We demonstrate a novel system that uses a piezoelectric transducer (PZT)-actuated mirror for laser stabilization. A combination of a simple mechanical design and electronic circuits is used to realize an ultra-flat frequency response, which enables an effective feedback bandwidth of 500 kHz. The PZT also performed well when used in a mode-locked laser with a GHz repetition rate, to which it is difficult to apply an electro-optic modulator (EOM).
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
The optical frequency stability of lasers has played a significant role in numerous applications, including metrology and high-precision spectroscopy. In such applications, the optical frequency fluctuations of lasers must be stabilized to decrease the measurement time and improve measurement accuracy. A fluctuation in the optical cavity length is one of the most important factors that can cause optical frequency instability. To compensate for such a fluctuation, mirrors actuated by a piezoelectric transducer (PZT) and electro-optic modulators (EOMs) are widely used. EOMs have an advantage over PZTs in terms of the frequency response, i.e. feedback bandwidth, which reaches at least several hundred kHz . However, we cannot always apply EOMs and other high-speed modulators , such as the cases of laser cavities with high powers, high quality factors, ultrashort pulses, and short path lengths, as well as situations where compensation of more than μm-level fluctuations is required; these are the possible cases in which PZTs can be used. Although a PZT-actuated mirror can be applied in a variety of circumstances, its bandwidth is typically limited to the few kHz-level. This restricts the stabilities of the lasers to which the EOMs cannot be applied. Therefore, there has been great demand for a PZT-actuated mirror with a broader feedback bandwidth.
The bandwidth of a PZT system is limited by strong mechanical resonances that typically lie in the frequency range slightly above 10 kHz. A PZT originally has only a self-resonance with in a much higher frequency region (depending on the thickness of the PZT). However, when a PZT is integrated into an optical system that includes a mirror and a mirror mount, other complex resonances arise as a result of acoustic vibration coupling with every component. This makes it difficult to achieve a broad feedback bandwidth. To damp these other resonances, various mirror mount structures have been demonstrated. A novel mount design was proposed by Briles et al. in 2010 . The design achieved damping of resonances up to 200 kHz, and a 180 kHz feedback bandwidth was obtained. They designed a mount structure made from copper-shielded lead, which acted as a damping material. However, their structure was complex and difficult to produce. In addition, the resonances above 200 kHz were still present. Another interesting approach was proposed by Chadi et al. in 2013 . They held their PZT via a side-clamping approach. Because the structure was vertically clamped in the main acoustic wave propagation direction, the structure should then suppress vibration coupling to the mount. The lowest resonant frequency was pushed up to more than 100 kHz. Although it appears to be easy to produce, the side-clamping system requires a thick PZT that strongly restricts the feedback bandwidth because of its relatively low self-resonance frequency. The third method using soft materials was demonstrated by Goldovsky et al. in 2016 . In their structure, the PZT was surrounded by elastic materials and a feedback bandwidth of approximately 200 kHz was achieved. In principle, this pre-load-like structure is suitable for operation of PZTs. However, this structure has also been unable to exceed the 200 kHz bandwidth. Note that, in these studies of PZTs, various sizes of mirrors and PZTs were used. The results of these systems are summarized in Table 1.
In this paper, we demonstrate a new PZT system design that uses a simple damping structure. This structure damps all mechanical resonances up to 500 kHz, which is the self-resonance frequency of the PZT itself. This simple resonance frequency at 500 kHz allows resonance compensation via an electronic circuit. Consequently, beyond 500 kHz, a flat frequency response is achieved. To verify the bandwidth of the proposed PZT system, the PZT is used as an intensity modulator. The residual intensity noise (RIN) of a laser is stabilized using the PZT and the effective feedback bandwidth is estimated to be 500 kHz, which represents a record for a PZT feedback bandwidth to the best of our knowledge. Finally, to demonstrate the practical use of our PZT, the PZT is installed in a solid-state mode-locked laser with a GHz repetition rate. The laser is then stabilized to an optical reference using the PZT, which demonstrates stabilization of the cavity length under conditions that would be unacceptable when using EOMs. As a result of the broad feedback bandwidth achieved, low residual phase noise of 183 mrad is obtained.
2. Design of the PZT system
The approach used to suppress the mechanical resonances of the PZT system involves impeding the acoustic wave propagation and reflection. The design of the proposed PZT system is shown in Fig. 1(a). The PZT is mounted on the mirror mount using a damping alloy, which is the main component used to absorb the acoustic waves. The damping alloy and the optimization of its damping ability are discussed in detail in the following section. To verify the PZT’s frequency response, a simple Michelson interferometer was used as shown in Fig. 1(b). When the PZT causes the length of one arm to vary, the resulting intensity at the photodetector also varies, which provides information about the amplitude and the phase of the PZT at the driving frequency.
