Optoelectronic oscillators (OEOs) are promising sources of low phase noise radio frequency (RF) signals. However, at X-band frequencies, the long optical fiber delay line required for a high oscillator Q also leads to spurious modes (spurs) spaced too narrowly to be filtered by RF filters. The dual injection-locked OEO (DIL-OEO) has been proposed as a solution to this problem. In this work, we describe in detail the construction of a DIL-OEO. We also present experimental data from our systematic study of injection-locking in DIL-OEOs. With this data, we optimize the DIL-OEO, achieving both low phase noise and low spurs. Finally, we present data demonstrating a 60 dB suppression of the nearest-neighbor spur without increasing the phase noise within 1 kHz of the 10 GHz central oscillating mode.
© 2011 Optical Society of America
1.1. The single-loop optoelectronic oscillator
An optoelectronic oscillator (OEO) is a radio frequency (RF) oscillator that utilizes an optical fiber delay line as a high-Q resonant cavity [1, 2]. The low loss per unit length of standard single-mode optical fiber of 0.2 dB/km indicates that it is should be possible in principle to construct OEOs with delay lines as long as 16 km and Q-factors as high as 4 × 106 . The best commercially available RF oscillators have Q-factors on the order of 1×105 . The high Q of an OEO implies that the phase noise that it produces should be very low.
The OEO’s Q-factor is approximately equal to 2πfτ, where f is the OEO’s oscillation frequency and τ is its round trip time . However, the frequency spacing between the oscillation modes of the OEO is inversely proportional to τ. For example, an OEO with a 4 km fiber delay line has a Q-factor of 200,000 but a mode spacing of only 50 kHz. Modes spaced so narrowly cannot be filtered using conventional RF filters.
1.2. Dual-cavity optoelectronic oscillators
Mode selectors with higher finesse than conventional RF filters are necessary to suppress the spurs of a high-Q OEO. Dual-cavity OEOs use a second optoelectronic loop or delay line as a high-finesse filter. Proposed dual-cavity designs include: the dual optoelectronic oscillator (DOEO), the coupled optoelectronic oscillator (COEO), and the dual injection-locked opto-electronic oscillator (DIL-OEO) [5–7].
The DOEO consists of a single optoelectronic loop with two fiber delay lines of different lengths. The lengths are chosen so that the two delay-lines only share a single common mode within the RF filter bandwidth. All other modes experience less gain per round trip and so are suppressed via gain competition.
The COEO consists of a fiber laser with a medium length delay-line of approximately 500 m length coupled to an optoelectronic loop via a common electro-optic modulator. The electro-optic loop locks the fiber laser’s mode spacing to the desired RF frequency and suppresses all but one of the fiber laser’s modes.
The DIL-OEO consists of a high-Q master OEO loop that is injection-locked to a relatively low-Q slave OEO loop. The slave OEO loop signal preferentially amplifies the desired master loop mode while suppressing all other spurious modes. In this work, we focus on the DIL-OEO, presenting the first systematic study of injection-locking in optoelectronic oscillators.
1.3. The dual injection-locked optoelectronic oscillator
Figure 1 shows a schematic illustration of the DIL-OEO. The DIL-OEO consists of two coupled OEO loops. The mode spacing of the master loop is typically between 10 and 100 kHz. The shorter slave loop is designed to support only a single mode within the bandwidth of its in-loop RF filter. We phase lock the two loops by injecting a portion of the master-loop signal into the slave loop, while, at the same time, injecting a portion of the slave-loop signal into the master loop. As we have shown in previous work, this bi-directional injection is required to achieve both low phase noise and low spurs . Injecting a portion of the master-loop signal into the slave loop ensures that the DIL-OEO maintains a high Q. Injecting a portion of the slave-loop signal into the master loop ensures spur suppression and maintains a stable phase-lock between both loops. We refer to injection from the master loop to the slave and injection from the slave to the master loop as forward and reverse injection respectively.
Our ultimate goal is to design an optimized DIL-OEO with both low phase noise and low spur levels. However, due to the complexity of the injection-locking process, it is difficult to determine the OEO parameter values that produce the best results. To assist us in accomplishing our objective, we have created a reduced model that provides qualitative insights into the injection-locking process in the DIL-OEO . From these insights and our quantitatively accurate full model  that has been described in detail elsewhere , we were able to construct our optimized DIL-OEO.
