1. Extended Abstract – Summer 2016 RiO REU
Mechanical Resonance Damping for Piezoelectric-Actuated Mirror
Mounts
Adam F. Moreau1,2,*, Jenna Bergevin1, Dr. R. Jason Jones1
1University of Arizona, Tucson AZ; 2University of San Diego, San Diego, CA
*adammoreau1@gmail.com
A piezoelectric-actuated mirror with greater than 380kHz servo bandwidth was developed, and the
principal factors that lead to low frequency mechanical resonances were examined. In order to keep the
gain cavity length of an ultrafast laser uniform, a small piezoelectric transducer (PZT) is attached to the
backside of one of the mirrors. A major difficulty encountered when working with PZT-actuated mirrors is
their very limited bandwidths, often < 20-40kHz. A number of variables were considered for the design of
the mount structure, such as the size of the mount head, the material used on the surface and the core of the
mount, the type and amount of adhesive applied, the methods of application, the mass of the mirror, and
fabrication techniques. Out of those analyzed, the two dominant factors, which most affect the frequency of
the first resonance, were the methods for applying the adhesive, and the thickness of the adhesive used.
When adhering the PZT to the mirror and mount head a large adhesive mound must be depressed, pushing
excess material to the sides thus eliminating irregularities within the adhesive itself, and ensuring that a thin
uniform layer is applied. With this addressed, secondary and tertiary factors have been shown to be the
presence of a damping core to prevent longitudinal resonance modes, and the Young’s Modulus of the
outer material respectively. The optimal mount design for a piezoelectric-actuated mirror was the 0.25ӯ
Tungsten-Carbide filled design, with an outermaterial of Brass.
INTRODUCTION
In ultrafast, high precision laser systems, stability of the gain cavity (Fig. 1) is a
major concern. A piezoelectric-actuated mirror mount design with over 380kHz servo
bandwidth is proposed to improve cavity stability. Major sources of low frequency
mechanical resonances were studied, and iterative design processes were used to identify
and dampen each source individually. The mount now proposed has been implemented
into the active servo loop of a Ti:Sapphire frequency comb to confirm these
measurements while in an active system.
In order to keep the gain cavity length uniform, a small piezoelectric transducer
(PZT) was attached to the backside of a fully reflective mirror. PZTs are crystals that
respond mechanically to an applied voltage signal. This PZT/mirror must then be adhered
to a mount in order to be placed and aligned into the system. Comparing the output of the
ultrafast laser with a second reference laser that maintains a constant frequency created a
feedback loop. Feedback controls compared the difference of the two to determine if the
cavity should be expanded or shortened to compensate for any changes. The cavity
environment always fluctuates via temperature changes, physical vibrations in the room,
etc. The final component of the control system, a piezoelectric driver, was connected to
the PZT and applied a measured voltage to precisely control the cavity length. The servo
bandwidth of the system is a measure of how quickly the PZT can respond to stimuli
while staying within the negative feedback regime.
Mechanical resonances present in the system (mirror, adhesive, PZT, and mount)
directly determine the useable servo bandwidth of the PZT actuated mirror. At the
frequency of a mechanical resonance or anti-resonance, a large spike in both amplitude
and phase occurs in either the positive or negative directions respectively. When the

2. Extended Abstract – Summer 2016 RiO REU
phase margin shifts by 180º positive feedback will occur and the cavity will no longer be
stable.
Figure 1. This figure depicts a Fabry-Pérot cavity in which a laser pulse is fed into the cavity containing
some type of gain medium, such as a solid-state crystal or semiconductor diode. A portion of the beam
comes out of the cavity and is coupled to the output, and a portion reflects back into the gain medium. The
outcome is such that an ultra short pulse train will be produced, and when the pulses are equally spaced the
laser is said to be mode locked, one common use of piezoelectric-actuated cavities.
EXPERIMENTAL DESIGN
Four mount designs were studied (Fig. 2), one control followed by three damping
designs. For the control mounts, a 1”Ø by 1” length cylinder was machined out of three
common mounting materials, Brass, Copper, and Aluminum. The cylindrical control
mounts allowed for the independent study of a number of possible limiting factors such
as adhesive wax thickness, mount material, radial position of the PZT/mirror, type of
mount holding, or choice of wax.
