Tuning forks with optimized geometries for quartz-enhanced photoacoustic spectroscopy

We report on the design, realization, and performance of novel quartz tuning forks (QTFs) optimized for quartz-enhanced photoacoustic spectroscopy (QEPAS). Starting from a QTF geometry designed to provide a fundamental flexural in-plane vibrational mode resonance frequency of ~16 kHz, with a quality factor of 15,000 at atmospheric pressure, two novel geometries have been realized: a QTF with T-shaped prongs and a QTF with prongs having rectangular grooves carved on both surface sides. The QTF with grooves showed the lowest electrical resistance, while the T-shaped prongs QTF provided the best photoacoustic response in terms of signal-to-noise ratio (SNR). When acoustically coupled with a pair of micro-resonator tubes, the T-shaped QTF provides a SNR enhancement of a factor of 60 with respect to the bare QTF, which represents a record value for mid-infrared QEPAS sensing. © 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement


Introduction
Optical techniques operating in the mid-infrared spectral regions are capable of excellent trace gas sensing performances, together with high sensitivity and selectivity [1,2] due to the presence of strong ro-vibrational absorption bands of many molecules.Photoacoustic spectroscopy (PAS) is a sensing technique that does not require the use of an optical detector and troublesome optical alignments, but nevertheless is capable of performing trace gas measurements at sub-parts-per-trillion concentration levels [3,4].PAS is based on the detection of sound waves generated by gas absorption of modulated optical radiation.Quartz tuning forks (QTFs) have shown a great potential as sound transducers, leading to a wellestablished variant of PAS, named quartz-enhanced photoacoustic spectroscopy (QEPAS) [5].The confinement of the acoustic energy between the prongs of the QTF, combined with high quality factors, enabled the detection of weak photoacoustic excitation within very small gas volumes.Since its introduction in 2002, standard low-cost QTFs with resonance frequencies at 32.7 kHz are typically employed in QEPAS sensors [6].The QTF is typically coupled with a pair of tubes, acting as an organ pipe resonator to probe the sound wave [7,8].The acoustic detection module composed of the QTF and micro-resonator tubes constitutes the QEPAS spectrophone, which is the core of any QEPAS sensor.In QEPAS sensing, the light source is focused between QTF prongs and sound waves produced by the modulated absorption of the gas are generated between the QTF prongs, forcing them to oscillate back and forth (in-plane anti-symmetrical modes).The main problem in the realization of a standard QEPAS sensor is the focalization of the laser beam within the 300 μm-gap between the standard QTF prongs without touching both micro-resonator tubes and the QTF.This is crucial in order to avoid the generation of a photo-thermal noise contribution which would be added to the piezoelectric signal [9].When laser modulation occurs at one of resonance frequencies of in-plane piezoelectrically active modes, the induced strain field generates surface electric charges proportional to the intensity of the sound waves incident on the QTF prongs.When the light is periodically absorbed by the gas, the energy excess is mainly dissipated through nonradiative relaxation processes, involving vibrational and rotational excited states.Sound waves are then generated via energy transfer from excited states to translational degrees of freedom.The ability of the gas target to periodically relax the excess of energy depends on the modulation frequency (i.e. the resonance frequency of the QTF in-plane mode) of the incident laser radiation and differs for each gas [10,11].With respect to the standard PAS, QEPAS operates at higher resonance frequencies.For slow relaxing gases, such as CO, CO 2 and NO a QEPAS sensor operational frequency as high as 32.7 kHz, like in standard QTFs, can limit the sound wave generation efficiency [12].These considerations suggested directions for the realization of improved QTFs: i) reduction of the QTF fundamental frequency, ii) increase the prongs spacing in order to facilitate the optical alignments and minimize the photo-thermal noise level.Starting in 2013, custom QTFs have been realized in QEPAS sensors following these two guidelines [13].Larger prongs spacing led to the use of the QEPAS technique with laser sources having a poor spatial beam quality as well as operating in the terahertz spectral range [13,14].The implementation of a single-tube as acoustic micro-resonator system is another achievement [15].Lowering the fundamental frequency also opened the way to the use of first overtone mode in QEPAS sensing [16,17], leading to a double-antinode QEPAS configuration [18] and simultaneous dual-gas detection by exciting with two laser sources both the fundamental and first overtone QTF flexural modes, simultaneously [19].However, guidelines for QTFs optimized for QEPAS operation are still not well defined.
This paper reports an investigation of the influence of prong sizes on both the resonance frequency and on the quality factor of the fundamental flexural mode, leading to the design of a quartz tuning fork optimized for QEPAS sensing.Starting from this design, two novel geometries were proposed: one with T-shaped prongs to optimize the strain field between the prongs and their support and the other one having prongs with grooves carved on the central sides in order to reduce the QTF electrical resistance.After determining the resonance properties, the investigated QTF samples were implemented in a QEPAS setup to test their photoacoustic response.The QTF providing the best performance in terms of signal-to-noise ratio (SNR) was acoustically coupled with a dual-tube micro-resonator system.The influence of the geometrical parameters on the photoacoustic response, namely the internal diameter and the length of the two tubes together with the spacing between the tube and the QTF, was also investigated to determine the optimal micro-resonator geometry.

