It is shown that the pressure sensitivity of a fiber-optic hydrophone is strongly dependent on the fiber's
strain configuration. Longitudinal strain is found to be much more effective than uniform strain, and conse-
quently modifications to the sensor's design are proposed. Environmental noise sources such as ocean mo-
tion and mechanical vibrations are then discussed, and a new double-cavity configuration, which is unaffect-
ed by those perturbations, is presented. A tunable-cavity detection method is finally proposed, and it is
shown how this method can overcome problems related to drift of the point of operation, laser intensity fluc-
tuations, and nonlinearity for high dynamic ranges.
1. Introduction
Fiber-optic hydrophones have recently been pro-posed1 -7 as a novel approach to underwater acousticsensing. The configuration considered most fre-quently1 -5 consists of two laser excited monomode fibersforming the two arms of an interferometer, with onefiber immersed in water as the sensing element and theother acting as a reference. The superposition of thetwo beams through a beam splitter and alignment de-vices results in a light-intensity modulation reproducingthe acoustic pressure fluctuations sensed by the im-mersed fiber. This scheme is very sensitive to envi-ronmental perturbations. If the maximum phase shiftAO5 induced by the pressure fluctuations has to satisfythe condition i4 << -r for linearity and a signal dynamicrange of 104 is required, optical path variations as smallas 10-5 Am must be detected. In underwater applica-tions, such small signals are likely to be overshadowedby mechanical vibrations of the optical elements relativeto each other.
Some alternative configurations avoiding most of theoptics have been proposed6 7 where the interferingbeams are transmitted through the same multimode ormonomode sensing fiber. However, these approachesare affected by problems such as excessive optical co-herence requirements for a given sensitivity and diffi-culty in setting and keeping the operating point (of theintensity response vs phase difference variations) in alinear region.
The author is with Defence Research Establishment Atlantic, P.O.
Other sources of environmental noise arise frompressure fluctuations near the surface due to oceanmotion, 8 as well as from elongations generated by dragforces on the fiber-cable link with the sensing ele-ment.9 10 These perturbations introduce random phasedifferences between the interfering beams, unless thelight beams are transmitted through the same mono-mode fiber. This can be done by including two reflec-tors along a single fiber so that the beams reflected backalong the highly perturbed portion of the fiber aresubject to the same random phase modulation. Un-fortunately, this simple scheme is faced with problemsof source coherence and drift of the operating point, aswill be explained in more detail later.
In this paper it is first shown that the sensitivity ofa fiber-optic hydrophone is strongly dependent on thestrain configuration. It is found that longitudinalcompression produces much higher sensitivity thanuniform 3-D compression. Consequently, some hy-drophone designs leading to longitudinal compressionand enhanced sensitivity are proposed. In Sec. III it isshown how the coherence requirements of a double-reflector configuration can be relaxed by the introduc-tion of a reference cavity along the same fiber. Envi-ronmental noise of the kind previously considered doesnot affect such a double-cavity configuration. More-over, the reference cavity-in the double-cavity con-figuration-can be tuned to avoid problems related todrift of the operating point, laser intensity fluctuations,and nonlinearity when the condition AO << 7r is notsatisfied.
II. Pressure Sensitivity
A number of investigations have been reported con-cerning the phase-modulation induced in the opticalbeam transmitted by an optical fiber subject to
stress.4 511-13 However, the sensitivity dependence onstress configuration has not been considered. It isshown here that widely different sensitivities are ob-tainable in the three cases of longitudinal, transverse,and uniform stress.
The transmission of a light wave through a fiber oflength L increases its phase by
shb=/3L, (1)
where ho- koneff is the propagation constant of a givenmode in the fiber, ho the free-space propagation con-stant, and neff the effective refractive index for thatmode. If the approximation neff n is made,13 wheren is the refractive index of the fiber's core, the pres-sure-induced phase shift may be written in the form
A = konAL + LkoAn, (2)
where the first term corresponds to the change in thefiber's length and the second term to the photoelasticeffect. Effects related to the mode structure are ne-glected in this approximation, as they are smaller thanthe terms appearing in Eq. (2) by 2 or 3 orders of mag-nitude.