2.1. The Yao-Maleki single-loop model
Our reduced model is based on the Yao-Maleki single-loop OEO model. In their original work, Yao and Maleki presented a reduced model of the single-loop OEO that allowed them to calculate the phase noise when the OEO operates in steady-state [1, 2]. We used similar methods to model the two coupled loops of the DIL-OEO. In order to better describe our DIL-OEO model, we begin with a review of the Yao-Maleki model.
We first define A(t), the complex envelope of the voltage at the output of the photodetector, by writing , where V(t) is the real voltage signal, R is the output impedance of the photodetector, and f0 is the carrier frequency, which is typically near 10 GHz. The envelope is normalized so that the oscillating power P(t) = |A(t)|2. Following the signal through one round trip of the OEO that is shown in Fig. 1, we find that A(t) must satisfy the delay-difference equation
In general, the gain saturation factor M [A(t – τ)] is a nonlinear function of the amplitude A(t). However, when the OEO operates at steady state, the gain GM is determined by the Barkhausen condition  and may be treated as a constant. Yao and Maleki assume that the gain saturation is due to the electro-optic modulator and has the formEq. (1) becomes linear, and its Fourier transform takes the form
From Eq. (4), we obtain immediatelyEq. (5) and taking an ensemble average over the noise we find
The minima of the denominator in Eq. (6) occur when ωτ = 2nπ, where n is an integer. If we assume strictly white input noise sources so that N(ω) = N0, then the power spectral density at each resonant frequency isEq. (6) reduces to the standard Lorentzian form
2.2. The reduced DIL-OEO model
We now present an overview of our reduced model of the DIL-OEO . Figure 2 is a schematic illustration of the DIL-OEO that shows the field injection ratios γij. In a manner analogous to the Yao-Maleki model, we represent the DIL-OEO amplitudes as
Taking the Fourier transform of Eq. (9) and solving for the steady-state amplitudes, we obtainEq. (10) and Eq. (11), we have incorporated the coefficients γ11 and γ22 into the terms (1 – Δ1) and (1 – Δ2). We assume that the noise sources are uncorrelated, so that the power spectral densities are given by Eq. (12). If we substitute the condition ω = 0 into Eq. (12), we find that the resonant power levels are given by Eq. (15), we determine that |D(ω)| ≪ |γ12γ21|.
Since the ratio of the noise power to the signal power is set by |D(ω)| ≪ |γ12γ21|, it is useful to writeEq. (12), it follows that with just white noise drivers when ωτ1 ≪ 1 and τ2 ≪ τ1. Therefore, is the noise-to-signal ratio at resonance of the injection-locked OEO.
Solving for the average oscillating powers in the master and slave loops, we find thatEq. (16) into Eq. (17), we find that ,
Due to injection locking, the quantities Δ1 and Δ2 are many orders of magnitude greater than Δ in the single-loop OEO . The magnitudes of Δ1 and Δ2, as well as their dependence on both γ12 and γ21 have important implications for spur suppression in DIL-OEOs, which we will explore in the following sections.
2.3. Effects of injection-locking on the close-in phase noise
From Eq. (12), we can extract qualitative information on both the phase noise and spurious mode levels in both loops of the DIL-OEO. In this section, we focus on the effects of injection-locking on the phase noise around the central oscillating tones of both the master and slave loops, where the mode number n = 0. We refer to the noise in this range as the close-in phase noise.
In order to simplify the analysis, we assume that W1 = W2, and N1 = N2. We also assume that γ21 ≫ γ12. Equation (12) is capable of quantitatively describing the DIL-OEO’s behavior over a wider range of parameters. We limit ourselves to the above assumptions to clarify the behavior. For frequencies close to the central resonant frequency of both the master and slave loops, we may writeEq. (19) into Eq. (12) we obtain the following asymptotic approximations of the power spectral densities in both loops:
Equation (20) shows that for radial frequencies less than ωL = |γ12|/τ1, the master and slave loop signals converge. Beyond ωL, the slave loop signal reaches a plateau, while the master loop’s signal continues to decrease with increasing frequency. Physically, the frequency ωL corresponds to the Leeson frequency, beyond which the phase of the slave loop is no longer locked to the phase of the master loop . Increasing the master-to-slave injection ratio increases the Leeson frequency thereby reducing the slave loop’s noise at high offset frequencies.
