidth under QP operation. By employing an adjustable RF filter driven by a time-varying voltage sequence, the COEO can generate frequency-hopping signals, as illustrated in the dashed box of Fig. 1(a).

In contrast to fixed-frequency OEOs, the suggested COEO exhibits exceptional frequency tuning attributes. For reliable switching of the operating frequency during the tuning process, it is imperative to guarantee continuous mode-locking of the optical pulses circulating in the fiber ring cavity. This implies that the oscillator requires a reliable locking mechanism to ensure that stability is maintained each time an oscillation is re-established, which is crucial for acquiring RF signals with low phase noise and minimal spurs. Here, reliable locking benefits from the extensive locking bandwidth present in the harmonic mode-locked lasers with a COA. Additionally, the RF loop requires precisely configured delays to minimize the time difference between the peak of the pulses entering the modulator’s gain medium and the peak of the gain modulation waveform. As shown in Fig. 1(a), assuming a pulse arrives at the modulator at a specific moment marked as the reference time point T0, it is evident that the feedback microwave signal, experiencing a delay within the RF loop, may not precisely synchronize with the pulse arrival. If there is a persistent mismatch between the two coupled loops, the RF delay after a time period T can be expressed as TRF=T0+δTTRT,(1)where δT is the transmission point shift with respect to the optical pulse by time interval; TR is the roundtrip time of the pulse in the loop. Equation (1) essentially indicates that the transmission point shifts by δT at each roundtrip. However, according to the principle of actively mode-locked lasers, a “pull-in” effect occurs when RF loop delays are maintained within specified tolerance ranges relative to the optical delays [42]. Figure 1(b) depicts the effect of different temporally modulated gain regions determined by the RF delay on the shaping of the same pulse. For smaller (larger) RF delays, the pulse behaves as a lag (advance) to the gain modulation region, and the gain modulation effectively resynchronizes the pulse by amplifying the pulse’s leading edge (trailing edge) above the peak [see panels II, IV in Fig. 1(b)]. The optimal situation is the synchronization of the modulation gain region and pulse [see panel III in Fig. 1(b)], which results in minimal timing jitter. Within a tolerable time range of δtm=(T+−T−)/2, the pulses are forcibly synchronized without introducing a large timing jitter. Conversely, a double pulse peak is formed when there is a substantial deviation in the RF delay from the ideal value, resulting in the temporal separation between the modulation gain region and pulses falling outside the pull-in range [see panels I, V in Fig. 1(b)]. This phenomenon arises from the higher gain change rate in the vicinity of the gain peak compared to the decay rate of the pulse tail. Concurrently, both peaks persist over multiple roundtrips, and the substantial temporal displacement between the two peaks induces a large timing jitter, potentially leading to either loss of lock or mode hopping of the oscillator. For a fixed-frequency COEO, the locking range exhibits a close relationship with the modulation depth and the pulse width, as estimated by [43] δtm<12βωmτ2,(2)where β is the modulation depth, ωm is the microwave frequency, and τ is the pulse duration. According to Eq. (2), the locking range can be enlarged by broadening the pulse duration and increasing the modulation depth. Here the oscillator operating at the QP inherently yields broad pulses with duration on the order of picoseconds through the incorporation of an intracavity COA, and the pulse duration could be further broadened by constraining the optical bandwidth of the mode-locked fiber laser. Within the RF loop, the RF amplifier operates in a state of deep saturation, and the RF loop delay is precisely designed to achieve the desired “pull-in” range.

Low-noise operation of the oscillator benefits from the incorporation of the COA. In a harmonic mode-locked fiber laser, the interaction between the fundamental longitudinal modes of the laser cavity induces fluctuations in the optical output intensity, giving rise to the generation of supermodes, which is reflected in the decrease of the SMSR and deterioration of phase noise of the beat note signal during the optical-to-microwave conversion process. The supermode noise could be effectively suppressed by the SOA with a fast carrier recovery rate and gain saturation effect [44–48]. As pulses enter the SOA, it induces changes in the carrier concentration, resulting in significant gain for pulses with smaller amplitude and reduced gain for larger ones—effectively mitigating amplitude fluctuations. The strength of the gain saturation effect correlates with the SOA carrier recovery time, with evident effects for signal frequencies close to or below this rate. Therefore, the SOA acts as an effective high-pass filter to suppress low-frequency supermode noise, enhancing the SMSR of microwave signals. Conversely, the longer carrier lifetime of an EDFA introduces power fluctuations, leading to strong spur noise in the oscillator. Figure 1(c) illustrates a spectrum comparison between a COEO with a single EDFA and one with COA along with the QP operation.

