OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 20 — Sep. 26, 2011
  • pp: 18842–18860
« Show journal navigation

Opto-acoustic behavior of coated fiber Bragg gratings

Massimo Moccia, Marco Pisco, Antonello Cutolo, Vincenzo Galdi, Pierantonio Bevilacqua, and Andrea Cusano  »View Author Affiliations


Optics Express, Vol. 19, Issue 20, pp. 18842-18860 (2011)
http://dx.doi.org/10.1364/OE.19.018842


View Full Text Article

Acrobat PDF (1597 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

In this paper, we present the study of the acousto-optic behavior of underwater-acoustic sensors constituted by fiber Bragg gratings (FBGs) coated by ring-shaped overlays. Via full-wave numerical simulations, we study the complex opto-acousto-mechanical interaction among an incident acoustic wave traveling in water, the optical fiber surrounded by the ring shaped coating, and the FBG inscribed the fiber, focusing on the frequency range 0.5-30 kHz of interest for SONAR applications. Our results fully characterize the mechanical behavior of an acoustically driven coated FBG, and highlight the key role played by the coating in enhancing significantly its sensitivity by comparison with a standard uncoated configuration. Furthermore, the hydrophone sensitivity spectrum exhibits characteristic resonances, which strongly improve the sensitivity with respect to its background (i.e., away from resonances) level. Via a three-dimensional modal analysis, we verify that the composite cylindrical structure of the sensor acts as an acoustic resonator tuned at the frequencies of its longitudinal vibration modes. In order to evaluate the sensor performance, we also carry out a comprehensive parametric analysis by varying the geometrical and mechanical properties of the coating, whose results also provide a useful design tool for performance optimization and/or tailoring for specific SONAR applications. Finally, a preliminary validation of the proposed numerical analysis has been carried out through experimental data obtained using polymeric coated FBGs sensors revealing a good agreement and prediction capability.

© 2011 OSA

1. Introduction

In recent years, optical technology developments have demonstrated that optical sensors can be used as acoustic detectors in a wide frequency range: from SONAR applications to ultrasonic imaging [1

1. C. K. Kirkendall and A. Dandridge, “Overview of high performance fibre-optic sensing,” J. Phys. D Appl. Phys. 37(18), R197–R216 (2004). [CrossRef]

3

3. G. Wild and S. Hinckley, “Acousto-ultrasonic optical fiber sensors: Overview and state-of-the-art,” IEEE Sens. J. 8(7), 1184–1193 (2008). [CrossRef]

]. Acousto-optic sensors have the advantage of compact size, in addition to electromagnetic interference immunity, stability in harsh environments, and multiplexing capability [3

3. G. Wild and S. Hinckley, “Acousto-ultrasonic optical fiber sensors: Overview and state-of-the-art,” IEEE Sens. J. 8(7), 1184–1193 (2008). [CrossRef]

].

Several sensing configurations have been proposed which rely on optical technology for acoustic detection in underwater scenarios. A promising approach was proposed by Hill et al. [4

4. D. J. Hill and P. J. Nash, “In-water acoustic response of a coated DFB fibre laser sensor,” Proc. SPIE 4185, 33–36 (2000).

], by using a distributed feedback fiber laser (DFB FL) as sensing element. The frequency of light produced by the DFB FL was extremely sensitive to acoustic perturbations. In [5

5. S. Fosters, A. Tikhomirova, M. Milnesa, J. van Velzena, and G. Hardyb, “A fibre laser hydrophone,” Proc. SPIE 5855, 627–630 (2005). [CrossRef]

], Foster et al. obtained a sensitivity of 100 nm/MPa by using a metal housing for the DFB FL sensor in order to enhance the hydrophone response. Even though DFB FL provides respectable sensitivities, and in-field demonstration of an FL hydrophone array has been also recently reported [6

6. S. Goodman, S. Foster, J. Van Velzen, and H. Mendis, “Field demonstration of a DFB fibre laser hydrophone seabed array in Jervis Bay, Australia,” Proc. SPIE 7503, 75034L1 (2009).

], sophisticated technologies are needed.

Simpler approaches have been proposed based on the use of fiber Bragg gratings (FBGs) in standard optical fibers for acoustic detection. Optical sensors based on FBG indeed demonstrated significant performance as underwater acoustic sensors by exploiting relatively cheap and well-established methodologies and technologies (i.e., multiplexing strategies, interrogation units, etc.) already developed for various FBG communication and sensing applications. In [7

7. N. Takahashi, A. Hirose, and S. Takahashi, “Underwater acoustic sensor with fiber Bragg grating,” Opt. Rev. 4(6), 691–694 (1997). [CrossRef]

] and [8

8. N. Takahashi, K. Yoshimura, S. Takahashi, and K. Imamura, “Development of an optical fiber hydrophone with fiber Bragg grating,” Ultrasonics 38(1-8), 581–585 (2000). [CrossRef] [PubMed]

], Takahashi et al. proposed a simple in-fiber FBG as underwater acoustic detector. The operational range and the pressure sensitivity of the hydrophone were systematically investigated [7

7. N. Takahashi, A. Hirose, and S. Takahashi, “Underwater acoustic sensor with fiber Bragg grating,” Opt. Rev. 4(6), 691–694 (1997). [CrossRef]

], and the frequency response was studied in various acoustic frequency ranges [8

8. N. Takahashi, K. Yoshimura, S. Takahashi, and K. Imamura, “Development of an optical fiber hydrophone with fiber Bragg grating,” Ultrasonics 38(1-8), 581–585 (2000). [CrossRef] [PubMed]

]. Improvements in the hydrophone response were obtained via temperature compensation [9

9. W. Thongnum, N. Takahashi, and S. Takahashi, “Temperature stabilization of fiber Bragg grating vibration sensor,” in OFS 2002, 15th Optical Fiber Sensors Conference Technical Digest, 2002. (2002), Vol. 1, pp. 223–226.

] by using feedback control. Multiplexing operation with FBG hydrophones with both time and wavelength division strategies was demonstrated in [10

10. N. Takahashi, K. Tetsumura, and S. Takahashi, “Multipoint detection of acoustical wave in water with WDM fiber Bragg grating sensor,” Proc. SPIE 3740, 270–273 (1999). [CrossRef]

] and [11

11. H. Yokosuka, S. Tanaka, and N. Takahashi, “Time-division multiplexing operation of temperature-compensated fiber Bragg grating underwater acoustic sensor array with feedback control,” Acoust. Sci. Technol. 26(5), 456–458 (2005). [CrossRef]

], respectively, in order to enable for multipoint detection.

The main limitation to the performance of FBG-based sensors in underwater applications stems from the high value (about 72 GPa) of the elastic (Young’s) modulus of the glass constituting the optical fiber. This was also the limiting factor for the application of FBGs as hydrostatic pressure sensors. In this framework, Hill et al. [12

12. D. J. Hill and G. A. Cranch, “Gain in hydrostatic pressure sensitivity of coated fiber Bragg grating,” Electron. Lett. 35(15), 1268–1269 (1999). [CrossRef]

] and Liu et al. [13

13. Y. Liu, Z. Guo, Y. Zhang, K. S. Chiang, and X. Dong, “Simultaneous pressure and temperature measurement with polymer-coated fiber Bragg grating,” Electron. Lett. 36(6), 564–566 (2000). [CrossRef]

], by exploiting the two-dimensional (2-D) model proposed by Hocker [14

14. G. B. Hocker, “Fiber optic acoustic sensors with composite structure: an analysis,” Appl. Opt. 18(21), 3679–3683 (1979). [CrossRef] [PubMed]

], demonstrated that FBGs coated by materials with Young’s modulus lower than that of the fiber glass may act as pressure sensors with enhanced sensitivity to the hydrostatic pressure. Their analyses were limited to the hydrostatic regime, and a dynamical extension to pressure acoustic waves is hitherto not available in the literature. From the experimental viewpoint, preliminary experimental studies by Cusano et al. [15

15. A. Cusano, S. D’Addio, A. Cutolo, S. Campopiano, M. Balbi, S. Balzarini, and M. Giordano, “Enhanced acoustic sensitivity in polymeric coated fiber Bragg grating,” Sensors Transducers 82, 1450–1457 (2007).

