measurement of pressure and temperature sensitivities of a bragg grating imprinted in a highly...

Measurement of pressure and temperaturesensitivities of a Bragg grating imprinted in ahighly birefringent side-hole fiber

Ewa Chmielewska, Waclaw Urbanczyk, and Wojtek J. Bock

The sensing characteristics of a Bragg grating imprinted in a specially developed highly birefringentside-hole fiber were investigated in detail. We showed that such a grating has almost identical sensi-tivities to temperature for both linearly polarized modes LP01

x and LP01y �approximately 5.9 pm�K� and

significantly different sensitivities to hydrostatic pressure ��1.93 pm�MPa for LP01x and �5.37 pm�MPa

for LP01y mode�. The sensitivity differences versus mode polarization are so high that this effect can be

employed for simultaneous sensing of temperature and pressure by interrogation of the wavelength shiftsat LP01

x and LP01y modes. Applying interferometric methods, we also measured the sensitivity of the

host side-hole fiber to temperature and hydrostatic pressure for each polarization mode. Our resultsshow that there is good agreement between the normalized sensitivities of the host side-hole fiber andthose of the grating for the same polarization modes. © 2003 Optical Society of America

OCIS codes: 350.2770, 060.2370.

1. Introduction

It has already been proved in many applications1 thatBragg gratings imprinted in standard single-modefibers are especially well suited for measuring tem-perature and strain. This is because the sensitivityof Bragg gratings to these two parameters is highcompared with other measurands and typically is inthe ranges of d�B�dT � 6.8–13 pm�K and d�B�d� �0.64–1.2 pm��strain, respectively, for temperatureand strain.1

In recent years many efforts have been undertakento expand the application area of Bragg gratings inthe measurement of hydrostatic pressure. The dif-ficulties in applying Bragg gratings for this purposeare mainly associated with their low sensitivity topressure, which for standard gratings is approxi-mately d�B�dp �3.4 pm�MPa.2 As a result, the

E. Chmielewska �[email protected]� and W. Ur-banczyk are with the Institute of Physics, Wroclaw University ofTechnology, 50-370 Wroclaw, Wybrzeze Wyspianskiego 27, Poland.W. J. Bock is with the Centre de Recherche en Photonique, Depar-tement d’Informatique et d’Ingenierie, Universite du Quebec enOutaouais, P.O. Box 1250, Station B, Gatineau Quebec J8X 3X7,Canada.

Received 20 May 2003; revised manuscript received 4 August2003.

0003-6935�03�316284-08$15.00�0© 2003 Optical Society of America

6284 APPLIED OPTICS � Vol. 42, No. 31 � 1 November 2003

use of such gratings is practically restricted to themeasurement of higher pressures. Furthermore, asthe grating is always exposed to ambient tempera-ture changes, it is difficult to separate the pressure-and temperature-related contributions to the overallwavelength shift in the reflected or transmissionspectrum. Several solutions have already been pro-posed3,4 to overcome the problem of low pressuresensitivity and the high temperature–pressure cross-sensitivity effect. The most promising ideas takeadvantage of specific features of the side-hole fiber,which was initially developed for polarimetric pres-sure measurements.5–7 A side-hole fiber has two airchannels located in parallel to the core, which can beeither cylindrical or elliptical �Fig. 1�. The air chan-nels cause high asymmetry of the in-plane principalstress components induced by hydrostatic pressurenear the core region.8 The stress asymmetry is re-sponsible for extremely high polarimetric sensitivityof the side-hole fiber to hydrostatic pressure, whichcan reach as much as �100 rad��MPa m�.8,9 Thenegative sign of pressure sensitivity indicates thatthe modal birefringence decreases with applied pres-sure. Another advantage of the side-hole fiber isthat its polarimetric sensitivity to temperature is rel-atively low approximately �0.5 rad��K m��. Thecombination of high sensitivity to pressure and lowsensitivity to temperature makes the side-hole fiber

especially well suited for hydrostatic pressure mea-surements by use of polarimetric techniques.5–7

Taking into consideration the above facts, it is rea-sonable to expect that the Bragg grating written inthe side-hole fiber will show significantly increasedsensitivity to pressure compared with those writtenin standard single-mode fibers. This expectationwas experimentally confirmed for the first time byCroucher et al.10 They demonstrated that the grat-ing, which couples energy between polarizationmodes in the side-hole fiber �rocking filter�, has apressure sensitivity 4 orders of magnitude higher �ap-proximately 100 pm�MPa� than the standard grat-ing. The rocking filter written in this fiber had to beas much as 100 cm long, which is not appropriate forpractical applications.