However, despite the considerable reduction in supermode competition achieved through SOA, it introduces additional phase noise arising from fluctuations in carrier density, stemming from both stimulated and spontaneous emissions. The single-sideband (SSB) phase noise induced by spontaneous emission and stimulated-emission-induced indirect fluctuation can be expressed as [49] Sϕ1(f)=(G−1)hvnsGPin,(3)Sϕ2(f)=(G−1)(2πKΓ/λA)24nsτc2PinGhv[(2πfτc)2+1],(4)where G represents the gain of SOA, h is Planck’s constant, v is the optical frequency, ns is the spontaneous emission factor, and Pin is the input optical power. K=Δnr(z,t)/Δne(z,t), where Δnr(z,t) is the real refractive index change and Δne(z,t) is the fluctuation of carrier density. Γ is the optical confinement factor, λ is the optical wavelength, A is the amplifier cross section, and τc is the carrier lifetime. Therefore, the total SOA-induced phase noise can be simply expressed as Sϕ(f)=Sϕ1(f)+Sϕ2(f). According to the theoretical analysis of Sϕ(f), the noise introduced by SOA can be effectively reduced when the SOA operates on the unitary gain regime (G=1). This means that there exists a QP where the phase noise introduced by the SOA can be minimized, thus optimizing the phase noise of the oscillator outputs, as shown in Fig. 1(d).

A technical illustration of the experiment and measurement setup used for FH-COEO is shown in Fig. 2. Here the operation and characteristics of the QP are elaborated, and a comprehensive validation is provided, showcasing the broadband tuning and frequency-hopping capabilities exhibited by the oscillator and high stability after synchronization with an external reference.

As shown in the dashed box in Fig. 2, the core component in the fiber laser is a COA consisting of an EDFA and an SOA, which serves as a light source, an optical gain medium, and the supermode absorber at the same time. The optical gain bandwidth is restricted by an optical bandpass filter with a 3 nm bandwidth. To ensure the low-noise operation of the oscillator, it is imperative to minimize the power jitter in the fiber laser arising from polarization perturbations. Hence, a σ-shaped laser cavity structure was employed to reduce polarization perturbations, with a polarization beam splitter (PBS) connecting a polarization-maintaining (PM) ring cavity to a non-PM branch [50]. Within the branch, a 150 m dispersion-shifted fiber (DSF) with a dispersion of ∼4psnm−1km−1 and a Faraday rotating mirror (FRM) introduce a significant delay to the pulses and effectively eliminate the impact of polarization variations through a roundtrip process. 20% of the light is extracted and photodetected into the RF loop for self-regenerative mode-locking. In addition to the fundamental configuration of the COEO, a phase-locked loop (PLL) with dual servo control was specifically devised to enhance long-term stability.

We first operated both the EDFA and SOA in the gain state by tuning their currents so that the average power of the transmitted pulses from the COA reached about 15 dBm. After closing the RF feedback loop, the oscillator started oscillating and generating optical pulses through self-regenerating harmonic mode-locking. We first investigated the COEO operating at a fixed frequency of 10 GHz, corresponding to approximately the 16,000th harmonic mode-locking state. To achieve an oscillator with optimal phase noise performance, we searched for the transparency region by adjusting the SOA’s bias current to enable quiet point operation. While adjusting the gain of SOA, the gain of EDFA changed accordingly, as the total gain of the COA remained constant. However, the EDFA always operated in a saturated state. Figure 3(a) depicts the phase noise of the oscillator with different gain states of the SOA, measured by the RF spectrum and phase noise analyzer (R&S FSWP50). When the SOA operated at a transparent gain (G=0dB), significant optimization of the phase noise spectrum confirmed the QP operating state. Comparison of the phase noise between the COEO operating with a single SOA and that operating with a single EDFA reveals that the QP operation effectively minimized the noise introduced by the SOA, achieving a similar level of phase noise to that of COEO operating with a single EDFA. The phase noise and SMSRs of the output signals were further tested against the SOA bias current. Figure 3(b) illustrates that the phase noise at 10 kHz offset is closely related to the current of SOA, reaching the optimum level of −140.2dBc/Hz under the QP operation. Whether the SOA operated in the gain region, transparency region, or absorption region near the transparency point, the supermode noise was effectively suppressed, with an average SMSR of ∼90dB. The high SMSRs proved that supermode suppression worked well in the fiber laser, so the application of relatively wideband RF filters for mode selection becomes a viable and practical option. Figure 3(c) depicts the RF spectrum produced by the QP-operated COEO utilizing RF bandpass filters with 3 dB bandwidths of 50 MHz, 500 MHz, and 1 GHz. The achieved SMSRs consistently exceed 80 dB. Another distinctive feature of employing a harmonic mode-locked laser with COA is the broadened pulse [51,52]. After obtaining a stable mode-locking operation, an investigation into its temporal characteristics was conducted through autocorrelation experiments. As shown in Fig. 3(d), the pulse has a duration of 13.52 ps and exhibits an asymmetric shape, which is attributed to the slow carrier dynamics and the introduced chirp of the SOA [43]. According to Eq. (2), the broad pulse results in an expanded locking bandwidth, which is crucial for enhancing the system stability, especially when the oscillator is flexibly tuned.

