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Highly precise stabilization of intracavity prism-based Er:fiber frequency comb using optical-microwave phase detector Shuangyou Zhang, Jiutao Wu, Jianxiao Leng, Shunnan Lai, and Jianye Zhao* Department of Electronics, School of Electronics Engineering and Computer Sciences, Peking University, Beijing 100871, China *Corresponding author:
[email protected] Received August 15, 2014; revised October 13, 2014; accepted October 15, 2014; posted October 16, 2014 (Doc. ID 221036); published November 10, 2014 In this Letter, we demonstrate a fully stabilized Er:fiber frequency comb by using a fiber-based, high-precision optical-microwave phase detector. To achieve high-precision and long-term phase locking of the repetition rate to a microwave reference, frequency control techniques (tuning pump power and cavity length) are combined together as its feedback. Since the pump power has been used for stabilization of the repetition rate, we introduce a pair of intracavity prisms as a regulator for carrier-envelope offset frequency, thereby phase locking one mode of the comb to the rubidium saturated absorption transition line. The stabilized comb performs the same high stability as the reference for the repetition rate and provides a residual frequency instability of 3.6 × 10−13 for each comb mode. The demonstrated stabilization scheme could provide a high-precision comb for optical communication, direct frequency comb spectroscopy. © 2014 Optical Society of America OCIS codes: (140.3500) Lasers, erbium; (140.3510) Lasers, fiber; (140.4050) Mode-locked lasers; (250.0250) Optoelectronics; (140.3425) Laser stabilization. http://dx.doi.org/10.1364/OL.39.006454
Optical frequency combs (OFCs) have attracted great attention for numerous research areas, such as time and frequency metrology [1,2], large-scale timing distribution [3,4], low noise signal synthesis [5], and fundamental constants measurement [6]. More recently, fiber-based frequency combs have become a popular research focus, due to their significant spectrum in the optical telecommunications band [4]. Moreover, they generally have relatively high robustness, compact architecture, and modest cost, because of their fiber-based structure. Accordingly, high-precision stabilization of fiber-based comb becomes more crucial for telecommunications, frequency metrology, and remote sensing applications. The frequency comb has two degrees of freedom, the repetition rate (i.e., f rep ), and the carrier-envelope offset frequency (i.e., f ceo ). A fully stabilized OFC is established by stabilizing both the f rep and the f ceo , to either a microwave reference or an optical reference. Much effort has been devoted to the stabilization of these two degrees of freedom [7–11]. The f rep can be stabilized through feedback to the cavity length [7,11], or the pump power [12]. However, using a piezoelectric transducer (PZT) to control the cavity length is often limited by the limited lengthtuning resolution, long response time, and large loop gain of PZT [13], while control of pump power is limited by the compensation range. For the control of the f ceo , it is common to tune the pump power to change the cavity dispersion [11]. It is also demonstrated that an intracavity electronics-optical modulator (EOM) could be used to lock the f ceo , which can improve the locking bandwidths [10]. In the phase locking of the f rep , the precision of its phase locking to the microwave reference is often limited by amplitude-to-phase (AM-to-PM) conversion, and shot noise inherent in the direct photodetection process [14]. A recently demonstrated optical-microwave phase detector (OM-PD) can directly extract the phase error, between the microwave signal and the optical pulse 0146-9592/14/226454-04$15.00/0
train, in the optical domain. As it can achieve sub-fs precision phase detection performance [15], using OM-PD as the phase detector can help to obtain highly precise and stable f rep locking when pump power is used to tune the f rep [16]. Since controlling the pump power is already used for highly precise locking of the f rep , another better way needs to be explored to control the f ceo for fully OFC stabilization. Using a pair of intracavity prisms to stabilize a comb is widely used in the solid-state mode-locked laser [7,17,18]. Compared with the intracavity EOM [10], it can achieve little or no influence on the f rep in the stabilization of the f ceo . To our knowledge, there is no report about the stabilization of the f ceo on the foundation of high-precision stabilization of the f rep , by using OM-PD. In this Letter, we employ a high-precision and ultralow noise OM-PD, to detect the phase difference between the f rep and the microwave reference. To ensure the longterm and high-precision phase locking of the f rep , we use the combination control of pump power and cavity length as the feedback. On the other side, we introduce a pair of intracavity prisms to change the group delay for f ceo control. With this method, the f ceo is stabilized by locking one element of the comb to a rubidium saturated absorption transition line, hence completely stabilizing the whole comb. The saturated absorption line is a convenient reference for us, and it can be replaced by other optical references or a self-referenced structure. The intracavity prism-based stabilization offers the advantage of altering the group delay, without significant changes to the cavity length. Although many studies had been reported by using intracavity prism pair for stabilization in solid-state lasers [7,17,18], to our knowledge, it is the first time to introduce intracavity prisms for the stabilization of fiber based comb. The experimental setup of the proposed stable OFC is illustrated in Fig. 1(a). A 74.5-MHz repetition rate, nonlinear polarization rotation mode-locked, Er-fiber laser is © 2014 Optical Society of America
November 15, 2014 / Vol. 39, No. 22 / OPTICS LETTERS
Fig. 1. (a) Schematic of the stable Er:fiber-based frequency comb: CM, collimator; EDF, erbium doped fiber; ISO, isolator; PBS, polarization beam splitter and (b) optical-microwave phase detector; FR, Faraday rotator; PM, phase modulator.
