Design and development of a temperature-compensatedfiber optic polarimetric pressure sensor based on photoniccrystal fiber at 1550 nm

Harneet K. Gahir and Dhiraj Khanna

Use of photonic crystal fibers (PCFs) in the field of sensing is relatively new. We propose the applicationof a PCF for pressure sensing. The fiber analyzed is a polarization-maintaining PCF that has negligiblesensitivity to temperature, making it an ideal candidate for pressure sensing in harsh environments. Onthe basis of theoretical and experimental analysis, PCF is proposed to be applied as a temperature-compensated pressure sensor. Detailed theoretical analysis and the experiment carried out are describedto show the concept of the sensor. © 2007 Optical Society of America

OCIS codes: 060.2370, 060.2420, 060.2310.

1. Introduction

Recently, research activities in the area of photoniccrystal fibers (PCFs) for sensing applications havegathered momentum because of the fibers’ uniquecharacteristics.1–3 Polarization-maintaining PCFs(PM-PCFs) are a relatively new class of fiber thatshow strong separation of polarization modes, andhence they may find application in fiber optic sensorsbased on the polarimateric technique. High birefrin-gence in PCFs can be introduced by having differentair-hole diameters along the two orthogonal axes orby asymmetric core design.4 This induced high bire-fringence of PCFs makes them potential candidatesfor polarimetric interferometric fiber optic sensors.The response of polarimetric fiber sensors to measur-ands arises from a change in the refractive index ofglass caused by various kinds of stress or strain.There is always a change in refractive index inducedby temperature-dependent strain in ordinary PMfiber-based polarimetric sensors.5 Various techniqueshave been reported in the past for temperature com-pensation in fiber optic pressure sensors.5–8 In PCFs

birefringence arises from nonaxisymmetric distribu-tion of the effective refractive index around the core;hence they are highly insensitive to temperaturevariations.9 It is reported that the temperature sen-sitivity of holey fibers is at least 1 order of magnitudelower than classical highly birefringent (HiBi)fibers.10–12 This low sensitivity of PCF is associatedwith a lack of thermal stresses in the fiber, thuseliminating the need for complicated temperature-compensation schemes.

In the present paper the high birefringence and lowtemperature sensitivity of a PM-PCF supplied byBlaze Photonics is exploited theoretically and exper-imentally for the design of a pressure sensor. Thebirefringence (form birefringence) in this fiber is in-duced by two air holes adjacent to the fiber core thathave diameters greater than the diameter of the clad-ding holes; the birefringence is insensitive to temper-ature variations. Also, in this fiber the temperaturecoefficient of birefringence is �30 times lower thanthat of conventional HiBi fiber,13 which leads to thetemperature compensation of the device.14 Recently,Bock et al.15 reported the first sensor based on PCFfor pressure measurement at 1618 nm. They splicedvarious segments of the PCF, which led to tempera-ture self-compensation. Studying optical propertiesof low-loss polarization-maintaining PCF, Suzukiet al.16 reported that PM-1550-01 has a transmissionloss and cross talk of 1.3 dB�Km and less than�22 dB, respectively, at 1550 nm.

A detailed theoretical model, developed by usingthe Mueller–Stokes polarization matrices is reportedin the present paper. The experiment was performed

The authors are with the Faculty of Applied Physcis, Institute OfArmament Technology, Simhgad Road, Girinagar, Pune 411025,Maharashtra, India. E-mail addresses are H. K. Gahir, gahir08@gmail.com, and D. Khanna, dhirajkhanna@gmail.com.

Received 4 October 2006; revised 1 December 2006; accepted 1December 2006; posted 6 December 2006 (Doc. ID 75789); pub-lished 20 February 2007.

0003-6935/07/081184-06$15.00/0© 2007 Optical Society of America

1184 APPLIED OPTICS � Vol. 46, No. 8 � 10 March 2007

on the basis of the proposed theoretical model. Re-cently Bock et al.15 reported a interesting sensorbased on PCF, which promises to greatly simplify theconstruction of the sensor while enhancing its perfor-mance. One of the motivations for the present paperis to present a setup that is significantly simpler thanthat reported by Bock et al.15 The model of the pres-sure sensor proposed here is simple, since it does notrequire the complicated scheme of splicing the vari-ous segments of PCF, which generally leads tosignificant losses. It is worth mentioning that the pro-posed sensor is novel in itself, as it operates in thetelecommunication window at 1550 nm with the ad-vantage of low temperature sensitivity with a simpledesign configuration. Experimental results obtainedby Bock et al. are evaluated on the basis of the the-oretical model proposed here.

