Abstract

A miniature Fabry-Perot interferometric sensor with an ultra-high temperature sensitivity was constructed by using an approximate 8-layer graphene diaphragm. The extremely thin diaphragm was transferred onto the endface of a ferrule with an inner diameter of 125 μm, and van der Waals interactions between the graphene diaphragm and its substrate created a low finesse Fabry-Perot interferometer with a cavity length of 42.86 μm. Temperature testing demonstrated a temperature-induced cavity length change of 352 nm/°C with a good linearity in the range of 20-60 °C. The result conformed well to the proposed analytical models relating to thermal expansion of trapped gas, thermal-optical property of graphene diaphragm and deflection behavior of bulged graphene blister. However, the ultra-thin diaphragm exhibited a small deflection deformation characteristic due to the applied higher loads.

© 2015 Optical Society of America

1. Introduction

Interest has increased in utilizing miniature fiber optic Fabry-Perot (FP) sensors in biomedical, environmental, microsystem applications due to their advantages over conventional sensors; such as immunity to electromagnetic interference, high resolution, fast response and compact size [1,2 ]. The FP sensor is typically constructed directly on a fiber end face and consists of a cleaved optical fiber and a sensitive diaphragm known as an extrinsic Fabry-Perot interferometric (EFPI) sensor structure. The sensitivity of the diaphragm in the FP sensor is defined as the ratio of the FP cavity’s length variation to the detected parameters [3], which is closely related with the used materials and the thickness of the diaphragm. Taking pressure measurement as an example, several of the miniature FP pressure sensors referred to in the research literature used different types of elastic materials as a pressure-sensitive diaphragm, such as metal, SiO2/silica, polymer, silver and graphene membrane [4–8 ]. Compared with other materials, the ultra-thin thickness of graphene can significantly improve the pressure sensitivity of FP sensors. Recently, Ma et al. fabricated a FP acoustic sensor with a dynamic pressure sensitivity of 1100 nm/kPa by using a ~100-nm-thick graphene diaphragm with a diameter of 125 μm [8]. Then Li et al. further achieved a dynamic pressure sensitivity of 2380 nm/kPa using a 13-layer graphene diaphragm with a diameter of 125 μm, which was the highest reported [9]. Hence, graphene, with a single-layer thickness of ~0.335 nm, is being utilized more since it was first isolated by Novoselov et al. [10] because of its extreme elasticity [11], ultrastrong adhesion [12], impermeability to gases [13] and optical far-infrared properties [14]. The unique combination of optical and mechanical properties makes graphene an ideal material for FP sensor applications. However, it is no denying that the temperature sensitivity of FP sensors should be investigated to enhance the thermal applicability of such sensors. Recently, multiple FP temperature sensors employing various smart structures and non-graphene materials have been reported. A single micro-air-gap based intrinsic FP interferometric fiber-optic sensor exhibited an optical path difference of 2.9 μm from 50 °C to 700 °C [15]. And a FP temperature sensor with a sensitivity of 0.95 pm/°C was developed by etching a multimode graded index fiber [16]. Also, an ultra-high sensitivity of ∼5.2 nm/°C was obtained by using a partially polymer-filled glass capillary to form an air micro-cavity [17]. These aforementioned FP sensors are adequate to measure high temperature variation whereas not suitable for measuring small temperature variation. In contrast, it is possible that graphene diaphragm is much more sensitive to low temperature fluctuations due to the properties of extremely thinness, high strength and large deflection deformation to allow the thermal expansion of air micro-cavity. In a recent study [18], it was stated that a miniature FP temperature sensor had a resonant wavelength sensitivity of 1.56 and 1.87 nm/°C at the temperature range of 500 - 510 °C and 1000 - 1008 °C respectively, by using a more than 4-layer graphene diaphragm with a diameter of 125 μm. However, the physics behind the cavity length variation verse temperature is not discussed in detail. Moreover, based on the thin-film optical theory and the Fresnel’s equations for reflection and refraction [19], the stated reflectivity (9.04%) of graphene film should indicate an approximate thickness above 12 nm. The thicker diaphragm in a miniaturized sensor head imposes a limit on its temperature sensitivity due to the restriction of thermal expansion of trapped gas in FP cavity.

In this paper, we fabricate a FP cavity using an ultra-thin ~8-layer graphene diaphragm with a diameter of 125 μm. The sensor proposed here exhibits an ultra-high temperature sensitivity of 352 nm/°C in the tested range of 20-60 °C. The diaphragm structure breaks the sensitivity limitations imposed by the increased thickness and the decreased dimension of a diaphragm used in traditional FP temperature sensors. Furthermore, thermal tests show that the cavity length variation of the FP sensor conforms well to the theoretical model on basis of the thermal expansion of trapped gas, thermal optical property of graphene diaphragm and the spherical shell equation used for the geometrically nonlinear response of a clamped circular elastic graphene diaphragm subjected to a pressure difference across the diaphragm.

2. Sensor fabrication and temperature-sensitive principle

Figure 1(a) shows the schematic diagram and the physical picture of the presented FP sensor that comprises of a zirconia ferrule, a standard single mode fiber (SMF) and a multi-layer graphene diaphragm. The diaphragm, working as a light reflector made directly on the end of the SMF, is adhered to the zirconia substrate by van der Waals forces as shown in Fig. 1(b), and the separation between the fiber end and the ferrule endface is controlled by using a 1-μm resolution translation stage. The ferrule and the SMF are held together by an epoxy adhesive (3M®). The graphene diaphragm is prepared from a 5~8-layer commercial Trivial Transfer Graphene sample in which the graphene film is grown by chemical vapor deposition (CVD) on a 20-μm thick Cu foil deposited on a polymer substrate (ACS Material®, www.xfnano.com). The process for preparing the graphene membrane and transferring it onto the fiber tip to an FP cavity is similar to that in [19].

 

Fig. 1 (a) Schematic diagram and physical picture of the FP sensor and (b) microscopic image of the graphene diaphragm adhered on ferrule.

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When external temperature occurs to change, the thermal expansion of trapped gas and the different thermal expansion coefficients between the zirconia ferrule and the SMF will cause the change of the length of FP cavity and then generate the FP interference. Referring to the theory of multiple-beam interference, the interference intensity Ir in FP cavity can be expressed as

where R 1 and R 2 are respectively the reflectivities of graphene membrane and fiber end face, and R 2 is measured to be 0.025; Ii is the incident intensity; ξ is the coupling coefficient of cavity length loss. When ignoring the half-wave loss, the phase difference δ between two adjacent beams in micro-air cavity can be written by
δ=4πL/λ
where L is the length of FP cavity, and λ is the wavelength of incident light. And the length L of FP cavity can be calculated by
where m and m + k are the interference order, respectively. In this case, Ir can reach the maximum value when δ equals to (2m + 1)π, wherein m = 0, 1, 2, etc.

As seen from Eq. (1), the temperature sensitivity for FP sensors shows a strong dependence on L and R 2. According to the law of thermal expansion of trapped gas and thermal deformation characteristics, the length change ΔL of FP cavity can be described as

ΔL=(βferruleLferruleβSMFLSMF)ΔT+ω
where βferrule and βSMF are the thermal expansion coefficients of ferrule and optical fiber, respectively; Lferrule and βSMF are the lengths of ferrule and optical fiber, respectively; and ω is the deflection deformation of graphene diaphragm resulted from thermal expansion of trapped gas, respectively. In view of the negative thermal expansion coefficient of graphene film [20], ω is supposed to consist of the deflection ωP caused by pressure change imposing on the clamped circular elastic graphene diaphragm and the deflection ωT caused by thermal expansion of the diaphragm.

After the graphene film is adhered to the ferrule endface at normal temperature T 0 and pressure p 0, the internal pressure in the micro-cavity, pint, is equal to the initial tension, resulted from adhesion energy between graphene film and ferrule substrate, plus the external pressure, pext, which is atmospheric pressure p 0. In other words, the graphene membrane is not flat, because a calibrated AFM tip test had showed a few nanometers of dip along the edges of the suspended regions where the graphene met the SiO2 sidewalls [13]. Considering the ideal gas law, when the temperature increases to T from T 0, the internal pressure pintT at T becomes

pintT=pintV0TVTT0=pintV0T(V0+ΔVT+ΔVω)T0
where V 0 and VT are the volumes of the cavity before and after the temperature changes, respectively; ΔVT is the equivalent cylindrical volume caused by different thermal expansion coefficients of ferrule and optical fiber; and ΔVω denotes the volume of deflection-dependent bulged graphene blister, which can be solved by a spherical cap volume as follows:
{ΔVω=πC3[4a3(3aω)ω2]a=r2+ω22ω
where r is the radius of the diaphragm, and C is the correction factor similar to that in [21].

