## Temperature effects in tuning fork enhanced interferometric photoacoustic spectroscopy |

Optics Express, Vol. 21, Issue 18, pp. 20911-20922 (2013)

http://dx.doi.org/10.1364/OE.21.020911

Acrobat PDF (2836 KB)

### Abstract

Temperature dependent measurements with a compact fiber coupled sensor for trace gas detection in the near-infrared based on tuning fork enhanced interferometric photoacoustic spectroscopy are presented. The temperature effects on the sensor have been investigated in a range from *T* = −41°C to *T* = 107°C, in particular the influence on the resonance frequency and the Q-factor of the micro tuning fork. The refined sensor head contains a combination of a silicon tuning fork and an acoustic off-beam resonator and permits methane detection with a detection limit of *S* = (3.85 ± 0.01) ppm. The functional capability of a numerical model for the optimization of acoustic off-beam resonators in COMSOL Multiphysics^{®} is presented.

© 2013 OSA

## 1. Introduction

1. A. A. Kosterev, Y. A. Bakhirkin, R. F. Curl, and F. K. Tittel, “Quartz-enhanced photoacoustic spectroscopy,” Opt. Lett. **27**(21), 1902–1904 (2002). [CrossRef] [PubMed]

2. A. A. Kosterev, F. K. Tittel, D. V. Serebryakov, A. L. Malinovsky, and I. V. Morozov, “Applications of quartz tuning forks in spectroscopic gas sensing,” Rev. Sci. Instrum. **76**(4), 043105 (2005). [CrossRef]

3. A. A. Kosterev, L. Dong, D. Thomazy, F. K. Tittel, and S. Overby, “QEPAS for chemical analysis of multi-component gas mixtures,” Appl. Phys. B **101**(3), 649–659 (2010). [CrossRef]

4. K. Liu, X. Guo, H. Yi, W. Chen, W. Zhang, and X. Gao, “Off-beam quartz-enhanced photoacoustic spectroscopy,” Opt. Lett. **34**(10), 1594–1596 (2009). [CrossRef] [PubMed]

5. L. Dong, A. A. Kosterev, D. Thomazy, and F. K. Tittel, “QEPAS spectrophones: design, optimization, and performance,” Appl. Phys. B **100**(3), 627–635 (2010). [CrossRef]

1. A. A. Kosterev, Y. A. Bakhirkin, R. F. Curl, and F. K. Tittel, “Quartz-enhanced photoacoustic spectroscopy,” Opt. Lett. **27**(21), 1902–1904 (2002). [CrossRef] [PubMed]

## 2. Experimental

*λ*= 1650 nm with an output power of

*P*= 9.95 mW is used (NEL Laser Diodes NLK1U5EAAA). It is driven by a combined temperature and current controller (Thorlabs ITC110). A frequency generator (Agilent U2761A) is used for sinusoidal modulation of the laser current at half the resonance frequency of the TF for 2-f-modulation spectroscopic measurements. Methane excitation is done at

*λ*= 1650.959 nm where the absorption cross section is

*S*= 1.278 ∙ 10

^{−21}cm

^{−1}/(molecule cm

^{−2}) [6

6. L. S. Rothman, I. E. Gordon, A. Barbe, D. C. Benner, P. E. Bernath, M. Birk, V. Boudon, L. R. Brown, A. Campargue, J.-P. Champion, K. Chance, L. H. Coudert, V. Dana, V. M. Devi, S. Fally, J.-M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, I. Kleiner, N. Lacome, W. J. Lafferty, J.-Y. Mandin, S. T. Massie, S. N. Mikhailenko, C. E. Miller, N. Moazzen-Ahmadi, O. V. Naumenko, A. V. Nikitin, J. Orphal, V. I. Perevalov, A. Perrin, A. Predoi-Cross, C. P. Rinsland, M. Rotger, M. Simeckova, M. A. H. Smith, K. Sung, S. A. Tashkun, J. Tennyson, R. A. Toth, A. C. Vandaele, and J. Vander Auwera, “The HITRAN 2008 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. **110**(9-10), 533–572 (2009). [CrossRef]

*λ*= 1570 nm (EM4 AA1401-190600-063-PM900-FCA-NA) with an optical output power of

*P*= 63 mW is applied, driven by a second ITC110. The detection of the optical readout signal is realized by an InGaAs photodiode with adjustable preamplifier (Thorlabs PDA10CS-EC). For all measurements described below, an amplification setting of

*g*= 10dB is used corresponding to a current to voltage gain of

*G*= 2.38 ∙ 10

^{3}V/A. The resulting voltage is fed into a lock-in-amplifier (Stanford Research Systems SR830) detecting in 2-f-mode. Measurement control and data acquisition is done by LabView

^{®}software and a PC.