2.4. Effects of injection-locking on spurious modes
Finally, we investigate the power at the spurs. When we are close to a spur of the master loop, so that ω = ωn = 2πn/τ1, where n = 1, 2, 3, we find
Spur suppression in the master loop occurs because the denominator in Eq. (12) only approaches its minimum value when both master and slave loops are resonant. The master loop spurs are attenuated by increasing the reverse injection ratio, reducing the forward injection ratio, and by increasing the slave loop length. The experimental data we will present in this work is consistent with these results. However in the optimal operating regime in which γ21 ∼ γ12 and both are large we found that it is necessary to use a full model to achieve quantitative accuracy .
3. Experimental setup
In this section we present a detailed description of the DIL-OEO. We describe the master and slave loops as well as the bi-directional injection bridge. We also outline steps taken to optimize the phase noise and stability of the DIL-OEO.
3.1. Master and slave loops
Figure 1 shows a schematic illustration of the DIL-OEO. The master and slave loops each contain a CW laser, a lithium niobate modulator, a length of optical fiber, a photodetector, a series of RF amplifiers, directional couplers leading to and from the bi-directional injection bridge, an RF filter, and output couplers to the measurement system. The CW lasers are distributed feedback (DFB) semiconductor diode lasers with wavelengths of 1550 nm. We used a 20 mW laser in the master loop, and an 80 mW laser in the slave loop.
We used standard Corning SMF28e single-mode optical fiber in all our experiments. High-Q OEOs typically have loop lengths between 2 km and 20 km. For our injection-locking study, we used a 4 km fiber spool in the master loop. We used two different slave loop lengths: 44 m and 547 m. We chose the slave loop lengths so that the slave loop supported no spurs within 500 kHz of the central RF oscillating tone. The 547 m slave supported approximately 16 spurs within the RF filter bandwidth, whereas the 44 m slave loop supported none.
We used semiconductor p-i-n photodetectors in both loops. Our photodetector responsivities were approximately 0.7 A/W at 1550 nm. The photodetectors we used had bandwidths of 12 GHz at their 3 dB rolloff frequencies. We used AML1010PNA2101 low-phase-noise RF amplifiers in both loops. These amplifiers have phase noise levels of −155 dBc/Hz at 1 kHz offset frequency, and noise figures of 6.5 dB. All amplifiers had 22 dB of small-signal gain, saturation output powers of 24 dBm at 10 GHz, and bandwidths of 2 GHz at their 3 dB rolloff frequencies. The RF filters ensured that the DIL-OEOs oscillated in an 8-MHz-wide frequency range around 10 GHz. The slave loop also included a tunable RF phase shifter. We used the phase shifter to tune the resonant frequency of the slave loop close enough to one of the resonant modes of the master loop to ensure phase-lock between both lops.
We placed output couplers in both loops so that we could measure their oscillating signals independently. We placed the output couplers immediately after the RF amplifiers so that we measured the RF signal at its maximum amplitude in each loop. The output powers were approximately 15 dBm. We required high output powers to drive the modulators and mixers in our phase noise measurement system with minimal amplification. In all of our experiments, the equilibrium oscillating power at the output couplers of the master and slave loops were within 1 dB of each other. We achieved nearly identical equilibrium powers in both master and slave loops by using RF amplifiers with similar saturation powers in both loops.