To validate the tuning characteristics of the oscillator, a commercially available two-stage YIG filter with a tunable range of 2–20 GHz was employed in the RF loop. The fiber laser was operated at the QP, and the detuning of the feedback signal and repetition rate of the pulse were calibrated by adjusting the RF phase shifter. Subsequently, the RF signal turned into a low-noise state with minimal spurs.

Despite the fact that the wide bandwidth of the filter (∼50MHz) leads to the existence of numerous oscillating modes, the COA operated at QP effectively functioned as a noise eater and a supermode suppressor within the laser cavity. Consequently, the oscillator can operate in a single-mode configuration, achieving a high SMSR without introducing additional noise. The generation of high-purity microwave signals spanning the 2–18 GHz range was demonstrated by adjusting the center frequency of the YIG filter. Figure 4(a) illustrates the overlapping RF spectrum with a tuning step of 1 GHz. Figure 4(b) provides a more detailed view of the spectra, revealing a side-mode distance from the carrier of approximately 625 kHz, with the SMSRs typically exceeding 85 dB. At each operating frequency, optical pulses with corresponding repetition rates were generated in the fiber loop, and parts of their spectra are depicted in Fig. 4(c). During the tuning process, variations in modulation rate led to differences in intracavity power. However, since the EDFA consistently operated in saturation, these power changes were compressed and did not lead to loss of locking or significant degradation in phase noise. The phase noise of the beatnote signals ranging from 2 to 18 GHz was then evaluated. As illustrated in Fig. 4(d), the typical phase noise level ranges from −131dBc/Hz to −142dBc/Hz, with an average value of about −138dBc/Hz at a 10 kHz frequency offset. Notably, the operating frequency range of the oscillator was confined to 2–18 GHz due to the restricted gain bandwidth of the cascaded RF amplifiers. The decrease in SMSRs and deterioration of phase noise at 17 GHz and 18 GHz signals are attributed to the excessive insertion loss of the YIG filter in the high-frequency tuning band.

This configuration establishes a highly reliable oscillator with the capability to achieve any discrete frequency aligned with the fiber ring modes within the tuning range by manipulating the driving voltage across the YIG filter. Furthermore, precise tuning of the oscillator frequency is achievable by adjusting the voltage of the VPS or the tunable optical delay line within the locking bandwidth, thus enabling continuous tuning of the oscillator within frequencies corresponding to the mode separation of the loop length.

Tunable COEOs serve as exceptional sources for generating FH signals. However, it is imperative to validate the consistency of FH signals across a broad spectrum. The COEO requires a sufficiently extensive locking bandwidth to maintain mode-locking stability during frequency switching. Here, the utilization of intracavity COA and imposition of constraints on the optical bandwidth resulted in the formation of pulses with an approximate duration of 10 ps within the fiber loop. The secondary RF amplifier operated in saturation with a high gain of 23 dB, enabling feedback to the modulator with a signal power of 18 dBm or higher to increase the modulation depth. According to Eq. (2), considering the modulation depth of 1 and an operating frequency of 12 GHz, for example, it is estimated that a stable single-mode oscillation can be sustained within a range of ∼3.77ps delay variations in the RF loop.

To verify this, the relationship between RF loop delay and operating mode was initially tested. The frequency and power of the oscillating mode were measured near the 12 GHz operating frequency. This was achieved by temporarily disconnecting the RF feedback loop, and then re-closing it after adjusting the voltage of the RF phase shifter to change the RF delay. As shown in Fig. 5(a), 15 modes were switched within a 55 ps delay variation, allowing an average delay change of approximately 3.67 ps, which is in general agreement with theoretical predictions. The amplitude-frequency response (S21) of the filter and the spectrum of the oscillation mode were recorded, revealing that modes with higher amplitude response tended to oscillate primarily, as shown in Fig. 5(b). When the RF delay was altered beyond the locking range, the mode switched to the next one to re-oscillate. It is noteworthy that the locking state was consistently maintained during adjustment, and the modes switched almost continuously. To explain this phenomenon, we measured the group delay within the range of approximately 10 MHz [gray area in Fig. 5(b)] around the center frequency of the filter. The group delay varies in a range of 1.26 ns due to the non-ideal transmission characteristics of the YIG filter, and there are about 16 modes within the specified region. Therefore, when the previous mode lost locking, it became feasible to identify a mode nearby with a suitable delay among the densely populated modes around the center frequency of the filter, facilitating smooth re-oscillation. The average group delay of the filter was tested over a frequency range of 10 GHz (from 6 to 16 GHz), as illustrated in Fig. 5(c). The results reveal that the average delay fluctuates within a range of less than 5 ns, and the delay variation within a bandwidth of 10 MHz at each frequency point is quite small. Therefore, reliable and low-noise oscillations are readily achievable when the center frequency of the YIG filter is tuned within several gigahertz.