Guidelines for the design of quartz tuning forks
The photoacoustic signal is proportional to the product Q•P•α, where Q is the QTF resonance quality factor, α is the gas target absorption coefficient and P is the laser power [17].The straightforward approach to design QTFs optimized for QEPAS sensing is to reduce the resonance frequency while keeping high the quality factor.The dependence of the resonance frequency and related quality factor on the QTF relevant dimensions has been investigated in [20], where a set of QTFs with different values of spacing between the prongs and their sizes was analyzed.This study showed that resonance frequencies of in-plane flexural modes can be well predicted by using the Euler-Bernoulli equation.Considerations about the quality factor are more challenging.The Q-factor depends on all the energy dissipation mechanisms occurring in a vibrating prong of a QTF.The main contributions are due to damping by the surrounding fluid, the interaction of the prong with its support and thermo-elastic damping [21].All these loss mechanisms strongly depend on the QTF prongs size.Although several theoretical models have been proposed to describe the dependence of each loss mechanism on the prongs geometry [22][23][24], there is no theoretical model capable to take into account all the dissipation mechanisms in one, consistent formulation.An experimental investigation described in [21] on the QTF fundamental flexural mode resonance at atmospheric pressure demonstrates that the overall quality factor can be phenomenologically related to the prong sizes by: 5 3.78 10 where w, T and L are the crystal thickness, the prongs width and the prongs length, respectively, all expressed in mm-units.This relation suggests that the overall quality factor of the fundamental mode can be increased by reducing the prong length and increasing both thickness and crystal width.Conversely, according to Euler-Bernoulli model, the resonance frequency of the fundamental flexural mode increases as the ratio between the prong thickness and its squared length [20].When the crystal thickness is fixed, the quality factor scales linearly as the ratio T/L and Eq.The graph clearly shows that for a selected resonance frequency, different prong sizes can be chosen, providing quality factors values spanning in a certain range.Moving to low resonance frequencies, this range of possible quality factor values, as well as the Q-factor values itself, is reduced.In particular, QTFs with a resonance frequency lower than 10 kHz cannot ensure a Q-factor higher than 15,000, at atmospheric pressure.For a novel generation of QTFs optimized for QEPAS operation, a resonance frequency of ~16 kHz (a half of the standard 32.7 kHz) was selected.At f = 16 kHz, L and T values (with w = 0.25 mm) maximizing the quality factor (18,000) are 9.4 mm and 2.0 mm, respectively.In a first step, starting with this prong geometry we designed two QTFs differing only in the prong spacing: QTF-S08 having a prong spacing of 0.8 mm, and QTF-S15 with a prong spacing of 1.5 mm.With all other geometrical parameters being identical, a comparison between them in terms of QEPAS performance will allow establishing the influence of the prong spacing on the QTF frequency and Q-factor, as well as on the amount of radiation incident on the prong surface, which typical affects the QEPAS sensor noise level.

T-shaped
When prongs produced alon surface.This QTF prongs.An increase o induced charg no analytical when the pro commercial f geometry and derived in pre stress field dis These gro the width of th to 100 µm, stiffness.The