built as an optical master oscillator for the frequency comb. In the MLL, a pair of prisms is employed in the intracavity, for stabilization of one comb mode. Because of the intracavity prisms, there are two optical pulse outputs (marked as outputs 1 and 2) in the system. An external cavity diode laser (ECDL), stabilized to a rubidium saturated absorption transition, is used as the optical reference. An OM-PD [Fig. 1(b)] performs the phase detection between the optical pulse train and the microwave reference, based on a Sagnac-loop interferometer. The OM-PD can mitigate the shot noise and the AM-to-PM conversion; it is widely used in low noise signal synthesis [19], and timing and frequency distribution [20]. More detailed information about the OM-PD can be found in [15]. To stabilize the f rep to a microwave reference, we use a high-resolution OM-PD as the phase detector, instead of using a high-speed photodiode and a mixer. The optical pulse train from the MLL output 1 is ∼10 mW, and applied to the OM-PD. An 18 dBm, 5.2 GHz microwave, which is the 70th harmonic of the f rep , is used as the reference source, and applied to a phase modulator in the OMPD. The 5.2 GHz microwave signal is referenced to a 10 MHz signal, from a passive hydrogen maser (OSA3700). By using the high harmonic signal as the phase comparison frequency, a large noise reduction of the fundamental repetition frequency is accomplished, due to the frequency division relationship. It is easy to achieve low-noise stabilization by using harmonics of the f rep [13]. The phase error, between the optical pulse train and the reference microwave signal, is converted to the intensity imbalance between the two output ports from the Sagnac loop, and detected by a balanced photodetector.
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The error signal generated from the OM-PD is filtered by a 100 kHz low-pass filter, amplified, and proportion-integration-differentiation (PID) regulated. Because it is hard to achieve high-accuracy frequency/phase tuning via the PZT control of cavity length, due to the limited length-tuning resolution, long response time, and large loop gain, we use the combination of pump modulation and PZT controlling as actuators. A commercial current source is used for sub-fs high-precision stabilization, while a PZT has an adjustment range of 40 μm, and can ensure ∼1 KHz large scale and long-term compensation of frequency drifts. This f rep stabilization technique has the advantage that the error signal, generated from the OM-PD, avoids the most of noise inherent in the photodetection process. A combination of pump and PZT control ensures both the high-precision and large locking range of the f rep . After the f rep is stabilized by the OM-PD, we use an optical reference for f ceo locking. The optical reference reported in this Letter is an ECDL, referenced to the rubidium saturated absorption resonance at 780 nm (Rb D2 line). We use an Er-doped fiber amplifier (EDFA) to amplify output 2 to ∼50 mW. The output pulses are compressed by a silicon prism pair [not shown in Fig. 1(a)]. The compressed pulses are frequency doubled by a periodically poled lithium niobate (PPLN) waveguide. After the PPLN, the pulses have a center wavelength of ∼780 nm. This frequency doubled pulses are directed to beat with the continuous wave from the ECDL. A signal analyzer is used to measure the generated beat signal (f beat ), with a measurement bandwidth of 10 kHz. The 3 dB linewidth of the beat signal is subMHz, and the SNR exceeds 20 dB. The only missing link, to stabilize the comb mode frequency, is now a mechanism for external control of the comb mode frequency. Because the pump power is already used in the stabilization of the f rep , we use a pair of intracavity prisms as the actuator, to change the group delay for control the comb mode frequency. This method is widely used for stabilization in solid-state mode-locked lasers [7,17,18]. This stabilization scheme offers the advantage of altering the group delay, without significant changes to the cavity length. Furthermore, this stabilization technique has a potential for independent group and phase delay changes. To lock the comb mode frequency, the locking electronics part [Fig. 1(a)] is used to filter and amplify the detected beat signal, and mix it with a synthesizer, to generate the error signal. The error signal is fed back to tilt the high reflector mirror mounted on a PZT, following the intracavity double-pass silicon Brewster prism pair, at an apex-to-apex separation of 80 mm. The prism apex angle is 32°060 , which ensures that the laser could arrive at and depart the prisms at Brewster angle. Tilting the mirror causes the different spectral components to spread out spatially; therefore it produces a controllable group delay, and alters the effective difference between group and phase velocities in the laser cavity, which leads to a change in the comb mode frequency. Figure 2 shows the impact on the f rep and f beat , when tilting the PZT. It has a big impact on the f beat on the order of MHz, and Hz order of magnitude on the f rep . After closing the servo loop, we achieved comb mode frequency stabilizing to the rubidium saturated absorption resonance.