Fiber Bragg gratings imprinted in side-hole fibershave been shown11,12 to be good candidates for simul-taneous sensing of hydrostatic pressure and temper-ature. Unfortunately, researchers used a side-holefiber with a cylindrical core, which resulted in itssmall initial birefringence. Recently Kreger et al.13

investigated a Bragg grating imprinted in the side-hole fiber with much higher initial birefringence en-sured by an elliptical core. Such gratings reflect twodifferent wavelengths �B

x and �By associated with

LP01x and LP01

y polarization modes, respectively.

Owing to the high initial birefringence of the hostfiber, the two reflected wavelengths are easily sepa-rable by use of a standard optical spectrum analyzer.They13 demonstrated that the differential sensitivityof the grating to pressure d��B

x � �By��dp is much

higher than that of standard gratings ��8.7 pm�MPa� and that such gratings can be successfully usedin pressure measurements with a resolution of ap-proximately 11 kPa.

In this paper we report on measurements of tem-perature and pressure sensitivities of the Bragg grat-ing imprinted in a side-hole fiber for LP01

x and LP01y

polarization modes. Our results show that such agrating has almost identical sensitivities to temper-ature for both polarization modes and significantlydifferent sensitivities to hydrostatic pressure. Thiseffect can potentially be employed for simultaneousmeasurements of temperature and pressure by inter-rogation of wavelength shifts at LP01

x and LP01y

modes. A similar concept has already been used forsimultaneous sensing of strain and temperature.14–17

Using interferometric methods, we also measuredthe sensitivity of the host side-hole fiber to tempera-ture and hydrostatic pressure for both polarizationmodes. The results for the host fiber show goodagreement with those for the grating. This suggeststhat, on the basis of sensitivity measurements of thehost fiber, we can fully predict the sensing character-istics of a grating imprinted in birefringent fiber witha complicated structure, even before such grating isactually manufactured.

2. Measurements of the Grating Sensitivity

The grating under test was written in a side-holefiber specially developed by the Laboratory of FiberOptic Technology, University of Marie Curie–Sklodowska, Lublin, Poland. This fiber has an ellip-tical core doped with 14.2 mol.% of GeO2. Otherfiber parameters were as follows: core dimensionsa 2.33 �m, b 1.33 �m, 8-�m distance betweenthe edges of the air channels located symmetricallywith respect to the fiber core, cutoff wavelength of 650nm, and beat length of 8.2 mm at 830 nm. The fibercladding had the shape of an ellipse with dimensionsof 105 �m � 124 �m. The cross section of the fiberobtained in the scanning electron microscope isshown in Fig. 1. At room temperature and at atmo-spheric pressure, the peak reflected wavelengths forLP01

x and LP01y modes were separated by �B

x ��B

y 87 pm, and the average wavelength ��Bx �

�By��2 was equal to 829.25 nm.The setup for measuring the grating sensitivity to

temperature and pressure is shown in Fig. 2. Forthe light source, we used a superluminescent diodewith the central wavelength �0 830 nm and � � 30nm �FWHM�, so that the source spectrum containsthe wavelengths reflected by the grating. The lightsource was pigtailed with a 3M polarizing fiber,which in turn was connected to the side-hole fiber bythe polarization-maintaining connector. It was pos-sible to excite a specific polarization mode in the side-hole fiber by alignment of its polarization axes at 0° or

Fig. 1. �a� Cross section of the side-hole fiber and �b� the enlargedview of the core region with the indicated coordinate system. Thephotograph was taken with the scanning electron microscope.