For the purpose of modeling the load-deflection behavior, the graphene diaphragm is approximated as a clamped circular membrane made of a linear isotropic elastic material based on the spherical shell equation. The relationship between the diaphragm deflection ω and the pressure change ΔP may be expressed as [22]

ΔP=4σ0tr2ωP+8EtωP33(1υ)r4
where E is the Young’s modulus of graphene (~1 TPa); t, υ and σ0 are the the thickness, the Poisson’s ratio (~0.17) and the prestress of the graphene diaphragm, respectively.

It is noted that ΔL can be measured by the interference spectrum. In combination with the available calculated ω and ΔVT, the pressure difference ΔP between internal and external sides of the diaphragm can be solved using Eq. (7), as well as the volume ΔVω under the bulge using Eq. (6). However, the relationship between the internal pressure and the volume under the pressurized blister should be in agreement with Eq. (5).

3. Experiment and analysis

It can be inferred from Eq. (1) that it is necessary to determine the reflectivity R 1 of the graphene diaphragm suspended onto the fiber-tip so as to analyze the change of cavity length because of the multiple optical interference. Moreover, the reflectance and transmittance of graphene in the optical region are a function of frequency, temperature and carrier density; i.e., R 1 is affected by the temperature. In terms of the wavelength range (1528-1608 nm) of used broadband source (ALS-CL-17), R 1 can be calculated by the complex refractive index, which depends on the temperature-dependent dynamical conductivity for high frequencies [23, 24 ]. Thus, the calculated reflectivities of 7- and 8-layer graphene diaphragm verse temperature are shown in Fig. 2 . Since the visibility of the fringe pattern for the FP cavity is related to the reflectivity of the fiber end and the graphene diaphragm, R 1 can be fitted by the measured interference spectrums of a FP sensor. Firstly, R 2 was measured to be approximately 2.5% with an optical spectrum analyzer (AQ6370C). Next, R 1 was measured to be within the range of 0.613% to 0.683%, as shown in Fig. 2. The result showed that the measured R 1 was not much sensitive to the temperature, which agreed well with the theoretical solution. The average value of R 1 was approximately 0.652%, in close proximity to the calculated reflectivity of 0.727% for an 8-layer graphene diaphragm. Therefore, the thickness of the diaphragm was approximated as 2.68 nm, i.e. an 8-layer thickness. It could also be inferred that the interference intensity was mostly generated by the cavity length variation.

 

Fig. 2 The measured and calculated film reflectivities.

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Referring to Fig. 3 , the developed FP sensor and a thermocouple sensor were put inside a thermostat. The reference temperature for the FP sensor was offered by a thermocouple thermometer (testo 925) with an accuracy of ± (0.5 °C + 0.3% of measured value) in the range of −40 °C to + 900 °C and an associated Type K thermocouple probe with an accuracy of Class 2 in the range of −60 °C to + 400 °C according to standard EN 60584-2. A broadband laser was used to illuminate the FP sensor, and the interference intensity was received by a photoelectric detector (PD) with a preamplifier through the use of an optical circulator. The 3dB bandwidth of the PD was up to 200 kHz. The reflection spectrum was then monitored by an optical spectrum analyzer (AQ6370C) with a wavelength resolution of 0.02 nm. In consideration of the use of room temperature curable adhesive and common SMF, the tested temperature was arranged as 20-60 °C, where the set interval was 2 °C in the first 10 °C and 5 °C in the remaining range, respectively.

 

Fig. 3 Schematic diagram of temperature experimental rig.

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Figures 4(a)-4(c) illustrate the cavity length change verse temperature at three cycles of temperature rise/drop measurements, respectively. Although the increased cavity length was not uniform as the temperature rose, the temperature sensitivity of the FP sensor was estimated to be 352 nm/°C by using a least square fitting method with a fitting R-square of 99.83%, in combination with the measured average cavity lengths respectively corresponding to the three cycles of temperature rise and drop measurements. And the sensor’s hysteresis error was calculated to be 2.79% in the tested range of 20-60 °C. Then derived by Eqs. (5) and (7) , the corresponding internal pressure in the cavity and the diaphragm deflection in Fig. 5 indicated that the volume thermal expansion under pressurized graphene blister made the pressure in the cavity, PintT, become slightly larger as the temperature rose, therefore leading to a slight increase in ωP. The thermal expansion of air micro-cavity induced the enlargement of bulged film deformation ω. Hence as shown by the symbol ‘Δ’ in Fig. 5, another factor ωT, in relation to the thermal expansion of the diaphragm, was introduced to examine the thermal mechanical behaviors of the FP sensor. This factor was solved by ω-ωP, and its fitted result was close to 208 nm/°C, which was a major contribution to the measured temperature sensitivity of 352 nm/°C. It could also be concluded from Fig. 5 that the higher load applied to the diaphragm, instead of the prestress, exerted a dominating effect on the pressure-deflection behavior of graphene membrane as a result of thermal expansion. That is to say, the diaphragm exhibited a small deflection characteristic at higher loads.

 

Fig. 4 Cavity length verse temperature at (a) the first cycle, (b) the second cycle and (c) the third cycle of temperature rise/drop measurements.

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Fig. 5 Pressure and deflection verse temperature.

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Taking the interference intensities at 35°C, 36°C and 37°C as examples, the measured reflection spectrums of the fabricated FP sensor is presented in Fig. 6 , where the average shift of dip wavelengths 1541 nm, 1555 nm and 1566 nm is 12.5 nm /°C. Furthermore, due to the variation in temperature, the theoretical dip wavelength shift can be approximated as

dλmdT=2m(βferruleLferruleβSMFLSMF+dωdT)2m(βferruleLferruleβSMFLSMF+nR(1-υ)r48EtVTω2)
where n and R are the number of moles of gas in the container (2.2274 × 10−11) and the universal gas constant (8.31441 J·mol−1·K−1), respectively. Thus the shift of dip wavelength will be not obvious at higher temperatures, thereby reducing the temperature sensitivity while extending temperature adaptable range. In contrast, the shift will grow larger at common temperatures, thereby making the interference intensity to form a periodic appearance in spite of a small temperature fluctuation.

 

Fig. 6 The measured reflection spectrums of the FP sensor.

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As demonstrated in Fig. 7 , the fitted period of temperature variation is less than 3 °C at the wavelength of 1541 nm. This phenomenon is not suitable for use of the wide-temperature intensity demodulation. For a typical wavelength of 1550 nm, a maximum linear range is generally defined as 387.5 nm, i.e., λ/4, which means that a variation of less than 1 °C for the temperature sensitivity mentioned here will possibly enable the order of interference spectrum to move forward or backward.

 

Fig. 7 The intensity signal in the range of 30-40 °C.

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Therefore, the change of FP cavity length is available to effectively estimate the current temperature. The possible error existing in the distribution of measured sensitivity is mainly due to the ideal gas modeling and thermal deformation induced by the transferring of graphene sheets suspended onto the ferrule substrate, which is dependent on the kinetic adhesion characteristics and mechanical properties [25, 26 ]. As a result, further research on the thermal deformation of graphene diaphragm in FP sensors over a wider temperature range is needed to investigate the physics behind it.

4. Conclusion

This study demonstrated the effectiveness of designing and analyzing an ultra-high temperature sensitivity sensor using a nanothick graphene diaphragm. A sensitive FP cavity of 42.86 μm in length was fabricated by suspending the graphene diaphragm and adhering it onto the endface of a ferrule with a bore diameter of 125 μm. The diaphragm, whose reflectivity was essentially independent of temperature, was equivalent to an 8-layer thickness. The thermal variation of cavity length was measured to be approximately 352 nm/°C in the tested range of 20-60 °C, which was primarily induced by the thermal deformation of graphene diaphragm on basis of the established analytical models. However, the intensity and phase shifts at common temperatures featured a periodic appearance even due to a narrow thermal fluctuation. Thermal adaptability analysis presented here would be applicable in highly sensitive graphene-based FP temperature, pressure or other sensors for biomedical and aerospace applications.

Acknowledgments

This work is supported by the National Nature Science Fund of China (61573033), the Program for Changjiang Scholars and Innovative Research Team in University (IRT1203), the China Academy of Space Technology (CAST) Innovation Foundation and the Graduate Innovation Fund of Beihang University (YCSJ-01-2015-01).