*l*= 45 mm, a width of

*w*= 28 mm, and a height of

*h*= 10 mm. Figure 2 shows a 3D-sketch of the optical elements and the acoustic off-beam resonator. The silicon TF is glued to the brass off-beam resonator. It is cut out of silicon (111) with a diamond precision saw (Bühler Isomet 4000). A typical resonance curve is shown in Fig. 3 which contains a sketch of the TF, too. This measurement was done at room temperature and ambient pressure with the setup presented in detail by Köhring et al. in [7

7. M. Köhring, A. Pohlkötter, U. Willer, M. Angelmahr, and W. Schade, “Tuning fork enhanced interferometric photoacoustic spectroscopy: a new method for trace gas analysis,” Appl. Phys. B **102**(1), 133–139 (2011). [CrossRef]

*f*= (18798.3 ± 0.5) Hz and a Q-factor of Q = 7063 ± 76. No acoustical resonator was attached to the TF during this measurement; therefore shifting of its resonance is negligible. The only additional damping effect results from the mounting of the TF in the interferometer. This fact will be important for the results of the temperature dependent measurements.

*d*= 300 µm is placed above of the resonator to connect the TF to the amplified acoustic wave inside the off-beam resonator. The TF is too long to be entirely mounted directly on top of the resonator. To omit undesirable effects of the overhanging part of the TF on the acoustic wave, the excitation light axis is shifted by an angle of

_{so}*α*= 22.5° with respect to the TF. This configuration ensures optimum signal amplification. Up to now, off-beam resonators are only used for quartz TFs with their fundamental resonance at

*f*= 32.768 kHz [8

8. K. Liu, H. Yi, A. A. Kosterev, W. Chen, L. Dong, L. Wang, T. Tan, W. Zhang, F. K. Tittel, and X. Gao, “Trace gas detection based on off-beam quartz enhanced photoacoustic spectroscopy: Optimization and performance evaluation,” Rev. Sci. Instrum. **81**(10), 103103 (2010). [CrossRef] [PubMed]

^{®}using the acoustics module and acoustics solid interaction. Due to the GRIN lens used for collimation, The inner resonator diameter was chosen to

*d*= 1 mm as the beam waist of the collimated excitation laser beam leaving the GRIN lens can be expected to be smaller than this value. For manufacturing-orientated reasons, the resonator wall thickness in TF direction was set to

_{i}*t*= 200 µm and the distance between the TF and the resonator was set to

_{w}*d*= 100 µm. The diameter of the sonic output was chosen to be

*d*= 300 µm according to the spacing of the TF prongs. Figure 4(a) shows the pressure field for the acoustic resonator with optimized length

_{so}*L*. At

_{opt}*L*= 11.6 mm the acoustic pressure between the TFs prongs reaches its maximum. The distribution of the sound field inside the resonator resembles well the expected behavior. Firebaugh et al. derived the sound field of an on-beam AR using a COMSOL Multiphysics

_{opt}^{®}model [9

9. S. L. Firebaugh, F. Roignant, and E. A. Terray, “Enhancing Sensitivity in Tuning Fork Photoacoustic Spectroscopy Systems,” Sensors Applications Symposium (SAS) (2010). [CrossRef]

10. M. Köhring, U. Willer, S. Böttger, A. Pohlkötter, and W. Schade, “Fiber Coupled Ozone Sensor Based on Tuning Fork Enhanced Interferometric Photoacoustic Spectroscopy,” IEEE J. Sel. Top. Quantum Electron. **18**(5), 1566–1572 (2012). [CrossRef]

10. M. Köhring, U. Willer, S. Böttger, A. Pohlkötter, and W. Schade, “Fiber Coupled Ozone Sensor Based on Tuning Fork Enhanced Interferometric Photoacoustic Spectroscopy,” IEEE J. Sel. Top. Quantum Electron. **18**(5), 1566–1572 (2012). [CrossRef]