1 November 2003 � Vol. 42, No. 31 � APPLIED OPTICS 6285

90° with respect to the azimuth of the mode guided inthe polarizing fiber. The part of the side-hole fiberwith the Bragg grating was installed in a high-pressure pipe sealed with epoxy glue at its ends andconnected to a Harwood DWT-35 pressure generator.This made it possible to generate the desired pres-sure with a precision of 0.1%. The pipe with thegrating was immersed in a thermostatic bath whosetemperature was controlled with a precision of 0.1 K.The wavelength shifts in the transmission spectruminduced by the change in temperature or hydrostaticpressure acting on the grating were registered by theAgilent optical spectrum analyzer with a resolution of1 pm. As illustrated in Fig. 3, applied pressure shiftsthe transmission-loss peak corresponding to the LP01

x

mode toward shorter wavelengths, in contrast to theLP01

y mode for which the spectrum was shifted towardlonger wavelengths. In consequence, the sensitivitiesto pressure for these two modes have opposite signs,negative for the LP01

x mode and positive for the LP01y

mode. In Fig. 4 we show the temperature-inducedshifts of transmission spectra for both polarizationmodes. In this case both shifts are toward longerwavelengths and are almost identical.

During measurements of the grating sensitivity,we changed temperature in the range from 0 °C to100 °C while varying hydrostatic pressure from 0 to15 MPa. Responses of the grating to those temper-ature and pressure changes are shown in Fig. 5.The wavelength difference �B

x � �By diminishes with

applied pressure and at 12.6 MPa becomes equal tozero. This effect is related to decreasing of modalbirefringence with applied pressure, which is an al-ready well-known feature of the side-hole fiber.

We determined the pressure and temperature sen-sitivities of the grating for each polarization mode bylinear fitting the data displayed in Fig. 5 and then byaveraging seven measurement series. The averagedvalues of the normalized sensitivities �1��B��d�B�dX��together with standard deviations are presented inTable 1. These results show that sensitivity of thegrating to temperature for LP01

x and LP01y polariza-

tion modes differs only by 1%, which roughly corre-sponds to the measurement accuracy. On the other

Fig. 2. Schema of the system for measuring sensitivities of theBragg grating for LP01

x and LP01y polarization modes. SLD, su-

perluminescent diode; PM, polarization-maintaining; and OSA, op-tical spectrum analyzer.

Fig. 3. Pressure-induced shifts of the transmission spectrum for�a� LP01

x and �b� LP01y polarization modes.

Fig. 4. Temperature-induced shifts of the transmission spectrumfor �a� LP01

x and �b� LP01y polarization modes.


hand, the sensitivity to pressure versus mode polar-ization is so high that it can be employed for simulta-neous measurement of temperature and pressure.

To recover information about these two parametersacting on the grating, one must measure the wave-length shifts �B

x, �By for both polarization modes

simultaneously. They are related to the measurandchanges by the following set of linear equations:

� �x

�y� � �

��x

�T��x

�p��y

�T��y

�p�� T

p� . (1)

The determinant of the sensitivity matrix appearingin the above expression should be possibly great toachieve high resolution in simultaneous measure-ments of pressure and temperature. After inserting

the sensitivity coefficients from Table 1 and takinginto account that the spectral shifts for both polar-ization modes can be resolved with a precision of 1 pmby the optical spectrum analyzer used in this exper-iment, we can estimate that the resolution in simul-taneous measurements of temperature and pressurewill be equal, respectively, to 0.2 °C and 1 kPa.These values are so small that the concept of simul-taneous measurements of temperature and pressureby interrogation of LP01

x and LP01y polarization

modes becomes quite attractive.The physical reasons for the low dependence of the

grating’s temperature sensitivity on mode polariza-tion can be easily understood by an analysis of theexpression for the normalized sensitivity:

1�B

i

d�Bi

dX� � 1

ni

dni

dX�

1�

d�

dX� for i � x, y, (2)

where � is the grating period. The main factor re-sponsible for an increase of the Bragg wavelengthwith temperature is a thermal coefficient dn�dT,which for pure silica glass is equal to 1 � 10�5 1�K.The second term in the above equation brings a neg-ligible contribution to the overall grating sensitivitybecause the thermal expansion coefficient of silicaglass is very small and equals �1��d��dT� 5 �10�7 1�K. The difference in temperature sensitivi-ties of the grating versus mode polarization is relatedto the stress caused by unequal thermal expansioncoefficients of the fiber core �SiO2 doped with GeO2�and the cladding �pure SiO2�. Via the elasto-opticeffect, the thermal stress introduces a differencebetween the refractive indices nx and ny for the re-spective polarization modes and contributes approx-imately 30%–50% to the overall birefringence of theelliptical core fiber.18 The thermal stress is releasedwith an increase of the fiber temperature, which inturn diminishes its birefringence. This effect isquantitatively represented by the parameter knownas the polarimetric sensitivity of the fiber to temper-ature:

KT �2�

�0

d�nx � ny�

dT. (3)

In an independent experiment we found KT �0.60rad��K m� at �0 830 nm for the side-hole fiber,which gives d�nx � ny��dT �7.9 � 10�8 1�K.This value is in very good agreement with the differ-ential sensitivity of the grating �1��B�d��B

x � �By��

dT. Assuming that n 1.453 and taking intoaccount the experimental data for the grating fromTable 1, we obtain d�nx � ny��dT �7.2 � 10�8

1�K. Good agreement between the polarimetric sen-sitivity of the host side-hole fiber and the differentialsensitivity of the grating leads to the conclusion thatboth effects are related to the same physical phenom-ena, i.e., release of the thermal stress with increasingtemperature.

A similar consistency exists for the sensitivities ofthe host fiber and the grating to hydrostatic pressure.

Fig. 5. Shifts of transmission spectra for orthogonally polarizedmodes �a� LP01

x and �b� LP01y versus applied �a� temperature and

�b� hydrostatic pressure.

Table 1. Normalized Sensitivity of the Bragg Grating �1��B��d�B�dX�and the Host Side-Hole Fiber ��L��1�1�L��d��dX� to Hydrostatic

Pressure and Temperature for Both Polarization Modes

Mode Units 1�B

d�B

dX ��

L��1 1

Ld�

dX

LP01x � 10�6 �K�1� 7.10 � 0.03 7.23 � 0.07

LP01y � 10�6 �K�1� 7.15 � 0.02 7.28 � 0.12

LP01x � 10�6 �MPa�1� �2.33 � 0.07 �3.82 � 0.29

LP01y � 10�6 �MPa�1� 6.47 � 0.05 7.08 � 0.42


From independent polarimetric measurements, weget Kp �82 rad��MPa m� at � 830 nm, whichgives d�nx � ny��dp �10.9 � 10�6 1�MPa for theside-hole fiber. From the experimental data dis-played in Table 1, we get almost the same value forthe grating: d�nx � ny��dp �12.7 � 10�6

1�MPa.It is far more difficult to explain the opposite signs

of the grating sensitivity to hydrostatic pressure forLP01

x and LP01y modes. Owing to the air channels,

hydrostatic pressure applied to the cladding inducesa concentration of compressive stress in the x direc-tion ��x �� y� near the core region, which leads to theincrease of refractive indices nx and ny for both po-larization modes. On the other hand, the domina-tion of the �x-stress component causes the fiber coreto become less elliptical with increasing pressure.Most probably the combination of geometrical andstress-associated effects gives rise to the oppositesigns of the pressure sensitivity for LP01

x and LP01y

modes. To analyze the problem quantitatively, onerequires reliable material data showing the depen-dence of the Young modulus and the Poisson ratio onGeO2 concentration in silica glasses. As reviewed inRef. 18, so far such data are not available in theliterature.

Good agreement between the polarimetric sensitiv-ity of the side-hole fiber and the differential sensitiv-ity of the grating to temperature and hydrostaticpressure suggests that the grating characteristics arefully predetermined by the structure of the host fiber.Indeed, it can be easily shown that the normalizedphase sensitivity of the fiber to external parameter Xfor a specific mode is formally represented by thesame expression as for the grating Eq. �2��:

1L

d�i

dX�i

L

� � 1ni

dni

dX�

1L

dLdX� for i � x, y, (4)

where �i is the phase shift experienced by the modeof specific polarization when it passes the distance Ldown the fiber length. It is reasonable to expect thatthe material constants such as thermal expansioncoefficients, the Young modulus, and the Poisson ra-tio, which indirectly influence the terms dn�dX anddL�dX, are not modified by UV radiation during theprocess of making the grating. If so, the expressionson the right sides in Eqs. �2� and �4� will take thesame values. The phase sensitivities of the host fi-ber can be easily measured with interferometricmethods or can be modeled if the material constantsfor SiO2�GeO2 glasses are known. Therefore itseems possible to predict the sensitivity of the grating�for each polarization mode� written in birefringentfibers having a complicated structure, even before thegrating is actually manufactured, simply by mea-surement of or modeling of the phase sensitivity ofthe host fiber. To verify this hypothesis, we mea-sured the sensitivity of the side-hole fiber to pressureand temperature for both polarization modes andcompared the results for the fiber with those for thegrating.