References and links

1. S. Avino, J. A. Barnes, G. Gagliardi, X. Gu, D. Gutstein, J. R. Mester, C. Nicholaou, and H.-P. Loock, “Musical instrument pickup based on a laser locked to an optical fiber resonator,” Opt. Express 19(25), 25057–25065 (2011). [CrossRef]   [PubMed]  

2. Y. Wang, D. N. Wang, C. Wang, and T. Hu, “Compressible fiber optic micro-Fabry-Pérot cavity with ultra-high pressure sensitivity,” Opt. Express 21(12), 14084–14089 (2013). [CrossRef]   [PubMed]  

3. F. Xu, D. Ren, X. Shi, C. Li, W. Lu, L. Lu, L. Lu, and B. Yu, “High-sensitivity Fabry-Perot interferometric pressure sensor based on a nanothick silver diaphragm,” Opt. Lett. 37(2), 133–135 (2012). [CrossRef]   [PubMed]  

4. G. Beheim, K. Fritsch, and R. N. Poorman, “Fiber-linked interferometric pressure sensor,” Rev. Sci. Instrum. 58(9), 1655–1659 (1987). [CrossRef]  

5. W. Wang, N. Wu, Y. Tian, C. Niezrecki, and X. Wang, “Miniature all-silica optical fiber pressure sensor with an ultrathin uniform diaphragm,” Opt. Express 18(9), 9006–9014 (2010). [CrossRef]   [PubMed]  

6. G. C. Hill, R. Melamud, F. E. Declercq, A. A. Davenport, I. H. Chan, P. G. Hartwell, and B. L. Pruitt, “SU-8 MEMS Fabry-Perot pressure sensor,” Sens. Actuators A Phys. 138(1), 52–62 (2007). [CrossRef]  

7. F. Guo, T. Fink, M. Han, L. Koester, J. Turner, and J. Huang, “High-sensitivity, high-frequency extrinsic Fabry-Perot interferometric fiber-tip sensor based on a thin silver diaphragm,” Opt. Lett. 37(9), 1505–1507 (2012). [CrossRef]   [PubMed]  

8. J. Ma, H. F. Xuan, H. L. Ho, W. Jin, Y. H. Yang, and S. C. Fan, “Fiber-optic Fabry-Perot acoustic sensor with multilayer graphene diaphragm,” IEEE Photonics Technol. Lett. 25(10), 932–935 (2013). [CrossRef]  

9. C. Li, X. Y. Gao, T. T. Guo, J. Xiao, S. C. Fan, and W. Jin, “Analyzing the applicability of miniature ultra-high sensitivity Fabry-Perot acoustic sensor using a nanothick graphene diaphragm,” Meas. Sci. Technol. 26(8), 085101 (2015). [CrossRef]  

10. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004). [CrossRef]   [PubMed]  

11. C. Lee, X. Wei, J. W. Kysar, and J. Hone, “Measurement of the elastic properties and intrinsic strength of monolayer graphene,” Science 321(5887), 385–388 (2008). [CrossRef]   [PubMed]  

12. S. P. Koenig, N. G. Boddeti, M. L. Dunn, and J. S. Bunch, “Ultrastrong adhesion of graphene membranes,” Nat. Nanotechnol. 6(9), 543–546 (2011). [CrossRef]   [PubMed]  

13. J. S. Bunch, S. S. Verbridge, J. S. Alden, A. M. van der Zande, J. M. Parpia, H. G. Craighead, and P. L. McEuen, “Impermeable atomic membranes from graphene sheets,” Nano Lett. 8(8), 2458–2462 (2008). [CrossRef]   [PubMed]  

14. L. A. Falkovsky and S. S. Pershoguba, “Optical far-infrared properties of a graphene monolayer and multilayer,” Phys. Rev. B Condens. Matter 76(15), 153410 (2007). [CrossRef]  

15. X. Chen, F. Shen, Z. Wang, Z. Huang, and A. Wang, “Micro-air-gap based intrinsic Fabry-Perot interferometric fiber-optic sensor,” Appl. Opt. 45(30), 7760–7766 (2006). [CrossRef]   [PubMed]  

16. P. A. R. Tafulo, P. A. S. Jorge, J. L. Santos, F. M. Araújo, and O. Frazão, “Intrinsic Fabry-Perot cavity sensor based on etched multimode graded index fiber for strain and temperature measurement,” IEEE Sens. J. 12(1), 8–12 (2012). [CrossRef]  

17. G. Zhang, M. Yang, and M. Wang, “Large temperature sensitivity of fiber-optic extrinsic Fabry-Perot interferometer based on polymer filled glass capillary,” Opt. Fiber Technol. 19(6), 618–622 (2013). [CrossRef]  

18. L. Li, Z. Y. Feng, X. G. Qiao, H. Z. Yang, R. H. Wang, D. Su, Y. P. Wang, W. J. Bao, J. C. Li, Z. H. Shao, and M. Hu, “Ultrahigh sensitive temperature sensor based on Fabry–Pérot interference assisted by a graphene diaphragm,” IEEE Sens. J. 15(1), 505–509 (2015). [CrossRef]  

19. C. Li, J. Xiao, T. T. Guo, S. C. Fan, and W. Jin, “Interference characteristics in a Fabry-Perot cavity with graphene membrane for optical fiber pressure sensors,” Microsyst. Technol. 21(11), 2297–2306 (2015). [CrossRef]  

20. D. Yoon, Y.-W. Son, and H. Cheong, “Negative thermal expansion coefficient of graphene measured by Raman spectroscopy,” Nano Lett. 11(8), 3227–3231 (2011). [CrossRef]   [PubMed]  

21. N. G. Boddeti, S. P. Koenig, R. Long, J. L. Xiao, J. S. Bunch, and M. L. Dunn, “Mechanics of adhered, pressurized graphene blisters,” J. Appl. Mech. 80(4), 040909 (2013). [CrossRef]  

22. J. W. Beams, The Structure and Properties of Thin Film (Wiley, 1959).

23. L. A. Falkovsky, “Optical properties of graphene,” J. Phys. Conf. Ser. 129, 012004 (2008). [CrossRef]  

24. A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011). [CrossRef]   [PubMed]  

25. A. Fasolino, J. H. Los, and M. I. Katsnelson, “Intrinsic ripples in graphene,” Nat. Mater. 6(11), 858–861 (2007). [CrossRef]   [PubMed]  

26. M. A. N. Dewapriya, A. Srikantha Phani, and R. K. N. D. Rajapakse, “Influence of temperature and free edges on the mechanical properties of graphene,” Model. Simul. Mater. Sci. Eng. 21(6), 065017 (2013). [CrossRef]  