## 3. Thermal influences

10. M. Köhring, U. Willer, S. Böttger, A. Pohlkötter, and W. Schade, “Fiber Coupled Ozone Sensor Based on Tuning Fork Enhanced Interferometric Photoacoustic Spectroscopy,” IEEE J. Sel. Top. Quantum Electron. **18**(5), 1566–1572 (2012). [CrossRef]

### 3.1 Temperature dependence of the acoustic resonator

*c*in an ideal gas can be described by:where

_{s}*κ*is the adiabatic exponent of the gas under test,

*k*the Boltzmann constant, and

_{B}*m*the molecular mass of the gas inside the resonator. For the most common case of a gas mixture filling the resonator the parameters

*κ*and

_{i}*m*can be summed up under consideration of the concentration

_{i}*C*of each gas. It can be seen from Eq. (1) that a temperature change, a change of molecular mass, or a change of

_{i}*κ*have influence on the speed of sound. The relation between the resonator properties and the speed of sound is given by the optimal length

*L*of the AR which is proportional to the half of the sound wavelength

_{opt}*λ*and not as theoretically expected an integer of

_{s}*λ*/2 for an isolated acoustic resonator:Under consideration that the length of the acoustic resonator is fixed to the previously determined value

_{s}*L*during the measurements, Eqs. (1) and (2) illustrate that lower temperatures are connected to lower resonance frequencies and higher temperatures are connected to higher resonance frequencies as well. The optimization process for the off-beam resonator, described in section 2, was done for a temperature of

_{opt}*T*= 25°C. Therefore the resonance frequency at room temperature should be near

*f*= 18.8 kHz.

_{r}### 3.2 Temperature dependence of the tuning fork resonance

13. G. Stemme, “Resonant silicon sensors,” J. Micromech. Microeng. **1**(2), 113–125 (1991). [CrossRef]

14. M. L. Nandanpawar and S. Rajagopalan, “Wachtman’s equation and temperature dependence of bulk moduli in solids,” J. Appl. Phys. **49**(7), 3976 (1978). [CrossRef]

15. J. B. Wachtman, W. E. Tefft, D. G. Lam, and C. S. Apstein, “Exponential Temperature Dependence of Young's Modulus for Several Oxides,” Phys. Rev. **122**(6), 1754–1759 (1961). [CrossRef]

16. Y. P. Varshni, “Temperature Dependence of the Elastic Constants,” Phys. Rev. B **2**(10), 3952–3958 (1970). [CrossRef]

17. U. Gysin, S. Rast, P. Ruff, E. Meyer, D. Lee, P. Vettiger, and C. Gerber, “Temperature dependence of the force sensitivity of silicon cantilevers,” Phys. Rev. B **69**(4), 045403 (2004). [CrossRef]

*E*follows the equation:where

*E*represents the Young’s modulus at a temperature of

_{0}*T*= 0 K. From the literature a value of

*E*= 169 GPa can be found for silicon (111) [18

_{0}18. N. Ono, K. Kitamura, K. Nakajima, and Y. Shimanuki, “Measurement of Young's Modulus of Silicon Single Crystal at High Temperature and Its Dependency on Boron Concentration Using the Flexural Vibration Method,” Jpn. J. Appl. Phys. **39**(Part 1, No. 2A), 368–371 (2000). [CrossRef]

*B*and

*T*are empirical parameters, whereat

_{0}*T*should be in the range of half the Debye temperature, which has a value of

_{0}*T*= 645 K for silicon [23].

_{d}24. W. E. Newell, “Miniaturization of Tuning Forks,” Science **161**(3848), 1320–1326 (1968). [CrossRef] [PubMed]

25. Y. Qin and R. Reifenberger, “Calibrating a tuning fork for use as a scanning probe microscope force sensor,” Rev. Sci. Instrum. **78**(6), 063704 (2007). [CrossRef] [PubMed]

*k*is the spring constant,

*m*the effective mass of the beam,

_{eff}*ρ*the density of the material, w the beam width, and

*l*the length of the beam. The inequality of the length of the beam and the effective length is considered by the value 1.015 [25

25. Y. Qin and R. Reifenberger, “Calibrating a tuning fork for use as a scanning probe microscope force sensor,” Rev. Sci. Instrum. **78**(6), 063704 (2007). [CrossRef] [PubMed]

*w*= 710 µm the width of the TF`s prong,

*l*= 6.8 mm the length of the TF`s prong and a density for silicon of

*ρ*= 2.336 g/cm

^{3}, the parameter

*A*can be calculated to be

*A*= 5.13 ∙ 10

^{−2}m

^{1/2}kg

^{-1/2}.