3. Measurements of the Fiber Sensitivity

The sensitivities of the host side-hole fiber were mea-sured in the system based on the Michelson inter-ferometer shown in Fig. 6. For a light source, weused the same superluminescent diode that was ap-plied for characterization of the grating. The lin-early polarized light from the source was coupled intoone polarization mode of the polarization-maintaining coupler. The reference and the testedside-hole fibers were connected to the outputs of thecoupler through the polarization-maintaining con-nectors. The same polarization modes were excitedin both interferometer arms by proper angular align-ment of the coupler outputs with respect to the ref-erence and the tested side-hole fibers. The mirrorsplaced at the ends of both arms reflected back the

Fig. 6. Schema of the system for measuring sensitivities of the host side-hole fiber to temperature and hydrostatic pressure for LP01x and

LP01y polarization modes.


excited modes, which finally interfered at the fourthoutput of the polarization-maintaining coupler. Weanalyzed the result of interference by splitting theoutput light versus wavelength with the diffractiongrating and registering the spectrum with the CCDcamera �Fig. 6�. In this way the group retardationbetween interfering modes can be determined in arather straightforward way:

Ri ��0

2

�i for i � x, y, (5)

where � is the separation between successive inter-ference minima in the spectrogram registered by theCCD camera and �0 is a central wavelength of thelight source. By group imbalance of the interferom-eter, we mean Ri Ni L, where Ni is a grouprefractive index for a specific polarization mode and L is a difference in arm lengths of the interferome-ter.

To find the relation between pixels and nanometersin the registered spectrogram, we used a special cal-ibration procedure. As shown in Fig. 6, we intro-duced a delay plate made of crystalline quartztogether with a polarizer and analyzer into the colli-mated beam coming out of the coupler output. Thegeometry of the system was kept fixed during themeasurements and the calibration procedure. Thebirefringent plate acted like an unbalanced inter-ferometer with an optical path delay arising betweenits orthogonally polarized eigenwaves. The azimuthof the plate was aligned at 45° with respect to thetransmission directions of the polarizer and analyzer,causing the eigenwaves to interfere. The quartzplate introduced an optical group delay R dq N,where N 0.009334 is a quartz group birefringencefor the central wavelength �0 830 nm and dq is aplate thickness. The intensity modulation regis-tered by the CCD camera during the calibration pro-cedure is shown in Fig. 7. The locations of theintensity minima in the registered spectrogram ex-pressed in pixels were found by use of a simple nu-merical procedure. For known group imbalance R,the spectral separation � between successive inter-ference fringes can be easily found from Eq. �5�. Ascaling coefficient was determined by linear fitting ofthe relation between the spectral separation offringes and their position expressed in pixels �Fig. 7�.The calibration procedure was repeated several timesfor different thicknesses of the delay plates �59.2,34.2, and 84.2 mm�, yielding the averaged scalingfactor equal to 0.0168 � 0.0001 nm�pixel.

To measure the sensitivity of the fiber for bothpolarization modes, we installed unequal lengths ofthe tested and the reference fibers, respectively, Ltand Lr, in a special chamber and subjected them totemperature and pressure changes. Outside and in-side the chamber the two fibers were located as closeto each other as possible, which made the measure-ment less sensitive to temperature gradients. Todetermine the fiber sensitivity for specific mode d�i�dX, we first measured the group imbalance versus

applied measurand Ri�X� �see Fig. 8�, and then, bylinear fitting these experimental data, we found theproportionality coefficient d Ri�X��dX. Finally, thefiber sensitivity was calculated with the followingformula:

1L

d�i

dX�

�

�0�Lt � Lr�

d Ri�X�

dXfor i � x, y, (6)

where

d Ri�X�

dX� 2�Lt � Lr� Ni� 1

Ni

dNi

dX

�1

Lt � Lr

d�Lt � Lr�

dX �for i � x, y. (7)

In the described experiment, owing to the use of adetection method based on spectral analysis, we ac-tually measured the susceptibility of the group re-fractive index to external parameter dNi�dX insteadof dni�dX. Therefore, when calculating the phasesensitivity according to expression �6�, we make asystematic error assuming that Ni ni and dNi�dX dni�dX. In the case of the refractive index, such asimplification introduces an error of a few percent.