There are four important sections in our PZT system: the damping material and its structure, the acoustic impedance matching between the damping alloy and the mirror mount, the selection and modification of the mirror and the PZT, and the electronic circuit used for compensation.
2.1 Damping alloy and structure
Typically, a metal such as aluminum is used for mirror mounts; acoustic waves propagate very well in this type of metal, which leads to strong resonances at frequencies as low as a few kHz. Therefore, a damping alloy is inserted between the PZT and the mirror mount. Although lead is well known as a classical vibration damping metal, there are a variety of better damping alloys, such as the Al-Fe alloy . Al-Fe alloy is commercially available and shows the best damping ability according to our measurements. In addition, Al-Fe alloy is quite a rigid material, in contrast to lead, and machine working of this alloy is also possible. By inserting a simple plate composed of Al-Fe, resonances below 100 kHz were suppressed very well. However, resonances at more than 100 kHz still appeared. To suppress these resonances, the frequency responses of the alloy in various shapes were measured experimentally. Ultimately, a 1° wedged plate with a thickness of 3 mm showed the best performance. The wedged damping alloy is the most important and essential to achieve our PZT performance. The damping ability was not improved by increasing the angle and/or the thickness of the structure. Although the PZT position is also strongly related to mechanical resonances, any significant position dependence was not observed in our final design. Note that PZT positions tested in our experiment were always off-centered because the bolt was placed at center.
2.2 Impedance matching
The contact between the mirror mount and the damping alloy is also important. If there is strong reflection of acoustic waves from the contact area, strong resonances will even occur when the damping alloy is used. Acoustic impedance matching helped to solve this problem. High-Z (Sonotech), which is commercially available, was used as an impedance matching gel. High-Z offers the highest acoustic impedance of such gels. The gel was used to fill the airgap between the mirror mount and the alloy and it suppressed acoustic reflection at the contact area. The frequency responses with/without impedance matching gel are shown in Fig. 2. The strong resonances above 100 kHz were clearly damped by the gel. In fact, we do not fully understand this phenomenon yet, because strong acoustic reflection from the edge of the mirror mount still occurs. However, reducing the numbers of surfaces that have strong reflection properties should help to suppress the number of mechanical resonances. Because High-Z is not a glue, a bolt was used to fix the alloy to the mount. Despite concerns this bolt may make the frequency response worse, no significant resonances caused by the bolt have been observed in our measurements. To attach the PZT and the mirror, Torr seal was used, and the glue layer must be thin.
2.3 Mirrors and PZTs
The thicknesses of the mirror and the PZT are very important factors because the thickness is directly related to the resonance frequency. To push the resonance toward a higher frequency, both the PZT and the mirror should be thin. A dielectric mirror was cut into a 2 mm square with a thickness of 0.7 mm using a diamond wheel saw and no significant distortion of the mirror surface was observed; this was confirmed by the results of a GHz comb experiment that will be described in the following section. The thickness of the PZT has a more significant effect. After application of the various improvements to the mounting structure, only the self-resonance of the PZT remained. A PZT with an original thickness of 2 mm (CMAP11, Noliac) was used in this experiment that had a self-resonance around 300 kHz. Therefore, the PZT’s frequency response was limited by the thickness of the PZT. The PZT was thus also cut and polished into smaller pieces with thicknesses of 0.7 mm (red) and 1.0 mm (blue) using the diamond wheel saw. Note that this technique sacrifices a PZT stroke and can only be applied to some multilayer PZTs. As shown in Fig. 3 the self-resonance frequency was pushed up to 500 kHz and the frequency response was clearly improved. During these measurements, the same wedged damping alloy and impedance matching gel were applied in all cases.
2.4 Compensation circuit
Although the lowest resonance frequency was pushed up to 500 kHz, the self-resonance of the PZT still remained, as shown in Fig. 3. For general feedback operation, the 20-dB amplitude peak around 500 kHz must be suppressed using a suitable low-pass filter at a lower cut-off frequency, which then restricts the feedback bandwidth. To circumvent this issue, the 500 kHz PZT resonance was compensated using an electronic circuit. The PZT self-resonance was similar to that of a second-order low-pass filter with a quality factor of 10. Suitable compensation filters composed of a simple analog circuit were designed, and the frequency response was improved as shown in Fig. 4. Comparison with the red curves in Fig. 3 shows that a 500 kHz peak was suppressed, and the corresponding phase was also recovered. Finally, the desired ultra-flat frequency response beyond 500 kHz was achieved.
