Sensitive acoustic vibration nsor using
房屋危房鉴定
single-mode fiber tapers
Yi Li,Xiaozhen Wang,and Xiaoyi Bao*
Department of Physics,University of Ottawa,150Louis Pasteur,Ottawa K1N6N5,Ontario Canada
*Corresponding author:Xiaoyi.Bao@uottawa.ca
Received11November2010;revid1March2011;accepted1March2011;
posted2March2011(Doc.ID138047);published25April2011 Optical fiber nsors are a good alternative to piezoelectric devices in electromagnetic nsitive envir-onments.In this study,we reported a fiber acoustic nsor bad on single-mode fiber(SMF)tapers.The fiber taper is ud as the nsing arm in a Mach–Zehnder interferometer.Benefiting from their micro-meter dimensions,fiber tapers have shown higher nsitivities to the acoustic vibrations than SMFs.
Under the same conditions,the thinnest fiber taper in this report,with a diameter of1:7μm,shows a20dB improvement in the signal to noi ratio as compared to that of an SMF.This acoustic vibration nsor c
an detect the acoustic waves over the frequencies of30Hz–40kHz,which is limited by the acous-tic wave generator in experiments.We also discusd the pha changes of fiber tapers with different diameters under acoustic vibrations.©2011Optical Society of America
OCIS codes:060.2370,060.4005.
1.Introduction
Piezoceramic nsors have been widely ud for passive acoustic monitoring.However,in a total elec-tromagnetic nsitive environment,the fiber optic acoustic nsor will be a good alternative.Another advantage of fiber optic acoustic nsors is their sim-plicity.The signal processor and electric power parts of piezoceramic nsors need to be located near the nsor head for low transmission loss.Also,the optic fibers are easier to be deployed and recovered.The majority of the fiber optic vibration nsors reported to date are bad on interferometric techniques,such as Mach–Zehnder(MZ),Michelson,Fabry–Perot or Sagnac interferometer,and fiber Bragg grating (FBG)techniques.Recently,Zhou[1]propod and demonstrated a temperature-innsitive acceler-ometer bad on a strain-chirped FBG.Instead of demodulation of the FBG’s wavelength shifts,they converted the wavelength shift to the reflection power change by fixing the FBG on a triangle canti-le
ver beam.Guo[2]reported a new type of acoustic nsor bad on a distributed Bragg reflector(DBR)fiber lar.A pair of FBGs was ud as the reflection mirrors to form a DBR lar,which was utilized as the acoustic nsor head.But limited by the line-width of the DBR lar,it was not capable of detect-ing low frequency vibrations,such as kHz.
In this study,we propod an MZ interferometer nsor,and a single thin fiber taper was ud as the nsing arm to detect acoustic vibrations.Micro-meter sized optical fiber tapers are of interest to many photonic areas due to their small dimensions, strong evanescent fields,and high nonlinearities[3]. They have been successfully applied in directional fi-ber couplers,exciting whispering gallery modes in microcavities[4],bionsors[5],high-order mode fil-ters[6],generating supercontinuum light[7]and acousto-optic modulator[8].Also,SMF tapers can be applied as acoustic and ultrasound vibration n-sors[9].In their experiments,the vibration was de-tected by directly measuring the transmission power of a piece of adiabatic fiber taper,which was ud as the nsing medium.When the environmental acous-tic wave frequency is equal to the modes frequency differences between the fundamental mode and the cladding modes,the environmental acoustic wave gives ri to the mode coupling from the fundamental
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©2011Optical Society of America
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mode to higher-order cladding modes and the trans-mission power thus changes.However,the acoustic waves of other frequencies were not demonstrated in their studies.Chen[10]reported a vibration n-sor bad on tapered fiber couplers,in which the acoustic wave was detected by measuring the power ratio changes of the coupler’s two output ports.The acoustic wave stretches and compress the fud ta-per ction of the coupler and varies the power ratios between the two outputs.They predicted that smaller fud taper waists should have higher nsi-tivities.However,limited by the fabrication condi-tions,the smallest fud taper waist in their experiments was only10μm.