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Fig. 2. Impact on the f beat and f rep when tilting the PZT following the prisms.
In order to evaluate the stabilization performance of the proposed OFC, we conducted long-term measurements of both the repetition rate and one comb mode. Because we use a passive hydrogen maser (OSA3700) as the reference for the f rep , it is hard to perform an independent and absolute instability measurement for the f rep , without a more stable microwave reference. Therefore, the stability of the f rep is characterized by the residual instability. The residual instability of the f rep is conducted by another OM-PD. The details of its operation are in [16]. We also use a frequency counter referenced to the passive hydrogen maser, to record the frequency drift of the f beat signal. The two frequency measurements were carried out for a couple of hours, and we utilized the recorded frequency data to calculate the Allan deviations. The curve (i) in Fig. 3(a) shows the fractional frequency drifts of the fundamental repetition rate at 74.5 MHz, when the OFC is free-running. The curve (ii) shows the residual timing drift, between the f rep and the reference signal. We calculated the frequency instabilities, of the optical mode and the f rep of the comb, from the series of recorded values (in terms of overlapping Allan deviation). Figure 3(b) shows the measured fractional frequency instabilities. The filled squares line is the result of f rep for the free-running OFC, and the filled circles line is the residual instability of the f rep in the stabilization situation. The filled diamonds line and filled triangles line represent the frequency stabilities of the optical mode of comb and the reference clock, respectively. The instability of the f rep when free-running reaches 8.1 × 10−9 for a 1 s gate time, and goes higher than 2.3 × 10−6 for 2000 s. The residual instability of the stable f rep is 7.3 × 10−16 and 6.3 × 10−18 , for averaging times of 1 and 2000 s, respectively. Its instability is lower by two orders of magnitude than that of the passive hydrogen maser. As a consequence, we can draw a conclusion that the stabilization technique has no stability loss, in term of the stability of the hydrogen maser; therefore the instability of the f rep is the same as the reference. The residual instability of the optical mode of comb is 8.3 × 10−12 and 3.6 × 10−13 , for 1 and 2000 s gate time, respectively. The high stability of the proposed OFC could improve the performance of
Fig. 3. (a) Time records of the fractional drift of the freerunning f rep and timing drift of the stabilized f rep and (b) fractional frequency instabilities for the reference clock, freerunning f rep , stabilized f rep , and a mode of stabilized comb.
high-precision direct frequency comb spectroscopy (DFCS) [21], and frequency dissemination [4]. In summary, we have demonstrated a new approach to generate a fully stable fiber-based frequency comb, at communication band, by using a high-precision phase detector OM-PD. The combination of pump power and PZT control as the actuator can ensure high-precision and long-term stabilization of the repetition rate. For locking one comb mode of the OFC to an optical reference, we introduce a pair of intracavity prisms to change the cavity dispersion. From the view of the results, the excellent locking performance of the OFC, based on the OM-PD, could easily transfer the stability of the most stable active hydrogen maser [22] to the OFC, without stability loss. The proposed highly stable fiber-based comb can be widely used in various scientific areas, such as highprecision optical communications, timing and frequency dissemination, and DFCS. As a future work, we will apply the proposed frequency comb structure, based on OMPD and intracavity prisms, to the self-referenced structure. This Letter was supported in part by the National Natural Science Foundation of China under Grant No. 61371074. We thank Professor Zhigang Zhang from the Department of Electronics, Peking University, for helpful discussions. References 1. T. W. Hänsch, Rev. Mod. Phys. 78, 1297 (2006). 2. J. Ye, H. Schnatz, and L. W. Hollberg, IEEE J. Sel. Top. Quantum Electron. 9, 1041 (2003). 3. J. Kim, J. A. Cox, J. Chen, and F. X. Kärtner, Nat. Photonics 2, 733 (2008). 4. G. Marra, H. S. Margolis, and D. J. Richardson, Opt. Express 20, 1775 (2012).
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