,16

16. S. Campopiano, A. Cutolo, A. Cusano, M. Giordano, G. Parente, G. Lanza, and A. Laudati, “Underwater acoustic sensors based on fiber Bragg gratings,” Sensors (Basel Switzerland) 9(6), 4446–4454 (2009). [CrossRef]

] demonstrated that coated FBGs may outperform (in terms of acoustic sensitivity) standard uncoated configurations.

Against this background, in this paper, we carry out a systematic numerical analysis of the response of a coated FBG acting as an acoustic wave sensor. More specifically, we study the complex opto-acousto-mechanical interaction among an incident acoustic wave traveling in water, the optical fiber surrounded by the ring-shaped coating, and the FBG inscribed in the fiber, via full-wave numerical simulations by means of a multiphysics software package based on the finite-element method (FEM). In order to provide a full characterization of the sensor performance, we also carry out a comprehensive parametric analysis of the hydrophone sensitivity, by varying the geometrical and mechanical properties of the coating. Finally, we present a preliminary experimental validation.

2. Theoretical background

The operational scenario of our underwater optical fiber hydrophone, schematically illustrated in Fig. 1
Fig. 1 Schematic description of the operational scenario for the underwater optical-fiber hydrophone (details in the text).
, inherently involves a complex interplay of different physical phenomena.

2.1 Acoustic domain: acoustic wave propagation

Acoustic waves are small perturbations (P,ρ) with respect to a constant equilibrium state (P0,ρ0) of a compressible ideal fluid [17

17. L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Pergamon Press, 1987).

], viz.,

(P,ρ)=(P,ρ)+(P0,ρ0),
(1)

where P=P(t,x,y,z) and ρ=ρ(t,x,y,z) are the scalar pressure field and the density of propagation medium, respectively, while P = P(t,x,y,z)P0 and ρ = ρ(t,x,y,z)ρ0 denote small perturbations with respect to the corresponding constant components P0 and ρ0, respectively.

The propagation of pressure acoustic waves in compressible ideal fluids (e.g., water) is ruled by fundamental laws, known as the continuity equation and the Euler’s equation respectively [17

17. L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Pergamon Press, 1987).

]:

ρt+ρ0(Ut)=0,ρ02Ut2=P,
(2)

where U=U(t,x,y,z) is the displacement vector.

P=c2ρ,
(3)

where c is the speed of sound in the fluid. By combining Eqs. (2) and (3), we obtain the wave equation

2P1c22Pt2=0,
(4)

which, in the time-harmonic regime, yields the Helmholtz equation

2p+(ωc)2p=0,
(5)

with ω denoting the angular frequency, and p denoting the frequency-domain pressure.

2.2 Mechanical domain: elastic wave propagation

In an elastic medium, waves propagate in the form of small oscillations of the stress field. The vector displacement U in an elastic medium is described by the following elasto-dynamic equilibrium (Navier’s) equation [18

18. F. Ihlenburg, Finite Element Analysis of Acoustic Scattering (Springer, 1998).

]:

μ2U+(λ+μ)(U)+F=ρs2Ut2,
(6)

λ=νE(1+ν)(12ν),μ=E2(1+ν).
(7)

εij=12(Uij+Uji),
(8)

σ=Dε,
(9)

where D is the elastic constant matrix.

Finally, the elasto-dynamic equation governing the time-harmonic elastic wave propagation in a solid is given by [18

18. F. Ihlenburg, Finite Element Analysis of Acoustic Scattering (Springer, 1998).

]

μ2u+(λ+μ)(u)+ρsω2u=f,
(10)

where u and f are the frequency-domain displacement vector and the applied dynamic load, respectively.

2.3 Boundary conditions: acousto-mechanical interactions

In order to calculate the full response of the system, we need to connect the acoustic and mechanical domains via proper boundary conditions. Such conditions, enforced at the interface between the water domain and the cylindrical sensor may be summarized as follows [18

18. F. Ihlenburg, Finite Element Analysis of Acoustic Scattering (Springer, 1998).

]:

  • 1. The normal displacement in the solid and fluid must be equal at the interface:
    ρ0ω2un=pn.
    (11a)
  • 2. The pressure must be in static equilibrium with the stress normal to the solid boundary:
    σn=p.
    (11b)
  • 3. In an ideal fluid, no tangential stresses must occur at the boundary:
    σ=0.
    (11c)

    In Eqs. (11a)-(11c), n is the unit vector normal to the boundary surface, while σn and σ are the components of the stress vector normal and tangential to the boundary surface, respectively. Furthermore, within the mechanical domain, we assume perfect bonding between the optical fiber and the coating, which implies the additional boundary condition

  • 4. The stresses and displacements at the fiber-coating interface must be continuous [17

    17. L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Pergamon Press, 1987).

    ]:
    σc=σf,Uc=Uf,
    (11d)

where the subscripts c and f identify the coating and fiber, respectively.

2.4 Optical domain

It is well known that an FBG is a strain sensor, and a mechanical deformation of the FBG results in a shift of the Bragg wavelength [7

7. N. Takahashi, A. Hirose, and S. Takahashi, “Underwater acoustic sensor with fiber Bragg grating,” Opt. Rev. 4(6), 691–694 (1997). [CrossRef]

]. The relationship between strain and induced changes in the wavelength reflected in an FBG, normalized to its central wavelength, is given by [20

20. C. J. S. de Matos, P. Torres, L. C. G. Valente, W. Margulis, and R. Stubbe, “Fiber Bragg grating (FBG) characterization and shaping by local pressure,” J. Lightwave Technol. 19(8), 1206–1211 (2001). [CrossRef]

]

Δλλ0=εzneff22[p11εx+p12(εz+εy)],
(12)

where Δλ is the Bragg wavelength shift, λ0 is the central wavelength of the FBG, p11 and p12 are the elasto-optic parameters, neff is the effective refractive index, and εi (i=x,y,z) are the Cartesian strain components evaluated at the FBG location. It is noteworthy that Eq. (12) well describes the elasto-optic response of FBGs in most practical cases when no significant birefringence is induced (εx=εy), and the strain components are uniform along the FBG length [21

21. A. Minardo, A. Cusano, R. Bernini, L. Zeni, and M. Giordano, “Response of fiber Bragg gratings to longitudinal ultrasonic waves,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52(2), 304–312 (2005). [CrossRef] [PubMed]

]. The condition of uniformity of the strain components along the grating length is fulfilled when the acoustic wavelength is much larger than the FBG length [21

21. A. Minardo, A. Cusano, R. Bernini, L. Zeni, and M. Giordano, “Response of fiber Bragg gratings to longitudinal ultrasonic waves,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52(2), 304–312 (2005). [CrossRef] [PubMed]

], and when the border effects on the strain distribution, due to the composite cylinder ends, are negligible.