Figure 2. Back (top) and front (bottom) views of the four mounts, shown with a Copper outer shell
material. From left to right: cylindrical control, Solid center of mass design, 0.125ӯ Tungsten-Carbide
filled center of mass design,and 0.25ӯ Tungsten-Carbide filled design.
The first damping design considered was the solid center of mass design with
three made, one each of Brass, Copper and Aluminum. This design was utilized to study
the effectiveness of damping both drumhead and deflection resonance modes. Drumhead
resonance modes occur as the front face to which the PZT/mirror is bonded flexes
similarly to a drum. The frequency of the first drumhead resonance scales as the inverse
of the diameter and thus the front face of the mount was tapered down to increase this
frequency [1]. Deflection resonance modes occur because traditional mounts are only
clamped at one end, and thus the mount can vibrate similarly to a cantilever beam. To

3. Extended Abstract – Summer 2016 RiO REU
counter these resonance modes, the center of mass design includes a tail which extends
out the back of the mount holder and keeps the center of mass directly above the
clamping point.
Building upon the center of mass design, a second damping design was
constructed, the 0.125ӯ Tungsten-Carbide filled center of mass design. In addition to
the drumhead and deflection resonance modes, longitudinal mode damping was
investigated with this mount. Longitudinal waves propagate along the length of the
mount, and the resonant frequency of these waves depends upon the material properties
of the mount [1,2]. A damping core of 0.125ӯ Tungsten-Carbide was inserted into a
Copper center of mass design in order to break up low frequency longitudinal resonance
modes. Tungsten-Carbide was chosen for the core material due to its advantageous
damping properties, and it’s rigidity for fabrication processes. Higher rigidity (compered
with other common damping materials such as lead) allowed for a simple fabrication
process that prevented the formation of air gaps in the mount, which would negatively
affect performance.
The final damping design investigated was the 0.25ӯ Tungsten-Carbide filled
design. This design further perused the dampening of longitudinal resonances by
increasing the Tungsten-Carbide core diameter and by shortening the overall mount
length, as the frequency of the first resonance is inversely proportional to length of the
mount.
MEASUREMENT
A Michelson Interferometer was constructed such that one arm went to a
stationary mirror, and the PZT-actuated mirror varied the second arm length. The output
of the interferometer came to a photodiode to record amplitude and phase data. The PZT
was connected to a network analyzer, and a wide spectrum sweep (1Hz-500kHz) was
performed. Each frequency sweep was averaged to increase the signal to noise ratio.
In all experiments described herein, the same silvered mirror and PZT were used
to reduce contributing variables. These two components were permanently adhered
together with a thin layer of Torr Seal. The mirror was chosen to be as light as possible,
and when other mountings with larger mirrors were compared those with smaller mirrors
had larger bandwidths, as supported by literature [3,4].
RESULTS
Of the factors investigated, thickness of the adhesive wax layer has been found to
be the primary dominant factor determining the first mechanical resonance of the system.
When the wax layer and the PZT/mirror are modeled as a mass-spring system, the
resonant frequency of this system is given by 𝑓 ∝ 𝐶 ∙ ℎ−1
2⁄
where h was the height of the
wax layer [5]. As seen in figure 3, the results from an experiment in which the height of
the wax was varied fit this model well. When applying the wax it has been found that it
was imperative to ensure that a uniform layer had been applied to prevent low frequency
resonances caused by air gaps. By depressing a large mound of hot wax with the
PZT/mirror, the excess wax was pushed to the sides, and a thin uniform layer of wax
would remain. For all investigations into other factors, the thinnest layer able to be
applied was used.

4. Extended Abstract – Summer 2016 RiO REU
Figure 3. Using Crystal Bond 509 adhesive wax, a pillar was constructed and the frequency response
measured as the height was varied. Solid fit line shows congruence with theory as a dependence upon
ℎ−1
2⁄
.
The frequencies of the first mechanical resonances were found to vary with mount
materials. The three materials chosen for study are all commonly found in optical
systems. It was found that the useable bandwidth of the Brass cylinder was the largest,
with Aluminum having the smallest (Fig. 4). It can be concluded therefor that optimal
mounts would best be made from Brass, or secondarily from Copper.
Figure 4. The traces above are from cylindrical mounts using Crystal Bond 509 wax with mounts of
Aluminum, Brass and Copper. Three sets of averaged data were taken for each material, resulting in the
following resonance peaks: Aluminum: 84kHz; Brass: 106kHz; Copper: 96kHz.