### 3.3 Temperature dependence of the resonator system

*A*of a driven oscillation as a function of the driving frequency

*ω*can be described by the square root of a Lorentzian function:where

*A*is the amplitude of the driving force,

_{drive}*ω*is the resonance frequency and

_{0}*γ*is the damping coefficient of the oscillator. The phase

*φ*between the driving force and the response of the oscillator as a function of the driving frequency can be described as:As mentioned above, the resonator system can be described by a set of two driven damped harmonic oscillators. Each of them follows the Eq. (6) and (7). The main difference between them is the damping factor, which is significantly higher for the AR leading to its lower Q-factor compared to the TF. However, the theoretical treatment of this problem would be trivial if both oscillators could be investigated separately. The measurements have shown that there is an important temperature dependent coupling between both resonators that causes strong changes in the resonant properties of the whole resonator system; therefore the coupling must not be neglected.

### 3.4 Temperature dependent measurements

*T*= −41°C and

*T*= 107°C. All measurements described in this section were done with a concentration of

*C*= 5% of methane with purity of

_{methane}*p*= 99.995% (Westfahlen AG) in nitrogen with purity of

_{methane}*p*= 99,999% (Westfahlen AG) at atmospheric pressure. The gas mixture was provided by two calibrated mass flow controllers (MKS, 1179BX12CS1BV) actuated by a multi gas controller (MKS, 647C). An overall gas flow of

_{nitrogen}*F*= 100 sccm results in a sufficiently fast gas exchange and was kept constant during the measurements.

*T*= 100 ms and a slope efficiency of 24dB. The resonance frequency and Q-factor were extracted from the data by fitting the square root of a Lorentian line shape to the data of each measurement as described in section 2.

_{c}*T*= 307.9 K corresponding to a resonance frequency of

*f*= 18791.6 Hz which was extracted from the data shown in Fig. 6. The upper x-scale in Fig. 5 shows the resultant resonance frequencies of the AR over the measured temperature range. Due to the change in the speed of sound, the AR resonance changes drastically over a range of about 5000 Hz. This leads to the behavior of the curve in Fig. 5 and can be illustrated with an examination of the coupling between both resonators. Two cases are of main interest: The frequency where the minimum of the curve occurs and the opposite case at much higher or lower frequency, where the Q-factor reaches its maximum. In the latter case, the resonance maximum of the AR is far away from the resonance of the TF. As the AR resonance is much wider than the TF resonance, there is still a part of the excitation energy which can be transferred from the AR to the TF due to the high Q of the TF. The reverse process, routing energy from the TF back to the AR can be neglected in this case, as the very sharp TF resonance has nearly no overlap with the AR resonance and the backward coupling coefficient is very small. In the second case where both resonances overlap, energy can be transferred in an efficient way from the AR to the TF, but also in the other direction: As the sharp TF resonance frequency coincides perfectly with the AR resonance frequency, energy can also be routed back into the AR. This is the explanation, why the Q-factor of the TF recorded in the shown measurements drops to a minimum. But this fact does not imply that energy is lost at this point, as the energy is stored in the AR. The change of energy stored in the TF`s oscillation and the change of its Q is in direct connection to an inverse change of the energy stored in the AR`s oscillation. Therefore, the overall amplification of the whole resonator system stays constant over the whole temperature range. This fact will be further confirmed at the end of section 4. Corresponding to the described assumptions, the square root of a Lorentian function was fitted to the data in Fig. 5, shown in the solid line. This curve represents the inverse resonance curve of the AR. Its Q-factor can be determined to 9.28 which is in good agreement with former publications [26

_{r}26. H. Yi, W. Chen, S. Sun, K. Liu, T. Tan, and X. Gao, “T-shape microresonator-based high sensitivity quartz-enhanced photoacoustic spectroscopy sensor,” Opt. Express **20**(8), 9187–9196 (2012). [CrossRef] [PubMed]

*k*represents the loading of both parts of the function. The parameters

*E*,

_{0}*T*and

_{0}*A*were fixed to the values presented in section 3.2.