Resonanc
The QTFs re generation of will be compa vibrating at th setup used to    frequencies (f 0 ), q G, QTF-S08-T, Q the Euler-Bernoulli model and the empirical dependence of the quality factor with prong width/length ratio is an efficient tool for the prediction of the quality factor values.Even if the resonance frequency of both QTF-S08 and QTF-S15 is almost a half of the standard 32.7 kHz-QTF, higher quality factors were measured.QTF-S08-G showed a resonance frequency about 4% lower than QTF-S08.Although the Euler-Bernoulli model does not predict a dependence of the resonance frequency on the crystal thickness w, 50 μm-grooves carving on both surface slightly affects the rectangular geometry of the prong and produces a small shift of the resonance frequency.For QTF-S08-T, a lower resonance frequency was measured with respect to QTF-S08 and QTF-S15, as predicted by COMSOL simulations, due to the nonuniformity of the moments of inertia along the prong section.For QTF-S08-T, a quality factor of 15,260 was measured.Although the prong T-geometry leads to a decrease of the prong width from 2 mm to 1.4 mm starting from 2.4 mm far from prong top, the quality factor was not affected.A comparison of the QTF#2 with the new generation QTFs shows that the latter exhibits higher quality factors and higher resonance frequencies, in agreement with the calculation shown in Fig. 1.A more interesting comparison can be performed when considering QTF#1 operating at the first overtone mode.QTF#1 has the fundamental flexural mode at 2.87 kHz with a quality factor of ~ 5,000 and the first overtone mode at 17.8 kHz with a quality factor as high as ~ 14,890.Therefore, by moving from the fundamental to the overtone mode leads to an increase of the resonance quality factor.This behavior can be explained by considering that air damping is strongly reduced when the resonance frequency increases [29] and support losses start to dominate when overtone modes are excited [30].
The new generation QTFs reached the same Q-factor values range of QTF#1 when they vibrate at the fundamental mode and this is useful in terms of QEPAS performance.Tshaping the prongs does not affect the electrical resistance, being nearly identical the electrical resistance measured for QTF-S08 and QTF-S08-T.While, a comparison of QTF-S08 and QTF-S08-G, clearly demonstrates that adding grooves on the prongs surfaces reduces the electrical resistance from 162.9 kΩ (QTF-S08) to 104.3 kΩ (QTF-S08-G), while Q-factor and resonance frequency are only slightly affected and thereby providing an improvement in terms of the QEPAS performance.

Photoacoustic response
To verify all assumptions, we employed all QTFs in the QEPAS setup, depicted in Fig. 4

(b).
A single-mode continuous-wave quantum cascade laser (QCL) was used as the excitation source to generate photoacoustic signals.The QCL targeted a water vapor absorption line falling at 1297.19 cm −1 , having intensity of 3.6•10 −22 cm/molecule [31].The laser beam was focused between the QTF prongs using a ZnSe lens with a focal length of 50 mm.An aluminum enclosure equipped with two mid-IR AR-coated windows was realized in order to accommodate and easily switch the QTFs.The housing was filled by standard air with a fixed 1.7% water vapor concentration at atmospheric pressure.The QEPAS sensor operated with a wavelength modulation and dual-frequency detection approach, i.e. the laser beam is wavelength-modulated at a half of the selected resonance frequency while the lock-in amplifier demodulates the QTF signal at the resonance frequency.The absorption line is acquired by applying a slow ramp to the current driver allowing a linear wavelength-scan.As a first step, the vertical position of the laser beam focus along the QTF axis (as shown in Fig. 6(a)) has to be optimized in terms of the QEPAS signal.To study the dependence of the QEPAS signal intensity (proportional to the total momentum generated by the pressure wave) as a function of the vertical position of the laser beam, the laser beam focus was moved from the top to the bottom along the QTF axis between the two prongs.The exper QTF-S08-T a position maxi prongs.The fundamental m respect to the can be explain spherical-like prong [17].In mm far from obtained for t Fig. 7(a)-(d).The        have been high is a from the combined esigns for cy of 15.8 is design, s adopted erties and ltiPhysics mulations increased ed prong factor was coupling he quality ed for the ped QTF ce, it was he aim to n internal e the best cement of ancement ral range.rified and redict the re precise heoretical capable to pect to the d the QTF prongs should be related with the geometrical properties of both acoustic resonators.Hence, the experimental results achieved in this work can be also used as a basis for theoretical and computational approaches (for example, finite element method analysis), mandatory for a precise prediction of an acoustic detection module performance.
(1) becomes Q = 9.45•10 4 T/L, for w = 0.25 mm, at atmospheric pressure.A MATLAB-based software was realized to relate the quality factor and the resonance frequency at different prong geometries.For each fixed prong geometry (T, L), the software calculates the resonance frequency and the related Q-factor, and plots ordered points on the x-(frequencies, f) and y-(Q-factors) axis of the coordinate plane.By ranging L from 3 mm to 20 mm and T from 0.2 mm to 3.0 mm, while keeping w at a fixed value of 0.25 mm, the calculated ordered points (Q, f) are shown in Fig. 1.

Fig. 1 .
Fig. 1.Q-factor values plotted as a function of the resonance frequency for different prong lengths and thicknesses of quartz tuning fork of crystal width w = 0.25 mm, at atmospheric pressure.
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4 s
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Fig. 7 mode record 6 .
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