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Optoelectronic oscillators (OEOs), based on optical fiber loops to act as a high-Q cavity, are capable of generating stable radio-frequencies (RF). The long-term frequency stability of the OEO is then limited by the cavity variation that is mainly induced by temperature sensitivity of the optical fiber. In order to actively stabilize the OEO cavity, we employ the technique of RF transfer over optical fibers. We propose and experimentally demonstrate a dual-loop-OEO scheme to enhance the long-term stability with an injected probe signal to monitor the phase variation in the fiber loops. The experimental results show that the resulting spread-spectrum signal is useful in monitoring the fiber delay without observable interference. The relationships between the measured frequency and the monitored delay are theoretically and numerically discussed. We also estimate the long-term stability of the proposed OEO scheme with the cavity phase correction. The corrected result shows the long-term frequency stability of the proposed OEO is within 8.4×10−8 at one day.
©2012 Optical Society of America
1. Introduction
High performance oscillators are important means for modern communications, navigation, radar and precise scientific measurements. The optoelectronic oscillator (OEO) is one of the most potential technologies to generate radio-frequency (RF) signals with very high spectral purity [1, 2]. The OEO is commonly based on a long optical fiber loop that acts as a high quality factor (Q) cavity. Since a fiber loop cavity supports low loss transmission over a wide spectrum, capable frequencies ranging from 50 MHz to 100 GHz can be generated by this optical and electronic hybrid system. In such schemes, single-mode operation and the desired oscillation frequency strongly depend on the selection of components and filter technologies. Various OEO architectures that can achieve below −140 dBc/Hz at 10 kHz offset have been successfully demonstrated with multi-loop OEO [3, 4], coupled OEO [5, 6], and OEOs with photonic filters [7].
Although the very short-term (τ < 0.4 s) frequency stability of the OEOs is guaranteed by its ultra-low phase noise, the long-term performance of these oscillators is limited by the fiber loops’ phase sensitivities to the environmental perturbations. Nowadays, it is still a challenge to achieve a good long-term frequency stability of the OEO without a thermal stabilized chamber [8–10]. Meanwhile, the ultra-stable frequency transmission over an optical fiber link has developed rapidly in the recent years. An RF transfer using amplitude modulation of the laser carrier has demonstrated a frequency stability of the 10−15 level at 1-s averaging time and the range of 10−18 at one day [11–14]. An optical carrier transfer can reach the stability below 10−18 after 1000 s [15–17]. For compensating the delay variation of the outdoor optical fiber paths, a phase correction is employed by means of the phase information of the round-trip signal. In this study we propose a novel architecture by utilizing the RF transfer technology to investigate the influence of phase variations in the OEO optical fiber loop. We experimentally demonstrate the use of an injected probe signal for monitoring the fiber delay and evaluate the performance of OEO by stabilizing its loop delay. With the proposed architecture, it can lead to a better understanding of long-term dynamic characteristics of the OEOs.
2. Theory
To illustrate the operation principle of the proposed architecture, a dual-loop OEO is shown in Fig. 1 . The OEO consists of a laser source, followed by an optical modulator, two spools of optical fiber to provide differential optical delays, a photodetector in each fiber route and a feedback circuit to form the resonating oscillators. Since there are two fiber paths with different time delays, two oscillators simultaneously exist in the dual-loop architecture. In this scheme, after being separately detected by the photodetectors, the two signals are combined, amplified by an RF amplifier to compensate the loss in the oscillating loops and filtered by a band-pass filter to achieve a single mode oscillation and then sent back to the modulator. If we assume the propagation delays of the long fiber and the related optical components be represented as , the short optical delay as , and all the rest common delays from the electrical components in the feedback loop be lumped as , then, these two loop delays can be expressed as , and , respectively.
The oscillating frequency is given by the relation:
where k and m are integers. The mode spacing of the OEO is then determined by the short loop delay , and the phase noise is dictated by the long loop delay . Since the oscillating frequency should match the resonations in both loops, this leads to the oscillator having narrow spectral width with suppressed spurious mode levels, as illustrated in Fig. 2 . After the oscillation starts, the stability of the oscillating frequency mainly depends on the environmental sensitivity of the high-Q elements, such as the optical fibers and the RF filter in the oscillators. Because of the frequency pulling effect between the narrow spectral width of the long loop and the broader one of the short loop, a small tuning of oscillating frequency is dominated by the long loop delay fluctuation. The cavity pulling is continuous unless a frequency hopping happens [3, 18]. Therefore, the following investigation will focus on the relation between the OEO frequency and the fluctuation of the long loop delay.