^{®}model for the optimization of the AR length to the resonance frequency of TFs. Although an optimum AR should lead to a minimum in Fig. 5 at 25°C, the measured minimum at a temperature of

*T*= 34.8 °C is a good value for the simulation.

## 4. Calibration measurements

27. A. A. Kosterev, R. F. Curl, F. K. Tittel, C. Gmachl, F. Capasso, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, and A. Y. Cho, “Effective Utilization of Quantum-Cascade Distributed-Feedback Lasers in Absorption Spectroscopy,” Appl. Opt. **39**(24), 4425–4430 (2000). [CrossRef] [PubMed]

28. A. Grossel, V. Zeninari, L. Joly, B. Parvitte, D. Courtois, and G. Durry, “New improvements in methane detection using a Helmholtz resonant photoacoustic laser sensor: A comparison between near-IR diode lasers and mid-IR quantum cascade lasers,” Spectrochim. Acta A Mol. Biomol. Spectrosc. **63**(5), 1021–1028 (2006). [CrossRef] [PubMed]

*T*= −21,5 °C up to

_{min}*T*= 35.7 °C. In order to reduce the measurement time, only three calibration steps were set for each calibration. Additionally, the measurements were performed with a smaller lock-in amplifier time constant of

_{max}*T*= 300 ms. All other parameters used for those measurements were kept equal to these of the calibration described earlier. Figure 8 shows the detection limits derived from the data. The appendent standard deviation (1

_{c}*σ*) of a measurement in pure nitrogen for each temperature is shown as error bars. It can easily be seen, that there is no significant change in the detection limit of the sensor in the investigated temperature range, as the fluctuations are only within the range of the error bars. This fact strengthens the assumptions in the previous section that imply that the resonator system stores the same amount of photoacoustically induced energy at each temperature.

## 5. Conclusion

*f*= 18.8 kHz, which was realized in COMSOL Multiphysics

^{®}, provided an efficient way to adapt the resonator dimensions to new frequencies. Calibration measurements at different temperatures showed that the effects mentioned earlier do not influence the detection limit of the sensor; this is connected to the complementary development of the amplifying properties of both resonators.

## Acknowledgments

## References and links

1. | A. A. Kosterev, Y. A. Bakhirkin, R. F. Curl, and F. K. Tittel, “Quartz-enhanced photoacoustic spectroscopy,” Opt. Lett. |

2. | A. A. Kosterev, F. K. Tittel, D. V. Serebryakov, A. L. Malinovsky, and I. V. Morozov, “Applications of quartz tuning forks in spectroscopic gas sensing,” Rev. Sci. Instrum. |

3. | A. A. Kosterev, L. Dong, D. Thomazy, F. K. Tittel, and S. Overby, “QEPAS for chemical analysis of multi-component gas mixtures,” Appl. Phys. B |

4. | K. Liu, X. Guo, H. Yi, W. Chen, W. Zhang, and X. Gao, “Off-beam quartz-enhanced photoacoustic spectroscopy,” Opt. Lett. |

5. | L. Dong, A. A. Kosterev, D. Thomazy, and F. K. Tittel, “QEPAS spectrophones: design, optimization, and performance,” Appl. Phys. B |

6. | L. S. Rothman, I. E. Gordon, A. Barbe, D. C. Benner, P. E. Bernath, M. Birk, V. Boudon, L. R. Brown, A. Campargue, J.-P. Champion, K. Chance, L. H. Coudert, V. Dana, V. M. Devi, S. Fally, J.-M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, I. Kleiner, N. Lacome, W. J. Lafferty, J.-Y. Mandin, S. T. Massie, S. N. Mikhailenko, C. E. Miller, N. Moazzen-Ahmadi, O. V. Naumenko, A. V. Nikitin, J. Orphal, V. I. Perevalov, A. Perrin, A. Predoi-Cross, C. P. Rinsland, M. Rotger, M. Simeckova, M. A. H. Smith, K. Sung, S. A. Tashkun, J. Tennyson, R. A. Toth, A. C. Vandaele, and J. Vander Auwera, “The HITRAN 2008 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. |

7. | M. Köhring, A. Pohlkötter, U. Willer, M. Angelmahr, and W. Schade, “Tuning fork enhanced interferometric photoacoustic spectroscopy: a new method for trace gas analysis,” Appl. Phys. B |

