1. Introduction

The ability to lock an optical cavity to a specific length is essential to fix a laser to a preselected frequency and phase [1–7]. It has great importance in many applications, such as stabilization of frequency combs [7–10], quantum information networks [11], atomic interference [12,13], atomic clocks [14,15] and ultrafast optics [16,17]. The simplest method to lock an optical cavity is to mount one of the end mirrors of the cavity on a piezoelectric transducer (PZT) [5,18–20], which is then controlled by a servo-loop to correct frequency and phase fluctuations by actively adjusting the length of the cavity.

Due to the electro-mechanical nature of the PZT, the locking performance is highly sensitive to acoustic resonances of the surrounding environment, including its own mount and even the optical table. This fact normally introduces a serious limitation on the PZT’s servo bandwidth, as mechanical resonances are generally accompanied by a 180° phase shift of the optical response, which transforms the negative feedback into positive and prevents locking in a closed loop. Therefore, and despite the fact that the natural resonant frequency of a bare PZT is typically in the range of 400 – 800 KHz, actual PZT based locks are traditionally limited to a low-bandwidth servo-loop (in the range of a few KHz), leaving the high-frequency control to more complicated methods, such as electro-optic modulation (EOM) [18,21], acousto-optic modulation (AOM) [18,22] or laser - current control (in semiconductor lasers) [23]. However, the use of EOM, AOM or current is not always possible and may add complications and extra limitations, such as dispersion in pulsed lasers or added intensity noise in semiconductor lasers. Piezo actuators, on the contrary, are much simpler, always applicable and do not introduce any interference within the laser cavity. Thus, the desire is clear for piezoelectric actuated mirrors with higher locking bandwidth, as was recognized in previous work [19,24].

The available bandwidth of feedback is of critical importance for minimization of the residual in-loop noise and to obtain a stable and robust lock even in the presence of strong transient interfering noise (e.g. touching the optical table, door slam, etc.). Due to the integrative nature of feedback loops, the response gain at low frequencies increases like $G\left(\omega \right)\sim \frac{1}{\omega }$ [25], indicating that to achieve high gain at the important low-frequency bands of noise, such as 50/60 Hz of the electrical mains or the acoustic vibrational band of 0.1 – 2KHz, it is critical to extend the available gain as high as possible in frequency. Since the physical limit to a PZT locking bandwidth normally arises from the first mechanical resonance that is excited by the PZT, the main challenge is to push the lowest resonance up, ideally to the natural resonance of the PZT-mirror compound alone, which can easily be in the 100 – 500KHz range, depending on the physical dimensions of the mirror and the PZT.

The main major difficulty in designing a PZT lock is the lack of complete understanding of the origin of low frequency resonances due to the acoustic complexity of opto-mechanical mounts. Consequently, mechanical designs for PZT-mounts are generally based on “good intuition” rather then on educated calculations. Previous attempts to overcome the low frequency resonances by different acoustic approaches reached servo-bandwidth of 180KHz by shaping the mount in an asymmetric form, filling it with lead to damp resonances and distorting the piezo-mount contact surface [19]. In addition, reducing the physical dimensions of the mirror and PZT was often required to reach high frequency performance, which renders it less comfortable to work with, and reduces the dynamic range of the PZT, and its mechanical force.

We offer a different approach to increase the available PZT bandwidth by completely decoupling the actuated mirror from the optical mount using soft materials under pressure as mechanical isolation. While the pressure allows long term stability of the mirror, the soft material itself (e.g. rubber, soft silicone gel, etc.) blocks the high frequency sound-waves from reaching the mount, and the PZT - mirror compound effectively floats in “mechanical vacuum”. This reduces tremendously the acoustic complication, allowing to reach record-high servo bandwidth with relatively large mirrors and PZTs, as described below.

We applied this design in our lab to lock a home made cavity for high-power frequency doubling of 1560nm CW light from a fiber laser to generate nearly 7W of 780nm light with >65% efficiency. The robustness of the lock to external noise is demonstrated in the online supplementary material ( Visualization 1).

2. The design

The philosophy behind the mechanical design is to prevent any direct contact between the parts that must vibrate (the mirror and the PZT) and the rest of the mount in order to minimize sources of resonant behavior. Thus, to mount the actuated mirror, we surround it with soft elastic substance, such as rubber o-rings or rubber pads which are pressured against the rigid optical mount as shown in Fig. 1. In addition, to ease the damping task of the rubber, all the mount materials in the vicinity of the piezo and mirror are relatively damped (e.g Black Delrin or other plastic materials of high rigidity). The mirror and PZT are glued together with an adhesive of minimal thickness (super glue), but are detached from the mount itself by a rubber padding on the back and a rubber o-ring in front. The whole configuration is sealed by applying pressure from the back of the mount.