These improvements were intended to achieve the broadest feedback bandwidth possible. One disadvantage of cutting the PZT is the reduction of the stroke for the compensation. The stroke of the sliced PZT was estimated to be 3 nm/V, and the applied peak-to-peak voltage in the experiment above was approximately 10 V. The last two techniques (cutting of the PZTs and use of the compensation circuit) are optional for extreme applications. The first two mechanical designs can be applied to a greater variety of cases. Even when a 20-mm-long PZT was used, the frequency response was still improved.
3. Feedback performances of the PZTs
To verify the feedback performance of the proposed PZT system, two independent experiments were performed. To measure the feedback bandwidth of the PZT, the residual intensity noise (RIN) of an Yb:fiber laser was stabilized using a simple Michelson interferometer. The experimental details are illustrated in Fig. 5(a). The PZT was placed in one arm of the interferometer to modulate the intensity of the output. The output was detected by a photodetector, and the RIN obtained was suppressed by referencing it to a voltage reference chip via a feedback loop that included the PZT. In this measurement, the noise spectrum during free running was obtained easily. Therefore, the feedback bandwidth can be estimated clearly. The RIN spectra are shown in Fig. 5(b). The free-running RIN spectrum of the Yb:fiber laser is consistent with that reported in the literature . The crossing frequency between the stabilized (blue line) and free-running (red line) spectra should be the effective feedback bandwidth, which reached more than 500 kHz. In this experiment, a PI (proportional-integral) corner of the loop filter is designed around 10 kHz with the aim of maintaining the flat phase response of the loop filter up to 500 kHz. To the best of our knowledge, the bandwidth is a record for such feedback provided using PZTs. However, this is not a practical approach because the amount of noise reduction is not very large. In contrast, as shown by the green line, by modifying the PI corner of the loop filter to around 200 kHz, noise reduction of more than 20 dB was observed at 10 kHz with a 100 kHz effective feedback bandwidth. This feedback achieved extremely high gain for a PZT, which corresponded to a 10-dB gain improvement at 10 kHz when compared with the results in the literature .
The other experiment involves optical frequency stabilization of a GHz repetition rate comb to an optical reference. Gigahertz combs offer considerable advantages over conventional 50-200 MHz combs. For example, their potential for obtaining a high signal-noise-to-ratio is helpful for applications in optical clocks [8,9] and their lower peak powers can suppress nonlinearities at photodetectors, which is important for low-noise photonic microwave generation [10,11]. However, EOMs cannot be applied easily to such tiny and (typically) high-finesse cavities, so the stability of GHz combs has been restricted by the relatively lower PZT feedback bandwidth. Therefore, one promising application of our PZT system should be the stabilization of GHz combs. Our experimental setup is illustrated in Fig. 6(a). An Yb:Y2O3 ceramic mode-locked laser was built with a 1.2 GHz repetition rate. The cavity configuration was similar to that in . One mirror was actuated by the PZT and stable Kerr-lens mode-locking was achieved, which supported the proposal that no significant distortion was present at the sliced mirror. As an optical reference, an external-cavity diode laser operating at 1074 nm and stabilized to a high-finesse cavity was used . An optical heterodyne beat note between the GHz comb and the optical reference was obtained. By modulating the PZT, the optical frequency of a longitudinal mode of the GHz comb can also be controlled. The relative phase of the heterodyne beat note was stabilized to a radio frequency (RF) reference via a feedback circuit. Note that this kind of phase stabilization need a high-speed actuator such as our PZTs, and cannot be achieved by conventional PZTs because the laser linewidth is typically broader than the feedback bandwidth of the PZTs. The residual phase noise power spectral density (PSD) and the integrated phase noise are shown in Fig. 6(b). The feedback bandwidth may exceed 200 kHz and residual phase noise integrated over the range from 100 Hz to 3 MHz was then down as low as 183 mrad. Although the noise of the frequency combs scaled with the square of the repetition rate , this value was comparable to that of well-stabilized 100 MHz Yb:fiber combs . The difference of the feedback bandwidth comparing with the RIN-feedback experiment (Fig. 5) is mainly caused by the different shape of free-running spectra. Higher feedback gain at low frequency is necessary for the laser-cavity control since the free-running phase noise decays much faster as it gets higher frequency in this case, which makes the feedback difficult to reduce higher frequency noise .