3. Problem geometry, observables, and methods

In our simulations, in order to model the multi-physical (acoustic and mechanical) interactions between an acoustic wave propagating in water and the composite structure constituting the hydrophone, we use the FEM-based commercial software package COMSOL Multiphysics® [22

22. COMSOL Multiphysics, User’s Guide (COMSOL AB, 2008).

].

The underwater acoustic sensor under investigation is schematically represented by a 3-D structure (Fig. 2
Fig. 2 3-D geometry considered in the numerical simulations (details in the text).
) composed by an inner cylinder (the optical fiber), with height h and radius Rf, and an outer annular cylinder (the ring shaped coating), with same height h and coating radius RC. From the acousto-mechanical viewpoint, no distinction is made between the core and the cladding of the fiber. The sphere of radius Rw in Fig. 2 represents the water-filled acoustic domain surrounding the hydrophone.

Basically, the full-wave 3-D investigation of the acoustic-mechanical response of the underwater acoustic sensor, under the effect of a incident acoustic plane wave, is carried out in COMSOL by solving Eq. (5) in the acoustic domain, and by using the principle of virtual work (equivalent to the equilibrium equation in Eq. (10)) [22

22. COMSOL Multiphysics, User’s Guide (COMSOL AB, 2008).

] in the mechanical domain. The resulting equations are coupled via the boundary conditions described in Eqs. (11). Moreover, at the spherical surface of the water domain, a radiation condition is set, so as to mimic an infinite water domain. At the external boundary, an acoustic plane wave (of amplitude p0=1MPa) is set as a source. The analysis is carried out within the frequency range 0.5-30 kHz.

The FEM-based 3-D analysis yields the strain distribution ε along the x, y, and z axes into the optical fiber where the FBG is inscribed. The strain components evaluated at the FBG location (x,y,z)=(0,0,0) are then used in the optical model to calculate the Bragg wavelength shift according to Eq. (12), whose conditions of applicability (cf. Section 2.4) are always fulfilled in the simulations below.

The observable “sensitivity” can be defined as

S=Δλλ0p0=1p0{εzneff22[p11εx+p12(εz+εy)]},
(13)

where p11=0.121, p12=0.265, and neff=1.465 [12

12. D. J. Hill and G. A. Cranch, “Gain in hydrostatic pressure sensitivity of coated fiber Bragg grating,” Electron. Lett. 35(15), 1268–1269 (1999). [CrossRef]

]. Moreover, from the ratio between the calculated sensitivity and that pertaining to the bare (i.e., uncoated) fiber in the hydrostatic case (following [12

12. D. J. Hill and G. A. Cranch, “Gain in hydrostatic pressure sensitivity of coated fiber Bragg grating,” Electron. Lett. 35(15), 1268–1269 (1999). [CrossRef]

]), a sensitivity gain may be defined as

Sensitivity Gain=20log10(|SSBARE|),
(14)

whereSBARE=2.76·106MPa−1 [12

12. D. J. Hill and G. A. Cranch, “Gain in hydrostatic pressure sensitivity of coated fiber Bragg grating,” Electron. Lett. 35(15), 1268–1269 (1999). [CrossRef]

,14

14. G. B. Hocker, “Fiber optic acoustic sensors with composite structure: an analysis,” Appl. Opt. 18(21), 3679–3683 (1979). [CrossRef] [PubMed]

].

For a comprehensive characterization of the sensor performance, we carried out a series of parametric studies, by varying the geometrical and physical parameters such as the coating height h, the coating radius RC, the Young’s modulus E, the Poisson’s ratio ν, the density ρ, and the loss factor η. In all the simulations below, we assume an optical fiber radius Rf=62.5μm, and an identical length h for the fiber and the coating. The remaining mechanical and acoustic parameters listed in Table 1

Table 1. Mechanical and Acoustic Constants of the Analyzed Structure

table-icon
View This Table
| View All Tables
are kept constant.

The computational domain is discretized using a tetrahedral mesh. Numerical convergence was achieved for a discretization of at least five elements per acoustic wavelength. The simulations were performed by using the iterative Generalised Minimal Residual (GMRES) solver with the algebraic multi-grid pre-conditioner [22

22. COMSOL Multiphysics, User’s Guide (COMSOL AB, 2008).

].

4. Numerical analysis

4.1 Resonant behavior of the coated fiber Bragg gratings

In order to analyze the opto-acoustical response of our proposed sensor, we begin considering a specific configuration with fixed coating size and material properties, and investigate the interaction with an acoustic wave from the phenomenological viewpoint.

4.1.1 Harmonic analysis

The configuration of interest features a ring-shaped coating with an outer radius Rc=1.25mm (i.e., 20 times larger than the fiber radius) and a height h=4cm. The elastic properties of the coating, given in Table 2

Table 2. Elastic Properties of the Ring-Shaped Coating

table-icon
View This Table
| View All Tables
, are consistent with the nominal properties of a specific thermosetting polyurethane (Electrolube UR5041) considered in [16

16. S. Campopiano, A. Cutolo, A. Cusano, M. Giordano, G. Parente, G. Lanza, and A. Laudati, “Underwater acoustic sensors based on fiber Bragg gratings,” Sensors (Basel Switzerland) 9(6), 4446–4454 (2009). [CrossRef]

]. The structure is excited by an acoustic plane wave normally-incident with respect to the cylinder axis. Numerical simulations are performed within the frequency range 500 Hz to 30 kHz (with steps of at least 1 kHz) of interest for typical SONAR applications. For all observables shown below, we also compute, as a reference, the zero-frequency values via the hydrostatic model [12

12. D. J. Hill and G. A. Cranch, “Gain in hydrostatic pressure sensitivity of coated fiber Bragg grating,” Electron. Lett. 35(15), 1268–1269 (1999). [CrossRef]

,14

14. G. B. Hocker, “Fiber optic acoustic sensors with composite structure: an analysis,” Appl. Opt. 18(21), 3679–3683 (1979). [CrossRef] [PubMed]

].

Figure 3(a)
Fig. 3 (a) Spectra of the strain components (parameters detailed in the text). (b), (c) Magnified details along the strain and frequency axes, respectively.
shows the simulation results in terms of strain components along the x, y, and z axes over the whole frequency range of interest. Four sharp peaks are clearly visible in the strain components at frequencies 5.6, 14.8, 21.8 and 28.7 kHz. For better visualization of the background response (away from resonances) that is hidden by the strength of the resonant peaks, we show in Fig. 3(b) a magnified detail with the strain scale saturated. Similarly, in Fig. 3(c), we show a magnified detail around 14.8kHz, so as to illustrate with a finer sampling (down to 1Hz) the line-shape of the resonance. All the observed resonances clearly resemble the Fano line-shape and may be accurately fitted with a Fano-type model [23

23. U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124(6), 1866–1878 (1961). [CrossRef]

]. Recalling that Fano resonances stem from the interference between a discrete state with a continuum of states [23

23. U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124(6), 1866–1878 (1961). [CrossRef]

], we can infer that the resonances observed are attributable to the interaction between one of the vibration modes of the sensor and the impinging acoustic wave.

As an illustration of the opto-acoustic response of the sensor to the impinging plane wave, Fig. 4
Fig. 4 Pressure distribution in water and z-strain distribution on the cylinder surface, for different frequencies of the acoustic wave (see also the animation Media 1), away from resonances: (a) 10 kHz, (b) 20 kHz, (c) 30 kHz, and around the second resonance: (d) 14.792 and (e) 14.800kHz
shows the pressure distribution in water (on the sphere boundary) and the z-strain distribution on the cylinder surface, for different frequencies (10, 20 and 30 kHz) away from resonances. As evident from Figs. 4(a-c), the cylindrical sensor responds to the impinging plane wave through a mechanical deformation, according to its elastic properties (see also the animation Media 1). The resulting strain at the FBG location determines a Bragg wavelength shift according to Eq. (12).