The paper is structured as follows: Section 2 givesa description of the theoretical analysis of the sensordesign. In Section 3, the experimental setup of thesensor is described. Section 4 contains the importanttheoretical and experimental results, and Section 5finally summarizes the paper with important conclu-sions.

2. Theoretical Analysis of Sensor Design

Most of the schemes for temperature compensation ina fiber optic pressure sensor are complicated, as men-tioned above. Use of PM-PCF for a pressure-sensingapplication provides a solution for the complicatedtemperature-compensating techniques. We have ex-plored this very important property of PM-PCF for apolarimetric-based pressure sensor that is compen-sated relative to temperature variations.

The basic configuration of the proposed fiber opticsensor system is illustrated in Fig. 1. The systemincludes a highly polarized light source, PM-PCF,polarization beam splitters (PBSs), photodetectors(D1 and D2), a data aquistion card, and the LabVIEWenvironment. We have assumed that linearly polar-ized light from the source with intensity Iin is irradi-ated on the PM-PCF at an angle of � to the fast axisof the fiber, which is taken to be the X axis in the XYZcoordinate system. The slow axis of fiber is consideredto be along the Y direction, and the direction of prop-agation is taken to be the Z axis. After traversing adistance L, which is the length of the fiber beingsubjected to pressure, the light is incident on a po-larization beam splitter aligned at an angle of � to thefast axis of the fiber. The role of the polarization beamsplitter is to separate the two orthogonally linearlypolarized components in mutually perpendicular di-

rections. The state of polarization (SOP) is a conve-nient way of measuring the signal independent of theinput intensity fluctuations.

A detailed theoretical analysis of the light propa-gation through various optical elements as men-tioned above is carried out by using Jones and Mullermatrices. The input and output Stokes vectors arerelated as

Sout � TP · TL · Sin, (1)

where

Sin � Iin�1 cos 2� sin 2� 0�t, (2)

Sout � �S0out S1

out S2out S3

out�t (3)

stand for the Stokes vectors of input and output light,respectively; t is the transpose of the matrix; and TP

and TL represent the Mueller matrix of the PBS andthe PCF segment, respectively. Fiber is treated as aretarder, as it shows a phase retardance due to in-trinsic and pressure-induced birefringence. Hence,the total phase retardance is given by

� � �0 � �P � �T, (4)

where

�0 ��ns � nf�2�L

�, �P �

PKP2�L�

, (5)

�T �TKT2�L

�, (6)

with

KP ��ns

�P ��nf

�P , KT ��ns

�T ��nf

�T .

Here ns and nf are the refractive indices along theslow and fast axes of the fiber; L is the length of thefiber; P and T are the pressure and temperature ap-plied on the fiber, respectively; and � is the wave-length of the light used. In the present formulationwe have neglected the retardance due to change intemperature, as it has already been reported byseveral authors that the temperature sensitivity ofPM-1550-01 is very small.13,14

The Mueller matrix for fiber becomes

TL � �1000

0100

00

cos �

�sin �

00

sin �

cos ��. (7)

Fig. 1. Schematic diagram of the proposed sensor.

10 March 2007 � Vol. 46, No. 8 � APPLIED OPTICS 1185

After traversing the fiber, the light passes from thePBS, which is oriented at an angle � to the X axis, thetwo transmitted beams will be mutually perpendicu-larly polarized at angles � and � � 90°�. Thus theMuller matrices of the PBS are

TP�� �12�

1cos 2

sin 2

0

cos 2

cos2 2

sin 2 cos 2

0

sin 2

sin 2 cos 2

sin2 2

0

0000�

(8)

TP� � 90°� �12�

1�cos 2

�sin 2

0

�cos 2

cos2 2

sin 2 cos 2

0

�sin 2

sin 2 cos 2

sin2 2

0

0000�.

(9)

The parameter of interest is the total transmittedintensity from the PBS, collected at detectors D1and D2, which is given by the first element of thematrix S0

out. The intensity at detectors D1 and D2 isfound to be

D1,2 � Iout �Iin

2 1 � cos�ns � nf�2�L�

�PKP2�L

� ��.

(10)

We have considered the simplistic case when thepolarizer and PBS are aligned such that � �� 45°. For this condition the output of detectors D1and D2 are

D1,2 � Iout �Iin

2 �1 cos ��. (11)

To overcome input intensity fluctuations, we havecalculated the SOP of the output beam, which is de-fined as

SOP �D1 � D2

D1 � D2� cos �. (12)

It is clear from the above equation that the SOPdepends only on the phase factor �, which is measur-and dependent and is totally independent of inputintensity. This also shows that the SOP ocsillates atthe frequency of 2�LKp��, and thus there will be aconstant phase shift term due to �0.