When the strain configuration is taken into account,Eq. (2) becomes
1 6A = konS 1 L - Lkon 3 L p2 jSj, (3)
2 ,=1
where S is the strain vector and p the photoelastic ten-sor in the standard contracted notation.14 The sub-script 1 of the strain vector refers to the longitudinaldirection, i.e., along the fiber's axis. The transversecomponents 2 or 3 of the optical indicatrix are equiva-lent here because of the radial symmetry. For an iso-tropic medium, ij has only two numerical values, des-ignated , and P12. The strain vector in the three casesof a longitudinal, transverse, and uniform 3-D strainconfiguration is given by
0 0 L0where ,u is the Poisson's ratio. The strain is relatedto the applied pressure p by the value of Young'smodulus.
The longitudinal, transverse, and uniform strain areobtained through the substitution of Eqs. (4) into Eq.(3) and are, respectively,
(A~~~~ 1= -I kon - - kon3 [(1 - A)P12 - P1]~EI 2
( 0) = -2gkon - -kon3[(l - 3 )p12 + (1 -)P11
( 4 = (1 - 2)kon - I kon3 [(1 - 2A)(pil + 2p12)]
(5)
If the numerical values (2-r)/ko = 0.63 gum, p11 P12 0.2, n = 1.5, and ,tz 0.25 are assumed, 1 1"13" 5 to-gether with a value of 7 X 1010 N/M2 for Young's mod-
ulus, the pressure sensitivities corresponding to Eqs. (5)are
(-L)= 2.14 X 10 - 0.24 X 1010
= 1.9 X 0-10 rad/,Pa m
itL) = - 1.07 X 10-10 - 0.47 X 1010 , (6)\pLt 6= -1.5 X 10-10 rad/,Pa m
(-). 1.07 X 10-10 - 0.71 X 0-")
= 0.36 X 10-10 rad/,uPa mfor longitudinal, transverse, and uniform pressure, re-spectively. In the uniform pressure case the two termscorresponding to the change in the fiber's length and tothe photoelastic effect have the same order of magni-tude and are opposite in sign, which account for thesmall value obtained for the sensitivity.
Hence, longitudinal pressure is about 5 times moreefficient than uniform pressure. This fact is importantparticularly when the design of the acoustic sensor hasto be chosen. A fiber coil surrounded by water expe-riences uniform compression and must be avoided.
Longitudinal compression much larger thantransverse compression can be obtained by coiling andcementing the fiber around a compliant cylinder, so thatits axial strain is related to the cylinder's contraction indiameter. For an air-filled cylinder, for example, azi-muthal stress is larger than the external stress normalto the cylinder's walls by a factor approximately equalto the radius-to-thickness ratio.16 A radius-to-thick-ness ratio not greater than 10 is generally required toavoid the cylinder's collapse under high hydrostaticpressure. Even with this limitation, very compliantcylinders can be obtained by using a compliant materialsuch as plastic.
The ultimate limit to the fiber's longitudinal stressis set by the failure of the fiber itself at large depths.For practical applications it is reasonable to assume thatthe fiber's elastic limit, which corresponds to a strainof the order of 1%,10 must not be exceeded for an ex-ternal hydrostatic pressure up to Pext = 107 Pa, i.e., fora depth of 1000 m. In this case the substitution of
AL AO- C = 10-L nk0L
in the first of Eqs. (6) leads to the result that the gainP/Pext of longitudinal to external pressure must be amaximum of 70.
111. Double-Cavity ConfigurationAs mentioned in Sec. I, environmental noise can be
reduced by using a single monomode fiber with two re-flectors inserted along the fiber to form a remote fibercavity. The portion of the fiber between the reflectorscan be coiled around a compliant cylinder in order toincrease the sensitivity to the acoustic field, as discussedabove. Each reflector may be a fiber connector, or adistributed-feedback reflector,1 7 1 8 or even a partiallysilvered mirror located between two couplers.