3.2. Bi-directional injection bridge
For the purposes of our study, the key feature of the DIL-OEO is the bi-directional injection bridge. We designed the injection bridge to allow us to vary the forward and reverse injection ratios independently. Figure 2 shows a schematic illustration of the bi-directional injection bridge. Both the master and slave loops contain output and input couplers. The bi-directional bridge consists of two arms. One arm leads from the master loop’s output coupler to an isolator, a variable attenuator and into the slave loop’s input coupler. The other arm of the bridge leads from the slave loop’s output coupler to a variable isolator, and ends at the input coupler of the master loop. The isolators in each arm provide 1 db of loss in their forward directions while providing 20 dB of loss in their reverse directions. These isolators ensure that 99% of the master-to-slave injection occurs in the forward injection arm, and that 99% of the slave-to-master injection occurs in the reverse injection arm. The effective forward and reverse injection ratios are determined by the input and output couplers as well as the variable attenuators in the injection bridge. The couplers used in this work are all bi-directional RF power dividers/combiners. For weakly coupled DIL-OEOs, we used −6 dB dividers were used as input and output couplers in both master and slave loops. We varied the forward and reverse injection ratios by varying the attenuation in each arm of the injection bridge. We used −6 dB couplers to construct our weakly-coupled bridge, and −3 dB couplers in our strongly-coupled bridge. In weakly-coupled DIL-OEOs, the attenuation in the injection bridge did not affect the signal levels in the DIL-OEO at steady state. However, when using −3 dB dividers for strong coupling, attenuation in the bridge did affect the power levels in both master and slave loops at steady state. Changes in the steady-state power levels in either loop altered both the phase noise and spur levels of the DIL-OEO. When building our strongly coupled DIL-OEO, we found it best to place the bridge after the final RF amplifier in both loops. Gain saturation in the final RF amplifier ensured that the input signal levels into the bridge at steady state remained constant even as we varied the forward and reverse injection ratios.
4. Experimental results
In this section, we present experimental data on the effects of forward injection, reverse injection, and slave loop length on the DIL-OEO’s phase noise and spurs. We collected all experimental data using a cross-correlation photonic delay line measurement system . Our goal was determine the forward and reverse injection ratios that led to maximum spur suppression while maintaining low phase noise in the DIL-OEO.
In our reduced model, the bi-directional injection bridge is represented by a 2-by-2 matrix that couples the oscillating fields in the master and slave loops. The complex coupling coefficients are given by γij, where subscripts 1 and 2 refer to the master and slave loops respectively. Experimentally, we measure the signal powers not the electric fields; so we will use the power coupling coefficients
We define the forward injection level as the ratio of the power of the signal injected from the master loop to the slave loop to the power of the master loop signal at the point of injection. Conversely, we define the reverse injection level as the ratio of the power injected from the slave loop to the master loop to the power of the slave loop signal at the point of injection. Given Eq. (23), the forward and reverse injection ratios are equal to Γ21 and Γ12 respectively.
4.1. Forward and reverse injection
As noted above, the forward injection ratio is defined as the ratio of the master-to-slave injected power to the oscillating power in the master loop at the point of injection. From Eq. (23), the forward injection level is
To test the effects of forward injection on phase noise and spurious mode levels, for fixed master and slave loops lengths, we vary the forward injection ratio while keeping the other injection ratios fixed. For this forward injection test, the injection ratios Γ11 and Γ22 were fixed at −3 dB. The reverse injection ratio Γ12 was fixed at −15 dB. The forward injection ratio Γ21 was set to the following values: −15 dB, −18 dB, −25 dB, and −35 dB. For each forward injection ratio, phase noise and spurious mode data was collected from both the master and slave loops of the DIL-OEO.
We performed the same procedure to test the effects of reverse injection on phase noise and spurious mode levels. In the case of reverse injection, the forward injection ratio Γ21 was fixed at −15 dB, while the reverse injection ratio Γ12 was set to the following values: −15 dB, −18 dB, −25 dB, and −35 dB. As with forward injection, the phase noise and spurious mode data was collected from both the master and slave loops of the DIL-OEO.
Figure 3 shows the dependence of the master loop signal parameters on both forward and reverse injection. Figure 3(a) shows that forward injection is 4 times more effective than reverse injection at altering master loop phase noise at 1 kHz. Similarly, Fig. 3(b) shows that the effect of forward injection on phase noise at 10 kHz is 8 times greater than that of reverse injection. Finally, Fig. 3(c) shows that reverse injection is 8 times more effective than forward injection at altering spur levels in the master loop. In Fig. 3 we have included theoretical data for comparison. This theoretical data was calculated using Eq. (12) which is valid for all values of γ12 and γ21 used.