We have developed a PZT-actuated mirror system with a flat frequency response up to 500 kHz. This system was realized by making four vital improvements, i.e., using a wedged damping alloy, performing acoustic impedance matching, cutting the PZT, and using a compensating electronic circuit. The maximum effective feedback bandwidth also reached 500 kHz, which is a record for a PZT. We also demonstrated stabilization of a GHz comb, in which it is difficult to apply EOMs. Although the size of the mirror and the PZT stroke were restricted, our design is still useful for numerous applications. This ultra-high-speed PZT system could be applied not only to laser feedback systems but also to a variety of applications that require high-speed displacement.
Ministry of Education, Culture, Sports, Science and Technology; Japan Society for the Promotion of Science (Research Fellowships for Young Scientists).
We would like to thank F. Quinlan for helpful comments on the manuscript and English proof reading.
The authors declare no conflicts of interest.
1. D. D. Hudson, K. W. Holman, R. J. Jones, S. T. Cundiff, J. Ye, and D. J. Jones, “Mode-locked fiber laser frequency-controlled with an intracavity electro-optic modulator,” Opt. Lett. 30(21), 2948–2950 (2005). [CrossRef]
2. T. Nakamura, S. Tani, I. Ito, and Y. Kobayashi, “Magneto-optic modulator for high bandwidth cavity length stabilization,” Opt. Express 25(5), 4994–5000 (2017). [CrossRef]
3. T. C. Briles, D. C. Yost, A. Cingöz, J. Ye, and T. R. Schibli, “Simple piezoelectric-actuated mirror with 180 kHz servo bandwidth,” Opt. Express 18(10), 9739–9746 (2010). [CrossRef]
4. A. Chadi, G. Méjean, R. Grilli, and D. Romanini, “Note: Simple and compact piezoelectric mirror actuator with 100 kHz bandwidth, using standard components,” Rev. Sci. Instrum. 84(5), 56112–56113 (2013). [CrossRef]
5. D. Goldovsky, V. Jouravsky, and A. Pe’er, “Simple and robust phase-locking of optical cavities with > 200 KHz servo-bandwidth using a piezo-actuated mirror mounted in soft materials,” Opt. Express 24(25), 28239–28246 (2016). [CrossRef]
6. Y. Okanda, “NOVEL Fe-Al ALLOY AND METHOD FOR PRODUCING THE SAME.” U.S. Patent Application No. 11/815,946.
7. L. Nugent-Glandorf, T. A. Johnson, Y. Kobayashi, and S. A. Diddams, “Impact of dispersion on amplitude and frequency noise in a Yb-fiber laser comb,” Opt. Lett. 36(9), 1578–1580 (2011). [CrossRef]
8. S. A. Diddams, T. Udem, J. C. Bergquist, E. A. Curtis, R. E. Drullinger, L. Hollberg, W. M. Itano, W. D. Lee, C. W. Oates, K. R. Vogel, and D. J. Wineland, “An optical clock based on a single trapped 199Hg+ ion,” Science 293(5531), 825–828 (2001). [CrossRef]
9. M. Takamoto, F.-L. Hong, R. Higashi, and H. Katori, “An optical lattice clock,” Nature 435(7040), 321–324 (2005). [CrossRef]
10. F. N. Baynes, F. Quinlan, T. M. Fortier, Q. Zhou, A. Beling, J. C. Campbell, and S. A. Diddams, “Attosecond timing in optical-to-electrical conversion,” Optica 2(2), 141–146 (2015). [CrossRef]
11. J. Davila-Rodriguez, X. Xie, J. Zang, C. J. Long, T. M. Fortier, H. Leopardi, T. Nakamura, J. C. Campbell, S. A. Diddams, and F. Quinlan, “Optimizing the linearity in high-speed photodiodes,” Opt. Express 26(23), 30532–30545 (2018). [CrossRef]
12. M. Endo, I. Ito, and Y. Kobayashi, “Direct 15-GHz mode-spacing optical frequency comb with a Kerr-lens mode-locked Yb:Y2O3 ceramic laser,” Opt. Express 23(2), 1276–1282 (2015). [CrossRef]
13. I. Ito, A. Silva, T. Nakamura, and Y. Kobayashi, “Stable CW laser based on low thermal expansion ceramic cavity with 4.9 mHz/s frequency drift,” Opt. Express 25(21), 26020–26028 (2017). [CrossRef]
14. M. Endo, T. D. Shoji, and T. R. Schibli, “Ultralow Noise Optical Frequency Combs,” IEEE J. Sel. Top. Quantum Electron. 24(5), 1–13 (2018). [CrossRef]
15. T. Nakamura, I. Ito, and Y. Kobayashi, “Offset-free broadband Yb:fiber optical frequency comb for optical clocks,” Opt. Express 23(15), 19376–19381 (2015). [CrossRef]