In our experiments,as a respon to the acoustic vibrations,the fiber tapers are stretched and con-tracted,and their lengths and diameters are thus de-formed,which changes the modes and conquently the mode index and optical path length difference (OPD).Since the stress is inverly proportional to the square of the fiber diameters,a thinner fiber taper should be elongated more.The taper length change directly leads to the OPD change between the two arms of the MZ interferomete
r.At the same time,the physical stress results in the refractive in-dex changeΔn of the fiber taper.This also varies the OPD and finally makes the output power change. Our simulation results show that the pha change of a piece of fiber taper under longitudinal strain is mainly from fiber length change when the fiber taper is assumed to be elastic and mechanically homoge-neous.The experimental results show that the acous-tic vibrations can be detected by fiber tapers with the signal to noi ratio(SNR)as high as59dB,which is much higher than nsitivities of the SMF using the same experimental tup.Such high SNR cannot be achieved with intensity measurement due to the lim-ited dynamic range of photodetectors.Different di-ameter’s fiber tapers are studied in the experiments. As we expected,smaller fiber tapers have higher SNRs.The measurement results are then compared with the simulation results of taper pha change un-der longitudinal strain,and they were found to be in good agreement.
2.Principle
For an MZ interferometer,the resultant intensity I0 is from the superposition of intensities I1and I2of the two arms:
幼儿推拿I0¼I1þI2þ2
ffiffiffiffiffiffiffiffiffi
I1I2
p
cosφ;ð1Þ
whereφis the total pha difference of the OPD of the two arms.Under the acoustic vibrations,the fiber taper is bent and stretched.It can be considered as the forced longitudinal stress acting on the fiber taper.To simplify the analysis,lateral deflections of fiber tapers were not considered in the following discussion,and the transmitted light is assumed to be at the fundamental mode when the fiber taper is stretched.At the same time,the refractive index n of the fiber taper was also conquently changed byΔn.Thus,the OPD changes are mainly compod of the fiber length change and the refractive index change.Under the acoustic wave perturbation,an additional pha changeΔφis introduced for an MZ interferometer:
I0¼I1þI2þ2
ffiffiffiffiffiffiffiffiffi
I1I2
p
cosðφ0þΔφÞ;ð2Þwhereφ0is the pha bias term,or the working point. To maintain the working point around the quadra-ture point,a piezoelectric fiber stretcher is ud in the reference arm and driven by a feedback circuit. Then we haveφ0¼ð2mþ1Þπand
I0¼I1þI2−2
弘扬传统文化作文ffiffiffiffiffiffiffiffiffi
I1I2
p
Δφ;ð3Þ
for a small pha change.Thus,the pha change is converted to the intensity change via an MZ interferometer.
3.Experiments
In the experiments of the prent report,biconical fiber tapers were manufactured by elongating an SMF heated by a hydrogen gas flame[11].A constant hot-zone approach[12]was ud in the fabrication. Therefore,all the fabricated tapers have the uniform waist length(about8mm)with the diameters ran-ging from1.7to50μm.The average transmission loss is less than0:2dB.A typical fiber taper profile is shown in Fig.1.The theoretical taper profile is also calculated and shown in Fig.1for comparison[13]. The schematic experimental tup is exhibited in Fig.2.An MZ interferometer was compod of two 50/50couplers.A10m long SMF was coiled around a piezoelectric stretcher and was ud as the refer-ence arm,while a piece of fiber taper was attached on a square metal plate ud as the nsing arm. The dimension of the metal plate is9cm×7cm×1mm and is weighted about50g.Actually,the mid-dle taper waist part is hanged over the plate since only the125μm fiber parts can be firmly stuck on the flat surface.In order to control the working point of the MZ interferometer,parts of the two output signals from the cond50/50couple are led out to the feedback circuit.This circuit filters out the
AC
Fig.1.(Color online)Actual fiber taper profile(black dots)is plotted against the theoretical profile line(red solid curve).The measurement error is reprented by the dots’radius.