The sensitivity of this basic transduction principle is strongly enhanced at the resonant frequencies, where a Fano-type strain response occurs at the FBG location. In Fig. 4(d-e), we show the pressure distribution in water and the z-strain distribution on the cylinder surface around the second resonance (14.792 and 14.800kHz), with color scales suitably saturated so as to allow correct visualization of all distributions. From the pressure distribution, it can be observed the outgoing pressure radiated by the excited resonance (the discrete state) which, interfering with the impinging plane wave (the continuum), generates the Fano-resonance phenomenon.

Figures 5(a)
Fig. 5 (a) Sensitivity (cf. Eq. (13)) and (b) sensitivity gain (cf. Eq. (14)) spectra. The inset in (a) highlights the Fano-type line-shape of the sensitivity around the resonant frequencies.
and 5(b) show the sensitivity (cf. Eq. (13)) and corresponding sensitivity gain (cf. Eq. (14)), respectively, as a function of frequency, computed on the basis of the εx, εy, and εz strain distributions obtained from the simulations.

As expectable, at the resonant frequencies (5.6, 14.8, 21.8 and 28.7 kHz), the sensitivity also exhibits a resonant behavior, which retains the Fano-type line-shape (see the inset in Fig. 5(a)). The sensitivity gain in Fig. 5(b) is characterized by peaks of amplitude up to 110 dB, superimposed onto a ~50dB background which is slowly decreasing with frequency.

Note that, in Fig. 5, the sensitivity value at zero-frequency computed via the hydrostatic model [12

12. D. J. Hill and G. A. Cranch, “Gain in hydrostatic pressure sensitivity of coated fiber Bragg grating,” Electron. Lett. 35(15), 1268–1269 (1999). [CrossRef]

,14

14. G. B. Hocker, “Fiber optic acoustic sensors with composite structure: an analysis,” Appl. Opt. 18(21), 3679–3683 (1979). [CrossRef] [PubMed]

] is in very good agreement with our low-frequency predictions.

It is also worth noting that the high sensitivity values observed in Fig. 5 at the resonant frequencies strongly rely on the assumption of zero damping in the composite cylindrical structure, for which an excited resonance yields a lossless vibration. Moreover, the resonances are very narrow (e.g., the sensitivity gain in Fig. 5(b) exceeds 80dB over bandwidths narrower than 0.5kHz).

To sum up, the numerical results above indicate that the ring-shaped coating is capable of significantly improving the sensitivity of the optical hydrophone, over the whole investigated frequency range, when compared with an uncoated FBG. Furthermore, the hydrophone sensitivity spectrum also exhibits characteristic resonant peaks, which yield a further strong enhancement.

4.1.2 Modal analysis

In particular, we computed the vibration modes of the composite cylindrical structure under investigation up to 30kHz. Figure 6
Fig. 6 Deformed geometry and z-strain distribution (in color scale) of the resonant modes.
shows the only nonzero (z) component of the longitudinal resonant modes, visualized in terms of deformed shape (retrievable from the displacement vector) and strain distribution (in color scale). More specifically, the composite cylindrical structure of the sensor supports four longitudinal vibration modes (at frequencies 5.7, 15, 21.9 and 27.9kHz) characterized by even symmetry along the z-axis, and three longitudinal vibration modes (at frequencies 10.8, 18.7 and 25kHz) with odd symmetry along the z-axis. It is interesting to note that the sensitivity peaks observed in Fig. 5 occur at frequencies associated to the even modes only.

As a concluding remark on this analysis, it should be noted that other vibration modes are supported by the composite structure (i.e., bending modes at frequencies 0.4, 1.0, 1.8, 2.9, 4.3, 5.7, 7.3, 9.0, 10.8, 12.7, 14.6, 16.5, 18.5, 20.5, 22.5, 24.5, 26.6 and 28.6kHz), which, however, do not give rise to sensitivity enhancements because they have intrinsically weaker longitudinal strain components with respect to the radial ones, and the Bragg wavelength is less sensitive to radial strain components with respect to the longitudinal one.

Moreover, for different physical and geometrical parametric configurations, other modes (of same and different kinds) may occur in the frequency range considered (e.g., transversal modes may fall within the range if larger radii are assumed). Nevertheless, an exhaustive study of the natural frequencies of free-standing (and composite) elastic cylinders [26

26. G. M. L. Gladwell and D. K. Vijay, “Natural frequencies of free finite length circular cylinders,” J. Sound Vibrat. 42(3), 387–397 (1975). [CrossRef]

] is beyond the scope of this paper, which is instead focused on the effects induced by the excitation of such modes in the sensing performance.

4.2 Effects of the coating properties on the sensing performance

4.2.1 Size

We now move on to exploring the influence of the geometrical parameters of the structure (height and diameter) on the hydrophone frequency response, by maintaining the coating physical parameters fixed (see Table 2).

In Fig. 8(b), with focus on the first resonance, we also show the effects of changing the coating radius (RC=1.25, 2.5 and 5mm). By increasing the coating height, a decrease of the resonant frequency is still observed, and the slowest decrease is obtained for the largest coating radius.

Overall, regardless the coating radius, an increase of the height yields a decrease of the resonant frequencies, which eventually saturates. Consequently, the height of the ring-shaped coating may be a useful parameter for tuning the gain sensitivity peaks without affecting meaningfully the background sensitivity.

All the variations of the resonant frequencies with the geometrical features of the ring-shaped coating were found to be in substantial agreement with the free vibration modes variations of a finite-length elastic composite cylinder [26

26. G. M. L. Gladwell and D. K. Vijay, “Natural frequencies of free finite length circular cylinders,” J. Sound Vibrat. 42(3), 387–397 (1975). [CrossRef]

].

Moreover, increasing the coating radius has two further main effects on the sensor performance: i) the enhancement of the background sensitivity at low frequencies, and ii) the progressive reduction of the background sensitivity at high frequencies.

In connection with the former effect, observing the low-frequency (below 3kHz) regions of the spectra in Fig. 9, it is evident that increasing the coating radius yields a significant enhancement of the sensitivity gain, up to a saturation value of about 60dB. To better highlight this aspect, in Fig. 11(a)
Fig. 11 (a) Sensitivity gain at first local minimum as a function of coating radius. (b) Sensitivity gain spectra around the first local minimum, for different coating radii.
we show the minimum values of the sensitivity gain between the first and second peaks, for various coating radii (up to RC/Rf=60). Basically, the sensitivity gain background increases with the coating radius until it reaches a constant value. This is in agreement with the hydrostatic model exploited in [12

12. D. J. Hill and G. A. Cranch, “Gain in hydrostatic pressure sensitivity of coated fiber Bragg grating,” Electron. Lett. 35(15), 1268–1269 (1999). [CrossRef]

,14

14. G. B. Hocker, “Fiber optic acoustic sensors with composite structure: an analysis,” Appl. Opt. 18(21), 3679–3683 (1979). [CrossRef] [PubMed]

], and may be attributed to the role played by the ring-shaped coating in contrasting the stiffness of the optical fiber glass.