3. Experimental Setup of the Sensor

To test the feasibility of the proposed model, a pre-liminary experimental setup was developed, which isshown in Fig. 1. The system comprises a highly po-larized source at 1550 nm with output power of�680 �W; PM-PCF supplied by Blaze Photonics,Denmark; a polarization controller; a polarization ex-tinction ratio meter; and a light-wave measurementsystem with power sensor model 81635, which is usedas a detector and powermeter. The high-precision fiberlaunch system is used for coupling light into the PCF,

which resolves the general problem of lossy claddingmodes in PCF. This is suggested to be the most suit-able way of coupling light to a small-core PCF. Thecross-sectional view of the fiber is shown in Fig. 2.Various parameters of fiber used are that the diam-eter of the holes adjacent to the fiber core is 2ah

� 4.5 �m and the cladding holes are of diameter2acl � 2.2 �m and pitch length � � 4.4 �m. Theadvantage of using this fiber is its negligible temper-ature sensitivity along with high pressure sensitivity.On the basis of the negligible temperature sensitivityof PM-1550-01 reported in several papers,13,14,17 thepresent experimental setup does not require the com-plicated temperature compensation scheme of splic-ing the various segments of PCF. Instead a single

Fig. 2. Cross-sectional view of PM-1550-01 PM-PCF.

Fig. 3. Output intensity variation with applied pressure for PCF.

1186 APPLIED OPTICS � Vol. 46, No. 8 � 10 March 2007

piece of PCF served the purpose. Marcin Szpulaket al.17 calculated the value of intrinsic birefringenceand pressure sensitivity of the PM-PCF used in thepresent paper, which they found to be 0.0004 and�2.34 10�6 MPa�1, respectively, at � � 1550 nm.

Linearly polarized light from the source islaunched into the PM-PCF at an angle of 45° to thefast axis of the fiber by using the fiber launch sys-tem and polarization extinction ratio meter. Fiberof length 4.2 m is coiled in a circle of diameter40 mm on a styrofoam sheet of dimensions 17 cm 17 cm on which another styrofoam sheet has beenplaced. On this sheet the different weights are ap-plied. This pressure arrangement has made it easy toapply the pressure to the complete 4.2 m length offiber. It has the drawback that uniform pressurecould not be applied, and hence the experimentalsetup does not exactly match the proposed theoreticalmodel. The light, after traversing through the PM-PCF, passes through the analyzer, which is set at anangle of 45°, and then is detected by the light-wavemeasurement system.

4. Results and Discussions

A. Theoretical Results

It is seen from Eq. (11) that the output intensity of thesensor depends on the input intensity and pressure-induced phase shifts. Computation of the theoreticalequations has been done by simulating the proposedtheoretical model in LabVIEW. The simulated resultof the output intensity of the sensor as a function ofthe applied pressure is shown in Fig. 3. The graphshows the sinusoidal variation. In limited pressureranges, the output intensity follows a relatively lin-ear curve, which is shown in Fig. 4. This indicatesthat the sensor can be designed to work in linearpressure ranges.

It is found that the output intensity fluctuates withrespect to the input intensity. Thus it is imperative toconsider the SOP to rule out any ambiguity in mea-surements due to input intensity fluctuations. Wehave plotted the SOP versus pressure in Fig. 5, whichalso shows the same behavior as in Fig. 4

The performance of PM-PCF fiber is compared withconventional fibers as well as specially designed HiBifibers on the basis of the SOP versus pressure plot forfour different types of fiber, namely, PM-PCF, bow-tie, side-hole, and elliptical-core fibers, in Fig. 6. Whileplotting the figure, the length of all the fibers were keptthe same, �4.2 m. As is evident from the figure, thesensitivity of the side-hole fiber is maximum. Polari-metric sensitivity of the PM-PCF to pressure is rela-tively higher than the rest of the highly birefringentfibers except for the specially designed side-hole

Fig. 4. Output intensity variation with applied pressure for PCFup to the linear range.

Fig. 5. Variation of SOP with applied pressure for PCF.

Fig. 6. (Color online) Variation of SOP with applied pressure forvarious fibers.

