sensors
Article Corrugated-Diaphragm Based Fiber Laser Hydrophone with Sub-100 µPa/Hz1/2 Resolution
Wen-Zhao Yang, Long Jin *, Yi-Zhi Liang, Jun Ma and Bai-Ou Guan Guangdong Provincial Key Laboratory of Optical Fiber Sensing and Communications, Institute of Photonics Technology, Jinan University, Guangzhou 510632, China; [email protected] (W.-Z.Y.); [email protected] (Y.-Z.L.); [email protected] (J.M.); [email protected] (B.-O.G.) * Correspondence: [email protected]; Tel.: +86-020-8522-1606
Academic Editors: George Rodriguez, Joseba Zubia and Paulo S. André Received: 18 April 2017; Accepted: 23 May 2017; Published: 26 May 2017
Abstract: In this work, a beat-frequency encoded fiber laser hydrophone is developed for high-resolution acoustic detection by using an elastic corrugated diaphragm. The diaphragm is center-supported by the fiber. Incident acoustic waves deform the diaphragm and induce a concentrated lateral load on the laser cavity. The acoustically induced perturbation changes local optical phases and frequency-modulates the radio-frequency beat signal between two orthogonal lasing modes of the cavity. Theoretical analysis reveals that a higher corrugation-depth/thickness ratio or larger diaphragm area can provide higher transduction efficiency. The experimentally achieved average sensitivity in beat-frequency variation is 185.7 kHz/Pa over a bandwidth of 1 kHz. The detection capability can be enhanced by shortening the cavity length to enhance the signal-to-noise ratio. The minimum detectable acoustic pressure reaches 74 µPa/Hz1/2 at 1 kHz, which is comparable to the zeroth order sea noise.
Keywords: fiber laser sensors; acoustic sensors; fiber optic hydrophones; fiber Bragg grating
1. Introduction Fiber optic hydrophones have been developed to detect underwater acoustic waves for engineering and defense applications. Compared to their piezoelectric counterparts, fiber optic hydrophones have exhibited high sensitivity and immunity to electromagnetic interference. Their multiplexing capability has been improved by using fiber Bragg gratings and fiber lasers as sensing elements [1–4]. A number of sensor configurations have been demonstrated and optimized for better detection capability. The implementation of interferometric fiber optic hydrophones relies on the translation of acoustic pressure into a change in optical phase difference between the sensing and reference arms [4]. Recently, the responsivity has been greatly enhanced by using a hollow-core photonic bandgap fiber with a high air-filling ratio in transverse geometry as a sensing fiber [5]. In addition, fiber-tip Fabry-Perot cavities based on deformable diaphragms can be utilized as photonic hydrophones. The diaphragms can be made of metal nanolayers [6,7], photonic crystals [8,9], and even mono- or multi-layer graphenes [10]. The diaphragms deform and thus change the round-trip phase in response to acoustic waves. The noise-equivalent-acoustic pressure (NEAP) can reach µPa/Hz1/2 level, taking advantage of the highly deformable nature of the diaphragms. A fiber laser has been exploited as a hydrophone by measuring its lasing frequency variation as a result of acoustically induced longitudinal strain [11]. The frequency change can be demodulated with an imbalanced interferometer with high resolution. As a result, the pressure sensitivity at 1 kHz is typically 58.0 dB re µPa/Hz1/2, corresponding to a minimum detectable acoustic pressure of 800 µPa [12]. Further sensitivity enhancement has been achieved by using a hollow rugby-ball-like transducer [13].
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Different from the single-frequency ones, a fiber laser sensor can also work in a beat-frequency encoding manner, that is, the x- and y- polarized lasing modes yield a beat signal whose frequency can shift in response to external perturbations [14–16]. This manner reserves multiplexing capability and the sensors can be cascaded to form an array [17]. The radio-frequency (RF) beat signal can be demodulated with methods that have been used in radio and microwave systems. This drift of carrier signal does not affect the extraction of the fast-varying signal and, therefore, the sensor offers inherent immunity to environmental perturbations. The beat-frequency encoded fiber laser has been used for underwater acoustic detection, as described in [14], but its detection capability was not fully exploited. In this work, we successfully pushed the detection limit to sub 100 µPa/Hz1/2 level. A corrugated diaphragm is used to concentrate uniform acoustic pressure to a point load on the laser cavity and induces optical response in beat-frequency variation. Experiment results show that the average acoustic sensitivity is 185.7 kHz/Pa with a working bandwidth of about 1 kHz. Sensors with shorter laser cavities can present better detection capability to a point load, due to a higher sensitivity-to-noise ratio. As a result, the detection limit at 1 kHz reaches 74 µPa/Hz1/2, which is comparable to the zeroth order sea noise.