Fig. 1. Double-cavity configuration: L, light source coupled to thefiber; R, reflectors; D, photodetector; S, servo-control electronics.The left portion of the figure represents the local part of the detecting
apparatus; the right portion represents the underwater part.
However, if the reflected beams are to interfere, ahighly coherent source with coherence length muchlonger than twice the cavity length is required. It isshown below how such coherence requirements can berelaxed considerably by introducing a second cavityalong the same fiber. Moreover, in a double-cavityconfiguration the detection method can be improved bytuning the local reference cavity.
The proposed configuration is shown in Fig. 1. Alight beam is coupled into an optical fiber and undergoesmultiple reflections within a local reference cavity sit-uated on the surface with the electronics apparatus.The transmitted beam propagates through the under-water portion of the fiber and undergoes multiple re-flections within the remote cavity. Each cavity consistsof a portion of the fiber coiled around a cylinder andbounded by two reflectors. A control voltage may beextracted from the detected signal and used to tune thelocal cavity, as will be explained in next section.
The spectral distribution of the light beam trans-mitted by the first cavity is given by the following ex-pression 19 :
* clo(oa)1 + Fsin231 (7)
1.0
where Io(co) is the power spectrum of the incident beam,and w is the optical angular frequency. The quantitiesa, F, and 61 are given by
T2S 4RS -Li,
(1 -RS) 2 (1 -RS) 2 Vl
where R is the reflectivity, T is the transmissivity ofeach reflector, S is the one-way attenuation between thereflectors, L1 is the fiber's length within the cavity, andv1 is the phase velocity of light along the fiber. Figure2 shows the typical spectral response of the cavity asgiven by Eq. (7) for values of R equal to 0.6 and 0.9, T= 1 - R, and L1 = 10 in. In the computation, an at-tenuation of 5 dB/km was assumed for the fiber. Anumber of peaks appear in the spectrum of the lighttransmitted by the cavity; each peak corresponds to a
value of the wavelength, which is a submultiple of twicethe optical length of the cavity.
The analysis leading to Eq. (7), as well as previousanalyses,1- 7 assumes that the interfering beams are inthe same state of polarization. The presence of cou-pling between the two polarization modes in ordinaryfibers20 '21 may require the use of suitable polarizingelements22 and of polarization-maintaining fibers23 toavoid depolarization of the light beam transmittedthrough the fiber. It should be noted here that in thehollow-cylinder sensor described in the previous section,hydrostatic pressure leads to anisotropic strain of thefiber coiled around the cylinder. For example, at adepth of 100 in and for a radius-to-thickness ratio of 10the fiber is subject to transverse strain of the order of10-4 in the direction parallel to the cylinder's axis andof 10-5 in the radial direction. Advantage could betaken of such an anisotropic strain to avoid depolar-ization of the light transmitted through the cavitywithout recourse to special fibers.
After transmission through the second cavity thedetected intensity integrated over all frequencies isgiven by the following expression:
(8)I = alow)acoo (1 + F sin261)(1 + F sin2
82)
where 2 is the equivalent of '3 for the second cavity.The resultant intensity is plotted in Fig. 3 as a functionof the difference 1 - 2, assuming a power spectrumbandwidth for the light source equal to 0.1 A. Maximain the detected intensity are obtained when the spectralresponses of the two cavities, each given by a curve ofthe type shown in Fig. 2, have their peaks exactly su-perposed.