Fig. 2 Illustration of the frequency selection in the dual-loop OEO. and are the mode spacings of the long and short loops respectively.
If the long loop delay changes by an amount of , which may be caused by temperature or temporal strain, the oscillating frequency will be deviated by due to the change of round-trip time in the loop, and then the change of the oscillating frequency can be expressed as:
For a typical single-mode fiber, the corresponding temperature dependent values are found to be [8, 19]. If we put the OEO in a well-controlled chamber within a 0.001 temperature stability, the long-term frequency stability may still be limited to several ppb (part per billion, 10−9).From Eq. (2), the frequency stability is negatively related to the stability of long loop delay. If there is any possibility to monitor the loop delay in real time, one can stabilize the fiber delay by using the optical or RF compensation approach [13, 14]. Then, the frequency stability over long period will depend on how precise the monitoring and cavity tuning systems in the OEO can be. Therefore, an approach to precisely monitoring the long fiber delay is proposed and demonstrated in the following sections.
3. Experiment
Figure 3 shows the schematic diagram of the proposed frequency stabilizing system using a dual-loop OEO with a probe signal. The probe signal is inserted by an RF coupler (HP 15104A) in front of the optical modulation. The light source used in this experiment is a distributed feedback (DFB) laser with wavelength at 1310 nm. The probe signal, along with the resonating frequency is converted from electrical domain to optical domain by directly modulating the source laser. After direct modulation, the optical signal is divided into two loops by a 50/50 optical coupler. The longer one is a 10 km spool of standard single-mode fiber (SMF), and the short one is a 40 m SMF jumper cable. The short length was chosen to support only one mode in the short loop within the applied RF filter bandwidth. The optical signals in the two paths are individually recovered by the corresponding phtodetector in each optical path. After photodetection, an RF power splitter, followed by the photodetector in the long fiber, provides the output of the probe signal for monitoring the phase variation. Since the loss of the short fiber is much less than it of the long one, an additional RF attenuator is essential to balance the loop gains. After combining the signals from these two loops, two cascaded RF amplifiers (Agilent 11909A) provide the required signal gain to compensate the power loss of all the components in the system for reaching the oscillation condition. By using the attenuators 1 (−12 dB) and 2 (−22 dB), the power of long loop was set to reach its saturation and the other one in the short loop was set to about 10 dB weaker than its saturation. Because of the relatively short length, the strong power in the short loop will increase the phase noise within 10 kHz of the oscillating mode and degrade the short-term stability of the OEO. Here, we chose a weaker power to ensure good short-term frequency stabilities. An RF band-pass filter (K&L microwave, 5B111-70/T4), having 4 MHz bandwidth centered at 70 MHz, selects an oscillation mode around this intermediate frequency. Finally, a half of the RF power is taken off by a power splitter (Agilent 11667B) and used as an OEO output. The other part of the RF signal is combined with the probe tone and sent back for optical modulation to form the feedback loops. The output is measured by a spectrum analyzer and a frequency counter (SR 620).
Fig. 3 Experimental setup. Laser: 1310 nm direct modulation laser module; PD: photodetector module; SMF: single-mode fiber; AMP: amplifier; ATT: variable attenuator.
We employ a pseudo-random noise (PRN) encoded signal to monitor the long fiber loop delay of the OEO. The PRN signal is based on the spread spectrum techniques [20], resulting in a signal with a wider bandwidth and a lower spectral power density. The probe signal is generated by a modem (TimeTech SATRE), which is used for two-way satellite time and frequency transfer (TWSTFT) [21, 22] and acts as a time interval counter. The modem transmits a signal whose timing phase is synchronized to its reference clock. After the signal passing through the long fiber and returning back to the modem, the propagation delay between the input and output ports of the probe signal is measured by the spread spectrum technique. The reference of our measurement instruments is based on a Hydrogen maser (CH1-75A).