Fig. 7. �a� Spectrogram registered during calibration procedure�dq 59.2 mm� and �b� the relation between the spectral separa-tion of interference fringes and their position expressed in pixels.


Owing to a relatively uniform distribution of stressinduced by pressure and temperature, it may be alsoexpected that the fiber sensitivity to these parame-ters is weakly dependent on wavelength and that thetotal systematic error in our measurement method isbelow 10%.

The normalized values of temperature and pres-sure sensitivities of the side-hole fiber are presentedin Table 1. Each result from Table 1 was obtainedby our averaging seven measurement series. As thesign of initial group imbalance Ri�X 0� cannot bedetermined directly from the output spectrogram, weused a special procedure to recognize it. By elongat-ing the reference fiber, we induced an increase ofoptical path delay. If, in response to this perturba-tion, the fringes in the spectrogram become wider,the imbalance Ri has a positive sign. If they be-come narrower, the imbalance has a negative sign.This procedure ultimately allowed us to identify thesigns of all measured sensitivities.

Similarly to the case of the grating, the normalizedsensitivities of the fiber to temperature for both po-larization modes have a positive sign and are equal toeach other. Furthermore, the measured sensitivi-ties for the fiber agree within a 2% error with thosefor the grating. We also detected a negative sign ofthe fiber sensitivity to pressure for the LP01

x modeand a positive sign for the LP01

y mode, just as for the

grating. Furthermore, the measured sensitivities topressure for the fiber and for the grating agree rea-sonably well. These results confirm our earlier sug-gestions that it is possible for one to predict thesensitivity of gratings written in highly birefringentfibers having a complicated structure simply by mea-suring or by modeling the sensitivity of the host fiberto the required physical parameters.

4. Conclusions

We measured the sensitivities �d�B�dX� of the Bragggrating and of the host side-hole fiber �d��dX� totemperature and hydrostatic pressure for both polar-ization modes. We detected opposite signs of pres-sure sensitivity versus mode polarization for both thegrating and the host fiber. We also suggested that,owing to the high difference in the pressure sensitiv-ities and the small difference in the temperature sen-sitivities versus mode polarization, this type ofgrating can be utilized for simultaneous temperatureand pressure measurements by interrogation of thewavelength shifts at the LP01

x and LP01y modes. We

demonstrated that such an approach can ensure arelatively high resolution, 0.2 °C and 1 kPa for tem-perature and pressure measurements, respectively.Furthermore, we proved in an experimental way thatthere is a close relation between the sensitivity of thegrating and that of the host fiber. This relation canbe used for predicting the grating sensitivities to dif-ferent physical parameters simply by measurementof or modeling of the response of the host fiber.

We are grateful to the Laboratory of Fiber OpticTechnology, University of Marie Curie–Sklodowska,Lublin, Poland, for providing the samples of the side-hole fiber. We also acknowledge support of this re-search by the Polish Committee for ScientificResearch under grant 4 T10C 039 23 and by theNatural Sciences and Engineering Research Councilof Canada.

References1. Y.-J. Rao, “In-fiber Bragg grating sensors,” Meas. Sci. Technol.

8, 355–357 �1997�.2. M. G. Xu, L. Reekie, Y. T. Chow, and J. P. Dakin, “Optical

in-fiber grating high pressure sensing,” Electron. Lett. 29,398–399 �1993�.

3. Y. Liu, Z. Guo, Y. Zhang, K. S. Chiang, and X. Dong, “Simul-taneous pressure and temperature measurement withpolymer-coated fiber Bragg grating,” Electron. Lett. 36, 564–566 �2000�.

4. A. Frank, K. Haroud, E. Rochat, K. Bohnert, and H. Brandle,“High resolution fiber laser sensor for hydrostatic pressure,” inProceedings of 15th International Conference on Optical FiberSensors �Optical Society of America, Washington, D.C., 2002�,pp. 359–362.