2. Working Principle The sensing element is a dual-polarization-mode fiber laser, fabricated by photoinscribing two wavelength-matched Bragg gratings in a single mode Er-doped optical fiber (M-12, Fibercore, Southampton, UK) to form a Fabry-Perot cavity. The fiber has a cutoff wavelength at around 935 nm and an absorption of 12 dB/m at 980 nm. The reflective wavelength of each grating is located at 1530 nm. The grating lengths are 3.5 and 4 mm, respectively. The coupling strength of each grating is higher than 25 dB (99.7% in reflectivity) to provide strong optical feedbacks for lasing oscillation. The output power of the laser is typically 100 µW with a pump power of 200 mW. The grating separation Ls is less than 8 mm in our experiment to obtain single-longitudinal mode output. With the injection of pump light at 980 nm, such a cavity intrinsically emits two orthogonal polarization lasing modes at frequencies νx and νy, respectively. The beat frequency can be expressed by ∆ν = νx − νy = cB/n0 λ, where B represents the fiber birefringence, c is the speed of light in vacuum, n0 is the average effective modal index, and λ denotes the lasing wavelength. Acoustic pressure is translated into birefringence change, which induces a beat-frequency variation. The beat signal is mixed with two local RF signals with 90 degree phase offset. This down-conversion treatment generates I/Q data which depicts the phase of the beat signal [18]. The frequency variation is obtained by taking a derivation of the phase change over time. Figure1 shows the schematic of the present sensor. An elastic corrugated diaphragm is selected to effectively translate the acoustic wave into a lateral load on the fiber. This kind of diaphragm has been widely used as a basic pressure sensitive element in engineering applications. The diaphragm has a circularly symmetrical geometry with three corrugation periods along the radial direction. As shows in Figure1a, the diaphragm has a point contact with the optical fiber at the rigid center. The diaphragm is made of beryllium bronze. It has a radius r = 19 mm, a thickness h = 0.2 mm, and a corrugation depth of H = 2 mm. Figure1b,c demonstrates side views of the sensor package. The fiber laser is fixed in a cylindrical base and a metal block is used to support the fiber to give a pre-charge for better stability. Figure1d shows the photograph of the sensor package. Sensors 2017, 17, 1219 3 of 9 Sensors 2017, 17, 1219 3 of 9
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Figure 1. (a) Schematic of the radial profile of the elastic corrugated diaphragm and the sensing Figure 1. (a) Schematic of the radial profile of the elastic corrugated diaphragm and the sensing element, i.e., the fiber grating laser. The laser is placed beneath and in contact with the rigid center of element, i.e., the fiber grating laser. The laser is placed beneath and in contact with the rigid center of Figurethe diaphragm. 1. (a) Schematic The diaphragm of the radial translates profile applied of the acoustic elastic pressure corrugated into diaphragm a lateral load and on the lasersensing via the diaphragm. The diaphragm translates applied acoustic pressure into a lateral load on the laser element,point contact; i.e., the (b )fiber Sectional grating view laser. (y-z The plane) laser of is the pl packagedaced beneath sensor; and ( cin) Sectionalcontact with view the (x-z rigid plane) center of theof via point contact; (b) Sectional view (y-z plane) of the packaged sensor; (c) Sectional view (x-z plane) thepackaged diaphragm. sensor; The (d )diaphragm Photograph translates of the packaged applied sensor. acoustic pressure into a lateral load on the laser of the packaged sensor; (d) Photograph of the packaged sensor. via point contact; (b) Sectional view (y-z plane) of the packaged sensor; (c) Sectional view (x-z plane) of the packaged sensor; (d) Photograph of the packaged sensor. AcousticAcoustic pressurepressure appliedapplied atat thethe upperupper surfacesurface tendstends toto deformdeform thethe diaphragmdiaphragm andand induceinduce aa verticalvertical deflectiondeflection at at the the rigid rigid center center (See (See Appendix AppendixA). In contrast,A). In contrast, a concentrated a concentrated force −F forcenormally − Acoustic pressure applied at the upper surface tends to deform the diaphragm and induce a appliednormally at applied the rigid at center the rigid can center induce can a deflection induce a deflectiond0 [19] d0 [19] vertical deflection at the rigid center (See Appendix A). In contrast, a concentrated force − normally applied at the rigid center can induce a deflectionr 2 d0 [19] d 0 ==− −F (1)(1) A 0′π Eh3 =− (1) ′ = 1 2 /3 1 − / ′ wherewhere A0 = (1 + q) /3 1 − µ2/q2.. Figure Figure 22 showsshows thethe numerical result result of of the the deformation deformation of of a center-supported diaphragm. In the present hydrophone, the center-supported/edge clamped wherea center-supported ′ = 1 diaphragm. /3 1 − / In . the Figure present 2 shows hydrophone, the numerical the center-supported/edge result of the deformation clamped of a diaphragm has a zero deflection as a result of the balance between the applied pressure and the center-supporteddiaphragm