To avoid the interference between the oscillating and probe signals, the frequency of the probe signal should be away from the oscillating frequency as well as the band-pass filter’s bandwidth. Moreover, the power density of the probe must be much lower than that of the oscillating signal to avoid the frequency beatings between them. However, the probe signal should maintain a certain carrier-to-noise ratio (CNR) for an acceptable monitoring precision. In this experiment, the signal and probe’s RF spectrum is shown as Fig. 4(a) . The oscillating frequency is set at 69.3 MHz with a peak power of 4 dBm. The central frequency of the probe signal is placed at 88 MHz, which is 18.7 MHz away from the oscillation. When the chip rate of the probe signal is 10 MHz, the actual bandwidth with RF power larger than the background is 15 MHz. The total channel power of the probe signal is −20 dBm. The peak power occurred near 88 MHz is −59 dBm, which is about 63 dB lower than that of the oscillation signal. Thus due to the limited input bandwidth of the modem, the CNR of the received probe signal reaches 62 dB/Hz. In addition, the probe signal can be easily eliminated by a filter following the RF output. Figure 4(b) shows the corresponding RF spectrum that is further filtered using another filter and an amplifier with a total gain of 7 dB.
Fig. 4 RF spectrum of OEO tone at 69.3 MHz and probe signal centered at 88 MHz (a) Direct RF output. (b) Further filtered RF output.
4. Experimental results
4.1. Influence of the probe signal
It is necessary to verify that the probe signal used for monitoring the fiber delay does not increase the phase noise of the OEO before we apply it to enhance the stability of the resonant frequency. We use a signal source analyzer (Agilent E5052B) to perform the phase noise measurement. Figure 5 shows the phase noise spectrum of the free-running OEO, the setup is as illustrated in Fig. 3. The RF signal without adding a probe signal is shown as the blue line in Fig. 5. Because the gain from the short loop is much weaker, the first spur at 20 kHz is as large as −83 dBc/Hz. After adding a probe signal, shown as the red line, the phase noise spectrum plot shows the corresponding phase noise data nearly overlaps the original one at less than 10 MHz offset frequencies. Due to the modulation bandwidth of the probe signal, there is a bump in the phase noise spectrum from 10 MHz to 26 MHz. Its peak is only −128 dBc/Hz, and can be eliminated by an RF filter. The green line shows the phase noise data after passing a surface acoustic wave (SAW) filter which is centered at 70 MHz with 2 MHz bandwidth.
Fig. 5 Phase noise data of a dual-loop OEO. Various RF outputs, without and with probe signal, and with probe signal after a SAW filter, are compared.
The phase noise measurement demonstrates that the probe signal does not increase the phase noise at close-in offset frequencies. In order to confirm there was no frequency pulling effect between the oscillation and the probe signals, we scanned the central frequency of the probe signal from 85 MHz to 88 MHz gradually, and observed the oscillation frequencies of the OEO by a frequency counter. There is no observable resonating frequency shift during the frequency scan of the probe signal. Though the existence of this probe does not affect the stability of OEO for the period larger than 1 s, the probe signal must be continuously injected to keep the stable gain balance in the loops because a change of injection power would cause a change of oscillation frequency due to the gain competition in the loop.
4.2. Temperature sensitivity for delays
The OEO and the measurement system were placed in an air conditioned room so that the temperature was roughly kept at 24.5±0.6°C. We measured the delay of the long optical fiber and the delay of electrical components in the open loop, respectively. In the same period, the temperature data with a resolution of 0.1°C were also recorded. The temperature-dependent delay coefficient of the long fiber is about 377 ps/°C, or 7.6 ppm/°C relative to its typical delay, i.e. ns. The electric circuit consists of RF filter, amplifiers, power splitter, attenuator and electric cables of about 4 m long and contributes 289 ns delay totally, in which 261.2 ns of electric delay was introduced by the high-Q RF filter. As the temperature changes, the electrical delay varies by about −52 ps/°C, or −180 ppm/°C relative to its typical delay. The temperature sensitivity of the electrical delay was in the opposite direction compared with that of the optical fiber. Table 1 summarizes the temperature sensitivity of the introduced delays for various parts in the OEO.