 

Fig. 1 PZT mounting concept. The mirror and PZT are glued together and held by applying pressure from the back and the front of the mount. The PZT is separated from the back of the mount by a soft padding disk, and from the front by a soft ring. Mechanical pressure stabilizes the mirror and improves damping of the high PZT-mirror self resonances.

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The employment of soft materials for mechanical damping is of course well-known and vastly applied, from nano-mechanical structures to domestic washing machines; and yet, it is very rarely used in precision opto-mechanical mounts. Probably the main reason that prevented incorporation of soft materials, such as rubber, in opto-mechanics is the concern that this will hamper the pointing stability of the mount. As we show below, this concern can be adequately lifted by applying pressure on the damping layers.

2.1. Mirror and PZT considerations

Due to the finite mass of the mirror, not all the momentum of the PZT can be transferred to the mirror, leaving some residual momentum exerted on the back of the piezo mount. Since the PZT - mirror compound in our design is isolated mechanically, the only back weight that the mirror can act on is the PZT itself, indicating that the PZT should be chosen with a mass that matches approximately the mass of the mirror (a PZT too small will barely move the mirror, while a PZT too large will introduce low self resonance frequency and high capacitive load for the driver). After several attempts, we found that for a mirror of 8mm diameter and 2mm thickness a 3 × 3 × 2mm PZT of 60nF electrical capacitance and 2.2μm travel range at 150V produced decent results.

2.2. Damping material considerations

In order to understand the function of the soft damping material, it is convenient to separate the operation of the servo-loop into two regimes - the very low and the very high frequency vibrations.

At low frequencies near DC, the damping material (rubber) is tightly pressed, and is rather stiff with high resistance to movement. If the damper is entirely rigid, which can happen if the pressure is too high, the actuated mirror will not be able to move at all. If instead, the pressure is soft enough to allow some movement, the net shift of the mirror will be governed by the ratio of stiffness between the back soft pad and the front soft ring. It is therefore desired that at low frequencies the front ring will be softer (lower spring constant) then the back pad.

At high frequencies on the other hand, the resistance of the damper to fast micro-movement is drastically reduced, and the above considerations are no longer needed. It is important, however, to have sufficiently soft and thick dampers that can block completely sound waves from reaching the mount itself. Due to the proximity to the piezo, the back side of the mount suffers stronger vibrations, and therefore requires a thicker rubber padding. We find that 2–3mm thick pads were sufficient for our design.

As mentioned above, the front rubber ring also aligns the mirror to the optical axis. While operating, the PZT can produce strong vibrations that may tilt and displace the mirror if the front rubber is too soft.

A good compromise between all the above considerations was to use the same material and thickness for back and front damping. After various of substances were tested, we found that the exact soft material is not very critical. Pads and rings molded from a simple general-purpose grey acrylic sealant gave very good results, both on damping abilities (208KHz servo bandwidth) and long term stability. General-purpose hot glue served very well also (195KHz servo bandwidth), and even Teflon backed with simple rubber o-rings did an OK job (100KHz servo bandwidth).

3. Final design and results

Figure 2 shows the final mechanical design. The Mount itself was molded from Acetal homopolymer (Delrin). The front was threaded externally to fit a commercial mount for 1″ optics (GM100 from Thorlabs). The pressure was applied by a back screw, also made of black Delrin. To prevent the piezo from rotating while turning the screw, a Teflon plate (white) was attached to the end of the screw that was free to rotate (see Fig. 2(b)). The Teflon plate was padded with a 2mm soft plate (grey, acrylic sealant), and the mirror was held in a 1.5 mm thick custom made soft holder (grey, acrylic sealant). As an extra damping precaution (though its necessity is not clear), another rubber pad and rubber o-ring were added between the PZT-mirror compound and the mount (yellow).

 

Fig. 2 (a) Schematic illustration of the final mounting design. (b) A zoom into the mount. From right to left: The mount (black), front 6.8mm inner diameter, 2mm thick rubber o-ring (yellow), a 6.5mm inner diameter, 2mm thick soft positioning ring (grey, molded from acrylic sealant), an 8mm diameter, 2mm thick mirror (blue), a cubic PZT of 3 × 3 × 2 dimensions, 60nF electrical capacitance and 2.2μm dynamic travel range at 150V (red), a 10.5mm diameter, 3mm thick back soft padding (grey, made of acrylic sealant), extra rubber padding (yellow), a Teflon supporting back (white) and the pressure screw (black).