has a zerodiaphragm. deflection In asthe a resultpresent of hydrophone, the balance between the center-supported/edge the applied pressure clamped and the reacting force from the fiber. Combining Equations (1) and (A2), the balance between the acoustic diaphragmreacting force has from a zero the deflection fiber. Combining as a result Equations of the balance (1) and between (A2), the the balance applied between pressure the acousticand the pressure and the point load given by the fiber can be expressed as reactingpressure force and thefrom point the loadfiber. given Combining by the fiber Equations can be (1) expressed and (A2), as the balance between the acoustic pressure and the point load given by the fiber =− ∙ can be expressed as (2) F = −P·Ae (2) where = denotes the effective area =− ∙ of corrugated diaphragm, = 1 /2 3 (2) is 2 wheredefinedA eas= aΓπ transductionr denotes thefactor. effective Equation area of(2) corrugated suggests that diaphragm, the uniformΓ = (pressure1 + q)/2 (P3 is+ concentratedq) is defined where = denotes the effective area of corrugated diaphragm, = 1 /2 3 is to a point load F onto the laser cavity. The transduction efficiency scales with the area of the definedas a transduction as a transduction factor. Equation factor. Equation (2) suggests (2) suggests that the uniformthat the pressureuniform Ppressureis concentrated P is concentrated to a point diaphragm πr2 as well as the factor which is determined by the shape of the corrugation. 2 toload a pointF onto load the laserF onto cavity. the Thelaser transduction cavity. The efficiency transduction scales efficiency with the areascales of with the diaphragm the area ofπr theas diaphragmwell as the factorπr2 as Γwellwhich as the is determinedfactor which by the is shapedetermined of the by corrugation. the shape of the corrugation.
Figure 2. FEM calculated deformations of an edge-clamped/center-supported corrugated diaphragm Figurein response 2. FEM to calculated10 Pa static deformations pressure. of an edge-clamped/center-supported corrugated diaphragm Figure 2. FEM calculated deformations of an edge-clamped/center-supported corrugated diaphragm in response to 10 Pa static pressure. in response to 10 Pa static pressure. The optical response in beat-frequency change induced by the point load F can be written as [20] The optical response in beat-frequency change induced by the point load F can be written as [20] δ ∆ = ∙ (3) δ ∆ = ∙ (3)
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The optical response in beat-frequency change induced by the point load F can be written as [20] Sensors 2017, 17, 1219 cγη 4 of 9 δ(∆ν) = ·F (3) n0λ where denotes the birefringence change rate with unit linear force density (N/m), which is wheremainlyγ denotesdetermined the birefringenceby the elastic change properties rate with and unitdiameter linear forceof the density glass (N/m),fiber [21]. which The is product mainly determined / has byan theamplitude elastic propertiesof around 10 and GHz/(N/mm). diameter of theThe glass factor fiber η is [the21]. normalized The product localcγ /intensity,n0λ has L /2 an amplitude of around 10 GHz/(N/mm).c ez(z) The2 factord η is the normalized local intensity, which can R +Lc/2 2 |e(z)|dzLc /2 2 bewhich expressed can be byexpressedη = lim by −Lc/2 lim , where |e(,z where)|2 represents |e(z)| represents the laser the mode laser profile, mode profile,L is the Lc LLc0 c Lc→0 c Lc contactis the contact length length between between the fiber the and fiber the and diaphragm. the diaphragm. Here we Here assume we assume that the that laser the mode laser is mode totally is confinedtotally confined by the gratings by the andgratings has a and nearly has uniform a nearly intensity uniform over intensity the blank over region the blank between region the gratings.between This approximation is reasonable with Ls > 2 mm, considering the strong grating back coupling and the gratings. This approximation is reasonable with Ls > 2 mm, considering the strong grating back the relatively low fiber gain [20]. This approximation leads to η = 1/Ls and the optical response in coupling and the relatively low fiber gain [20]. This approximation leads to =1/ and the beat-frequency change induced by the point load F can be written as [20], optical response in beat-frequency change induced by the point load F can be written as [20], . cγ F δ ( ∆∆ v) =≐ ∙· (4)(4) n 0 λ L s
LLss,, onceonce again,again, denotesdenotes thethe gratinggrating separationseparation thatthat representsrepresents the the length length between between two two gratings. gratings. FigureFigure3 3shows shows thethe calculatedcalculated frequency response response,, based based on on Equations Equations (2), (2), (4) (4)and and (A4). (A4). The Thefirst-order first-order resona resonantnt frequency frequency is isf00f 00= =1269 1269 Hz. Hz. The The calculated calculated static static pressure pressure sensitivitysensitivity isis 164.3164.3 kHz/Pa kHz/Pa for Lss = 3 3 mm. mm. In In the calculation, the damping factor isis setset asas ξξ= = 0.04,0.04, whichwhich isis aa resultresult ofof thethe dampingdamping effecteffect of of the the vibrating vibrating diaphragm diaphragm in in water. water.