Table 1. Temperature Sensitivity of Delays of Various Parts
4.3. Frequency versus monitored fiber delay
The frequency measurements with a 1-s gate time were recorded once per second, and no frequency hopping was observed during the 3-day measurement period. In the meantime, the delay of the long fiber was monitored via the probe signal and recorded every second. The standard deviation of the monitored delay data is about 10 ps. Such a precision was not enough to represent the actual delay variation in short term. In practice, we used the 600-s moving averages of the monitored data, whose standard deviation is 17 fs, to represent the delay of the fiber in this paper. We chose the averaging time of 600 s for having enough precision but sacrifice less real-time properties of the monitoring.
Figure 6(a) shows the comparison between the measured frequency deviation (i.e. ) and the monitored long fiber delay variation. It is clear that the frequency varied along with the fluctuation of the fiber delay. Figure 6(b) displays their correlation, which shows a linear dependency between the frequency and the delay variations. For each delay value, the corresponding frequency is not exactly one-to-one matched but exhibits some hysteresis. Since we observed that the RF filter with a metal shell was highly sensitive to the instant temperature fluctuation, while the 10-km fiber spool with a plastic cover responds relatively slowly to the change of room temperature, we suspect this hysteresis may be attributed to the asynchronous thermal response between the fiber spool and electrical components, which were not taken into consideration in our delay monitoring data. Moreover, the slope of 0.65 is less than the expected value of 0.86 (i.e. 325/377, obtained from Table 1). An explanation is given in section 5.1.
Fig. 6 Measured fractional frequency variation of the OEO versus negative value of long fiber delay variation. (a) Comparison of the frequency (red curve) and negative long fiber delay variation (blue curve). (b) Correlation between them.
For evaluating the long-term frequency stability, the Allan deviation is adopted here for its common popularity [23]. The overlapping Allan deviation results are shown in Fig. 7 where the frequency fluctuation of the measured data is represented as the red curve. The frequency stability is 2.4×10−10 at 1-s averaging time. Due to the thermal drift, the curve monotonically increases to 10−7 after 4000-s averaging time. There is a peak at 4×104 s, which corresponds to a half day due to the diurnal periodicity of room temperature. Following the relation obtained in Fig. 6(b), the corrected frequency data were calculated according to the monitored delay data. Its Allan deviation is shown in the blue line in Fig. 7. The plot shows that the corrected data are helpful to improve the stability for the averaging times of larger than 400 s. The frequency stability could be reduced from 5.5×10−7 to 8.4×10−8 at the half-day averaging time. For the averaging times from 12 hours to one day, the frequency stability could be kept within 8.4×10−8.
Fig. 7 Allan deviation of measured and corrected frequencies of a dual-loop OEO. The correction are made according to the relation in Fig. 6(b).
5. Discussion
5.1. Pulling effect by the short loop
In section 2, for a dual-loop OEO, we assume that the small frequency fluctuation is dominated by the long loop delay fluctuation. However, the frequency pulling due to the short loop is determined by its quality factor Q [18], and will influence the resulting stability of the oscillator. The overall Q of a dual-loop OEO could be regarded as an average between the long-loop’s high Q and the short loop’s low Q [4]. Due to the gain competition between dual loops, if we vary the gain condition in the short loop, the phase noise of a dual-loop OEO changes as the “weight” of short loop changes.
Figure 8 shows the phase noise under different gain conditions in the short loop, the green line represents the results for the gain (Gs) that the short loop reaches its saturation. The red and blue lines are the cases with 10 dB stronger than saturation (Gs + 10 dB) and 10 dB weaker than saturation (Gs–10 dB), respectively. The plot demonstrates that with a stronger gain in the short loop, the phase noise increases in lower offset frequencies (e.g. <20 kHz) but decreases in higher offset frequencies region (e.g. >20 kHz). For the OEO with a 10 dB stronger gain, the first spur at 20 kHz is reduced to −96 dBc/Hz.