1874APPLIED OPTICS/Vol.50,No.13/1May2011
components above10Hz,which is assumed as the acoustic vibration noi range.Then the two signals are compared and procesd in the circuit,and the feedback signal was finally nt to the piezoelectric
fiber stretcher to maintain the MZ interferometer working around the quadrature point[14].A20mW 1550nm DFB lar source with the3MHz spectral linewidth was ud as the light source.A conven-ti
onal speaker was ud as an acoustic vibration
source,which was placed underneath the metal plate.To compare the performance of the fiber taper nsor and the conventional electric nsor,a com-mercial piezoelectric accelerometer was attached on the plate near the fiber taper.An amplifier circuit of bandwidth from30Hz to100kHz filtered DC com-ponents of the electric signal from p-i-n photodiode and amplified the AC components.The time domain signal was collected by the data acquisition card without averaging and was then converted to a fre-quency spectrum through fast Fourier transform (FFT).A Labview program performed the data collec-tion and processing.
All the experiments were performed at room temperature.The measured SNR of the signals within the detection bandwidth is as high as59dB without any averaging.Two reprentative fre-quency spectra of the1:7μm fiber taper and their corresponding time domain spectra are shown in Figs.3(a)and3(b).The time domain spectra are of quite flat amplitude contour,which indicates that the feedback circuit actually works.We also mea-sured the SNRs of fiber tapers with different dia-meters as shown in Fig.4.All the measurements were performed under the same conditions and the speaker was tuned to3000Hz with the output power of3W.It was found that higher SNR and n-sitivity can be obtained in thinner tapers.The SMF was also tested using the same experimental tup. Compar
ed with the SMF,the smallest taper(1:7μm) has an SNR improvement by about20dB.
The labeled working bandwidth of the speaker is from30Hz to6kHz.Hence,the generated acoustic waves at low frequency,30Hz,and higher frequency,40kHz,have much lower power.The measured fre-quency respon characteristic of the fiber nsor is displayed in Fig.5.The measured SNRs are from 15to59dB over frequencies from30Hz to40kHz. The piezoelectric accelerometer results are also shown for comparison.It is en that the trend of the SNR curve of the fiber nsor is similar to that of the accelerometer,both of which depend on the frequency respon of the speaker.However,the piezoelectric nsors are not applicable in an electro-magnetic nsitive environment,while optical fiber nsors are.Our experiments also show that this fiber taper nsor is a good complement to the re-ported fiber coupler nsor[10],which has a fre-quency respon from veral tens of kHz to veral hundred kHz.
伤心的回忆
We also studied the fiber nsor’s respon to the acoustic vibration intensity at a certain frequency.By tuning the input voltage of the speaker from100mV to5V at the frequency of3kHz,different acoustic wave intensities were generated.The piezoelectric accelerometer was also employed as the reference. The SNRs of the fiber nsor and the accelerometer are shown in Fig.6.Both of the SNR curves have the similar trend that the SNR increas with the rising input volt
ages to the speaker.This measurement is conducted for the single frequency detection.
山药的作用4.Theoretical Discussions
Assuming the fiber tapers are elastic and mechani-cally homogeneous,the pha change,Δφ,is induced by an elongation,ΔL,which is given by[15]
Δφ¼kðnΔLþΔnLÞ;ð4Þ
where k¼2π
λ
is the wave vector,L andΔL are the ori-ginal fiber length and the change in fiber length when the fiber is stretched or contracted.Hereafter, we assume that the fiber tapers and common fi-bers have the same length,L.The first term on the right side of Eq.(4)reprents the physical length changes,and the cond term reprents the refrac-tive index change of the taper itlf.Under the long-itudinal strain,we have[15
]
Fig.2.Schematic of the experimental tup.The probe head of the piezoelectric device is also attached on the plate near the fiber taper.