Figure 3. Calculated frequency response of fiber laser hydrophone with Ls = 3 mm and ξ = 0.04. Figure 3. Calculated frequency response of fiber laser hydrophone with Ls = 3 mm and ξ = 0.04. 3. Experimental Setup 3. Experimental Setup Figure4 shows the experimental setup of acoustic detection with a corrugated-diaphragm based Figure 4 shows the experimental setup of acoustic detection with a corrugated-diaphragm fiber laser hydrophone. The fiber laser is pumped with a 980 nm laser diode via a wavelength-division based fiber laser hydrophone. The fiber laser is pumped with a 980 nm laser diode via a multiplexer (WDM). The inner space of the transducer is filled with water for pressure balance. wavelength-division multiplexer (WDM). The inner space of the transducer is filled with water for The water tank is a cylindrical one with a height of 0.4 m and a radius of 0.16 m. The water depth is pressure balance. The water tank is a cylindrical one with a height of 0.4 m and a radius of 0.16 m. 0.36 m. A waterproof speaker (UWS-045, KHZ Corporation, Zhongshan, China) is placed at the bottom The water depth is 0.36 m. A waterproof speaker (UWS-045, KHZ Corporation, Zhongshan, China) of a water tank as an acoustic source. The distance between the acoustic source and the transducer is is placed at the bottom of a water tank as an acoustic source. The distance between the acoustic 0.2 m in our experiment. The sensor is in the far field of the acoustic source. A stable stationary wave source and the transducer is 0.2 m in our experiment. The sensor is in the far field of the acoustic field can be formed by the upward acoustic wave emitted by the source and the reflected wave by source. A stable stationary wave field can be formed by the upward acoustic wave emitted by the the surface of water. The amplitude and frequency of the acoustic wave can be adjusted by a digital source and the reflected wave by the surface of water. The amplitude and frequency of the acoustic signal generator. The acoustic frequency scans from 110 to 2010 Hz with a step of 50 Hz. A commercial wave can be adjusted by a digital signal generator. The acoustic frequency scans from 110 to 2010 Hz hydrophone (8104, Brüel&Kjær, Copenhagen, Denmark) is used for calibration. with a step of 50 Hz. A commercial hydrophone (8104, Brüel&Kjær, Copenhagen, Denmark) is used for calibration.
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Figure 4. Schematic of acoustic detection with the fiber grating laser hydrophone. WDM: Figure 4. Schematic of acoustic detection with the fiber grating laser hydrophone. WDM: FigureWavelength-division 4. Schematic multiplexer; of acoustic ISO: detection Optical isolat withor; the PD: fiber Photodetector; grating laser PC: Polarization hydrophone. controller. WDM: Wavelength-division multiplexer; ISO: Optical isolat isolator;or; PD: Photodetector; Photodetector; PC: PC: Polarization Polarization controller. controller. 4. Results and Discussion 4. Results and Discussion Figure 5a shows measured acoustically induced beat-frequency variations as a function of Figure 5a shows measured acoustically induced beat-frequency variations as a function of appliedFigure acoustic5a shows pressure. measured The acoustically result of two induced fiber beat-frequency laser hydrophones variations with as L as function= 3 and of6 appliedmm are applied acoustic pressure. The result of two fiber laser hydrophones with Ls = 3 and 6 mm are acousticexhibited. pressure. The applied The acoustic result of wave two fiberhas a laserfrequenc hydrophonesy of 800 Hz. with TheL amplituds = 3 andes 6 vary mm arein proportion exhibited. exhibited. The applied acoustic wave has a frequency of 800 Hz. The amplitudes vary in proportion Thewith applied applied acoustic acoustic wave pressure. has a frequency The measured of 800 Hz.sensitivities The amplitudes are 181 vary and in 83 proportion kHz/Pa, withrespectively, applied with applied acoustic pressure. The measured sensitivities are 181 and 83 kHz/Pa, respectively, acousticestimated pressure. from the The linear measured fits. Figure sensitivities 5b shows are 181 the and output 83 kHz/Pa, sinusoidal respectively, waveforms estimated for an fromacoustic the estimated from the linear fits. Figure 5b shows the output sinusoidal waveforms for an acoustic linearsignal fits.of 800 Figure Hz, 525b showsPa. the output sinusoidal waveforms for an acoustic signal of 800 Hz, 25 Pa. signal of 800 Hz, 25 Pa.