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Due to its high capacitive load, the PZT could not be driven with a standard commercial driver. To maintain fast enough electro-mechanic response, we designed and realized a custom home-made driver. The appendix contains further details on the electrical design of the driver.

3.1. Time and frequency response

To test the performance of the PZT-actuated mirror, we incorporated it in a Michelson interferometer that was actively locked to an interference fringe. During the lock, we introduced an additional step to the input error signal of the control loop, and recorded the in-loop response.

Figure 3 shows the time and frequency response to a step perturbation, with a proportional-integrator corner (PI) set to 30KHz and 300KHz, with the loop gain raised to the verge of self oscillation. The frequency of self oscillation of the loop was 320KHz and 290KHz accordingly, and the servo bandwidth, defined as the maximal frequency of positive loop-gain was > 200KHz with PI corner set to 30KHz (and > 100KHz with the PI corner at 300KHz).

 

Fig. 3 Time and frequency response for a step perturbation, PI corner set to 30KHz and 300KHz. (a) Frequency response with PI at 30KHz. (b) Frequency response with PI at 300KHz. (c) Time response with PI at 30KHz. (d) Time response with PI at 300KHz.

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Although the servo bandwidth for the PI corner 300KHz was lower (106KHz for the first zero-crossing, with a near zero-touch at 77KHz), its performance at low frequencies was significantly better, which is evident from the fast time response in Fig. 3(d), showing a response time of ~ 3μs. It is clear therefore that although the maximal servo-bandwidth is an important measure of the achievable performance, the best temporal response is not necessarily obtained with the highest servo-bandwidth, but rather with the highest gain at low frequencies, which may be offered by a slightly higher PI corner.

Note that the mechanical design is very robust and there is no principal restriction on the materials used. While we found that the best gain bandwidth (208KHz) was obtained with dampers molded from acrylic sealant, very good results were obtained also with a large variety of soft dampers, such as hot glue (195KHz), soft silicone gel, soft Teflon, rubber o-rings etc.

3.2. long term stability

Despite initial concerns for the of long term stability of optical elements that are mounted on soft materials, our observations show that the mechanical pressure keeps the mirror remarkably stable. Several tests of overnight operation, and even 2.5 days of continuous operation showed almost no evidence of loss of optical alignment.

The long term pointing stability was qualitatively tested by measuring the angular drift and noise of the interferometer output beam over a period of 18 hours by imaging the focal spot (far field) of the beam on a CCD camera behind an f = 600mm lens. The angular shift was calculated from the spatial deviation of the center of mass of each frame from the average centroid of all frames. The interferometer was locked and filmed for seven hours, then stayed locked over night (8 hours) and was filmed again for additional three hours on the following day, to a total of 18 hours of operation. It is clear from Fig. 4 that no meaningful angular shift occurred. The maximal average angular deviation during the entire 18h period was < 2 × 10⁻²mRad, of order 0.01 of the diffraction limited beam divergence.

 

Fig. 4 Pointing stability of the PZT-mirror as a function of time.

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4. Conclusions

We demonstrated that mechanical isolation by soft materials enables record high bandwidth of optical servo-locking. Even though mechanical damping with soft materials is widely used in many engineering applications, the adoption of these principles to optics was generally avoided so far. Our experiments show that significant advantages of soft materials can be exploited, with no evident compromise of optical stability, enjoying the best of both worlds.

Appendix - PZT driver outline

The PZT, acts electrically as a relatively large capacitor. Thus, to obtain fast optical response, a driver should be able to provide sufficient current to drive the capacitance.

Figure 5 shows a simplified scheme of our home-built driver design. First, the input signal is pre-amplified (AD823), followed by two power amplifiers (OPA458) in parallel, one non-inverting and the other inverting, that feed the two leads of the PZT. The configuration above allows output current up to 5A at an operating bandwidth of > 1MHz and a maximum differential voltage of about ~ 60V. When driving the actual PZT, a voltage rise time of less then 1μs was obtained.

 

Fig. 5 Basic scheme of the PZT driver. The input signal is pre-amplified and split into inverting and non inverting amplifiers. The outputs are then feed the two leads of the piezo, producing a differential voltage with an overall gain of ×4 (after preamp).

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Funding

Israel Science Foundation (Grant #46/14).

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