Table 1. Polarimetric Sensitivities of Various HiBi Fibers

Type dB�dP (MPa�1)

PM-PCF �2.34276 � 10�6

Elliptical core 1.90986 � 10�7

Bow tie 1.08225 � 10�6

Side hole �1.27324 � 10�5

10 March 2007 � Vol. 46, No. 8 � APPLIED OPTICS 1187

fiber.18 At the same time, PM-PCF has the advantageof having negligible temperature sensitivity as com-pared with the other fibers mentioned. The cor-responding values of polarimetric sensitivity topressure of each fiber is presented in Table 1.

To compare our results with Bock et al.,15 we haveplotted the graph of the SOP with respect to pressurefor temperature T � 14 °C in Fig. 7. We have takenthe same values of all the parameters that Bock et al.used. Results obtained by Bock et al. are shown inFig. 8. It is clearly seen from both figures that thereis a satisfactory match between the theoretical re-sults obtained by us and the experimental resultsobtained by Bock et al.

Also, the graph of output voltage versus pressurefor finite temperature �T � 14 °C� has been obtainedas shown in Fig. 9, while Fig. 10 represents the ex-perimental plot obtained by Bock et al. for outputvoltage versus pressure at the same temperature. Itis observed that both figures show almost the samebehavior in the given pressure range. It is obviousfrom Fig. 9 that the SOP of the sensor has a very lowtemperature dependence and hence does not affectthe pressure measurements. The reason behind thenegligible change in curves with respect to tempera-ture variation is that the ratio of KP and KT is ap-proximately 370 K�MPa for the PCF used in the

present paper. Kim and Kang19 also studied experi-mentally the temperature dependence of PCF (PM-1550-01) and found an exceptionally low dependenceon temperature changes in PCF.

The results obtained on the basis of theoretical analy-sis clearly prove the advantage of the low temperaturesensitivity of PCF and hence obviate the complicatedtemperature compensation scheme in which splicing offiber segments is required. On the basis of the theo-retical analysis and the result obtained, we have pro-posed a more simplified experimental setup.

B. Experimental Results

The experimental setup has been designed as men-tioned in Section 3. We have applied known weightson the fiber, which in turn have generated pressure ofa few kilopascals. The output power measured as afunction of the applied pressure is shown in Fig. 11.The experimental curve obtained shows the drop inintensity with increasing pressure. This trend of theexperimental graph (Fig. 11) and theoretical plot(Fig. 4) for output intensity versus applied pressurematches qualitatively. However, because of couplinglosses, absorption loss inside the fiber, and the as-sumption of uniform applied pressure, the experi-mental values do not agree quantitatively with theobtained theoretical values.

Fig. 7. Output intensity versus pressure for T � 0 °C.

Fig. 8. Experimental results obtained by Bock et al.15

Fig. 9. Output intensity of the sensor as a function of appliedpressure at T � 14 °C.

Fig. 10. Experimental results of Bock et al.15 at T � 14 °C.

1188 APPLIED OPTICS � Vol. 46, No. 8 � 10 March 2007

5. Conclusions

A new and simplistic method for a fiber optic pres-sure sensor compensated for temperature variationsbased on the polarimetric interferometric techniqueusing photonic crystal fiber has been described. Lowtemperature sensitivity is the inherent property ofthe PM-PCF manufactured by Blaze Photonics,which is used in the present setup. The feasibility ofthe proposed theoretical model has been demon-strated on the basis of the experiment. Theoreticalresults have been presented, and they are comparedwith the results obtained experimentally. It is worthmentioning that there is a satisfactory match be-tween our theoretical results and the experimentalresults reported by Bock et al.15 The present setuplacks an effective pressure-generating system. Re-search for the extensive design to affect the uniformpressure (megapascals) on the fiber is still going on.From the applications point of view, a PM-PCF pres-sure sensor with low temperature sensitivity can bejudiciously utilized in a wide range of pressure andstrain measuring applications, such as tsunami de-tection and structural health monitoring in harshenvironments.

The proposed scheme has many advantages overthe existing ones, which include a simpler design, lowtemperature sensitivity, high polarization sensitiv-ity, low losses, and the capability to work at the tele-communication wavelength of 1550 nm.

The authors are thankful to J. Nayak, ResearchCenter Imarat, Hyderabad, and Anuj Bhatnagar,Society for Applied Microwave Electronic Engineer-ing and Research, Mumbai, for fruitful discussionsand timely help offered. The authors are also thank-ful for the encouragement and help given by S. B.Phadke, Defence Institute of Advanced Technology,Pune. The financial support from the Ministryof Defence (Defence Research and DevelopmentOrganisation), New Delhi, is gratefully acknowl-edged.