8. | K. Liu, H. Yi, A. A. Kosterev, W. Chen, L. Dong, L. Wang, T. Tan, W. Zhang, F. K. Tittel, and X. Gao, “Trace gas detection based on off-beam quartz enhanced photoacoustic spectroscopy: Optimization and performance evaluation,” Rev. Sci. Instrum. |

9. | S. L. Firebaugh, F. Roignant, and E. A. Terray, “Enhancing Sensitivity in Tuning Fork Photoacoustic Spectroscopy Systems,” Sensors Applications Symposium (SAS) (2010). [CrossRef] |

10. | M. Köhring, U. Willer, S. Böttger, A. Pohlkötter, and W. Schade, “Fiber Coupled Ozone Sensor Based on Tuning Fork Enhanced Interferometric Photoacoustic Spectroscopy,” IEEE J. Sel. Top. Quantum Electron. |

11. | L. Dong, K. Liu, A. A. Kosterev, and F. K. Tittel, “Effect of Speed of Sound on Quartz-Enhanced Photoacoustic Spectroscopy Trace Gas Sensor Performance,” CLEO:2011 - Laser Applications to Photonic Applications: OSA, paper CThCC5 (2011). |

12. | S. Böttger, M. Köhring, U. Willer, and W. Schade, “Off-Beam Quartz-Enhanced Photoacoustic Spectroscopy with LEDs,” Appl. Phys. B (to be published). |

13. | G. Stemme, “Resonant silicon sensors,” J. Micromech. Microeng. |

14. | M. L. Nandanpawar and S. Rajagopalan, “Wachtman’s equation and temperature dependence of bulk moduli in solids,” J. Appl. Phys. |

15. | J. B. Wachtman, W. E. Tefft, D. G. Lam, and C. S. Apstein, “Exponential Temperature Dependence of Young's Modulus for Several Oxides,” Phys. Rev. |

16. | Y. P. Varshni, “Temperature Dependence of the Elastic Constants,” Phys. Rev. B |

17. | U. Gysin, S. Rast, P. Ruff, E. Meyer, D. Lee, P. Vettiger, and C. Gerber, “Temperature dependence of the force sensitivity of silicon cantilevers,” Phys. Rev. B |

18. | N. Ono, K. Kitamura, K. Nakajima, and Y. Shimanuki, “Measurement of Young's Modulus of Silicon Single Crystal at High Temperature and Its Dependency on Boron Concentration Using the Flexural Vibration Method,” Jpn. J. Appl. Phys. |

19. | J. J. Wortman and R. A. Evans, “Young's Modulus, Shear Modulus, and Poisson's Ratio in Silicon and Germanium,” J. Appl. Phys. |

20. | D. R. França and A. Blouin, “All-optical measurement of in-plane and out-of-plane Young's modulus and Poisson's ratio in silicon wafers by means of vibration modes,” Meas. Sci. Technol. |

21. | M. A. Hopcroft, W. D. Nix, and T. W. Kenny, “What is the Young's Modulus of Silicon?” J. Microelectromech. Syst. |

22. | J. Kim, D. Cho, and R. S. Muller, “Why is (111) silicon a better mechanical material for MEMS?” Proc. Transducers (2001). |

23. | C. Kittel, “Introduction to Solid State Physics,” 8th ed. Hoboken, New Jersey, USA: John Wiley & Sons, Ltd. (2004). |

24. | W. E. Newell, “Miniaturization of Tuning Forks,” Science |

25. | Y. Qin and R. Reifenberger, “Calibrating a tuning fork for use as a scanning probe microscope force sensor,” Rev. Sci. Instrum. |

26. | H. Yi, W. Chen, S. Sun, K. Liu, T. Tan, and X. Gao, “T-shape microresonator-based high sensitivity quartz-enhanced photoacoustic spectroscopy sensor,” Opt. Express |

27. | A. A. Kosterev, R. F. Curl, F. K. Tittel, C. Gmachl, F. Capasso, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, and A. Y. Cho, “Effective Utilization of Quantum-Cascade Distributed-Feedback Lasers in Absorption Spectroscopy,” Appl. Opt. |

28. | A. Grossel, V. Zeninari, L. Joly, B. Parvitte, D. Courtois, and G. Durry, “New improvements in methane detection using a Helmholtz resonant photoacoustic laser sensor: A comparison between near-IR diode lasers and mid-IR quantum cascade lasers,” Spectrochim. Acta A Mol. Biomol. Spectrosc. |