Multiple reflections between one cavity and the otherhave been neglected in the analysis leading to Eq. (8)for the following two reasons. First, the light beamgoing to the remote cavity, back to the first cavity, andback again to the remote cavity is subject to a greaterfiber absorption than the beam going straight throughthe two cavities. Second, the optical beam transmitted
.75
I -_ Oe.50 V
.25
0N7V1 (No1) r V, (N+2)1r V,
LI L, LI
ANGULAR FREQUENCY
Fig. 2. Spectral response of a single cavity. Each peak correspondsto a wavelength which is a submultiple of twice the optical wavelength
Fig. 3. Detected intensity as a function of the difference betweenthe phase delays introduced by the two cavities. The intensity ismaximum when the spectral responses of the two cavities are exactly
superposed.
by the first cavity and reflected back by the secondcavity has a spectrum constituted mainly of those fre-quency peaks that are transmitted again through thefirst cavity.
The previous analysis is valid no matter how large thelight source spectral bandwidth may be, i.e., no matterhow short its coherence length may be. Even very in-coherent sources such as a LED or a tungsten lamp havebeen used successfully in double-cavity modulationexperiments. 2 4
The detected signal is unaffected by any phase per-turbation in the fiber between the local and remotecavities, because the detected intensity depends onlyon the matching of the spectral responses of the twocavities. In other words, all the interfering beamspropagate through the same fiber and thus are subjectto the same phase perturbations.
IV. Signal Retrieval
Previous analyses1-7 of the fiber optic hydrophonehave assumed that the acoustic signal is recovered bysimply detecting the intensity-modulated optical beamresulting from the interferometric superposition. It ispossible to use a similar method here. Figure 4 showsa typical curve of the detected intensity as a functionof the acoustically induced phase shift in the remotecavity. This curve is similar to those shown in Fig. 3.The acoustic signal can be retrieved by setting the pointof operation at A, with phase excursions between A' andA" in order to avoid nonlinearity. This restriction setsa limit to the dynamic range. More important, the re-covered signal is highly dependent upon the position ofthe operating point. Even if the point of operation iscorrectly set at A initially, it will drift slowly with timebecause of small variations in the depth of the fibersensor or because of thermal fluctuations. This mayresult in large distortions or even a loss of the acousticsignal.
Such limitations can be overcome by using a laserheterodyne method to produce a frequency-modulated
>_ A B
(I'
Z II
A B p
1II1
Fig.4. Signal retrieval by cavity tuning. In the conventional methodthe point of operation is set at A, and good linearity is obtained if thephase excursions are sufficiently small. In the tunable-cavity methodthe point of operation is kept on B by applying a feedback voltage
proportional to the difference B - B'.
signal at an intermediate frequency.11,25 This signalcan subsequently be demodulated by standard tech-niques. However, such a method requires a separatereference beam, which will be susceptible to the envi-ronmental noise problems men tioned in Sec. I.
A third approach has been used in a previous opticalcommunication system.2 The first cavity is locked tothe second in that the length of the first is continuouslyequalized to that of the second. Thus, the operatingpoint is constantly kept in a position such as the pointB in Fig. 4. This can be achieved as shown in Fig. 1.The fiber in the first cavity is coiled around a piezo-electric cylinder, whose diameter can be varied by theapplication of a small control voltage. Depending onthe number of fiber turns around the piezoelectric cyl-inder, phase sensitivities of the order of radNV or morecan be obtained. 12 The control voltage essentially re-produces the phase fluctuations of the remote cavity,so that this voltage itself is the signal to be recovered.The servocircuit relating the control voltage to the de-tected signal can be described as follows. A fast ac os-cillation is superimposed on the control voltage, and thedetected intensity is sampled at the extremas to give thetwo values B and B in Fig. 4. If the two cavities arematched, the point of operation is exactly at B so thatB = B. If there is a mismatch, a variation of thecontrol voltage by an amount proportional to B - B'will bring the system back to equilibrium.