Considering the remarkable robustness of the implemented COEO, additional evaluations were carried out to measure the random FH signals it produces within a designated frequency range. A sequence of voltage signals, ranging from 3 V to 7 V, is generated from a random number generator. These signals were then input into a programmable DC power supply, generating a corresponding oscillation frequency of the COEO for each voltage jump. Measurements of phase noise and SMSRs were conducted for the random FH signals, yielding typical values of −138dBc/Hz at 10 kHz and 90 dB on average, as shown in Fig. 6(a). Figure 6(b) depicts the operating frequency in response to various voltage signals, demonstrating a linear relationship of 1.758 GHz/V. In addition, an assessment of the FH resolution was conducted. The theoretical resolution of the FH signal depends on the FSR of the fiber loop, which is approximately 625 kHz in our case. Continuous switching of the FH signals with a resolution of 1.25 MHz is demonstrated, which was limited by the 0.7 mV resolution of the DC power supply, as shown in Fig. 6(c). Furthermore, the FH speed was tested through transient analysis using FSWP50. The hopping time of the FH signal in a free-running state involves multiple variables, such as the electrical signal switching time, tuning response time, and the time required for switching and re-oscillating. Here the FH speed is notably influenced by the sluggish tuning response of the YIG filter. As depicted in Fig. 6(d), the results reveal that the switching time is approximately 1.5 μs for a 5.3 MHz step. Potential reductions in hopping time can be achieved by employing YIG filters with higher sweep speeds.

Table 1 provides a performance comparison of FH-COEO with other reported tunable OEOs. The results clearly illustrate that our approach exhibits the most favorable combination of the lowest phase noise and the highest SMSR characteristics, spanning a broad frequency tuning range. Notably, the FH-COEO employs a fiber delay line with a length of only 150 m, allowing for a compact packaging configuration. This highlights the potential for deploying low-phase-noise optoelectronic oscillators beyond laboratory settings, facilitating their application across diverse mobile platforms.Table 1.

Comparison of Low-Noise Frequency-Hopping Signal-Generation Schemes in OEOs

The ultralow phase noise exhibited by the COEO indicates exceptional short-term frequency stability. However, over longer timescales, the frequency stability is constrained by thermal and power fluctuations within the laser. The quiet point does not significantly improve close-in phase noise because our fiber loop is placed in an open environment without any temperature control or isolation measures, which allows external noise to couple into the system and limits the improvement of near-offset phase noise. To mitigate frequency drift, synchronization with an external reference source becomes imperative. The optical loop of the COEO generates pulses with a specific repetition rate, primarily determined by the mode-locked laser loop length and the microwave feedback phase. Consequently, independently locking the optical or electrical loop is impractical due to their dynamic correlation. In this context, a dual-channel feedback PLL is designed, and the error signal is fed back to both the optical fiber stretcher and the RF phase shifter for a stable lock. Figure 7(a) demonstrates a notable reduction below 100 Hz offset frequency when the phase-locked loop is synchronized at the 10 GHz operating frequency. The stability of the output frequency, assessed by the overlapping Allan deviation, exhibits an improvement of nearly three orders of magnitude, reaching 6.1×10−12 at 1 s averaging time, as shown in Fig. 7(b).

In summary, we demonstrate an ultralow-noise COEO with flexible tuning capability and high robustness. The oscillator has a tunable output frequency over 2–18 GHz and exhibits phase noise as low as −140dBc/Hz at 10 kHz. The low-phase-noise characteristic of such a short-fiber COEO is attributed to the enhanced Q-factor from the regenerative gain of the laser cavity, the anti-polarization perturbation structure, and the quiet point operation with intracavity SOA. Simultaneously, the inherent large locking bandwidth enhances the robustness of the oscillator, thereby enabling frequency-hopping operation. The demonstrated low-phase-noise (below −135dBc/Hz at 10 kHz), low-spuriousness (−85dBc), and broadband random FH signal generation proves that the proposed COEO is a strong candidate for FH microwave sources in wireless communication and radar systems, with the potential to enhance the communication capacity and improve interference immunity without compromising on the low-noise performance.