As for the latter effect, looking at the high-frequency (e.g., above 20 kHz, for RC/Rf=40) regions of the spectra in Fig. 9, an overall deterioration of the sensitivity gain can be observed, in spite of the appearance of additional resonances. In this framework, it is worth mentioning the appearance of transversal resonances (e.g., at 26.5 and 27.7 kHz for RC/Rf=30, and at 22.1 and 24.2kHz for RC/Rf=40) which, however, do not yield meaningful sensitivity enhancements. To highlight the deterioration of the sensitivity gain background, in Fig. 11(b) we show the spectra (extracted from Fig. 9) around the first local minima, from which a low-pass behavior is clearly observed, with a cut-off frequency that decreases when the coating radius increases, and the previously shown low-frequency gain level increasing with the coating radius. Note that such low-pass behavior could not be predicted by the hydrostatic model [12

12. D. J. Hill and G. A. Cranch, “Gain in hydrostatic pressure sensitivity of coated fiber Bragg grating,” Electron. Lett. 35(15), 1268–1269 (1999). [CrossRef]

,14

14. G. B. Hocker, “Fiber optic acoustic sensors with composite structure: an analysis,” Appl. Opt. 18(21), 3679–3683 (1979). [CrossRef] [PubMed]

], and is attributable to diffraction effects occurring when the acoustic wavelength approaches the cylinder diameter.

4.2.2 Mechanical properties

In order to explore the effects of the coating elastic properties, we compared, for a given coating size (h=4cm and Rc=1 .25mm), the sensitivities obtained by changing its Young’s modulus E, Poisson’s ratio ν, and density ρ. The values used in the analysis are consistent with (but not strictly limited to) the nominal properties of certain specific polymeric materials (thermosetting polyurethanes), like that considered in [16

16. S. Campopiano, A. Cutolo, A. Cusano, M. Giordano, G. Parente, G. Lanza, and A. Laudati, “Underwater acoustic sensors based on fiber Bragg gratings,” Sensors (Basel Switzerland) 9(6), 4446–4454 (2009). [CrossRef]

], which are particularly suited to underwater applications in view of their adhesion (on the fiber glass) and waterproof properties.

We start by considering two basic materials: the former (identical to that considered so far, cf. Table 2) is characterized by E=78MPa, ν=0.3, and ρ=1180 kg/m3; the latter features the same Poisson’s ratio, but E=970MPa and ρ=1070 kg/m3 (consistent with the thermosetting polyurethane Electrolube UR5528). Moreover, in order to separate the effects of the Young’s modulus variation from those due to the density variation, we also consider other two sets of physical parameters (not corresponding to specific existing materials) featuring E=500MPa, ν=0.3, ρ=1070kg/m3, and E=500MPa, ν=0.3, ρ=1180kg/m3, respectively. Figure 12(a)
Fig. 12 Sensitivity gain spectra, by varying (a) the coating Young’s modulus E and density ρ (for ν=0.3), and (b) the coating Poisson’s ratio ν (for E=78MPa and ρ=1180kg/m3).
shows the sensitivity-gain spectra pertaining to these four materials, from which it can be clearly seen that increasing the Young’s modulus yields a desensitization of the hydrophone, accompanied by a high-frequency shift of the peaks. Much less significant are the effects of the density variations, limited to a slight sensitivity increase (for decreasing density) and frequency shift of the resonant peaks.

Finally, Fig. 12(b) illustrates the effects of the Poisson’s ratio variations (from 0.3 to 0.4), for fixed E=78MPa and ρ=1180 kg/m3, which basically amount to a deterioration (for increasing values of ν) of the sensitivity-gain background (away from resonances), and a slight frequency shift of the resonant peaks.

Overall, the numerical results indicate that sensitivity enhancements may be obtained by using a ring-shaped coating characterized by low values of the Young’s modulus, Poisson’s ratio, and density. With reference to the Young’s modulus and Poisson’s ratio, this is in agreement with the hydrostatic analysis [12

12. D. J. Hill and G. A. Cranch, “Gain in hydrostatic pressure sensitivity of coated fiber Bragg grating,” Electron. Lett. 35(15), 1268–1269 (1999). [CrossRef]

,14

14. G. B. Hocker, “Fiber optic acoustic sensors with composite structure: an analysis,” Appl. Opt. 18(21), 3679–3683 (1979). [CrossRef] [PubMed]

]. Basically, decreasing the Young’s modulus and/or the Poisson’s ratio reduces the bulk modulus K of the ring-shaped coating (given by K=E/[3(12ν)], for homogeneous, isotropic, linear elastic materials) which, for a given acoustic pressure, yields in turn an increase of the coating compression, and hence an enhancement of the strain components acting on the FBG. Further insight may be gained by considering the characteristic acoustic impedance Z of the material composing the ring- shaped coating, defined as [18

18. F. Ihlenburg, Finite Element Analysis of Acoustic Scattering (Springer, 1998).

]

Z=ρ'cC=ρ'Kρ'=ρ'E3(1-2ν),
(15)

where cc is the bulk speed of an elastic wave in a linearly-elastic solid. It can readily be noticed that the sensitivity optimization criteria emerged from the parametric analysis are consistent with a minimization of the coating impedance. It is also worth noting that such minimization implies an increase of the impedance mismatch with the surrounding water, which is detrimental in terms of increased signal reflection, but is largely compensated by the increase of the strain energy endowed to the FBG.

4.2.3 Structural damping

All the results discussed so far are obtained considering lossless materials. In what follows, we consider the effects of damping in both the glass fiber and the coating material. The structural damping is expressed in terms of a loss factor η defined as the ratio between the imaginary and real parts of the complex Young’s modulus E [27

27. C. F. Beards, Structural Vibration Analysis and Damping (Butterworth Heinemann, 1996).

]. Following [27

27. C. F. Beards, Structural Vibration Analysis and Damping (Butterworth Heinemann, 1996).

], for the optical fiber, such loss factor assumed to be η=0.002. Figure 13
Fig. 13 Effects of the structural damping on the sensitivity gain spectrum, for a ring-shaped coating featuring ring-shaped coating featuring RC/Rf=20, h=4cm, ν=0.3, ρ=1180kg/m3, Re(E)=78MPa, and η=0.1.
illustrates the effects of damping with reference to a ring-shaped coating featuring RC/Rf=20, h=4cm, ν=0.3, ρ=1180kg/m3, Re(E)=78MPa, and η=0.1.

As expectable, it can be noted that the damping affects primarily the resonances (especially those at higher frequencies), yielding a strong sensitivity deterioration, while the baseline sensitivity gain turns out to be essentially unaffected. Since our model does not take into account the frequency-dependence of the coating elastic properties, the stronger deterioration effects observed at higher frequencies may be attributed to the corresponding longer acoustic paths in the coating. The effect of damping on the sensitivity must be carefully taken into account in the choice of the coating material, since a low Young’s modulus (useful to increase the sensitivity, cf. Figure 12(a)) is often competing with a low damping, because “soft” materials typically exhibit high damping.

4.3 Directivity

We conclude our parametric studies by considering the effects of oblique incidence, with specific reference to a parameter configuration featuring RC/Rf=20, h=3cm, ν=0.3, ρ=1180kg/m3, E=78MPa, and no damping. In view of the cylindrical symmetry of the structure, we only consider variations of the angle θ between the incidence direction and the x-y plane. Thus, θ=0 represents the normal-incidence case considered so far, while for θ=π/2 the acoustic wave travels parallel to the cylinder axis.