**OCIS Codes**

(300.0300) Spectroscopy : Spectroscopy

(300.6430) Spectroscopy : Spectroscopy, photothermal

**ToC Category:**

Spectroscopy

**History**

Original Manuscript: April 8, 2013

Revised Manuscript: May 16, 2013

Manuscript Accepted: May 17, 2013

Published: August 30, 2013

**Virtual Issues**

Vol. 8, Iss. 10 *Virtual Journal for Biomedical Optics*

**Citation**

M. Köhring, S. Böttger, U. Willer, and W. Schade, "Temperature effects in tuning fork enhanced interferometric photoacoustic spectroscopy," Opt. Express **21**, 20911-20922 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-18-20911

Sort: Year | Journal | Reset

### References

- A. A. Kosterev, Y. A. Bakhirkin, R. F. Curl, and F. K. Tittel, “Quartz-enhanced photoacoustic spectroscopy,” Opt. Lett.27(21), 1902–1904 (2002). [CrossRef] [PubMed]
- A. A. Kosterev, F. K. Tittel, D. V. Serebryakov, A. L. Malinovsky, and I. V. Morozov, “Applications of quartz tuning forks in spectroscopic gas sensing,” Rev. Sci. Instrum.76(4), 043105 (2005). [CrossRef]
- A. A. Kosterev, L. Dong, D. Thomazy, F. K. Tittel, and S. Overby, “QEPAS for chemical analysis of multi-component gas mixtures,” Appl. Phys. B101(3), 649–659 (2010). [CrossRef]
- K. Liu, X. Guo, H. Yi, W. Chen, W. Zhang, and X. Gao, “Off-beam quartz-enhanced photoacoustic spectroscopy,” Opt. Lett.34(10), 1594–1596 (2009). [CrossRef] [PubMed]
- L. Dong, A. A. Kosterev, D. Thomazy, and F. K. Tittel, “QEPAS spectrophones: design, optimization, and performance,” Appl. Phys. B100(3), 627–635 (2010). [CrossRef]
- L. S. Rothman, I. E. Gordon, A. Barbe, D. C. Benner, P. E. Bernath, M. Birk, V. Boudon, L. R. Brown, A. Campargue, J.-P. Champion, K. Chance, L. H. Coudert, V. Dana, V. M. Devi, S. Fally, J.-M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, I. Kleiner, N. Lacome, W. J. Lafferty, J.-Y. Mandin, S. T. Massie, S. N. Mikhailenko, C. E. Miller, N. Moazzen-Ahmadi, O. V. Naumenko, A. V. Nikitin, J. Orphal, V. I. Perevalov, A. Perrin, A. Predoi-Cross, C. P. Rinsland, M. Rotger, M. Simeckova, M. A. H. Smith, K. Sung, S. A. Tashkun, J. Tennyson, R. A. Toth, A. C. Vandaele, and J. Vander Auwera, “The HITRAN 2008 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat.110(9-10), 533–572 (2009). [CrossRef]
- M. Köhring, A. Pohlkötter, U. Willer, M. Angelmahr, and W. Schade, “Tuning fork enhanced interferometric photoacoustic spectroscopy: a new method for trace gas analysis,” Appl. Phys. B102(1), 133–139 (2011). [CrossRef]
- K. Liu, H. Yi, A. A. Kosterev, W. Chen, L. Dong, L. Wang, T. Tan, W. Zhang, F. K. Tittel, and X. Gao, “Trace gas detection based on off-beam quartz enhanced photoacoustic spectroscopy: Optimization and performance evaluation,” Rev. Sci. Instrum.81(10), 103103 (2010). [CrossRef] [PubMed]
- S. L. Firebaugh, F. Roignant, and E. A. Terray, “Enhancing Sensitivity in Tuning Fork Photoacoustic Spectroscopy Systems,” Sensors Applications Symposium (SAS) (2010). [CrossRef]
- M. Köhring, U. Willer, S. Böttger, A. Pohlkötter, and W. Schade, “Fiber Coupled Ozone Sensor Based on Tuning Fork Enhanced Interferometric Photoacoustic Spectroscopy,” IEEE J. Sel. Top. Quantum Electron.18(5), 1566–1572 (2012). [CrossRef]