Figure 5. (a) Measured beat-frequency variationsvariations as a function of applied acoustic pressure at 800 Hz. Figure 5. (a) Measured beat-frequency variations as a function of applied acoustic pressure at 800 Hz. LLss = 3 and 6 mm, respectively; ( b) Output waveforms of the fiberfiber laser hydrophones atat 800800 Hz,Hz, 2525 Pa.Pa. Ls = 3 and 6 mm, respectively; (b) Output waveforms of the fiber laser hydrophones at 800 Hz, 25 Pa.
We have tested the frequency responses of the fiber laser hydrophones with Ls = 3, 4 and 6 mm, We havehave testedtested thethe frequencyfrequency responsesresponses ofof thethe fiberfiber laserlaser hydrophoneshydrophones withwith LLss = 3, 4 and 6 mm, respectively. As shown in Figure 6a, the average sensitivities over the working bandwidth from 110 respectively. As As shown shown in in Figure Figure 6a,6a, the the average average sensitivities sensitivities over over the the working working bandwidth bandwidth from from 110 to 1210 Hz are 185.7, 159.6, and 85.9 kHz/Pa, respectively. According to Equation (4), the beat 110to 1210 to 1210 Hz Hzare are 185.7, 185.7, 159.6, 159.6, and and 85.9 85.9 kHz/Pa, kHz/Pa, respectively. respectively. According According to to Equation Equation (4), (4), the beat frequency change induced by a point load is in proportion to local intensity of the laser mode. As a frequency change induced by a point load is inin proportionproportion toto locallocal intensityintensity ofof thethe laserlaser mode.mode. As a result, shorter laser cavities enable higher local intensity and therefore higher sensitivities, because result, shorter laser cavitiescavities enable higher locallocal intensityintensity andand thereforetherefore higherhigher sensitivities,sensitivities, becausebecause the laser modes are more confined. The natural resonant frequency of the corrugated diaphragm is the laserlaser modesmodes areare moremore confined.confined. TheThe naturalnatural resonantresonant frequency of thethe corrugatedcorrugated diaphragmdiaphragm is 1310 Hz, determined by the elastic property and corrugation geometry. Figure 6a shows an abrupt 13101310 Hz, determined by the elastic property and corrugationcorrugation geometry. Figure 66aa showsshows anan abruptabrupt change in sensitivity at about 400 Hz, which is probably a result of the mechanical resonance of the change in sensitivity at about 400 Hz, which is probably a result ofof thethe mechanicalmechanical resonance of thethe metal package. This weak resonance is not relevant with the mechanical property of the diaphragm metal package. This weak resonance is not relevant with the mechanicalmechanical property of thethe diaphragmdiaphragm and can be seen in each independent test. The measured acoustic sensitivity as well as the and can be seen in each independent test. The measured acoustic sensitivity as well as the
Sensors 2017, 17, 1219 6 of 9 Sensors 2017, 17, 1219 6 of 9 andfirst-order can be seenresonant in each frequency independent are in test.good The agreemen measuredt with acoustic the calculated sensitivity result as well. The as slight the first-order difference resonantbetween frequency the calculated are in goodand measured agreement withsensitivities the calculated may be result. a result The slightof the difference deviation between from ideal the calculatedcorrugation and geometry. measured sensitivities may be a result of the deviation from ideal corrugation geometry.
FigureFigure 6. 6.( a(a)) Measured Measured frequency frequency responses responses of of fiber fiber laser laser hydrophones hydrophones with with different differentL Ls.s. In In addition, addition, measuredmeasured result result with with a flat a diaphragmflat diaphragm as transducer as transducer is plotted is forplotted comparison; for comparison; (b) Measured (b) frequencyMeasured noisefrequency spectra noise of fiber spectra lasers of withfiber Llaserss = 3, with 4, and Ls 6= mm.3, 4, and 6 mm.