5. Preliminary experimental validation

In order to validate the numerical modeling of the optical hydrophone, we carried out the experimental characterization of several coated FBGs in an instrumented water tank [29

29. M. Moccia, M. Pisco, A. Cutolo, V. Galdi, and A. Cusano, “Resonant hydrophones based on coated fiber Bragg gratings. Part I: numerical analysis,” Proc. SPIE 7753, 775384, 775384-4 (2011). [CrossRef]

,30

30. M. Moccia, M. Consales, A. Iadicicco, M. Pisco, M. Giordano, A. Cutolo, and A. Cusano, “Resonant hydrophones based on coated fiber Bragg gratings. Part II: experimental analysis,” Proc. SPIE 7753, 775383, 775383-4 (2011). [CrossRef]

].

Here we report the preliminary results of the experimental characterizations in terms of sensitivity gain for two sensors, designed to operate efficiently at “low” frequencies (<15kHz) by means of Damival® E 13650 [31

31. “Damival resins: polyurethane and epoxy systems for potting and encapsulation,” www.sibel.bg/upl_doc/DAMIVAL_E.pdf.

] coating (a polyurethane resin) and at “high” frequencies (15-30kHz) by means of Araldite® DBF [32] coating (an epoxy adhesive resin), respectively.

In particular, the optical hydrophones with Damival® and Araldite® are characterized both by a diameter of 5mm (RC/Rf=40), and a height of 3cm and 3.8cm, respectively.

Details on the setup for the experimental characterization can be found elsewhere [29

29. M. Moccia, M. Pisco, A. Cutolo, V. Galdi, and A. Cusano, “Resonant hydrophones based on coated fiber Bragg gratings. Part I: numerical analysis,” Proc. SPIE 7753, 775384, 775384-4 (2011). [CrossRef]

,30

30. M. Moccia, M. Consales, A. Iadicicco, M. Pisco, M. Giordano, A. Cutolo, and A. Cusano, “Resonant hydrophones based on coated fiber Bragg gratings. Part II: experimental analysis,” Proc. SPIE 7753, 775383, 775383-4 (2011). [CrossRef]

]. Basically, a train of sine-wave pulses with duration 0.5ms at increasing frequencies in the range 4-30kHz (with step of 1kHz) is generated by an acoustic source immersed in the water tank, while reference data have been retrieved using a reference PZT hydrophone [30

30. M. Moccia, M. Consales, A. Iadicicco, M. Pisco, M. Giordano, A. Cutolo, and A. Cusano, “Resonant hydrophones based on coated fiber Bragg gratings. Part II: experimental analysis,” Proc. SPIE 7753, 775383, 775383-4 (2011). [CrossRef]

]. The FBG hydrophones were placed and maintained in vertical position by means of a few gram weight. Consequently, the sound pressure was perpendicular to the fiber longitudinal axis. For each frequency, the resulting time responses of the coated FBGs sensors to the acoustic excitation were measured via a tunable laser locked to work at the edge of the FBG spectra [30

30. M. Moccia, M. Consales, A. Iadicicco, M. Pisco, M. Giordano, A. Cutolo, and A. Cusano, “Resonant hydrophones based on coated fiber Bragg gratings. Part II: experimental analysis,” Proc. SPIE 7753, 775383, 775383-4 (2011). [CrossRef]

]. From the time responses (corresponding to the acoustical sine-wave pulses), the amplitudes of optical sensor responses have been obtained through FFT analysis and used to reconstruct the sensitivity curve vs. frequency.

The obtained experimental sensitivity gains are reported in Fig. 15 (a-b)
Fig. 15 Numerical and experimental sensitivity gain of a coated FBG respect to bare fiber vs frequency (a) with the Damival ® E 13650 coating and (b) with the Araldite ® DBF coating. “Elaborated” data take into account the finite duration of the acoustic pulse
. In the same plots the corresponding numerical predictions are also shown for comparison. A good agreement between the experimental data and the numerically predicted sensitivity gains can be clearly observed. It is worth noting that the elastic properties of the polymeric coatings used to numerically reconstruct the experimental data are consistent with those found in literature for both class of materials: polyurethane resins for Damival® E 13650 and Araldite® based resins for Araldite® DBF, as observable in Table 3

Table 3. Properties of the Ring-Shaped Coatings

table-icon
View This Table
| View All Tables
. This last evidence and the good agreement observed clearly demonstrate the correctness of the proposed numerical modeling as well as its prediction capability.

The comparison primarily confirms the resonant behavior of the underwater acoustic sensor outlined by the numerical analysis, which in turn demonstrates to be able to supply physical insight in the sensor operation and at the same time to offer acceptable prediction capabilities both in terms of resonant frequencies and sensitivity values.

The disagreements between experimental and numerical data (particularly evident with the Araldite® coating) can be attributed to second order effects (physical imperfections, acoustically induced particle fluid motion, etc.), which have not been taken into account in the simulations, but that are not able to dominate the basic transduction mechanism.

A major difference between the experimental and numerical data can be found in the shape of the sensitivity gain peaks. Differently from the experimental observations, the numerical predicted Fano line shape in the sensitivity would imply a zero crossing for the sensitivity and thus a narrow dip in the sensitivity gain for each resonance (actually the dip is well observable in the numerical plots only when a fine frequency sampling is employed).

From the experimental viewpoint, these narrow spectral features cannot beobserveded due to the finite duration of a single acoustic tone (0.5ms) limiting the spectral resolution of the experimental characterization (in turn experimentally the pulse duration is limited in order to avoid the superposition of the direct wave with the reflected ones in the tank). To better explain the effect of the limited spectral resolution on the numerical predictions, in Fig. 15(a-b) we show (with the trace “elaborated”) the numerical sensitivity gain accounting for the finite duration of the acoustic pulse. It is evident in Fig. 15 that the finite time extent of the sine wave pulses smoothes the sharp spectral features by strongly deemphasizing the presence of the narrow dips and justifying the difference between numerical and experimental data in the peaks shapes when this effect is not taken into account. Finally, further analysis is currently under way to improve the correlation between numerical and experimental data.

6. Conclusions

The results from our comprehensive parametric studies also indicate that the coating height and radius may be effectively utilized in order to tune the resonant frequencies. Furthermore, larger coating radii may be beneficial in improving the low-frequency background sensitivity, but detrimental in the high-frequency region. In connection with the coating elastic properties, low values of the Young’s modulus, Poisson’s ratio, and density are desirable for enhancing the sensitivity, and the detrimental effect of structural damping on the resonant peaks needs to be carefully accounted for.

Finally, a preliminary validation of the proposed numerical analysis has been carried out through experimental data obtained using polymeric coated FBGs sensors. As matter of fact, a good agreement between the experimental characterizations and the numerically predicted sensitivity gains has been obtained, confirming the correct modeling of the hydrophone as well as its prediction capability.

Acknowledgments

We would like to acknowledge Dr. Marco Consales and Dr. Agostino Iadicicco for their kind support and active collaboration in the experimental measurements and the Whitehead Alenia Sistemi Subacquei (WASS) for the availability of the instrumented water tank.

References and links

1.

C. K. Kirkendall and A. Dandridge, “Overview of high performance fibre-optic sensing,” J. Phys. D Appl. Phys. 37(18), R197–R216 (2004). [CrossRef]

2.

E. Udd, Fiber Optic Sensors: An Introduction for Engineers and Scientists (Wiley, New York, 1990).

3.

G. Wild and S. Hinckley, “Acousto-ultrasonic optical fiber sensors: Overview and state-of-the-art,” IEEE Sens. J. 8(7), 1184–1193 (2008). [CrossRef]

4.

D. J. Hill and P. J. Nash, “In-water acoustic response of a coated DFB fibre laser sensor,” Proc. SPIE 4185, 33–36 (2000).

5.

S. Fosters, A. Tikhomirova, M. Milnesa, J. van Velzena, and G. Hardyb, “A fibre laser hydrophone,” Proc. SPIE 5855, 627–630 (2005). [CrossRef]

6.