- L. Dong, K. Liu, A. A. Kosterev, and F. K. Tittel, “Effect of Speed of Sound on Quartz-Enhanced Photoacoustic Spectroscopy Trace Gas Sensor Performance,” CLEO:2011 - Laser Applications to Photonic Applications: OSA, paper CThCC5 (2011).
- S. Böttger, M. Köhring, U. Willer, and W. Schade, “Off-Beam Quartz-Enhanced Photoacoustic Spectroscopy with LEDs,” Appl. Phys. B (to be published).
- G. Stemme, “Resonant silicon sensors,” J. Micromech. Microeng.1(2), 113–125 (1991). [CrossRef]
- M. L. Nandanpawar and S. Rajagopalan, “Wachtman’s equation and temperature dependence of bulk moduli in solids,” J. Appl. Phys.49(7), 3976 (1978). [CrossRef]
- J. B. Wachtman, W. E. Tefft, D. G. Lam, and C. S. Apstein, “Exponential Temperature Dependence of Young's Modulus for Several Oxides,” Phys. Rev.122(6), 1754–1759 (1961). [CrossRef]
- Y. P. Varshni, “Temperature Dependence of the Elastic Constants,” Phys. Rev. B2(10), 3952–3958 (1970). [CrossRef]
- U. Gysin, S. Rast, P. Ruff, E. Meyer, D. Lee, P. Vettiger, and C. Gerber, “Temperature dependence of the force sensitivity of silicon cantilevers,” Phys. Rev. B69(4), 045403 (2004). [CrossRef]
- N. Ono, K. Kitamura, K. Nakajima, and Y. Shimanuki, “Measurement of Young's Modulus of Silicon Single Crystal at High Temperature and Its Dependency on Boron Concentration Using the Flexural Vibration Method,” Jpn. J. Appl. Phys.39(Part 1, No. 2A), 368–371 (2000). [CrossRef]
- J. J. Wortman and R. A. Evans, “Young's Modulus, Shear Modulus, and Poisson's Ratio in Silicon and Germanium,” J. Appl. Phys.36(1), 153–156 (1965). [CrossRef]
- D. R. França and A. Blouin, “All-optical measurement of in-plane and out-of-plane Young's modulus and Poisson's ratio in silicon wafers by means of vibration modes,” Meas. Sci. Technol.15(5), 859–868 (2004). [CrossRef]
- M. A. Hopcroft, W. D. Nix, and T. W. Kenny, “What is the Young's Modulus of Silicon?” J. Microelectromech. Syst.19(2), 229–238 (2010). [CrossRef]
- J. Kim, D. Cho, and R. S. Muller, “Why is (111) silicon a better mechanical material for MEMS?” Proc. Transducers (2001).
- C. Kittel, “Introduction to Solid State Physics,” 8th ed. Hoboken, New Jersey, USA: John Wiley & Sons, Ltd. (2004).
- W. E. Newell, “Miniaturization of Tuning Forks,” Science161(3848), 1320–1326 (1968). [CrossRef] [PubMed]
- Y. Qin and R. Reifenberger, “Calibrating a tuning fork for use as a scanning probe microscope force sensor,” Rev. Sci. Instrum.78(6), 063704 (2007). [CrossRef] [PubMed]
- H. Yi, W. Chen, S. Sun, K. Liu, T. Tan, and X. Gao, “T-shape microresonator-based high sensitivity quartz-enhanced photoacoustic spectroscopy sensor,” Opt. Express20(8), 9187–9196 (2012). [CrossRef] [PubMed]
- A. A. Kosterev, R. F. Curl, F. K. Tittel, C. Gmachl, F. Capasso, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, and A. Y. Cho, “Effective Utilization of Quantum-Cascade Distributed-Feedback Lasers in Absorption Spectroscopy,” Appl. Opt.39(24), 4425–4430 (2000). [CrossRef] [PubMed]
- A. Grossel, V. Zeninari, L. Joly, B. Parvitte, D. Courtois, and G. Durry, “New improvements in methane detection using a Helmholtz resonant photoacoustic laser sensor: A comparison between near-IR diode lasers and mid-IR quantum cascade lasers,” Spectrochim. Acta A Mol. Biomol. Spectrosc.63(5), 1021–1028 (2006). [CrossRef] [PubMed]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.