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5. Extended Abstract – Summer 2016 RiO REU
Using the cylindrical mounts, it was found that a there is a minor dependence
upon the radial placement of the PZT/mirror. When the PZT/mirror is adhered to the edge
of the front face (center of mirror offset was 0.4”), the bandwidth was seen to drop by
approximately 10kHz as opposed to the center of the mount. When the PZT/mirror was
only slightly offset however this effect is indistinguishable. Cylindrical mounts were also
used to determine that the type of mount holding (ThorLabs or Newport 1” Mirror
Mounts) had no effect upon the frequency of the first resonance. This continued to hold
even when the holdings were placed backwards, thus indicating that this was not a
bandwidth-limiting factor. Additionally the type of adhesive wax used (Crystal bond 509
or Mounting Wax 80) did not affect the frequency of the first resonances found with the
cylindrical mounts. This was later confirmed during tests using additional mount designs.
The solid center of mass design further confirmed the results of the material
comparison performed with the cylinders, showing Brass to have the largest bandwidth
(Fig. 5). The bandwidth for the Brass and Copper mounts did not however improve from
the cylinder mounts. The Aluminum center of mass mound conversely, did see an
improvement in usable bandwidth. This suggests that deflection and drumhead resonance
modes play a diminished in role determining the bandwidth of a mount material with a
high young’s modulus, such as Brass or Copper, when compared to a less rigid material,
such as Aluminum.
The 0.125ӯ Tungsten-Carbide filled center of mass design did however improve
upon the copper solid center of mass mount, and the copper cylinder. This clearly
indicated that the presence of a longitudinal damping element positively impacted the
usable bandwidth for the PZT-actuated mirror mount.
Figure 5. Frequency responses of the four center of mass type designs, with the following resonance peaks
were found: Aluminum: 102kHz; Brass: 104kHz; Copper - Solid: 89kHz; Copper – Filled: 142kHz.
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6. Extended Abstract – Summer 2016 RiO REU
The mounting mount design proposed herein built upon the results of the copper
filled center of mass design to further dampen longitudinal resonances, and to choose
materials that do not show a strong dependence upon deflection and drumhead resonance
modes. The resulting frequency responses (Fig. 6) were highly stable in both amplitude
and phase, and approached the free resonance of the bare PZT (theoretical maximum for
any design) [3,4]. The front face of this design has been tapered to reduce possible
drumhead modes, however these resonance sources were not predicted to be bandwidth-
limiting factors for Brass and Copper mounts.
Figure 6. The 0.25ӯ Tungsten-Carbide filled mount frequency responses for Brass and Copper. The
largest servo bandwidth yet measured was this design with a Brass shell, depicted here (blue).
Brass– Filled: 392kHz; Copper - Filled: 380kHz
CONCLUSION
The optimal mount design for a piezoelectric-actuated mirror is the 0.25ӯ
Tungsten-Carbide cored filled design made of Brass. In all designs the adhesive wax
layer must be thin, as this was a principle factor in determining the first resonances. Our
design utilizes a rigid damping core, and tapered nose to minimize longitudinal, and
drumhead resonance modes respectively. Due to higher resonances of Brass, compared
with Copper or Aluminum, it was an optimal material for the outer shell. The objective of
this research was to design and fabricate a mount with ≥ 100kHz servo bandwidth. This
has been achieved, and the highest servo bandwidth yet measured by this group is
392kHz.
ACKNOWLEDGEMENTS
The authors would like to acknowledge funding support from the National
Science Foundation through and REU Site under grant #EEC-104331. We thank the
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Copper

7. Extended Abstract – Summer 2016 RiO REU
Research in Optics (RiO) Program, the Undergraduate Research Opportunities
Consortium (UROC), and the University of Arizona. We thank A. Agarwal for helpful
discussions.
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123703 1-8
[3] Millo, Jacques; Merzougui, Mourad; Di Pace, Sibilla; Chaibi, Walid; Applied Optics
2014, Vol. 53, 7761-7772
[4] Chadi, A.; Méjean, G.;Grilli, R.;Romanini, D.; Rev. Sci. Instrum. 2013, Vol. 84,
056112
[5] Li, Jie-Fang; Moses, P.; Viehland, D.; Rev. Sci. Instrum. 1995, Vol. 66, 215-221