The minimum detectable phase shift is related to thecapability of detecting the difference B - B. This isanalogous to the problem of detecting the differencebetween the intensities A' and A in the conventionalmethod, so that the sensitivity of the two methods isessentially the same. However, if the sampling rate ishigh enough the tunable-cavity method makes it pos-sible to follow phase excursions of several cycles, ratherthan being limited to 7r/2 as in the first method. An-other advantage is that the recovered signal dependsonly on the difference of the intensities B' and B,rather than the absolute values. Consequently, the
signal is unaffected by random variations of the laseroutput power. Finally, this method automaticallycompensates for the drift of the point of operation.Thermal fluctuations and depth variations in the re-mote cavity will still be sensed as if they were part of theacoustic signal. However, they will not affect the lin-earity and the sensitivity of the system and are usuallylow enough in frequency so that they can be filtered outof the acoustic signal.
The maximum detectable acoustic frequency is lim-ited by resonance considerations for the piezoelectriccylinder. Driving frequencies up to 30 kHz can be ob-tained with cylinders a few centimeters in diameter."This should be satisfactory in most cases of currentpractical interest. If this is not the case, frequencies inthe MHz range can be attained at the expense of a lowerphase sensitivity by operating at the thickness reso-nance of a thin piezoelectric cylinder. The fiber caneither be positioned along the axis of the cylinder,' 2 orcoiled around the cylinder.
V. Discussion and Conclusion
In this paper, a double-cavity single-fiber configu-ration is proposed for a fiber-optic hydrophone. It canbe considered as an extension of the configurationproposed in Ref. 6. It has the advantage that a low-coherence source can be used and that the system isinherently insensitive to phase perturbations arisingfrom environmental factors in the ocean; in addition,the reference cavity may be tuned to overcome a num-ber of practical limitations, as discussed in the lastsection. In particular, the removal of the condition AO<< r makes it possible to increase the pressure sensi-tivity by the methods discussed in Sec. II, without acorresponding dynamic range compression.
It should be noted that a tunable-cavity detectionmethod similar to that described in the last section canbe used in the double-monomode-fiber configuration.l- 5
This may be done by tuning the reference fiber with apiezoelectric cylinder. However, even with such animprovement, the double-fiber configuration requiresa complex optical apparatus which is affected by me-chanical vibrations; also, it is sensitive to random per-turbations such as ocean motion and cable elonga-tions.
The single-multimode fiber configurations7 elimi-nates the optics but requires a long fiber and a highlycoherent source and provides no tunable second cavity.Therefore, it suffers from drift of the operating point,dynamic range compression, and sensitivity to laseroutput fluctuations. Moreover, it is sensitive to oceanperturbations because the interfering beams travel withdifferent propagation constants through the fiber.
The double-cavity single-fiber configuration is pro-posed as a hydrophone element. Natural extensionsof the same concept lead to arrays consisting of a num-ber of acoustic sensors located along the same fiber,where each sensor consists of two reflectors and asensing cylinder. In such systems time-multiplexingis possible by using short optical pulses and recordingthe intensity of the echo signal reflected back by eachsensor. Also, wavelength-division-multiplexing can beachieved if the reflectors of each sensor are stronglyfrequency selective as in the case of distributed-feed-back reflectors.1 7 ' 18 A third possible scheme is cav-ity-length multiplexing.27 However, this last methodrequires widely different cavity lengths, which result indifferent sensitivities for the various sensors, so that thisapproach does not appear to be practical in this case.
In conclusion, this paper is concerned with fiber-opticsensing of small acoustic signals in an ocean environ-ment. Two approaches are proposed to discriminatebetween acoustic signal and system noise. The first isa modification of the strain configuration that makesuse of longitudinal compression to increase the pressuresensitivity of the fiber sensor. The second is a modifi-cation of the interferometric scheme that makes use ofa double-cavity single-fiber configuration to obtain asystem insensitive to ocean-induced random phaseperturbations.
The author is particularly grateful to G. W. McMahonof Defence Research Establishment Atlantic for manyvaluable interactions, to C. W. Bright of Defence Re-search Establishment Atlantic for his continuous en-couragement, and to K. 0. Hill of CommunicationsResearch Center, Ottawa, for helpful discussions.
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