Figure 4 shows similar results for the slave loop signal. Forward injection has a greater effect than reverse injection on close-in phase noise and the Leeson bandwidth. The effect of forward injection on Leeson bandwidth can be determined from Fig. 4(b) which shows the phase noise at 10 kHz. At 10 kHz, the phase noise in the slave is primarily determined by the noise plateau which in turn is determined by the Leeson bandwidth of the DIL-OEO. Figure 4(c) shows that, as we observed in the master loop, the slave spur level is more strongly affected by reverse injection than forward injection. However, unlike in the master loop, there exists an optimal reverse injection ratio above which spur levels rise. We observe no such optimal point for forward injection over the range of values investigated. The above data suggests that increasing both forward and reverse injection in unison reduces both phase noise and spurious mode levels. Again, in Fig. 4 we have included theoretical data for comparison. This theoretical data was calculated using Eq. (12) which is valid for all values of γ12 and γ21 used.
4.2. Slave loop length
The preceding experimental data was obtained from the DIL-OEO using a 44 m slave loop. The slave loop length was chosen to ensure that the slave supported only a one mode within the bandwidth of the 8 MHz bandpass filter. However, because of the relatively short delay, the free-running slave loop noise is 30 dB higher than the free-running master loop noise at 1 kHz. Theoretical models predict that increasing slave loop length should increase suppression of the first and second spurs of the DIL-OEO [9,10,14]. In this section, we present experimental data on the effects of increasing slave loop length on the phase noise and spurs in a DIL-OEO.
We replaced the 44 m fiber spool in the slave loop of the DIL-OEO with a 547 m fiber spool. Figure 5 shows a plot of the free-running phase noise data for both slave loops. The 547 m slave loop’s phase noise is 15 dB lower than the that of the 44m from 1 kHz to 100 kHz. However, the 547 m slave has a spur level of −88 dBc/Hz at 375 kHz. From the free-running data, we expect the longer slave to reduce the spurious modes of the DIL-OEO at 50 and 100 kHz while introducing an additional mode at 375 kHz. We constructed DIL-OEOs using both slave loops while fixing the master loop length at 4 km. We fixed the forward and reverse injection ratios at −18 dB.
Figure 6 shows phase noise data from both DIL-OEOs. Fig. 6(a) shows that increasing the slave loop’s length had no effect on the master loop phase noise. However, increasing the slave loop length reduced the first and second spurs in the master loop by 20 and 8 dB respectively. All of the master loop’s spurs were reduced by increasing slave loop length including the spur closest to the free-running slave loop spur at 375 kHz.
Figure 6(b) shows the phase noise data from the slave loop. Increasing slave loop length decreased the first and second spurs by 28 and 8 dB respectively. In the long-slave-loop DIL-OEO, the spur levels rose as their offset frequencies approached that of the free-running slave loop spur. At 354 kHz, the long-slave-loop spur level was 17 dB higher than that of the short slave loop. However, the maximum spur level in the long slave loop (−113 dBc/Hz at 354 kHz) was 8 dB lower than the maximum spur level in the short slave loop (−105 dBc/Hz at 50 kHz). Furthermore, the phase noise at offset frequencies greater than 10 kHz was also reduced by increasing the slave loop length.
We note that the Leeson bandwidth, remained unchanged. The master and slave loop signals diverged at 1.5 kHz regardless of the slave loop’s length. Nevertheless, the slave loop phase noise beyond the Leeson bandwidth decreased as we increased the slave loop length. At high offset frequencies, the injection-locked slave loop signal benefited from the reduced phase noise of the free-running slave loop. We conclude that, as in the master loop, increasing slave loop length improves the slave loop signal. In subsequent sections, we use a 547 m slave loop in the DIL-OEO because its benefits outweigh the disadvantage of the additional spurious mode at 354 kHz.
4.3. Coupling strength
In Sec. 4.1, we presented experimental data that suggests that the phase noise and spurious mode levels in both master and slave loops of the DIL-OEO may be reduced by increasing the forward and reverse injection ratios in unison. Both our full and reduced models also suggest that increased coupling should improve DIL-OEO performance [9, 10, 14]. In order to investigate the effects of increasing both forward and reverse injection, we constructed a strong-injection bridge. The weak-injection bridge used in the forward and reverse injection studies −6 dB couplers and could provide at most −15 dB forward and reverse injection. In the strong-injection bridge, we used −3 dB couplers in both the forward and reverse injection arms.