S. Goodman, S. Foster, J. Van Velzen, and H. Mendis, “Field demonstration of a DFB fibre laser hydrophone seabed array in Jervis Bay, Australia,” Proc. SPIE 7503, 75034L1 (2009).

7.

N. Takahashi, A. Hirose, and S. Takahashi, “Underwater acoustic sensor with fiber Bragg grating,” Opt. Rev. 4(6), 691–694 (1997). [CrossRef]

8.

N. Takahashi, K. Yoshimura, S. Takahashi, and K. Imamura, “Development of an optical fiber hydrophone with fiber Bragg grating,” Ultrasonics 38(1-8), 581–585 (2000). [CrossRef] [PubMed]

9.

W. Thongnum, N. Takahashi, and S. Takahashi, “Temperature stabilization of fiber Bragg grating vibration sensor,” in OFS 2002, 15th Optical Fiber Sensors Conference Technical Digest, 2002. (2002), Vol. 1, pp. 223–226.

10.

N. Takahashi, K. Tetsumura, and S. Takahashi, “Multipoint detection of acoustical wave in water with WDM fiber Bragg grating sensor,” Proc. SPIE 3740, 270–273 (1999). [CrossRef]

11.

H. Yokosuka, S. Tanaka, and N. Takahashi, “Time-division multiplexing operation of temperature-compensated fiber Bragg grating underwater acoustic sensor array with feedback control,” Acoust. Sci. Technol. 26(5), 456–458 (2005). [CrossRef]

12.

D. J. Hill and G. A. Cranch, “Gain in hydrostatic pressure sensitivity of coated fiber Bragg grating,” Electron. Lett. 35(15), 1268–1269 (1999). [CrossRef]

13.

Y. Liu, Z. Guo, Y. Zhang, K. S. Chiang, and X. Dong, “Simultaneous pressure and temperature measurement with polymer-coated fiber Bragg grating,” Electron. Lett. 36(6), 564–566 (2000). [CrossRef]

14.

G. B. Hocker, “Fiber optic acoustic sensors with composite structure: an analysis,” Appl. Opt. 18(21), 3679–3683 (1979). [CrossRef] [PubMed]

15.

A. Cusano, S. D’Addio, A. Cutolo, S. Campopiano, M. Balbi, S. Balzarini, and M. Giordano, “Enhanced acoustic sensitivity in polymeric coated fiber Bragg grating,” Sensors Transducers 82, 1450–1457 (2007).

16.

S. Campopiano, A. Cutolo, A. Cusano, M. Giordano, G. Parente, G. Lanza, and A. Laudati, “Underwater acoustic sensors based on fiber Bragg gratings,” Sensors (Basel Switzerland) 9(6), 4446–4454 (2009). [CrossRef]

17.

L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Pergamon Press, 1987).

18.

F. Ihlenburg, Finite Element Analysis of Acoustic Scattering (Springer, 1998).

19.

S. Timoshenko and J. N. Goodier, Theory of Elasticity (McGraw-Hill, 1951).

20.

C. J. S. de Matos, P. Torres, L. C. G. Valente, W. Margulis, and R. Stubbe, “Fiber Bragg grating (FBG) characterization and shaping by local pressure,” J. Lightwave Technol. 19(8), 1206–1211 (2001). [CrossRef]

21.

A. Minardo, A. Cusano, R. Bernini, L. Zeni, and M. Giordano, “Response of fiber Bragg gratings to longitudinal ultrasonic waves,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52(2), 304–312 (2005). [CrossRef] [PubMed]

22.

COMSOL Multiphysics, User’s Guide (COMSOL AB, 2008).

23.

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124(6), 1866–1878 (1961). [CrossRef]

24.

K. Sakoda, “Symmetry, degeneracy, and uncoupled modes in two-dimensional photonic lattices,” Phys. Rev. B Condens. Matter 52(11), 7982–7986 (1995). [CrossRef] [PubMed]

25.

A. Ricciardi, I. Gallina, S. Campopiano, G. Castaldi, M. Pisco, V. Galdi, and A. Cusano, “Guided resonances in photonic quasicrystals,” Opt. Express 17(8), 6335–6346 (2009). [PubMed]

26.

G. M. L. Gladwell and D. K. Vijay, “Natural frequencies of free finite length circular cylinders,” J. Sound Vibrat. 42(3), 387–397 (1975). [CrossRef]

27.

C. F. Beards, Structural Vibration Analysis and Damping (Butterworth Heinemann, 1996).

28.

A. Guran, J. Ripoche, and F. Ziegler, Acoustic Interactions with Submerged Elastic Structures (World Scientific, 1996).

29.

M. Moccia, M. Pisco, A. Cutolo, V. Galdi, and A. Cusano, “Resonant hydrophones based on coated fiber Bragg gratings. Part I: numerical analysis,” Proc. SPIE 7753, 775384, 775384-4 (2011). [CrossRef]

30.

M. Moccia, M. Consales, A. Iadicicco, M. Pisco, M. Giordano, A. Cutolo, and A. Cusano, “Resonant hydrophones based on coated fiber Bragg gratings. Part II: experimental analysis,” Proc. SPIE 7753, 775383, 775383-4 (2011). [CrossRef]

31.

“Damival resins: polyurethane and epoxy systems for potting and encapsulation,” www.sibel.bg/upl_doc/DAMIVAL_E.pdf.

32.

“Huntsman advanced materials,” www.huntsmanservice.com/Product_Finder/ui/PSDetailCompositeList.do?pInfoSBUId=9&PCId=1663

33.

“eFunda polymer material properties,”http://www.efunda.com/materials/polymers/properties/polymer_datasheet.cfm?MajorID=PU&MinorID=1.

34.

T. Pritz, “The Poisson’s loss factor of solid viscoelastic materials,” J. Sound Vibrat. 306(3-5), 790–802 (2007). [CrossRef]

35.

A. Sorathia, “Polyurethane-epoxy interpenetrating polymer network acoustic damping material,” U.S. Patent No. 5,331,062 (19 July 1994).

36.

F. A. Khayyat and P. Stanley, “The dependence of the mechanical, physical and optical properties of Araldite CT200/HT 907 on temperature over the range −10°C to 70°C,” J. Phys. D Appl. Phys. 11(8), 1237–1247 (1978). [CrossRef]

37.

F. J. P. Chaves, “Application of adhesive bonding in PVC windows,” MSc Thesis (University of Porto, Portugal, 2005), http://www.scribd.com/doc/37203644/MSc-Thesis.

38.