5. H. M. Xie, Ph. Dabkiewicz, R. Ulrich, and K. Okamoto, “Side-hole fiber for fiber-optic pressure sensing,” Opt. Lett. 11, 333–335 �1986�.

6. M. Turpin, M. Brevignon, J. P. Le. Pesant, and O. Gaouditz,“Interfero-polarimetric fiber optic sensor for both pressure andtemperature measurement,” in Proceedings of 8th Interna-tional Conference on Optical Fiber Sensors �Institute of Elec-trical and Electronic Engineers, New York, 1992�, pp. 362–365.

Fig. 8. Changes in retardation for the LP01x and LP01

y polariza-tion modes induced by �a� temperature �Lt � Lr 0.995 m� and �b�hydrostatic pressure �Lt � Lr 1.040 m�.


7. W. J. Bock, M. S. Nawrocka, and W. Urbanczyk, “Highly sen-sitive fiber-optic sensor for dynamic pressure measurements,”IEEE Trans. Instrum. Meas. 50, 1085–1088 �2001�.

8. W. J. Bock, W. Urbanczyk, and J. Wojcik, “Characterization ofelliptical-core side-hole fibers for interferometric pressuresensing,” in Interferometry ’94: Interferometric Fiber Sensing,E. Udd and R. P. Tatam, eds., Proc. SPIE 2341, 152–159�1994�.

9. W. Urbanczyk, M. S. Nawrocka, and W. J. Bock, “Digital de-modulation system for low-coherence interferometric sensorsbased on highly birefringent fibers,” Appl. Opt. 40, 6618–6625�2001�.

10. J. A. Croucher, L. Gomez-Rojas, S. Kanellopoulos, and V. A.Handerek, “High sensitivity pressure measurements usingside-hole fiber,” in Twelfth International Conference on OpticalFiber Sensors, Vol. 16 of 1997 OSA Technical Digest Series�Optical Society of America, Washington, D.C., 1997�, pp. 72–74.

11. R. J. Schroeder, T. Yamate, and E. Udd, “High pressure andtemperature sensing for the oil industry using fiber Bragggratings written onto side hole single mode fiber,” in 13thInternational Conference on Optical Fiber Sensors, B. Y. Kimand K. Hotate, eds., Proc. SPIE 3746, 72–74 �1999�.

12. T. Yamate, R. T. Ramos, R. J. Schroeder, and E. Udd, “Ther-mally insensitive pressure measurements up to 300 degrees Cusing fiber Bragg gratings written onto side-hole single mode

fiber,” in 14th International Conference on Optical Fiber Sen-sors, A. G. Mignani, ed., Proc. SPIE 4185, 628–631 �2000�.

13. S. Kreger, S. Calvert, and E. Udd, in Proceedings of FifteenthInternational Conference on Optical Fiber Sensors �Optical So-ciety of America, Washington, D.C., 2002�, pp. 355–358.

14. M. Sudo, M. Nakai, K. Himeno, S. Suzaki, A. Wada, and R.Yamauchi, “Simultaneous measurement of temperature andstrain using PANDA fiber grating,” in Twelfth InternationalConference on Optical Fiber Sensors, Vol. 16 of 1997 OSATechnical Digest Series �Optical Society of America, Washing-ton, D.C., 1997�, pp. 170–173.

15. W. Urbanczyk, E. Chmielewska, and W. J. Bock, “Measure-ment of temperature and strain sensitivities of a two-modeBragg grating in a bow-tie fiber,” Meas. Sci. Technol. 12, 800–804 �2000�.

16. L. A. Ferreira, F. M. Araujo, J. L. Santos, and F. Farahi,“Simultaneous measurement of strain and temperature usinginterferometrically interrogated fiber Bragg grating sensor,”Opt. Eng. 39, 2226–2234 �2000�.

17. T. Mizunami, T. V. Djambova, T. Niiho, and S. Gupta, “Bragggratings in multimode and few-mode optical fibers,” J. Light-wave Technol. 18, 230–235 �2000�.

18. W. Urbanczyk, T. Martynkien, and W. J. Bock, “Dispersioneffects in elliptical-core highly birefringent fibers,” Appl. Opt.40, 1911–1920 �2001�.


measurement of pressure and temperature sensitivities of a bragg grating imprinted in a highly...

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