We achieved forward and reverse injection ratios of up to −7 dB with the strong-injection bridge. However, the insertion losses Γ11 and Γ22 were increased to −7 dB. For the purposes of this study, we define a coupling coefficient C given by
In our experimental study of coupling strength, we fixed Γ11 and Γ22 of the DIL-OEO at −7 dB. We varied the coupling coefficient by varying Γ12 and Γ21 using the variable attenuators in the bi-directional bridge. The coupling coefficients used in the study were: 0 dB, −3 dB, −6 dB, −10 dB,and −20 dB. For each coupling coefficient, we measured the phase noise in both the master and slave loops of the DIL-OEO.
Figure 7 shows the phase noise at 1 kHz versus coupling coefficient for both free-running and injection-locked master and slave loops. Increasing coupling from −20 dB to 0 dB reduced the slave loop noise by 3 dB while leaving the master loop noise unchanged. Over the set of coupling coefficients used, the best noise performance at 1 kHz was obtained by setting the coupling coefficient to 0 dB. Setting C to either 0 dB or −6 dB ensured that the phase noise power spectral densities at 1 kHz of both master and slave loops were within 3 dB of the phase noise power spectral density of the free-running master loop.
Figure 8 shows the effect of coupling strength on the noise at 10 kHz. Again the effect of coupling on the slave loop signal is greater than the effect on the master loop signal. Increasing the coupling from −20 dB to 0 dB reduced the slave loop noise by 13 dB but had no effect on the master loop noise. The injection-locked master loop phase noise at 10 kHz was lower than the phase noise of the free-running master loop because the white noise power in the free-running slave loop was lower than that of the free-running master loop.
In the slave loop, we used a 19 dBm laser in order to minimize the white noise in the slave loop. In the master loop, on the other hand we used a 13 dBm laser that provides lower flicker noise than does the slave loop’s laser because the noise in the DIL-OEO is dominated by the master loop’s contribution at offset frequencies within the Leeson bandwidth. The noise beyond the Leeson bandwidth is a combination of the noise from the master and slave loops. As one consequence, the noise in the injection-locked slave loop for −20 dB coupling is higher than the noise in the free-running slave loop.
Figure 9 shows the spur level versus coupling strength in both master and slave loops. Using −6 dB coupling generated the lowest spurs in both loops. The lowest master loop spur level was −128 dBc/Hz, which is 50 dB lower than that of the free-running master loop. The lowest spur level in the slave was −134 dBc/Hz, which is within 4 dB of the noise level of the free-running slave loop at the same offset frequency.
Figure 10 shows the phase noise data of the optimized DIL-OEO. Using −6 dB coupling provided the best combination of low phase noise and low spur levels in both the master and slave loops. The slave loop signal, in particular, benefited from increased coupling. We succeeded in reducing the spur level to within 4 dB of the noise level of the free-running slave loop while reducing the phase noise at 1 and 10 kHz by 13 and 7 dB respectively. The noise penalty of the injection-locked slave relative to the free-running master loop was 8 dB at 10 kHz and less than 3 dB at 1 kHz, while the spur reduction was over 60 dB. Our experimental results are consistent with the predictions of both our full and reduced models [9, 10].
We investigated the effects of forward and reverse injection on the steady-state signal of the DIL-OEO. We found that increasing both forward and reverse injection in tandem reduced spur levels in the master loop while also reducing phase noise in the slave loop. Increasing slave loop length also reduced spur levels in the loop. The improved understanding of injection-locking obtained from our experimental data, coupled with insights from our theoretical models, enabled us to optimize the phase noise and spur levels of the DIL-OEO.
We have experimentally constructed a DIL-OEO with the low phase noise of a long-loop OEO and the spurious mode levels of a short-loop OEO. Our results demonstrate that the dual injection-locked OEO is capable of combining the high-Q of a long cavity OEO with the single-mode behavior of a short loop OEO. Having circumvented the tradeoff between Q and mode-spacing, we have demonstrated that the DIL-OEO is a practical source of low phase noise RF signals.
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