References1. R. Kotynski, T. Nasilowski, M. Antkowiak, F. Berghmans, and

H. Thienpont, “Sensitivity of holey fiber based sensors,” inProceedings of 5th International Conference on TransparentOptical Networks and 2nd European Symposium on PhotonicCrystals (IEEE, 2003), pp. 340–343.

2. W. Urbanczyk, M. Szpulak, G. Statkiewlcz, T. Martynkien,and J. Olszewski, “Sensing capabilities of the birefringentholey fibers,” in International Conference on Transparent Op-tical Networks 2004 (2004), pp. 91–94.

3. W. J. Bock and W. Urbanczyk, “Measurements of sensitivity ofbirefringent holey fiber to temperature elongation and hydro-static pressure,” in Proceedings of the 21st IEEE Instrumenta-tion and Measurement Technology Conference 2004 (IEEE,2004), pp. 1228–1232.

4. K. Suzuki, H. Kubota, and S. Kawanishi, “Optical properties ofa low loss polarization maintaining photonic crystal fiber,”Opt. Express 9, 676–680 (2001).

5. W. J. Bock, N. S. Nawrocka, and W. Urbakezyk, “Highly sen-sitive fiber optics sensor for dynamic pressure measurements,”IEEE Trans. Instrum. Meas. 50, 1085–1088 (2001).

6. W. J. Bock, W. Urbakezyk, R. Buczynski, and A. W. Domanski,“Cross-sensitivity effect in temperature compensated sensorsbased on highly birefringent fibers,” Appl. Opt. 33, 6078–6083(1994).

7. Y. Zhao, M. Zhao, and J. Yang, “Self-compensated high pres-sure sensor with high-birefringence fiber Bragg-grating and abulk modulus,” Opt. Eng. 44, 014401-1–014401-4 (2005).

8. W. J. Bock and W. Urbakezyk, “Temperature desensitization ofa fiber optic pressure sensor by simultaneous measurement ofpressure and temperature,” Appl. Opt. 37, 3897–3901 (1998).

9. R. Kotynski, T. Nosilawski, M. Antkoniak, F. Berghmansa,and H. Thienpart, “Sensitivity of holey fiber based sensors,” inInternational Conference on Transparent Optical Networks2003 (2003), pp. 340–343.

10. T. Wolinski, in Progress in Optics XL, E. Wolf, ed. (North-Holland, 2000).

11. T. Ritari, H. Ludnigsen, M. Wegmuller, M. Legre, N. Gisin,J. C. Folkenberg, and H. D. Nielsen, “Experimental study ofpolarization properties of highly birefringent photonic crystalfiber,” Opt. Express 12, 5931–5939 (2004).

12. T. Nasilwoski, P. Lesiak, R. Kotynski, M. Antkowiak, A. Ferna-nadez, F. Bergmans, and H. Thienpart, “Birefringent photoniccrystal fiber as a multi-parameter sensor,” in ProsymposiumIEEE�LEOS Belarus chapter (2003), pp. 29–32.

13. D. Kim and J. U. Kang, “Sagnac loop interferometer based onpolarization maintaining photonic crystal fiber with reducedtemperature sensitivity,” Opt. Express 12, 4490–4495 (2004).

14. C. Zhao, X. Yang, C. Lu, W. Jin, and M. S. Demokan,“Temperature-insensitive interferometer using a highly bire-fringent photonic crystal fiber loop mirror,” IEEE Photon.Tech. Lett. 16, 2535–2537 (2004).

15. W. J. Bock, J. Chen, T. Eftimov, and W. Urbanczyk, “A pho-tonic crystal fiber sensor for pressure measurements,” IEEETrans. Instrum. Meas. 55, 1119–1123 (2006).

16. K. Suzuki, H. Kubota, S. Kawanishi, M. Tanaka, and M. Fu-jita, “Optical properties of low-loss polarization maintainingphotonic crystal fiber,” Opt. Express 9, 676–680 (2001).

17. M. Szpulak, T. Martynkien, and W. Urbanczyk, “Effects of hy-drostatic pressure on phase and group modal birefringence inmicrostructured holey fibers,” Appl. Opt. 43, 4739–4744 (2004).

18. J. Chen and W. J. Bock, “A novel fiber optic pressure sensoroperated at 1300-nm wavelength,” IEEE Trans. Instrum.Meas. 53, 10–14 (2004).

19. D. Kim and J. U. Kang, “Sagnac loop interferometer based onpolarization maintaining photonic crystal fiber with reducedtemperature sensitivity,” Opt. Express 12, 4490–4495(2004).

Fig. 11. Pressure characteristics of sensor developed.

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