References

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  1. S. Avino, J. A. Barnes, G. Gagliardi, X. Gu, D. Gutstein, J. R. Mester, C. Nicholaou, and H.-P. Loock, “Musical instrument pickup based on a laser locked to an optical fiber resonator,” Opt. Express 19(25), 25057–25065 (2011).
    [Crossref] [PubMed]
  2. Y. Wang, D. N. Wang, C. Wang, and T. Hu, “Compressible fiber optic micro-Fabry-Pérot cavity with ultra-high pressure sensitivity,” Opt. Express 21(12), 14084–14089 (2013).
    [Crossref] [PubMed]
  3. F. Xu, D. Ren, X. Shi, C. Li, W. Lu, L. Lu, L. Lu, and B. Yu, “High-sensitivity Fabry-Perot interferometric pressure sensor based on a nanothick silver diaphragm,” Opt. Lett. 37(2), 133–135 (2012).
    [Crossref] [PubMed]
  4. G. Beheim, K. Fritsch, and R. N. Poorman, “Fiber-linked interferometric pressure sensor,” Rev. Sci. Instrum. 58(9), 1655–1659 (1987).
    [Crossref]
  5. W. Wang, N. Wu, Y. Tian, C. Niezrecki, and X. Wang, “Miniature all-silica optical fiber pressure sensor with an ultrathin uniform diaphragm,” Opt. Express 18(9), 9006–9014 (2010).
    [Crossref] [PubMed]
  6. G. C. Hill, R. Melamud, F. E. Declercq, A. A. Davenport, I. H. Chan, P. G. Hartwell, and B. L. Pruitt, “SU-8 MEMS Fabry-Perot pressure sensor,” Sens. Actuators A Phys. 138(1), 52–62 (2007).
    [Crossref]
  7. F. Guo, T. Fink, M. Han, L. Koester, J. Turner, and J. Huang, “High-sensitivity, high-frequency extrinsic Fabry-Perot interferometric fiber-tip sensor based on a thin silver diaphragm,” Opt. Lett. 37(9), 1505–1507 (2012).
    [Crossref] [PubMed]
  8. J. Ma, H. F. Xuan, H. L. Ho, W. Jin, Y. H. Yang, and S. C. Fan, “Fiber-optic Fabry-Perot acoustic sensor with multilayer graphene diaphragm,” IEEE Photonics Technol. Lett. 25(10), 932–935 (2013).
    [Crossref]
  9. C. Li, X. Y. Gao, T. T. Guo, J. Xiao, S. C. Fan, and W. Jin, “Analyzing the applicability of miniature ultra-high sensitivity Fabry-Perot acoustic sensor using a nanothick graphene diaphragm,” Meas. Sci. Technol. 26(8), 085101 (2015).
    [Crossref]
  10. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
    [Crossref] [PubMed]
  11. C. Lee, X. Wei, J. W. Kysar, and J. Hone, “Measurement of the elastic properties and intrinsic strength of monolayer graphene,” Science 321(5887), 385–388 (2008).
    [Crossref] [PubMed]
  12. S. P. Koenig, N. G. Boddeti, M. L. Dunn, and J. S. Bunch, “Ultrastrong adhesion of graphene membranes,” Nat. Nanotechnol. 6(9), 543–546 (2011).
    [Crossref] [PubMed]
  13. J. S. Bunch, S. S. Verbridge, J. S. Alden, A. M. van der Zande, J. M. Parpia, H. G. Craighead, and P. L. McEuen, “Impermeable atomic membranes from graphene sheets,” Nano Lett. 8(8), 2458–2462 (2008).
    [Crossref] [PubMed]
  14. L. A. Falkovsky and S. S. Pershoguba, “Optical far-infrared properties of a graphene monolayer and multilayer,” Phys. Rev. B Condens. Matter 76(15), 153410 (2007).
    [Crossref]
  15. X. Chen, F. Shen, Z. Wang, Z. Huang, and A. Wang, “Micro-air-gap based intrinsic Fabry-Perot interferometric fiber-optic sensor,” Appl. Opt. 45(30), 7760–7766 (2006).
    [Crossref] [PubMed]
  16. P. A. R. Tafulo, P. A. S. Jorge, J. L. Santos, F. M. Araújo, and O. Frazão, “Intrinsic Fabry-Perot cavity sensor based on etched multimode graded index fiber for strain and temperature measurement,” IEEE Sens. J. 12(1), 8–12 (2012).
    [Crossref]
  17. G. Zhang, M. Yang, and M. Wang, “Large temperature sensitivity of fiber-optic extrinsic Fabry-Perot interferometer based on polymer filled glass capillary,” Opt. Fiber Technol. 19(6), 618–622 (2013).
    [Crossref]
  18. L. Li, Z. Y. Feng, X. G. Qiao, H. Z. Yang, R. H. Wang, D. Su, Y. P. Wang, W. J. Bao, J. C. Li, Z. H. Shao, and M. Hu, “Ultrahigh sensitive temperature sensor based on Fabry–Pérot interference assisted by a graphene diaphragm,” IEEE Sens. J. 15(1), 505–509 (2015).
    [Crossref]
  19. C. Li, J. Xiao, T. T. Guo, S. C. Fan, and W. Jin, “Interference characteristics in a Fabry-Perot cavity with graphene membrane for optical fiber pressure sensors,” Microsyst. Technol. 21(11), 2297–2306 (2015).
    [Crossref]
  20. D. Yoon, Y.-W. Son, and H. Cheong, “Negative thermal expansion coefficient of graphene measured by Raman spectroscopy,” Nano Lett. 11(8), 3227–3231 (2011).
    [Crossref] [PubMed]
  21. N. G. Boddeti, S. P. Koenig, R. Long, J. L. Xiao, J. S. Bunch, and M. L. Dunn, “Mechanics of adhered, pressurized graphene blisters,” J. Appl. Mech. 80(4), 040909 (2013).
    [Crossref]
  22. J. W. Beams, The Structure and Properties of Thin Film (Wiley, 1959).
  23. L. A. Falkovsky, “Optical properties of graphene,” J. Phys. Conf. Ser. 129, 012004 (2008).
    [Crossref]
  24. A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011).
    [Crossref] [PubMed]
  25. A. Fasolino, J. H. Los, and M. I. Katsnelson, “Intrinsic ripples in graphene,” Nat. Mater. 6(11), 858–861 (2007).
    [Crossref] [PubMed]
  26. M. A. N. Dewapriya, A. Srikantha Phani, and R. K. N. D. Rajapakse, “Influence of temperature and free edges on the mechanical properties of graphene,” Model. Simul. Mater. Sci. Eng. 21(6), 065017 (2013).
    [Crossref]

2015 (3)

C. Li, X. Y. Gao, T. T. Guo, J. Xiao, S. C. Fan, and W. Jin, “Analyzing the applicability of miniature ultra-high sensitivity Fabry-Perot acoustic sensor using a nanothick graphene diaphragm,” Meas. Sci. Technol. 26(8), 085101 (2015).
[Crossref]

L. Li, Z. Y. Feng, X. G. Qiao, H. Z. Yang, R. H. Wang, D. Su, Y. P. Wang, W. J. Bao, J. C. Li, Z. H. Shao, and M. Hu, “Ultrahigh sensitive temperature sensor based on Fabry–Pérot interference assisted by a graphene diaphragm,” IEEE Sens. J. 15(1), 505–509 (2015).
[Crossref]

C. Li, J. Xiao, T. T. Guo, S. C. Fan, and W. Jin, “Interference characteristics in a Fabry-Perot cavity with graphene membrane for optical fiber pressure sensors,” Microsyst. Technol. 21(11), 2297–2306 (2015).
[Crossref]

2013 (5)

N. G. Boddeti, S. P. Koenig, R. Long, J. L. Xiao, J. S. Bunch, and M. L. Dunn, “Mechanics of adhered, pressurized graphene blisters,” J. Appl. Mech. 80(4), 040909 (2013).
[Crossref]

M. A. N. Dewapriya, A. Srikantha Phani, and R. K. N. D. Rajapakse, “Influence of temperature and free edges on the mechanical properties of graphene,” Model. Simul. Mater. Sci. Eng. 21(6), 065017 (2013).
[Crossref]

Y. Wang, D. N. Wang, C. Wang, and T. Hu, “Compressible fiber optic micro-Fabry-Pérot cavity with ultra-high pressure sensitivity,” Opt. Express 21(12), 14084–14089 (2013).
[Crossref] [PubMed]

J. Ma, H. F. Xuan, H. L. Ho, W. Jin, Y. H. Yang, and S. C. Fan, “Fiber-optic Fabry-Perot acoustic sensor with multilayer graphene diaphragm,” IEEE Photonics Technol. Lett. 25(10), 932–935 (2013).
[Crossref]

G. Zhang, M. Yang, and M. Wang, “Large temperature sensitivity of fiber-optic extrinsic Fabry-Perot interferometer based on polymer filled glass capillary,” Opt. Fiber Technol. 19(6), 618–622 (2013).
[Crossref]

2012 (3)

2011 (4)

S. Avino, J. A. Barnes, G. Gagliardi, X. Gu, D. Gutstein, J. R. Mester, C. Nicholaou, and H.-P. Loock, “Musical instrument pickup based on a laser locked to an optical fiber resonator,” Opt. Express 19(25), 25057–25065 (2011).
[Crossref] [PubMed]

S. P. Koenig, N. G. Boddeti, M. L. Dunn, and J. S. Bunch, “Ultrastrong adhesion of graphene membranes,” Nat. Nanotechnol. 6(9), 543–546 (2011).
[Crossref] [PubMed]

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011).
[Crossref] [PubMed]

D. Yoon, Y.-W. Son, and H. Cheong, “Negative thermal expansion coefficient of graphene measured by Raman spectroscopy,” Nano Lett. 11(8), 3227–3231 (2011).
[Crossref] [PubMed]

2010 (1)

2008 (3)

J. S. Bunch, S. S. Verbridge, J. S. Alden, A. M. van der Zande, J. M. Parpia, H. G. Craighead, and P. L. McEuen, “Impermeable atomic membranes from graphene sheets,” Nano Lett. 8(8), 2458–2462 (2008).
[Crossref] [PubMed]