Figure 9 shows the Allan deviation of a dual-loop OEO under various gain conditions in the short loop. With a 10 dB stronger gain, the short loop plays a significant role on the oscillated frequency. Its short-term stability is much poorer than the others. There is a bump at around 150 s, which corresponds to the half-cycle time of the air-condition operation. Compared with the long loop, the delay time contributed by electric components plays more important roles in the short loop, thus it is much more sensitive to the instantaneous thermal fluctuation. In the long loop, the variation of the electric part is almost neutralized by the long delay introduced by the long fiber spool. Nevertheless, after 1000 s of averaging time, the OEO with stronger gain in the short loop shows better stabilities. This may be even improved from the employment of the opposite thermal coefficients between the RF filter and fibers. These demonstrate that the long-term frequency fluctuation would also be affected by the short loop when the short loop was employed to suppress the spurious modes. This is the reason to explain for the measured slope in Fig. 6(b).
5.2. Performance evaluation of active stabilization on loop delays
According to the monitored fiber delay data, we are able to stabilize the fiber delay by compensating its variation. To carry out the active optical compensation, the fiber delay could be controlled by inserting a commercially available tunable fiber delay line. Since the fiber spool provides desirable longer thermal response, it is applicable to employ moving averages of the monitored data to enhance its precision. Based on the resolution provided by the probe signal with 10 MHz bandwidth, it is possible to stabilize a fiber delay within 25 fs, corresponding to a relative offset of 5 × 10−10 for a 10-km fiber delay. However, both the long loop and the short loop have to be stabilized concurrently. Then, it is helpful to increase the fiber length of the short loop. For a short loop of 800-m fiber delay, the estimated relative offset is within 6.25 × 10−9. Moreover, we should pay more attention on the influence of the RF filter, which introduced considerable delay variations but was not monitored. In practice, it can be overcome by employing a temperature-insensitive filter with a simple thermal insulation. Through the use of ceramic technology, some commercially available filters have superior temperature stability, with the corresponding temperature coefficient as small as a few ppm/°C. Finally, the long-term frequency stability of this dual-loop OEO is expected to be several ppb (10−9) without the need of a thermal-controlled chamber. This advantage avoids huge energy consumption, which is important for some specific applications, e.g. satellite system.
Since a dual-loop OEO is not effective to suppress the spurious modes, the dual injection-locked OEO (DIL-OEO) has been proposed as a good solution to reduce spurs [24]. The independent master and slave loops in a DIL-OEO make it more flexible to apply the probe signal for monitoring the loop delay. On the other hand, the delay monitoring can be realized by a flexible and low-cost software-defined method. The pseudo-random noise (PRN) probe signal could be generated by an arbitrary waveform generator and received by an analog-to-digital sampler. Precise delay can be obtained by the cross-correlation spectrum analysis. A new software modem based on graphics processing units (GPUs) had been demonstrated [25]. This enables us to perform the monitoring experiment by the real-time processing, and delay data could be obtained every 4 ms. Thus, the bandwidth of PRN signal would not be limited by the commercial modems, which are generally designed for the satellite communication system. In addition, the satellite bandwidth is an expensive resource. As wider bandwidth is employed, higher resolution of delay monitoring is obtained. Then, the level of 10−10 may be possible to be kept for a long-term frequency stability of this delay stabilized OEO.
6. Conclusion
A high performance OEO can act as a local oscillator that could lock the output of the absolute reference frequency, provided by the atomic transition. An OEO with a stabilized cavity could avoid the possible loss of lock which may be caused by the cavity pulling. In this paper, we have experimentally demonstrated a feasible method for monitoring the fiber delay of a dual-loop OEO with a spread-spectrum probe signal. Since the probe signal can keep a good carrier-to-noise ratio with a much lower power level than that of the oscillated signal, there is no observable interference in the oscillation loop. With the advent of novel tunable optical delay devices, the very precise tuning of the fiber delay has been an available technique. The cavity of the OEO can be stabilized by actively tuning the fiber delay according to the monitored data.
Through the better selection of components, we may employ a higher chip-rate PRN signal, which requires a broader bandwidth, to increase the precision of monitored delay data. The use of a thermal insensitive filter would make this OEO more reliable. Then, an OEO equipped with a monitoring and tuning function may have the potential to become even better than that predicted in this paper. This OEO may have great potential for special applications, such as satellite systems or the local oscillator of an atomic clock.
Acknowledgments
The authors would like to express their gratitude to Mr. P. L. (Allen) Chang of Agilent, Taiwan, for supporting the phase noise measurement.
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