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Δn ¼−1
n 3·ε·½p 12−νðp 11þp 12Þ ;
ð5Þ
where ε¼ΔL
L ;p 11and p 12are optoelastic constants of silica;and νis the Poisson ratio of silica.Equation (5)shows that Δn is negative,and has a negative con-tribution to the pha change.But the fiber length is positive under the longitudinal strain and has a positive contribution to the whole pha change.Therefore,the pha change of an SMF can be ex-presd as
Δφ¼kn ΔL 1− n
22
母亲的记忆½p 12−νðp 11þp 12Þ
:
ð6Þ
For the fiber tapers,the pha change is more complicated and can be shown as the following:Δφðz Þ¼k ·n ðz Þ·εðz Þ
· 1−
n ðz Þ2
·½p 12−νðp 11þp 12Þ ·d z ;ð7Þwhere n ðz Þis the n eff along the fiber taper,and εðz Þis the local strain.In order to simulate the综合素质评价自我评价
pha
Fig.3.(Color online)Frequency spectra of a 1:7μm fiber taper and their corresponding time domain spectra,(a)400Hz,(b)3100Hz.
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Fig.5.(Color online)Frequency respon to the studied fiber ta-per nsor and piezoelectric accelerometer.The frequency range is from 30Hz to 40
kHz.Fig.6.(Color online)FFT SNRs of fiber taper nsor and accel-erometer are plotted against the input speaker voltage.Both nsors have a similar
trend.
Fig.7.(Color online)Evolution of HE 11mode with the variation of taper sizes.The refractive index of fiber cladding is highlighted as red
curve.化学实验基本操作
Fig.4.(Color online)SNR increas with smaller tapers dia-meters.The measured SNR of an SMF is obtained using the same experimental tup and is plotted for
comparison.
Fig.8.(Color online)The comparison of experimental data (black dots)and theoretical values (red curve)with different taper diameters.
1May 2011/Vol.50,No.13/APPLIED OPTICS
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change under strain,the effective refractive index n eff at each point of a fiber taper is needed.Bad on the eigenvalue equations[16],the n eff of the HE11 mode(fundamental mode)was calculated and is shown in Fig.7.Here,it was assumed that the fiber taper is adiabatic,and the light propagates at the HE11fundamental mode.The n eff drops quickly when the taper diameter is smaller than20μm.In the experiments,the amplifier filtered the DC com-ponent.So large pha changes generate higher sig-nal intensities.From Eq.(3),we have
SNR taper=SNR SMF∝Δφtaper=ΔφSMF:ð8Þ
Bad on the measured taper profile(not shown here due to limited space)and the calculated n eff,the pha change of a taper fiber under strain was eval-uated.The calculatedΔφtaper=ΔφSMF was plotted against taper waist diameters in Fig.8and the mea-sured SNR taper=SNR SMF was also included for com-parison.The experimental data and theoretical values fit very well.This also proves that the main pha change of a taper fiber is resulted from long-itudinal strain and the taper length change is the main contribution of the whole pha change.
5.Conclusion
In this report,we demonstrated an MZ interfero-metric acoustic nsor bad on fiber tapers.The ex-
perimental results show that fiber tapers have higher SNR up to20dB than that of the SMF using the same experimental tup.The pha changes of fiber tapers with different diameters under longitu-dinal strain were investigated and agreed well with the experimental results.It is noted that the nsor’s performance may be slightly different if choosing dif-ferent metal materials or different dimensions as the attachment,as they will have different attenuations for different frequency components.To further im-prove the nsor performance,two improvements could be done in the future.First,the taper waist length can be incread and made thinner if using the variation flame scanning method[13].A longer and thinner taper waist should have larger pha change to the vibrations since the major pha change contribution is from the taper waist.Second, low refractive index polymer gel should be intro-duced in the nsor fabrication.In the current nsor, the taper waist does not touch the metal plate to avoid the high loss.Thus,acoustic vibrations cannot directly act on the fiber taper.Low refractive index polymer gel has been successfully utilized to protect fiber taper from the water and dust[17].Low refrac-tive index polymer gel can be ud to stick the fiber taper on the metal plate at low loss.Therefore,the acoustic wave can be directly conducted to the taper and increa the acoustic wave intensity.
Note:Part of the above content was reported in the Twentieth International Conference on Optical Fibre Sensors,Edinburgh,UK,2009.
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