Figure 6a also shows the measured frequency response with a flat diaphragm for comparison. Figure6a also shows the measured frequency response with a flat diaphragm for comparison. This diaphragm has the same diameter and thickness with the corrugated one. The natural resonant This diaphragm has the same diameter and thickness with the corrugated one. The natural resonant frequency of the flat diaphragm is about 1100 Hz. The average sensitivity is only 39.3 kHz/Pa with frequency of the flat diaphragm is about 1100 Hz. The average sensitivity is only 39.3 kHz/Pa with Ls = 6 mm, much lower than the corrugated-diaphragm one. The comparison between the result Ls = 6 mm, much lower than the corrugated-diaphragm one. The comparison between the result obtained with a flat and a corrugated diaphragm shows the effect of the amplification factor Γ, which obtained with a flat and a corrugated diaphragm shows the effect of the amplification factor Γ, which is determined by the diaphragm geometry. Specifically, a customized flat diaphragm with H/h = 0, is determined by the diaphragm geometry. Specifically, a customized flat diaphragm with H/h = 0, q = 1 enables an amplitude Γ = 0.25. In contrast, the corrugated one with H/h = 10, q = 12 has an q = 1 enables an amplitude Γ = 0.25. In contrast, the corrugated one with H/h = 10, q = 12 has an amplification factor Γ = 0.435, which is 74% higher than the flat one, in accordance with the measured amplification factor Γ = 0.435, which is 74% higher than the flat one, in accordance with the measured result. In addition, a higher H/h ratio can yield an increased natural resonant frequency f00, based on result. In addition, a higher H/h ratio can yield an increased natural resonant frequency f 00, based on the definition of Equations (A3) and (A5), which means the corrugated diaphragm can also provide the definition of Equations (A3) and (A5), which means the corrugated diaphragm can also provide a a wider working bandwidth than a flat one. wider working bandwidth than a flat one. The noise of the present hydrophone at the frequency range of interest mainly comes from the The noise of the present hydrophone at the frequency range of interest mainly comes from the frequency noise of the fiber laser. The frequency noise mainly comes from the random thermal frequency noise of the fiber laser. The frequency noise mainly comes from the random thermal fluctuation of Er-doped fiber [22]. The spectral density has a 1/f dependence on frequency f and the fluctuation of Er-doped fiber [22]. The spectral density has a 1/f dependence on frequency f spectrum is almost independent of pump power [23]. The beat signal has the same and the spectrum is almost independent of pump power [23]. The beat signal has the same frequency-dependent profile but reduced strength, as a result of partial compensation between the frequency-dependent profile but reduced strength, as a result of partial compensation between the two two orthogonal lasing modes which are generated from the same cavity. Figure 6b shows the orthogonal lasing modes which are generated from the same cavity. Figure6b shows the measured measured noise spectra of the beat signals with different cavity lengths. Here we simply write the noise spectra of the beat signals with different cavity lengths. Here we simply write the spectrum as spectrum as = / , where C is obtained by fitting lines in Figure 6b is used to characterize the S( f ) = C/ f , where C is obtained by fitting lines in Figure6b is used to characterize the noise level. 5 5 5 2 noise level. The noise levels5 are C = 25 × 10 , 1.6 ×5 10 2 and 1 × 10 Hz for Ls = 3, 4, and 6 mm, The noise levels are C = 2 × 10 , 1.6 × 10 and 1 × 10 Hz for Ls = 3, 4, and 6 mm, respectively. There respectively. There is a peak at around 104 Hz in the spectra, as a result of relaxation oscillation. The is a peak at around 104 Hz in the spectra, as a result of relaxation oscillation. The corresponding corresponding minimum detectable acoustic pressure Pmin can be simplyp estimated with minimum detectable acoustic pressure Pmin can be simply estimated with Pmin = S( f )/Sb, where Sb = / b is the beat-frequency , where sensitivity. S is the As abeat-frequency result, the minimum sensitivity. detectable As a acousticresult, the pressures minimum are estimateddetectable 1/2 asacoustic 74, 78, andpressures 112 µ Pa/Hzare estimated1/2 at 1 kHz,as 74, respectively, 78, and 112 which µPa/Hz are comparable at 1 kHz, respectively, to the zeroth which order seaare comparable to the zeroth order sea noise. With Ls = 3 mm, the minimum detectable acoustic1/2 pressure noise. With Ls = 3 mm, the minimum detectable acoustic pressure reaches 74 µPa/Hz at 1 kHz, 1/2 whichreaches is the74 µPa/Hz best achieved at 1result kHz so, which far. In is the the experiment, best achieved the maximum result so appliedfar. In the pressure experiment, is 30 Pa the in amplitude.maximum Theapplied dynamic pressure range is of30 thePa hydrophonein amplitude. is The around dynamic 112 dB. range of the hydrophone is around 112 ThedB. detection limit is also estimated via measuring a weak signal with an electronic spectrum The detection limit is also estimated via measuring a weak signal with an electronic spectrum analyzer. As shown in Figure7, when applying 10 mPa acoustic pressure at 1 kHz with Ls = 3 mm, theanalyzer. peak intensity As shown of in the Figure beat signal 7, when at 1applyi kHzng is about10 mPa− 18acoustic dBc/Hz pressure1/2 and at the 1 kHz phase with noise Ls = level 3 mm, is 1/2 −the39 dBc/Hzpeak intensity1/2. Considering of the beat that signal the measurementat 1 kHz is about bandwidth −18 dBc/Hz of 100 Hz and can the cause phase a 20 noise dB intensity level is −39 dBc/Hz1/2. Considering that the measurement bandwidth of 100 Hz can cause a 20 dB intensity reduction for a single-frequency signal, the true SNR is 41 dB at 1 kHz. Therefore, the SNR is 21 dB
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Sensors 2017, 17, 1219 7 of 9 reduction for a single-frequency signal, the true SNR is 41 dB at 1 kHz. Therefore, the SNR is 21 dB and theand NEAP the NEAP is estimated is estimated as 83 µ Pa/Hzas 83 1/2µPa/Hzat 1 kHz,1/2 at which1 kHz, basically which basically agrees with agrees theminimum with the detectableminimum acousticdetectable pressure acoustic 74 pressureµPa/Hz 1/274 µPa/Hzat 1 kHz.1/2 at 1 kHz.
Figure 7. Recorded spectrum when applying 10 mPa acoustic signal at 1 kHz via phase noise Figure 7. Recorded spectrum when applying 10 mPa acoustic signal at 1 kHz via phase noise measurement for Ls = 3 mm. measurement for Ls = 3 mm. 5. Conclusions 5. Conclusions In summary, we have demonstrated a high-resolution beat-frequency-encoded fiber laser In summary, we have demonstrated a high-resolution beat-frequency-encoded fiber laser hydrophone based on an elastic corrugated diaphragm. The corrugated diaphragms are more hydrophone based on an elastic corrugated diaphragm. The corrugated diaphragms are more pressure-sensitive than the flat ones, and therefore selected as a transducer to concentrate applied pressure-sensitive than the flat ones, and therefore selected as a transducer to concentrate applied acoustic pressure into a near point load on the laser cavity. A higher corrugation depth-thickness ratio acoustic pressure into a near point load on the laser cavity. A higher corrugation depth-thickness H/h enables a higher transduction efficiency. The concentrated load creates a local optical phase change ratio H/h enables a higher transduction efficiency. The concentrated load creates a local optical phase and induces an optical response in beat-frequency shift. Experimental results show that shorter cavity change and induces an optical response in beat-frequency shift. Experimental results show that length yields a higher sensitivity as well as a higher signal-to-noise ratio, as a result of more confined shorter cavity length yields a higher sensitivity as well as a higher signal-to-noise ratio, as a result of laser mode. As a result, the beat-frequency sensitivity reaches 185.7 kHz/Pa by use of a fiber laser more confined laser mode. As a result, the beat-frequency sensitivity reaches 185.7 kHz/Pa by use of with a grating separation length of 3 mm. The resolution of the hydrophone reaches 74 µPa/Hz1/2 at a fiber laser with a grating separation length of 3 mm. The resolution of the hydrophone reaches 1 kHz. The dynamic range of the hydrophone is estimated to 112 dB. The performance of the fiber 74 µPa/Hz1/2 at 1 kHz. The dynamic range of the hydrophone is estimated to 112 dB. The laser hydrophone can be further improved forming lasers with highly confined mode, which requires performance of the fiber laser hydrophone can be further improved forming lasers with highly rare-earth doped fibers with higher optical gain. confined mode, which requires rare-earth doped fibers with higher optical gain. Acknowledgments: This work is supported by National Natural Science Foundation of China (No. 61235005) andAcknowledgments: Guangdong Natural This Science work is Foundation supported (No.by National S20130300133022005). Natural Science Foundation of China (No. 61235005) and Guangdong Natural Science Foundation (No. S20130300133022005). Author Contributions: W.-Z.Y. and L.J. conceived and designed the experiments; W.-Z.Y. performed the experiments;Author Contributions: W.-Z.Y., Y.-Z.L. W.-Z.Y. and L.J. and analyzed L.J. conceived the data; and J.M. anddesigned B.-O.G. the contributed experiments; reagents/materials/analysis W.-Z.Y. performed the tools; W.-Z.Y. and L.J. wrote the paper. experiments; W.-Z.Y., Y.-Z.L. and L.J. analyzed the data; J.M. and B.-O.G. contributed reagents/materials/analysis Conflictstools; W.-Z.Y. of Interest: and L.J.The wrote authors the paper. declare no conflict of interest.
AppendixConflicts of TheoryInterest: ofThe a authors Center-Free declare Corrugated no conflict of Diaphragm interest.
AppendixA pressure A. Theory difference of a PCentcaner-Free deform Corrugated an edge-clamped Diaphragm diaphragm. The deformation can be simply depicted by the deflection d0 at the rigid center, which can be expressed by [19] A pressure difference P can deform an edge-clamped diaphragm. The deformation can be simply depicted by the deflection d0 at thePr4 rigid center,d whichd 3 can be expressed by [19] = A· 0 + B· 0 (A1) Eh 4 h h 3 (A1) = ∙ ∙ where E and µ represent Young’s modulus and Poisson’s ratio of the metal, respectively, 2 Awhere= 2(E3 +andq) ·(µ1 +representq)/3 1 − Young’sµ2/q2 , Bmodulus= 32(q + and6 − µPoisson’)/[(q + s3 )ratio·(q − ofµ) ],the and metal,q is a shaperespectively, factor =2 3 ∙ 1 /3 1− / , =32 6− / 3 ∙ − , and q is a shape factor defined as = 1 1.5 / ⁄ [16]. With the assumption of small deflection, the second term on the right side can be ignored, and Equation (1) can be simplified as = (A2)
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1/2 defined as q = 1 + 1.5H2/h2 [16]. With the assumption of small deflection, the second term on the right side can be ignored, and Equation (1) can be simplified as
r4 = d0 P 3 (A2) Sensors 2017, 17, 1219 AEh 8 of 9
Due to the similarity in d0-P dependence between Equation (2) and that of a flat diaphragm Due to the similarity in d0-P dependence between Equation (2) and that of a flat diaphragm d = Pr4/64D, where D = Eh3/12 1 − µ2 denotes the flexural rigidity, the deformation of the = /64 , where = /12 1 − denotes the flexural rigidity, the deformation of the corrugated diaphragm can be equivalently considered as a flat one with an effective flexural rigidity, corrugated diaphragm can be equivalently considered as a flat one with an effective flexural which can be expressed by rigidity, which can be expressed by AEh3 D = (A3) e f f 64 = (A3) A diaphragm under harmonic perturbation can be64 approximately treated as a damping oscillator, and theA induceddiaphragm harmonic under deformationharmonic perturbation (in amplitude) can can be be approximately simply described treated by [24 ]as a damping oscillator, and the induced harmonic deformation (in amplitude) can be simply described by [24] 2 ωmn d0 ω f = d0 r (A4) 2 = 2 2 2 2 2 ƒ ωmn − ω + 4ω ωmn ξ (A4) f f − ƒ 4 ƒ where ξ is the damping factor, ωf is the angular frequency of the acoustic wave, and ωmn is natural where ξ is the damping factor, ωf is the angular frequency of the acoustic wave, and ωmn is natural angular frequency which can be written as angular frequency which can be written as s 2 ϕ De f f = mn · ω mn = 2 ∙ (A5)(A5) r ρ h wherewhere ϕ mn isis aa constantconstant relatedrelated toto thethe vibrationvibration modemode ofof thethe diaphragm.diaphragm. ForFor thethe fundamentalfundamental 2 = mechanical mode, ϕ 00 =10.2110.21. Equation Equation (A4) (A4) enables enables a a flat flat response at belowbelow thethe lowestlowest orderorder natural resonantresonant frequency frequencyf 00 f00. Therefore,. Therefore, we we can can treat treat the harmonicthe harmonic deformation deformation at frequencies at frequencies lower thanlower the than resonant the resonant frequency frequency as a hydrostatic as a hydrostati problem.c problem. The diaphragmThe diaphragm deformation, deformation, as well as well as the as sensorthe sensor response, response, is calculated is calculated with with this this hydrostatic hydrostatic approximation approximation in the in text.the text. We havehave numericallynumerically calculated calculated the the deformation deformation induced induced by by a statica static pressure pressure difference difference of 10of Pa10 basedPa based on finite on finite element element method. method. Figure FigureA1 shows A1 theshows calculated the calculated deformation deformation of a center-free of a corrugatedcenter-free diaphragm.corrugated Itsdiaphragm. geometry Its is ingeometry accordance is within acco therdance one in ourwith experiment. the one in The our diaphragm experiment. presents The maximumdiaphragm deflection presents maximum at the rigid deflection center. at the rigid center.
Figure A1.A1. Calculated deformation deformation of of center-free corru corrugatedgated diaphragm in response to 10 PaPa staticstatic pressure.pressure.
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