Bodo Möller Chemie, “Technical data: PUR and epoxy” http://www.bm-chemie.de/content/de/download/pub/Elektrogiessharze_12_03_2009.pdf

OCIS Codes
(060.2370) Fiber optics and optical communications : Fiber optics sensors
(230.1040) Optical devices : Acousto-optical devices
(060.3735) Fiber optics and optical communications : Fiber Bragg gratings
(280.4788) Remote sensing and sensors : Optical sensing and sensors

ToC Category:
Sensors

History
Original Manuscript: June 30, 2011
Revised Manuscript: August 18, 2011
Manuscript Accepted: August 22, 2011
Published: September 13, 2011

Citation
Massimo Moccia, Marco Pisco, Antonello Cutolo, Vincenzo Galdi, Pierantonio Bevilacqua, and Andrea Cusano, "Opto-acoustic behavior of coated fiber Bragg gratings," Opt. Express 19, 18842-18860 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-20-18842


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. C. K. Kirkendall and A. Dandridge, “Overview of high performance fibre-optic sensing,” J. Phys. D Appl. Phys.37(18), R197–R216 (2004). [CrossRef]
  2. E. Udd, Fiber Optic Sensors: An Introduction for Engineers and Scientists (Wiley, New York, 1990).
  3. G. Wild and S. Hinckley, “Acousto-ultrasonic optical fiber sensors: Overview and state-of-the-art,” IEEE Sens. J.8(7), 1184–1193 (2008). [CrossRef]
  4. D. J. Hill and P. J. Nash, “In-water acoustic response of a coated DFB fibre laser sensor,” Proc. SPIE4185, 33–36 (2000).
  5. S. Fosters, A. Tikhomirova, M. Milnesa, J. van Velzena, and G. Hardyb, “A fibre laser hydrophone,” Proc. SPIE5855, 627–630 (2005). [CrossRef]
  6. S. Goodman, S. Foster, J. Van Velzen, and H. Mendis, “Field demonstration of a DFB fibre laser hydrophone seabed array in Jervis Bay, Australia,” Proc. SPIE7503, 75034L1 (2009).
  7. N. Takahashi, A. Hirose, and S. Takahashi, “Underwater acoustic sensor with fiber Bragg grating,” Opt. Rev.4(6), 691–694 (1997). [CrossRef]
  8. N. Takahashi, K. Yoshimura, S. Takahashi, and K. Imamura, “Development of an optical fiber hydrophone with fiber Bragg grating,” Ultrasonics38(1-8), 581–585 (2000). [CrossRef] [PubMed]
  9. W. Thongnum, N. Takahashi, and S. Takahashi, “Temperature stabilization of fiber Bragg grating vibration sensor,” in OFS 2002, 15th Optical Fiber Sensors Conference Technical Digest, 2002. (2002), Vol. 1, pp. 223–226.
  10. N. Takahashi, K. Tetsumura, and S. Takahashi, “Multipoint detection of acoustical wave in water with WDM fiber Bragg grating sensor,” Proc. SPIE3740, 270–273 (1999). [CrossRef]
  11. H. Yokosuka, S. Tanaka, and N. Takahashi, “Time-division multiplexing operation of temperature-compensated fiber Bragg grating underwater acoustic sensor array with feedback control,” Acoust. Sci. Technol.26(5), 456–458 (2005). [CrossRef]
  12. D. J. Hill and G. A. Cranch, “Gain in hydrostatic pressure sensitivity of coated fiber Bragg grating,” Electron. Lett.35(15), 1268–1269 (1999). [CrossRef]
  13. Y. Liu, Z. Guo, Y. Zhang, K. S. Chiang, and X. Dong, “Simultaneous pressure and temperature measurement with polymer-coated fiber Bragg grating,” Electron. Lett.36(6), 564–566 (2000). [CrossRef]
  14. G. B. Hocker, “Fiber optic acoustic sensors with composite structure: an analysis,” Appl. Opt.18(21), 3679–3683 (1979). [CrossRef] [PubMed]
  15. A. Cusano, S. D’Addio, A. Cutolo, S. Campopiano, M. Balbi, S. Balzarini, and M. Giordano, “Enhanced acoustic sensitivity in polymeric coated fiber Bragg grating,” Sensors Transducers82, 1450–1457 (2007).
  16. S. Campopiano, A. Cutolo, A. Cusano, M. Giordano, G. Parente, G. Lanza, and A. Laudati, “Underwater acoustic sensors based on fiber Bragg gratings,” Sensors (Basel Switzerland)9(6), 4446–4454 (2009). [CrossRef]
  17. L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Pergamon Press, 1987).
  18. F. Ihlenburg, Finite Element Analysis of Acoustic Scattering (Springer, 1998).
  19. S. Timoshenko and J. N. Goodier, Theory of Elasticity (McGraw-Hill, 1951).
  20. C. J. S. de Matos, P. Torres, L. C. G. Valente, W. Margulis, and R. Stubbe, “Fiber Bragg grating (FBG) characterization and shaping by local pressure,” J. Lightwave Technol.19(8), 1206–1211 (2001). [CrossRef]
  21. A. Minardo, A. Cusano, R. Bernini, L. Zeni, and M. Giordano, “Response of fiber Bragg gratings to longitudinal ultrasonic waves,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control52(2), 304–312 (2005). [CrossRef] [PubMed]
  22. COMSOL Multiphysics, User’s Guide (COMSOL AB, 2008).
  23. U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev.124(6), 1866–1878 (1961). [CrossRef]
  24. K. Sakoda, “Symmetry, degeneracy, and uncoupled modes in two-dimensional photonic lattices,” Phys. Rev. B Condens. Matter52(11), 7982–7986 (1995). [CrossRef] [PubMed]
  25. A. Ricciardi, I. Gallina, S. Campopiano, G. Castaldi, M. Pisco, V. Galdi, and A. Cusano, “Guided resonances in photonic quasicrystals,” Opt. Express17(8), 6335–6346 (2009). [PubMed]
  26. G. M. L. Gladwell and D. K. Vijay, “Natural frequencies of free finite length circular cylinders,” J. Sound Vibrat.42(3), 387–397 (1975). [CrossRef]
  27. C. F. Beards, Structural Vibration Analysis and Damping (Butterworth Heinemann, 1996).
  28. A. Guran, J. Ripoche, and F. Ziegler, Acoustic Interactions with Submerged Elastic Structures (World Scientific, 1996).
  29. M. Moccia, M. Pisco, A. Cutolo, V. Galdi, and A. Cusano, “Resonant hydrophones based on coated fiber Bragg gratings. Part I: numerical analysis,” Proc. SPIE7753, 775384, 775384-4 (2011). [CrossRef]
  30. M. Moccia, M. Consales, A. Iadicicco, M. Pisco, M. Giordano, A. Cutolo, and A. Cusano, “Resonant hydrophones based on coated fiber Bragg gratings. Part II: experimental analysis,” Proc. SPIE7753, 775383, 775383-4 (2011). [CrossRef]
  31. “Damival resins: polyurethane and epoxy systems for potting and encapsulation,” www.sibel.bg/upl_doc/DAMIVAL_E.pdf .
  32. “Huntsman advanced materials,” www.huntsmanservice.com/Product_Finder/ui/PSDetailCompositeList.do?pInfoSBUId=9&PCId=1663
  33. “eFunda polymer material properties,” http://www.efunda.com/materials/polymers/properties/polymer_datasheet.cfm?MajorID=PU&MinorID=1 .
  34. T. Pritz, “The Poisson’s loss factor of solid viscoelastic materials,” J. Sound Vibrat.306(3-5), 790–802 (2007). [CrossRef]
  35. A. Sorathia, “Polyurethane-epoxy interpenetrating polymer network acoustic damping material,” U.S. Patent No. 5,331,062 (19 July 1994).
  36. F. A. Khayyat and P. Stanley, “The dependence of the mechanical, physical and optical properties of Araldite CT200/HT 907 on temperature over the range −10°C to 70°C,” J. Phys. D Appl. Phys.11(8), 1237–1247 (1978). [CrossRef]
  37. F. J. P. Chaves, “Application of adhesive bonding in PVC windows,” MSc Thesis (University of Porto, Portugal, 2005), http://www.scribd.com/doc/37203644/MSc-Thesis .
  38. Bodo Möller Chemie, “Technical data: PUR and epoxy” http://www.bm-chemie.de/content/de/download/pub/Elektrogiessharze_12_03_2009.pdf

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.

Supplementary Material


» Media 1: MPG (1400 KB)     

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited