Open Access
Add to BibSonomyAbstract
Extraction of a microwave component from a low-time-jitter femtosecond pulse train has been attractive for current generation of spectrally pure microwave. In order to avoid the transfer from the optical amplitude noise to microwave phase noise (AM-PM), we propose to down-convert the target component to intermediate frequency (IF) before the opto-electronic conversion. Due to the much lower carrier frequency, the AM-PM is greatly suppressed. The target is then recovered by up-conversion with the same microwave local oscillation (LO). As long as the time delay of the second LO matches that of the IF carrier, the phase noise of the LO shows no impact on the extraction process. The residual noise of the proposed extraction is analyzed in theory, which is also experimentally demonstrated as averagely around −155 dBc/Hz under offset frequency larger than 1 kHz when 10-GHz tone is extracted from a home-made femtosecond fiber laser. Large tunable extraction from 1 GHz to 10 GHz is also reported.
© 2015 Optical Society of America
1. Introduction
Ultralow phase noise microwave and radio frequency (RF) sources are critical for various scientific and engineering applications, such as communications, navigations, high-performance antennas and radars, and precise scientific measurements. Direct generation rather than frequency multiplication is required for ultralow phase noise. Electronic high quality factor (Q-factor) resonators [1] are usually limited by the bulky and environment-sensitive cavities, as well as lack of tunability. Currently, significant efforts have been focused on developing new low-phase-noise microwave sources with high frequency and wideband tunability, which are based on photonics technology. Optoelectronic oscillator (OEO) is one of the potential schemes [2–4]. At present, state-of-the-art OEO has a record low-phase-noise (−163 dBc/Hz @ 6 kHz offset) by 16-km fiber [5]. Microwave extraction from an ultra-stable femtosecond laser is another promising approach [6–11]. Based on the fluctuation-dissipation theorem [12], the increase rate of the oscillation timing jitter variance is in proportion to optical pulse duration. Compared with a 10-GHz microwave oscillator (as well as OEO), for example, a mode-locked laser generating 100-fs pulse width has a scaling factor of 106 [13]. As a result, the cavity length can be greatly shortened. Synthesis of 10-GHz microwave from 78-MHz free-running mode-locked Er-fiber lasers with −142 dBc/Hz single-sideband (SSB) noise at 10-kHz offset frequency has been reported [10]. The phase stability can be further improved by locking the femtosecond laser with a cavity-stabilized optical reference via optical frequency division.
Though photo detection of such low-time-jitter optical pulse train generates electronic spectrum composed of harmonics of pulse repetition rate up to the cutoff bandwidth of photo detector (PD) in theory, PD nonlinearities degrades the spectral performance. Under pulsed illumination, PD can be easily saturated since the peak optical power is much higher than continuous-wave (CW) light. The high-density photo-generated carriers and finite carrier mobility inside PD result in intensity-dependent charge screening, which slows down the response time of PD [14]. Such nonlinearity degrades the extracted microwave both in strength and in phase stability. Firstly, additional loss, besides the linear frequency response fading, appears at the high order harmonics, especially in microwave range. Secondly, any intensity fluctuation of the pulse train results in different PD response time, which couples the optical amplitude noise to microwave phase noise (AM-PM). Such nonlinearity can be overcome by state-of-the-art high-power PDs with optimized input optical power [9]. Optical filtering and pulse interleaving have also been reported to increase the microwave signal power and to reduce AM-PM [15, 16], with the loss of tunability. Another effective way is to synchronize a low-noise voltage-controlled oscillator (VCO) to the mode-locked fiber laser using a specially designed balanced optical-microwave phase detector (BOMPD) [17, 18]. The employment of BOMPD complicates the extraction scheme, and the VCO also limits the microwave frequency range.
In this paper, we propose that a delay-matched frequency conversion pair combined with an intermediate frequency (IF) filter in between results in an equivalent narrowband microwave filter, by which any microwave frequency component from the femtosecond pulse train can be extracted with low additional phase noise. The femtosecond pulse train firstly passes through a Mach-Zehnder modulator (MZM) driven by a microwave local oscillation (LO), and is directly detected by a low-speed PD, through which the wanted microwave is down-converted to an IF tone. The IF tone is selected by an IF filter and finally up-converted under the same microwave LO to recover the desired microwave carrier. Theory shows two implementations guarantee low phase noise extraction: time delay match between the second LO and IF filtering, and opto-electronic conversion in the low-speed first Nyquist zone of the periodic femtosecond pulse train. Numerical study as well as experiment shows the low additional phase noise. Our extraction scheme lowers the requirement of PD significantly. Large tunability is also an advantage of our scheme.
2. Principle and simulation
Here in theory we illustrate the advantages of the proposed microwave extraction based on frequency conversion pair and IF-domain filtering. Assume that an ideal femtosecond pulse train is described by its angular repetition rate, ωO, and single pulse intensity profile, q(t), whose energy is normalized to 1. The real one, however, suffers from intensity fluctuation, ΑO(t), and time jitter, τO(t), which is described by
If the pulse train is received by an ideal, noise-free PD to recover the Nth-order harmonic tone, the above time jitter results in the minimum phase noise asIf the direct detection is employed however the AM-PM is considered, the intensity fluctuation induces additional time jitter, τΑ(ΑO), so that the microwave phase noise is enlarged asThe microwave extraction based on the proposed equivalent filtering is shown in Fig. 1.
Fig. 1 The proposed microwave extraction from femtosecond optical pulse train through delay-matched frequency conversion pair and IF-domain opto-electronic receiving and filtering.
The microwave LO is located at ωL with large phase noise, φL(t). The MZM is biased at its quadrature angle. Here we assume a linear electro-optical transfer curve with a modulation depth of β for simplicity. A full nonlinear transfer curve, employed in the following simulation, can result in the same conclusion. The optical intensity after MZM is then
The approximation stands when the duration of femtosecond pulse is much shorter than the period of the microwave LO. Equation (4) shows that the microwave LO is down-converted (specifically, the so-called “bandpass-sampled” [19]) by optical pulse train, where the carrier frequency is greatly decreased from ωL to ωIF,Physically, the microwave LO is mixed with its nearest microwave component inside the femtosecond pulse train, so that IF carrier should be inside the first Nyquist zone, which explains Eq. (5). Different from the conventional down-conversion, the IF tone, denoted by Α’O in Eq. (4), is still carried by optical pulses. After the opto-electronic conversion by PD, one can get the electronic pulse train asWe consider the nonlinear saturation effect of PD, where the output pulse width, qΑ’O and the time delay, τΑ(Α’O), are both disturbed by the energy of each optical pulse, Α’O. The approximation in Eq. (6) stands when the duration of electronic pulse is much shorter than the period of IF tone. After the following IF filter, only the carrier around ωIF is selected. In Eq. (6), the ΣqΑ’O part contributes only its direct-current (DC) component, which can be well described by the integration of each qΑ’O. Though the PD is saturated, the photo-generated current can still be fully collected due to the low-speed repetition rate. As a result, ΣqΑ’O results in a constant 1, despite the pulse width and delay jitter. A second concern is that the newly-generated phase perturbation, ωIFτΑ(Α’O) in Eq. (6), is mainly a periodic one. From Eq. (4), Α’O contains the DC part (ΑO) as well as carrier at ωIF, so does the corresponding ωIFτΑ(Α’O). With a relatively high ωIF, e.g. tens of MHz, such high-offset-frequency phase distribution can be well separated from the wanted IF tone and be suppressed by IF filter. Under a linear fitting between the AM-PM-induced time delay and optical pulse energy, only time jitter from ΑO should be considered, and the signal after IF filter isAt the up-conversion mixer, the IF tone is multiplied with the same but time-delayed microwave LO, so that the target microwave component is recovered as [20]which is also the final output. In Eq. (8), Δt is the time delay difference between two microwave LO transmissions from the common output to up-conversion mixer. Accordingly, the phase noise extracted by the proposed equivalent filtering isCompared with the minimum extraction phase noise in Eq. (2), phase noise extracted by the proposed scheme contains two additional noises. Firstly, the AM-PM in PD still appears with however greatly suppressed impact. Since the opto-electronic conversion occurs in the low-speed IF domain, the resulted phase noise is very small. For example, assume a 10-GHz component is extracted, while the IF tone is at 20 MHz. The actual AM-PM phase noise will be suppressed with around 54 dB if the same PD is used. Secondly, the noisy microwave LO may also result in phase noise during the frequency conversion pair. However, if the time delays of two conversions are well matched, such phase noise can also be minor: noise suppression ratio is ~|2πfΔt|2, where f is the offset frequency [20]. At 1-MHz/100-kHz offset frequency, the suppression can be larger than 44/64 dB if the delay mismatch is within 1 ns. Such delay control is easy to obtain in practice. Note the noise contribution from the electronic frequency up-conversion mixer is also negligible [21].
The above extraction is studied numerically. Assume that the repetition rate of femtosecond pulse train is 80 MHz. Each pulse randomly deviates from the ideal position with a normal distribution, where the standard deviation is 20 fs. The time jitter is then around 5 × 10−6 fs2/Hz within the whole spectrum (as shown in the inset of Fig. 2(a)). According to Eq. (2), the 125th-order harmonic tone, i.e. the 10-GHz microwave component, has a minimum phase noise of around −137 dBc/Hz, as shown in Fig. 2(a). Randomly fluctuated pulse energy is also assumed, which results in a flat relative intensity noise (RIN) distribution at −139 dBc/Hz. We assume that the average optical power hitting on PD is always 4 mW. The nonlinearity of PD results in a pulse-energy-dependent pulse delay, which is 2.5 ps/pJ [14]. According to Eq. (3), additional phase noise appears if the pulse train is directly detected by PD, which is as high as −120 dBc/Hz (as shown in Fig. 2(b)) and is almost 20 dB larger than the original phase noise. That is, the AM-PM dominates if 10-GHz tone is extracted directly. Here (and in the following simulation) we ignore the thermal and shot noise of PD.
Fig. 2 A numerical example for the proposed microwave extraction scheme. (a) The time jitter of the femtosecond source and the corresponding phase noise of its 10-GHz microwave component. (b) A phase noise comparison of direct detected 10-GHz tone and equivalently filtered one; the green lines show phase noise of the microwave LO and its suppression by delay match; the residual AM-PM noise is also shown. (c) PD output spectrum within its first Nyquist zone.
In order to extract the 10-GHz component by equivalent filtering scheme, a noisy microwave LO is employed. We assume that the carrier frequency of LO is normally distributed around 10.017 GHz with a standard deviation of 1 kHz. Figure 2(b) shows the corresponding phase noise, which is about −96 dBc/Hz at 10-kHz offset frequency. After the frequency conversion pair and IF filtering in between, the phase noise of extracted 10-GHz tone is shown in Fig. 2(b), which is the same as that of the minimum value shown in Fig. 2(a). In simulation we assume that the delay mismatch between the two frequency conversions is 1 ns.
Figure 2(b) shows the two residual phase noise illustrated in Eq. (9). Firstly, the delay mismatch results in phase noise transfer from noisy microwave LO. The 1-ns mismatch corresponds to about 84 dB suppression ratio at 10-kHz offset frequency, as shown in Fig. 2(b). Though the suppression ratio drops when the offset frequency increases, the phase noise of LO also decreases. So does a practical microwave source. As a result, the residual noise transferred from the LO is as low as −180 dBc/Hz. Secondly, since the IF tone frequency, 17 MHz, is much lower than the target microwave, 10 GHz, the AM-PM phase noise is also greatly suppressed (55 dB), which is only −176 dBc/Hz around. Both residual noises can be ignored totally.
In Eq. (4) we assume a linear electro-optical transfer curve of MZM. In practice, modulation depth of 1 (the applied peak-to-peak voltage is twice of the half-wave voltage of MZM) should be selected in order to maximize the down-conversion efficiency, so that nonlinearity of MZM should be considered. Figure 2(c) shows the resulted nonlinear spurs inside the 40-MHz first Nyquist zone after down-conversion. Due to the ultra-large sampling bandwidth property of femtosecond pulse, nonlinear harmonics of the microwave LO are all down-sampled into the first Nyquist zone. For example, the 3rd-order/5th-order harmonic, which is at 30.051 GHz/50.085 GHz, appears at 29 MHz/5 MHz. Note that since the MZM is biased at its quadrature point, the even-order harmonics should be zero. However, one can still observe the 2nd-order and 4th-order harmonics, which are at 34 MHz and 12 MHz, respectively. This is due to the AM-PM modulation which is driven by Α’O as shown in Eq. (6). The alternating current (AC) part of Α’O results in phase modulation with offset frequency of ωIF, so that the even-order harmonics appear. The simulation shows that it is reasonable in Eq. (7) to ignore the corresponding high-speed AM-PM. Note the nonlinear spurs are far away from the target, and may be further removed by narrowband filtering (either in IF or in final microwave domain).
3. Experiment result
We experimentally demonstrate the microwave extraction based on frequency conversion pair and IF processing. The setup is shown in Fig. 1, where an additional electronic amplifier is used after the IF filter. The home-made femtosecond fiber laser has a repetition rate around 80 MHz. The average optical power hitting on PD is 3 dBm. The IF filter, centered at 22 MHz, has a 3-dB bandwidth of 18 MHz and group delay of 50 ns. An electronic cable with about 50-ns delay and 16 dB loss is used for the matched delay. The common microwave LO comes from a commercial sinusoidal wave generator (Anritsu 68047C) at around 10 GHz. A 9.978-GHz microwave tone is extracted with power of 0 dBm. The absolute single-side-band (SSB) noise is measured by Agilent N9030A [22]. Figure 3(a) shows the SSB noise of the extracted 9.978-GHz microwave component. At 10-kHz offset frequency, the SSB noise is −113 dBc/Hz. As a comparison, SSB noise of LO is also plotted. One can find that the two noise spectrums are actually independent, which is predicted by Eq. (9) if the delay match is satisfied (Δt = 0). SSB noise suppression nearly 30 dB can be found in the extracted microwave. In the low offset frequency range, the free-running operation of the femtosecond laser results in larger noise. It is interesting to find that the SSB noise of 22-MHz IF tone follows that of the femtosecond laser in low offset frequency range, while it follows the noise of microwave LO in high offset frequency range, which agrees with Eq. (7): the phase noise of IF tone contains the both noises. The SSB noise spectrum changes after up-conversion illustrates that the LO noise is well subtracted by delay match.
Fig. 3 (a) The SSB noise of the extracted microwave, the IF tone, and the microwave LO, respectively. (b) The microwave spectrum after extraction.
Figure 3(b) shows the spectrum of final output. One can find the image tone (at 10.022 GHz) at the other side of the 10-GHz microwave LO. Such tone has much larger SSB noise. Other spurs are from the nonlinear modulation in MZM and from AM-PM inside PD, as shown in Fig. 2(c). The spurs are well separated from the extracted microwave tone, and can be removed by image-rejection mixing and narrowband filtering.
By tuning the carrier frequency of microwave LO, different microwave components can be extracted based on the same setup. The obtained tunable range is much larger than the scheme based on phase-locking a low-phase-noise VCO. Without considering the phase noise, one can achieve microwave LO with large tunability commercially. Figure 4 shows the measured SSB noises when the extracted microwaves are around 10 GHz and those from 1 GHz to 10 GHz.
Fig. 4 The measured absolute SSB noises of the extracted microwave components (a) around 10 GHz and (b) from 1 GHz to 10 GHz.
In Figs. 3 and 4, one still finds relatively large SSB noise due to the significant time jitter of the home-made femtosecond fiber laser, so that the final output contains both ΦO and the additional phase noise due to the extraction. Actually, based on our laser, the direct detection results in almost the same absolute SSB noise as the proposed extraction. In order to evaluate the extraction performance individually, we build two independent microwave extraction setups (including two microwave LOs) according to Fig. 1, which both extract the 9.978-GHz component from the same femtosecond laser. The resulted two tones have obviously the same ΦO but independent extraction-induced additional noises. Their residual noise is then measured by R&S®FSUP signal source analyzer [23], and the result is shown in Fig. 5. When the offset frequency is larger than 1-kHz, the residual SSB noise is averagely around −155 dBc/Hz. Such residual noise may support low-noise microwave extraction from femtosecond laser with a-few-fs time jitter or even less. If an ultra-stable optical source is used, e.g. that in [8], the residual will then be the limit of absolute noise after extraction.
Fig. 5 The measured residual SSB noise of two 10-GHz microwave component extracted from the same femtosecond laser when two independent extraction setups are used.
In our scheme, the power of 22-MHz IF tone after PD is −15 dBm. However, if the femtosecond pulse train is received directly by the same 20-GHz PD, the power of 10-GHz component is as low as −40 dBm. For both cases, the average optical power hitting on PD is 3 dBm. We believe the PD saturation leads to pulse broadening after opto-electronic conversion, as well as the much less power at microwave range. However, despite the saturation, the photo-generated current can still be fully collected due to the low-speed repetition rate, which benefits the opto-electronic conversion in IF domain. As a result, the extracted microwave power is enlarged greatly by the proposed scheme.
4. Conclusion
Aiming to extract a microwave component from a femtosecond pulse train with low phase noise, we here proposed and demonstrated experimentally an equivalent filtering scheme, employing a pair of frequency down- and up- conversions as well as IF-domain opto-electronic conversion and filtering. We used two implementations, time delay match between the conversion pair and direct opto-electronic detection in the low frequency, to greatly suppress the additional extraction phase noise due to the external LO and PD nonlinearity, respectively. Numerical study showed that additional phase noise can be neglectable under typical parameters. Experimentally the residual SSB noise was averagely around −155 dBc/Hz under offset frequency larger than 1 kHz. Large extraction tunability from 1 GHz to 10 GHz was also demonstrated.
References and links
1. C. R. Locke, E. N. Ivanov, J. G. Hartnett, P. L. Stanwix, and M. E. Tobar, “Invited article: Design techniques and noise properties of ultrastable cryogenically cooled sapphire-dielectric resonator oscillators,” Rev. Sci. Instrum. 79(5), 051301 (2008). [CrossRef] [PubMed]
2. X. S. Yao and L. Maleki, “Optoelectronic microwave oscillator,” J. Opt. Soc. Am. B 13(8), 1725–1735 (1996). [CrossRef]
3. A. J. Seeds and K. J. Williams, “Microwave photonics,” J. Lightwave Technol. 24(12), 4628–4641 (2006). [CrossRef]
4. L. Maleki, “The optoelectronic oscillator,” Nat. Photonics 5(12), 728–730 (2011). [CrossRef]
5. D. Eliyahu, D. Seidel, and L. Maleki, “Phase noise of a high performance OEO and an ultra-low noise floor cross-correlation microwave photonic homodyne system,” in Proceedings of IEEE Conference on Frequency Control Symposium (IEEE, 2008), pp. 811–814. [CrossRef]
6. J. Millo, R. Boudot, M. Lours, P. Y. Bourgeois, A. N. Luiten, Y. L. Coq, Y. Kersalé, and G. Santarelli, “Ultra-low-noise microwave extraction from fiber-based optical frequency comb,” Opt. Lett. 34(23), 3707–3709 (2009). [CrossRef] [PubMed]
7. J. Kim and F. X. Kärtner, “Microwave signal extraction from femtosecond mode-locked lasers with attosecond relative timing drift,” Opt. Lett. 35(12), 2022–2024 (2010). [CrossRef] [PubMed]
8. T. M. Fortier, M. S. Kirchner, F. Quinlan, J. Taylor, J. C. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. W. Oates, and S. A. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics 5(7), 425–429 (2011). [CrossRef]
9. T. M. Fortier, F. Quinlan, A. Hati, C. Nelson, J. A. Taylor, Y. Fu, J. Campbell, and S. A. Diddams, “Photonic microwave generation with high-power photodiodes,” Opt. Lett. 38(10), 1712–1714 (2013). [CrossRef] [PubMed]
10. K. Jung, J. Shin, and J. Kim, “Ultralow phase noise microwave generation from mode-locked Er-fiber lasers with subfemtosecond integrated timing jitter,” IEEE Photonics J. 5(3), 5500906 (2013). [CrossRef]
11. D. Hou, X. P. Xie, Y. L. Zhang, J. T. Wu, Z. Y. Chen, and J. Y. Zhao, “Highly stable wideband microwave extraction by synchronizing widely tunable optoelectronic oscillator with optical frequency comb,” Sci. Rep. 3, 3509 (2013). [CrossRef] [PubMed]
12. H. A. Haus and A. Mecozzi, “Noise of mode-locked lasers,” IEEE J. Quantum Electron. 29(3), 983–996 (1993). [CrossRef]
13. J. Kim and F. X. Kärtner, “Attosecond-precision ultrafast photonics,” Laser Photonics Rev. 4(3), 432–456 (2010). [CrossRef]
14. M. Currie and I. Vurgaftman, “Microwave phase retardation in saturated InGaAs photodetectors,” IEEE Photonics Technol. Lett. 18(13), 1433–1435 (2006). [CrossRef]
15. A. Haboucha, W. Zhang, T. Li, M. Lours, A. N. Luiten, Y. Coq, and G. Santarelli, “Optical-fiber pulse rate multiplier for ultralow phase-noise signal generation,” Opt. Lett. 36(18), 3654–3656 (2011). [CrossRef] [PubMed]
16. H. Jiang, J. Taylor, F. Quinlan, T. Fortier, and S. A. Diddams, “Noise floor reduction of an Er: fiber laser-based photonic microwave generator,” IEEE Photonics J. 3(6), 1004–1012 (2011). [CrossRef]
17. J. Kim, F. X. Kärtner, and F. Ludwig, “Balanced optical-microwave phase detectors for optoelectronic phase-locked loops,” Opt. Lett. 31(24), 3659–3661 (2006). [CrossRef] [PubMed]
18. A. H. Nejadmalayeri and F. X. Kärtner, “Mach-Zehnder based balanced optical microwave phase detector,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2012), paper CTu2A.1. [CrossRef]
19. P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, and A. Bogoni, “A fully photonics-based coherent radar system,” Nature 507(7492), 341–345 (2014). [CrossRef] [PubMed]
20. Y. Dai, R. Wang, F. Yin, J. Dai, Y. Zhou, J. Li, and K. Xu, “Hybrid radio-intermediate-frequency oscillator with photonic-delay-matched frequency conversion pair,” Opt. Lett. 40(12), 2894–2897 (2015). [CrossRef] [PubMed]
21. D. Jorgesen, Mariki microwave RFµwave Tech notes, http://www.markimicrowave.com/blog/2012/12/.
22. Keysight N9030A PXA signal analyzer specifications guide, http://literature.cdn.keysight.com/litweb/pdf/5990-3952EN.pdf?id=1759326
23. R&S®FSUP signal source analyzer specifications, http://www.electrorent.com/products/search/pdf/RS-fsup26.pdf