C. Lee, X. Wei, J. W. Kysar, and J. Hone, “Measurement of the elastic properties and intrinsic strength of monolayer graphene,” Science 321(5887), 385–388 (2008).
[Crossref] [PubMed]

L. A. Falkovsky, “Optical properties of graphene,” J. Phys. Conf. Ser. 129, 012004 (2008).
[Crossref]

2007 (3)

A. Fasolino, J. H. Los, and M. I. Katsnelson, “Intrinsic ripples in graphene,” Nat. Mater. 6(11), 858–861 (2007).
[Crossref] [PubMed]

L. A. Falkovsky and S. S. Pershoguba, “Optical far-infrared properties of a graphene monolayer and multilayer,” Phys. Rev. B Condens. Matter 76(15), 153410 (2007).
[Crossref]

G. C. Hill, R. Melamud, F. E. Declercq, A. A. Davenport, I. H. Chan, P. G. Hartwell, and B. L. Pruitt, “SU-8 MEMS Fabry-Perot pressure sensor,” Sens. Actuators A Phys. 138(1), 52–62 (2007).
[Crossref]

2006 (1)

2004 (1)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref] [PubMed]

1987 (1)

G. Beheim, K. Fritsch, and R. N. Poorman, “Fiber-linked interferometric pressure sensor,” Rev. Sci. Instrum. 58(9), 1655–1659 (1987).
[Crossref]

Alden, J. S.

J. S. Bunch, S. S. Verbridge, J. S. Alden, A. M. van der Zande, J. M. Parpia, H. G. Craighead, and P. L. McEuen, “Impermeable atomic membranes from graphene sheets,” Nano Lett. 8(8), 2458–2462 (2008).
[Crossref] [PubMed]

Araújo, F. M.

P. A. R. Tafulo, P. A. S. Jorge, J. L. Santos, F. M. Araújo, and O. Frazão, “Intrinsic Fabry-Perot cavity sensor based on etched multimode graded index fiber for strain and temperature measurement,” IEEE Sens. J. 12(1), 8–12 (2012).
[Crossref]

Avino, S.

Bao, W. J.

L. Li, Z. Y. Feng, X. G. Qiao, H. Z. Yang, R. H. Wang, D. Su, Y. P. Wang, W. J. Bao, J. C. Li, Z. H. Shao, and M. Hu, “Ultrahigh sensitive temperature sensor based on Fabry–Pérot interference assisted by a graphene diaphragm,” IEEE Sens. J. 15(1), 505–509 (2015).
[Crossref]

Barnes, J. A.

Beheim, G.

G. Beheim, K. Fritsch, and R. N. Poorman, “Fiber-linked interferometric pressure sensor,” Rev. Sci. Instrum. 58(9), 1655–1659 (1987).
[Crossref]

Boddeti, N. G.

N. G. Boddeti, S. P. Koenig, R. Long, J. L. Xiao, J. S. Bunch, and M. L. Dunn, “Mechanics of adhered, pressurized graphene blisters,” J. Appl. Mech. 80(4), 040909 (2013).
[Crossref]

S. P. Koenig, N. G. Boddeti, M. L. Dunn, and J. S. Bunch, “Ultrastrong adhesion of graphene membranes,” Nat. Nanotechnol. 6(9), 543–546 (2011).
[Crossref] [PubMed]

Bunch, J. S.

N. G. Boddeti, S. P. Koenig, R. Long, J. L. Xiao, J. S. Bunch, and M. L. Dunn, “Mechanics of adhered, pressurized graphene blisters,” J. Appl. Mech. 80(4), 040909 (2013).
[Crossref]

S. P. Koenig, N. G. Boddeti, M. L. Dunn, and J. S. Bunch, “Ultrastrong adhesion of graphene membranes,” Nat. Nanotechnol. 6(9), 543–546 (2011).
[Crossref] [PubMed]

J. S. Bunch, S. S. Verbridge, J. S. Alden, A. M. van der Zande, J. M. Parpia, H. G. Craighead, and P. L. McEuen, “Impermeable atomic membranes from graphene sheets,” Nano Lett. 8(8), 2458–2462 (2008).
[Crossref] [PubMed]

Chan, I. H.

G. C. Hill, R. Melamud, F. E. Declercq, A. A. Davenport, I. H. Chan, P. G. Hartwell, and B. L. Pruitt, “SU-8 MEMS Fabry-Perot pressure sensor,” Sens. Actuators A Phys. 138(1), 52–62 (2007).
[Crossref]

Chen, X.

Cheong, H.

D. Yoon, Y.-W. Son, and H. Cheong, “Negative thermal expansion coefficient of graphene measured by Raman spectroscopy,” Nano Lett. 11(8), 3227–3231 (2011).
[Crossref] [PubMed]

Craighead, H. G.

J. S. Bunch, S. S. Verbridge, J. S. Alden, A. M. van der Zande, J. M. Parpia, H. G. Craighead, and P. L. McEuen, “Impermeable atomic membranes from graphene sheets,” Nano Lett. 8(8), 2458–2462 (2008).
[Crossref] [PubMed]

Davenport, A. A.

G. C. Hill, R. Melamud, F. E. Declercq, A. A. Davenport, I. H. Chan, P. G. Hartwell, and B. L. Pruitt, “SU-8 MEMS Fabry-Perot pressure sensor,” Sens. Actuators A Phys. 138(1), 52–62 (2007).
[Crossref]

Declercq, F. E.

G. C. Hill, R. Melamud, F. E. Declercq, A. A. Davenport, I. H. Chan, P. G. Hartwell, and B. L. Pruitt, “SU-8 MEMS Fabry-Perot pressure sensor,” Sens. Actuators A Phys. 138(1), 52–62 (2007).
[Crossref]

Dewapriya, M. A. N.

M. A. N. Dewapriya, A. Srikantha Phani, and R. K. N. D. Rajapakse, “Influence of temperature and free edges on the mechanical properties of graphene,” Model. Simul. Mater. Sci. Eng. 21(6), 065017 (2013).
[Crossref]

Dubonos, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref] [PubMed]

Dunn, M. L.

N. G. Boddeti, S. P. Koenig, R. Long, J. L. Xiao, J. S. Bunch, and M. L. Dunn, “Mechanics of adhered, pressurized graphene blisters,” J. Appl. Mech. 80(4), 040909 (2013).
[Crossref]

S. P. Koenig, N. G. Boddeti, M. L. Dunn, and J. S. Bunch, “Ultrastrong adhesion of graphene membranes,” Nat. Nanotechnol. 6(9), 543–546 (2011).
[Crossref] [PubMed]

Engheta, N.

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011).
[Crossref] [PubMed]

Falkovsky, L. A.

L. A. Falkovsky, “Optical properties of graphene,” J. Phys. Conf. Ser. 129, 012004 (2008).
[Crossref]

L. A. Falkovsky and S. S. Pershoguba, “Optical far-infrared properties of a graphene monolayer and multilayer,” Phys. Rev. B Condens. Matter 76(15), 153410 (2007).
[Crossref]

Fan, S. C.

C. Li, J. Xiao, T. T. Guo, S. C. Fan, and W. Jin, “Interference characteristics in a Fabry-Perot cavity with graphene membrane for optical fiber pressure sensors,” Microsyst. Technol. 21(11), 2297–2306 (2015).
[Crossref]

C. Li, X. Y. Gao, T. T. Guo, J. Xiao, S. C. Fan, and W. Jin, “Analyzing the applicability of miniature ultra-high sensitivity Fabry-Perot acoustic sensor using a nanothick graphene diaphragm,” Meas. Sci. Technol. 26(8), 085101 (2015).
[Crossref]

J. Ma, H. F. Xuan, H. L. Ho, W. Jin, Y. H. Yang, and S. C. Fan, “Fiber-optic Fabry-Perot acoustic sensor with multilayer graphene diaphragm,” IEEE Photonics Technol. Lett. 25(10), 932–935 (2013).
[Crossref]

Fasolino, A.

A. Fasolino, J. H. Los, and M. I. Katsnelson, “Intrinsic ripples in graphene,” Nat. Mater. 6(11), 858–861 (2007).
[Crossref] [PubMed]

Feng, Z. Y.

L. Li, Z. Y. Feng, X. G. Qiao, H. Z. Yang, R. H. Wang, D. Su, Y. P. Wang, W. J. Bao, J. C. Li, Z. H. Shao, and M. Hu, “Ultrahigh sensitive temperature sensor based on Fabry–Pérot interference assisted by a graphene diaphragm,” IEEE Sens. J. 15(1), 505–509 (2015).
[Crossref]

Fink, T.

Firsov, A. A.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref] [PubMed]

Frazão, O.

P. A. R. Tafulo, P. A. S. Jorge, J. L. Santos, F. M. Araújo, and O. Frazão, “Intrinsic Fabry-Perot cavity sensor based on etched multimode graded index fiber for strain and temperature measurement,” IEEE Sens. J. 12(1), 8–12 (2012).
[Crossref]

Fritsch, K.

G. Beheim, K. Fritsch, and R. N. Poorman, “Fiber-linked interferometric pressure sensor,” Rev. Sci. Instrum. 58(9), 1655–1659 (1987).
[Crossref]

Gagliardi, G.

Gao, X. Y.

C. Li, X. Y. Gao, T. T. Guo, J. Xiao, S. C. Fan, and W. Jin, “Analyzing the applicability of miniature ultra-high sensitivity Fabry-Perot acoustic sensor using a nanothick graphene diaphragm,” Meas. Sci. Technol. 26(8), 085101 (2015).
[Crossref]

Geim, A. K.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref] [PubMed]

Grigorieva, I. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref] [PubMed]

Gu, X.

Guo, F.

Guo, T. T.

C. Li, X. Y. Gao, T. T. Guo, J. Xiao, S. C. Fan, and W. Jin, “Analyzing the applicability of miniature ultra-high sensitivity Fabry-Perot acoustic sensor using a nanothick graphene diaphragm,” Meas. Sci. Technol. 26(8), 085101 (2015).
[Crossref]

C. Li, J. Xiao, T. T. Guo, S. C. Fan, and W. Jin, “Interference characteristics in a Fabry-Perot cavity with graphene membrane for optical fiber pressure sensors,” Microsyst. Technol. 21(11), 2297–2306 (2015).
[Crossref]

Gutstein, D.

Han, M.

Hartwell, P. G.

G. C. Hill, R. Melamud, F. E. Declercq, A. A. Davenport, I. H. Chan, P. G. Hartwell, and B. L. Pruitt, “SU-8 MEMS Fabry-Perot pressure sensor,” Sens. Actuators A Phys. 138(1), 52–62 (2007).
[Crossref]

Hill, G. C.

G. C. Hill, R. Melamud, F. E. Declercq, A. A. Davenport, I. H. Chan, P. G. Hartwell, and B. L. Pruitt, “SU-8 MEMS Fabry-Perot pressure sensor,” Sens. Actuators A Phys. 138(1), 52–62 (2007).
[Crossref]

Ho, H. L.

J. Ma, H. F. Xuan, H. L. Ho, W. Jin, Y. H. Yang, and S. C. Fan, “Fiber-optic Fabry-Perot acoustic sensor with multilayer graphene diaphragm,” IEEE Photonics Technol. Lett. 25(10), 932–935 (2013).
[Crossref]

Hone, J.

C. Lee, X. Wei, J. W. Kysar, and J. Hone, “Measurement of the elastic properties and intrinsic strength of monolayer graphene,” Science 321(5887), 385–388 (2008).
[Crossref] [PubMed]

Hu, M.

L. Li, Z. Y. Feng, X. G. Qiao, H. Z. Yang, R. H. Wang, D. Su, Y. P. Wang, W. J. Bao, J. C. Li, Z. H. Shao, and M. Hu, “Ultrahigh sensitive temperature sensor based on Fabry–Pérot interference assisted by a graphene diaphragm,” IEEE Sens. J. 15(1), 505–509 (2015).
[Crossref]

Hu, T.

Huang, J.

Huang, Z.

Jiang, D.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref] [PubMed]

Jin, W.

C. Li, X. Y. Gao, T. T. Guo, J. Xiao, S. C. Fan, and W. Jin, “Analyzing the applicability of miniature ultra-high sensitivity Fabry-Perot acoustic sensor using a nanothick graphene diaphragm,” Meas. Sci. Technol. 26(8), 085101 (2015).
[Crossref]

C. Li, J. Xiao, T. T. Guo, S. C. Fan, and W. Jin, “Interference characteristics in a Fabry-Perot cavity with graphene membrane for optical fiber pressure sensors,” Microsyst. Technol. 21(11), 2297–2306 (2015).
[Crossref]

J. Ma, H. F. Xuan, H. L. Ho, W. Jin, Y. H. Yang, and S. C. Fan, “Fiber-optic Fabry-Perot acoustic sensor with multilayer graphene diaphragm,” IEEE Photonics Technol. Lett. 25(10), 932–935 (2013).
[Crossref]

Jorge, P. A. S.

P. A. R. Tafulo, P. A. S. Jorge, J. L. Santos, F. M. Araújo, and O. Frazão, “Intrinsic Fabry-Perot cavity sensor based on etched multimode graded index fiber for strain and temperature measurement,” IEEE Sens. J. 12(1), 8–12 (2012).
[Crossref]

Katsnelson, M. I.

A. Fasolino, J. H. Los, and M. I. Katsnelson, “Intrinsic ripples in graphene,” Nat. Mater. 6(11), 858–861 (2007).
[Crossref] [PubMed]

Koenig, S. P.

N. G. Boddeti, S. P. Koenig, R. Long, J. L. Xiao, J. S. Bunch, and M. L. Dunn, “Mechanics of adhered, pressurized graphene blisters,” J. Appl. Mech. 80(4), 040909 (2013).
[Crossref]

S. P. Koenig, N. G. Boddeti, M. L. Dunn, and J. S. Bunch, “Ultrastrong adhesion of graphene membranes,” Nat. Nanotechnol. 6(9), 543–546 (2011).
[Crossref] [PubMed]

Koester, L.

Kysar, J. W.

C. Lee, X. Wei, J. W. Kysar, and J. Hone, “Measurement of the elastic properties and intrinsic strength of monolayer graphene,” Science 321(5887), 385–388 (2008).
[Crossref] [PubMed]

Lee, C.

C. Lee, X. Wei, J. W. Kysar, and J. Hone, “Measurement of the elastic properties and intrinsic strength of monolayer graphene,” Science 321(5887), 385–388 (2008).
[Crossref] [PubMed]

Li, C.

C. Li, X. Y. Gao, T. T. Guo, J. Xiao, S. C. Fan, and W. Jin, “Analyzing the applicability of miniature ultra-high sensitivity Fabry-Perot acoustic sensor using a nanothick graphene diaphragm,” Meas. Sci. Technol. 26(8), 085101 (2015).
[Crossref]

C. Li, J. Xiao, T. T. Guo, S. C. Fan, and W. Jin, “Interference characteristics in a Fabry-Perot cavity with graphene membrane for optical fiber pressure sensors,” Microsyst. Technol. 21(11), 2297–2306 (2015).
[Crossref]

F. Xu, D. Ren, X. Shi, C. Li, W. Lu, L. Lu, L. Lu, and B. Yu, “High-sensitivity Fabry-Perot interferometric pressure sensor based on a nanothick silver diaphragm,” Opt. Lett. 37(2), 133–135 (2012).
[Crossref] [PubMed]

Li, J. C.

L. Li, Z. Y. Feng, X. G. Qiao, H. Z. Yang, R. H. Wang, D. Su, Y. P. Wang, W. J. Bao, J. C. Li, Z. H. Shao, and M. Hu, “Ultrahigh sensitive temperature sensor based on Fabry–Pérot interference assisted by a graphene diaphragm,” IEEE Sens. J. 15(1), 505–509 (2015).
[Crossref]

Li, L.

L. Li, Z. Y. Feng, X. G. Qiao, H. Z. Yang, R. H. Wang, D. Su, Y. P. Wang, W. J. Bao, J. C. Li, Z. H. Shao, and M. Hu, “Ultrahigh sensitive temperature sensor based on Fabry–Pérot interference assisted by a graphene diaphragm,” IEEE Sens. J. 15(1), 505–509 (2015).
[Crossref]

Long, R.

N. G. Boddeti, S. P. Koenig, R. Long, J. L. Xiao, J. S. Bunch, and M. L. Dunn, “Mechanics of adhered, pressurized graphene blisters,” J. Appl. Mech. 80(4), 040909 (2013).
[Crossref]

Loock, H.-P.

Los, J. H.

A. Fasolino, J. H. Los, and M. I. Katsnelson, “Intrinsic ripples in graphene,” Nat. Mater. 6(11), 858–861 (2007).
[Crossref] [PubMed]

Lu, L.

Lu, W.

Ma, J.

J. Ma, H. F. Xuan, H. L. Ho, W. Jin, Y. H. Yang, and S. C. Fan, “Fiber-optic Fabry-Perot acoustic sensor with multilayer graphene diaphragm,” IEEE Photonics Technol. Lett. 25(10), 932–935 (2013).
[Crossref]

McEuen, P. L.

J. S. Bunch, S. S. Verbridge, J. S. Alden, A. M. van der Zande, J. M. Parpia, H. G. Craighead, and P. L. McEuen, “Impermeable atomic membranes from graphene sheets,” Nano Lett. 8(8), 2458–2462 (2008).
[Crossref] [PubMed]

Melamud, R.

G. C. Hill, R. Melamud, F. E. Declercq, A. A. Davenport, I. H. Chan, P. G. Hartwell, and B. L. Pruitt, “SU-8 MEMS Fabry-Perot pressure sensor,” Sens. Actuators A Phys. 138(1), 52–62 (2007).
[Crossref]

Mester, J. R.

Morozov, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref] [PubMed]

Nicholaou, C.

Niezrecki, C.

Novoselov, K. S.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref] [PubMed]

Parpia, J. M.

J. S. Bunch, S. S. Verbridge, J. S. Alden, A. M. van der Zande, J. M. Parpia, H. G. Craighead, and P. L. McEuen, “Impermeable atomic membranes from graphene sheets,” Nano Lett. 8(8), 2458–2462 (2008).
[Crossref] [PubMed]

Pershoguba, S. S.

L. A. Falkovsky and S. S. Pershoguba, “Optical far-infrared properties of a graphene monolayer and multilayer,” Phys. Rev. B Condens. Matter 76(15), 153410 (2007).
[Crossref]

Poorman, R. N.

G. Beheim, K. Fritsch, and R. N. Poorman, “Fiber-linked interferometric pressure sensor,” Rev. Sci. Instrum. 58(9), 1655–1659 (1987).
[Crossref]

Pruitt, B. L.

G. C. Hill, R. Melamud, F. E. Declercq, A. A. Davenport, I. H. Chan, P. G. Hartwell, and B. L. Pruitt, “SU-8 MEMS Fabry-Perot pressure sensor,” Sens. Actuators A Phys. 138(1), 52–62 (2007).
[Crossref]

Qiao, X. G.

L. Li, Z. Y. Feng, X. G. Qiao, H. Z. Yang, R. H. Wang, D. Su, Y. P. Wang, W. J. Bao, J. C. Li, Z. H. Shao, and M. Hu, “Ultrahigh sensitive temperature sensor based on Fabry–Pérot interference assisted by a graphene diaphragm,” IEEE Sens. J. 15(1), 505–509 (2015).
[Crossref]

Rajapakse, R. K. N. D.

M. A. N. Dewapriya, A. Srikantha Phani, and R. K. N. D. Rajapakse, “Influence of temperature and free edges on the mechanical properties of graphene,” Model. Simul. Mater. Sci. Eng. 21(6), 065017 (2013).
[Crossref]

Ren, D.

Santos, J. L.

P. A. R. Tafulo, P. A. S. Jorge, J. L. Santos, F. M. Araújo, and O. Frazão, “Intrinsic Fabry-Perot cavity sensor based on etched multimode graded index fiber for strain and temperature measurement,” IEEE Sens. J. 12(1), 8–12 (2012).
[Crossref]

Shao, Z. H.

L. Li, Z. Y. Feng, X. G. Qiao, H. Z. Yang, R. H. Wang, D. Su, Y. P. Wang, W. J. Bao, J. C. Li, Z. H. Shao, and M. Hu, “Ultrahigh sensitive temperature sensor based on Fabry–Pérot interference assisted by a graphene diaphragm,” IEEE Sens. J. 15(1), 505–509 (2015).
[Crossref]

Shen, F.

Shi, X.

Son, Y.-W.

D. Yoon, Y.-W. Son, and H. Cheong, “Negative thermal expansion coefficient of graphene measured by Raman spectroscopy,” Nano Lett. 11(8), 3227–3231 (2011).
[Crossref] [PubMed]

Srikantha Phani, A.

M. A. N. Dewapriya, A. Srikantha Phani, and R. K. N. D. Rajapakse, “Influence of temperature and free edges on the mechanical properties of graphene,” Model. Simul. Mater. Sci. Eng. 21(6), 065017 (2013).
[Crossref]

Su, D.

L. Li, Z. Y. Feng, X. G. Qiao, H. Z. Yang, R. H. Wang, D. Su, Y. P. Wang, W. J. Bao, J. C. Li, Z. H. Shao, and M. Hu, “Ultrahigh sensitive temperature sensor based on Fabry–Pérot interference assisted by a graphene diaphragm,” IEEE Sens. J. 15(1), 505–509 (2015).
[Crossref]

Tafulo, P. A. R.

P. A. R. Tafulo, P. A. S. Jorge, J. L. Santos, F. M. Araújo, and O. Frazão, “Intrinsic Fabry-Perot cavity sensor based on etched multimode graded index fiber for strain and temperature measurement,” IEEE Sens. J. 12(1), 8–12 (2012).
[Crossref]

Tian, Y.

Turner, J.

Vakil, A.

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011).
[Crossref] [PubMed]

van der Zande, A. M.

J. S. Bunch, S. S. Verbridge, J. S. Alden, A. M. van der Zande, J. M. Parpia, H. G. Craighead, and P. L. McEuen, “Impermeable atomic membranes from graphene sheets,” Nano Lett. 8(8), 2458–2462 (2008).
[Crossref] [PubMed]

Verbridge, S. S.

J. S. Bunch, S. S. Verbridge, J. S. Alden, A. M. van der Zande, J. M. Parpia, H. G. Craighead, and P. L. McEuen, “Impermeable atomic membranes from graphene sheets,” Nano Lett. 8(8), 2458–2462 (2008).
[Crossref] [PubMed]

Wang, A.

Wang, C.

Wang, D. N.

Wang, M.

G. Zhang, M. Yang, and M. Wang, “Large temperature sensitivity of fiber-optic extrinsic Fabry-Perot interferometer based on polymer filled glass capillary,” Opt. Fiber Technol. 19(6), 618–622 (2013).
[Crossref]

Wang, R. H.

L. Li, Z. Y. Feng, X. G. Qiao, H. Z. Yang, R. H. Wang, D. Su, Y. P. Wang, W. J. Bao, J. C. Li, Z. H. Shao, and M. Hu, “Ultrahigh sensitive temperature sensor based on Fabry–Pérot interference assisted by a graphene diaphragm,” IEEE Sens. J. 15(1), 505–509 (2015).
[Crossref]

Wang, W.

Wang, X.

Wang, Y.

Wang, Y. P.

L. Li, Z. Y. Feng, X. G. Qiao, H. Z. Yang, R. H. Wang, D. Su, Y. P. Wang, W. J. Bao, J. C. Li, Z. H. Shao, and M. Hu, “Ultrahigh sensitive temperature sensor based on Fabry–Pérot interference assisted by a graphene diaphragm,” IEEE Sens. J. 15(1), 505–509 (2015).
[Crossref]

Wang, Z.

Wei, X.

C. Lee, X. Wei, J. W. Kysar, and J. Hone, “Measurement of the elastic properties and intrinsic strength of monolayer graphene,” Science 321(5887), 385–388 (2008).
[Crossref] [PubMed]

Wu, N.

Xiao, J.

C. Li, X. Y. Gao, T. T. Guo, J. Xiao, S. C. Fan, and W. Jin, “Analyzing the applicability of miniature ultra-high sensitivity Fabry-Perot acoustic sensor using a nanothick graphene diaphragm,” Meas. Sci. Technol. 26(8), 085101 (2015).
[Crossref]

C. Li, J. Xiao, T. T. Guo, S. C. Fan, and W. Jin, “Interference characteristics in a Fabry-Perot cavity with graphene membrane for optical fiber pressure sensors,” Microsyst. Technol. 21(11), 2297–2306 (2015).
[Crossref]

Xiao, J. L.

N. G. Boddeti, S. P. Koenig, R. Long, J. L. Xiao, J. S. Bunch, and M. L. Dunn, “Mechanics of adhered, pressurized graphene blisters,” J. Appl. Mech. 80(4), 040909 (2013).
[Crossref]

Xu, F.

Xuan, H. F.

J. Ma, H. F. Xuan, H. L. Ho, W. Jin, Y. H. Yang, and S. C. Fan, “Fiber-optic Fabry-Perot acoustic sensor with multilayer graphene diaphragm,” IEEE Photonics Technol. Lett. 25(10), 932–935 (2013).
[Crossref]

Yang, H. Z.

L. Li, Z. Y. Feng, X. G. Qiao, H. Z. Yang, R. H. Wang, D. Su, Y. P. Wang, W. J. Bao, J. C. Li, Z. H. Shao, and M. Hu, “Ultrahigh sensitive temperature sensor based on Fabry–Pérot interference assisted by a graphene diaphragm,” IEEE Sens. J. 15(1), 505–509 (2015).
[Crossref]

Yang, M.

G. Zhang, M. Yang, and M. Wang, “Large temperature sensitivity of fiber-optic extrinsic Fabry-Perot interferometer based on polymer filled glass capillary,” Opt. Fiber Technol. 19(6), 618–622 (2013).
[Crossref]

Yang, Y. H.

J. Ma, H. F. Xuan, H. L. Ho, W. Jin, Y. H. Yang, and S. C. Fan, “Fiber-optic Fabry-Perot acoustic sensor with multilayer graphene diaphragm,” IEEE Photonics Technol. Lett. 25(10), 932–935 (2013).
[Crossref]

Yoon, D.

D. Yoon, Y.-W. Son, and H. Cheong, “Negative thermal expansion coefficient of graphene measured by Raman spectroscopy,” Nano Lett. 11(8), 3227–3231 (2011).
[Crossref] [PubMed]

Yu, B.

Zhang, G.

G. Zhang, M. Yang, and M. Wang, “Large temperature sensitivity of fiber-optic extrinsic Fabry-Perot interferometer based on polymer filled glass capillary,” Opt. Fiber Technol. 19(6), 618–622 (2013).
[Crossref]

Zhang, Y.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref] [PubMed]

Appl. Opt. (1)

IEEE Photonics Technol. Lett. (1)

J. Ma, H. F. Xuan, H. L. Ho, W. Jin, Y. H. Yang, and S. C. Fan, “Fiber-optic Fabry-Perot acoustic sensor with multilayer graphene diaphragm,” IEEE Photonics Technol. Lett. 25(10), 932–935 (2013).
[Crossref]

IEEE Sens. J. (2)

P. A. R. Tafulo, P. A. S. Jorge, J. L. Santos, F. M. Araújo, and O. Frazão, “Intrinsic Fabry-Perot cavity sensor based on etched multimode graded index fiber for strain and temperature measurement,” IEEE Sens. J. 12(1), 8–12 (2012).
[Crossref]

L. Li, Z. Y. Feng, X. G. Qiao, H. Z. Yang, R. H. Wang, D. Su, Y. P. Wang, W. J. Bao, J. C. Li, Z. H. Shao, and M. Hu, “Ultrahigh sensitive temperature sensor based on Fabry–Pérot interference assisted by a graphene diaphragm,” IEEE Sens. J. 15(1), 505–509 (2015).
[Crossref]

J. Appl. Mech. (1)

N. G. Boddeti, S. P. Koenig, R. Long, J. L. Xiao, J. S. Bunch, and M. L. Dunn, “Mechanics of adhered, pressurized graphene blisters,” J. Appl. Mech. 80(4), 040909 (2013).
[Crossref]

J. Phys. Conf. Ser. (1)

L. A. Falkovsky, “Optical properties of graphene,” J. Phys. Conf. Ser. 129, 012004 (2008).
[Crossref]

Meas. Sci. Technol. (1)

C. Li, X. Y. Gao, T. T. Guo, J. Xiao, S. C. Fan, and W. Jin, “Analyzing the applicability of miniature ultra-high sensitivity Fabry-Perot acoustic sensor using a nanothick graphene diaphragm,” Meas. Sci. Technol. 26(8), 085101 (2015).
[Crossref]

Microsyst. Technol. (1)

C. Li, J. Xiao, T. T. Guo, S. C. Fan, and W. Jin, “Interference characteristics in a Fabry-Perot cavity with graphene membrane for optical fiber pressure sensors,” Microsyst. Technol. 21(11), 2297–2306 (2015).
[Crossref]

Model. Simul. Mater. Sci. Eng. (1)

M. A. N. Dewapriya, A. Srikantha Phani, and R. K. N. D. Rajapakse, “Influence of temperature and free edges on the mechanical properties of graphene,” Model. Simul. Mater. Sci. Eng. 21(6), 065017 (2013).
[Crossref]

Nano Lett. (2)

D. Yoon, Y.-W. Son, and H. Cheong, “Negative thermal expansion coefficient of graphene measured by Raman spectroscopy,” Nano Lett. 11(8), 3227–3231 (2011).
[Crossref] [PubMed]

J. S. Bunch, S. S. Verbridge, J. S. Alden, A. M. van der Zande, J. M. Parpia, H. G. Craighead, and P. L. McEuen, “Impermeable atomic membranes from graphene sheets,” Nano Lett. 8(8), 2458–2462 (2008).
[Crossref] [PubMed]

Nat. Mater. (1)

A. Fasolino, J. H. Los, and M. I. Katsnelson, “Intrinsic ripples in graphene,” Nat. Mater. 6(11), 858–861 (2007).
[Crossref] [PubMed]

Nat. Nanotechnol. (1)

S. P. Koenig, N. G. Boddeti, M. L. Dunn, and J. S. Bunch, “Ultrastrong adhesion of graphene membranes,” Nat. Nanotechnol. 6(9), 543–546 (2011).
[Crossref] [PubMed]

Opt. Express (3)

Opt. Fiber Technol. (1)

G. Zhang, M. Yang, and M. Wang, “Large temperature sensitivity of fiber-optic extrinsic Fabry-Perot interferometer based on polymer filled glass capillary,” Opt. Fiber Technol. 19(6), 618–622 (2013).
[Crossref]

Opt. Lett. (2)

Phys. Rev. B Condens. Matter (1)

L. A. Falkovsky and S. S. Pershoguba, “Optical far-infrared properties of a graphene monolayer and multilayer,” Phys. Rev. B Condens. Matter 76(15), 153410 (2007).
[Crossref]

Rev. Sci. Instrum. (1)

G. Beheim, K. Fritsch, and R. N. Poorman, “Fiber-linked interferometric pressure sensor,” Rev. Sci. Instrum. 58(9), 1655–1659 (1987).
[Crossref]

Science (3)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref] [PubMed]

C. Lee, X. Wei, J. W. Kysar, and J. Hone, “Measurement of the elastic properties and intrinsic strength of monolayer graphene,” Science 321(5887), 385–388 (2008).
[Crossref] [PubMed]

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011).
[Crossref] [PubMed]

Sens. Actuators A Phys. (1)

G. C. Hill, R. Melamud, F. E. Declercq, A. A. Davenport, I. H. Chan, P. G. Hartwell, and B. L. Pruitt, “SU-8 MEMS Fabry-Perot pressure sensor,” Sens. Actuators A Phys. 138(1), 52–62 (2007).
[Crossref]

Other (1)

J. W. Beams, The Structure and Properties of Thin Film (Wiley, 1959).

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Figures (7)

Fig. 1
Fig. 1 (a) Schematic diagram and physical picture of the FP sensor and (b) microscopic image of the graphene diaphragm adhered on ferrule.
Fig. 2
Fig. 2 The measured and calculated film reflectivities.
Fig. 3
Fig. 3 Schematic diagram of temperature experimental rig.
Fig. 4
Fig. 4 Cavity length verse temperature at (a) the first cycle, (b) the second cycle and (c) the third cycle of temperature rise/drop measurements.
Fig. 5
Fig. 5 Pressure and deflection verse temperature.
Fig. 6
Fig. 6 The measured reflection spectrums of the FP sensor.
Fig. 7
Fig. 7 The intensity signal in the range of 30-40 °C.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

δ = 4 π L / λ
Δ L = ( β f e r r u l e L f e r r u l e β S M F L S M F ) Δ T + ω
p i n t T = p i n t V 0 T V T T 0 = p i n t V 0 T ( V 0 + Δ V T + Δ V ω ) T 0
{ Δ V ω = π C 3 [ 4 a 3 ( 3 a ω ) ω 2 ] a = r 2 + ω 2 2 ω
Δ P = 4 σ 0 t r 2 ω P + 8 E t ω P 3 3 ( 1 υ ) r 4
d λ m d T = 2 m ( β f e r r u l e L f e r r u l e β S M F L S M F + d ω d T ) 2 m ( β f e r r u l e L f e r r u l e β S M F L S M F + n R ( 1 - υ ) r 4 8 E t V T ω 2 )

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