Optics & Laser Technology 33 (2001) 145151www.elsevier.com/locate/optlastec

Radio-over-$bre distribution using an optical D-$bre antennaA. Bhattia ;, H.S. Al-Raweshidyb, G. Murtazac

aREMEC Airtech, Smeaton Close, Aylesbury, Buckinghamshire HP19 3SU, UKbElectronic Engineering Laboratory, Communication Group, University of Kent, Canterbury, Kent CT2 2NT, UK

cDepartment of Engineering Technology, The Manchester Metropolitan University, John Dalton Building, Chester Street, Manchester, M1 5GD, UK

Received 26 September 2000; accepted 6 December 2000

Abstract

Finite element analysis has been used to characterise an all-$bre antenna using circular core D-$bre. The optical D-$bre carryinga transversely poled piezoelectric polyvinylidene 3uoride polymer coating was modelled by using three-dimensional stress analysis.The response of the D-$bre antenna was determined over a wide frequency range from 1 to 800MHz. The modelling predicts thatthe electric-$eld-induced strains will cause a phase shift of 2:43105 rad=(V=m) per metre at 5MHz. At frequencies higher than 8MHz, theoptical response is dominated by radial resonances of the D-$bre=coating composite. Using the simulation results, an electric-$eld-inducedphase shift of 7:35105 rad=(V=m) per metre has been obtained. An increase in phase modulation sensitivity by a factor of threecompared to conventional circular $bre has been achieved by utilising the unique properties of the D-$bre structure. The D-$bre antennahas potential applications in areas such as EMC testing and radio-over-$bre networks where it provides a convenient means of opticallygenerating radio signals. c 2001 Elsevier Science Ltd. All rights reserved.

Keywords: D-$bre; Antenna; Finite element analysis

1. Introduction

Radio-over-$bre (RoF) transmission systems, charac-terised by having elements of free-space radio and optical$bre, are expected to $nd an increasing role in telecommuni-cation networks over the next decade [1]. RoF systems workon the principle that an radio frequency (RF) subcarrier isused to modulate the optical signal, which is then distributedby optical $bre. Depending on the application, the radiosignals may be VHF, UHF, microwave or millimetre wave.One of the key issues in the realisation of RoF architectureis the development of an e@ective means of generating andtransmitting the radio subcarrier. The simplest method forthe generation of radio signals, for transmission through anoptical network is to directly modulate the light source withthe received electrical signal. This can be achieved in twoways; the laser bias current could be directly modulatedor alternatively the laser may be operated in continuouswave (cw) mode in conjunction with an external modulatorto modulate the intensity of the resulting output. Direct

Corresponding author. Tel.: +44-1296-319-367; fax: +44-1296-319-200.E-mail address: abhatti@remecairtech.com (A. Bhatti).

Fig. 1. Optical generation of microwaves using optical $bre antenna.

modulation of the laser can lead to a number of problemssuch as relative intensity noise (RIN), chirp and intermod-ulation distortion (IMD) [2]. However, by externally mod-ulating the laser source problems such as chirp and IMD inthe laser are virtually eliminated. A recent novel approachin generating an externally modulated optical signal hasused an optical $bre antenna based on piezoelectric poly-mer coated D-$bre. The D-$bre antenna is used to phasemodulate the lightwave with a received RF electrical signal[3]. The advantage of using the D-$bre antenna as shown inFig. 1 is that the RF signal can be directly detected whilstproviding a means for modulating the light within the $brethus bypassing the need for directly modulating the laser.The D-$bre has a D-shaped cross-section, with a 3at sur-

face parallel to the longitudinal axis of the $bre, as shownin Fig. 2. The unique property D-$bre which makes it more

0030-3992/01/$ - see front matter c 2001 Elsevier Science Ltd. All rights reserved.PII: S 0030 -3992(00)00130 -4

146 A. Bhatti et al. / Optics & Laser Technology 33 (2001) 145151

Fig. 2. D-$bre cross-section.

attractive than conventional circular $bre for sensing pur-poses originates from the greater interaction of the propagat-ing optical $eld with the external space on the planar side ofthe $bre geometry. In conventional circular $bres, the opti-cal $eld remains within the $bre structure due to the glasscladding layer, in the case of D-$bre the guiding region isnow closer to the outer surface of the $bre. Moreover, re-moving a small amount of the cladding layer from the 3atsurface will bring the optical $eld (known as the evanescent$eld) to the surface. In this way, the evanescent $eld allowsa much greater interaction between the optical lightwaveand any outside perturbation, thus allowing construction ofa far more sensitive device.

2. Modelling approach

Experimental measurements taken on a polymer-coatedelliptical core D-$bre with d-distance of 11m and doublecladding layer have shown an electric-$eld-induced phaseshift of 1:7rad=(V=m) per metre [2]. In this paper, wepresent an alternative approach using $nite element analysis(FEA) to study the response of a polymer-coated circularcore D-$bre with single cladding layer. The complex geo-metrical structure of the D-$bre does not allow the devel-opment of a straightforward mathematical model, whereasFE modelling techniques have been proven to characterisecomplex structures with relative ease and accuracy [4]. Withthe availability of increasingly sophisticated FEA software,this approach o@ers a very useful alternative for studyingthe response of the D-$bre antenna. One of the main ad-vantages of using FEA techniques is that test simulationsmay be performed to study the antenna structure in order todeduce an optimised design prior to fabrication.Previously, in order to validate the feasibility and accu-

racy of the FE model initial simulations were carried out fora circular singlemode $bre jacketed with a radially polarisedmaterial. The advantage of using this con$guration is that anexact mathematical solution can be obtained thus providingan e@ective comparison for the FEA. The FE model showedexcellent agreement with both theoretical and experimentalresults [5]. This work describes, for the $rst time, a novel ap-proach of using FEA to simulate the response of the D-$bre

antenna. Results showing the wide frequency response from1 to 800MHz of the phase shift induced in a circular coreD-shaped optical $bre jacketed with a transversely polarisedpiezoelectric material are presented.

3. Piezoelectric polymer coating

Piezoelectricity is the property possessed by some mate-rials of becoming electrically charged when subjected to amechanical stress. Such materials also exhibit the conversee@ect whereby on application of an electric $eld the mate-rial deforms. The large piezoelectric coeKcients in polarisedpolyvinylidene 3uoride (PVDF) have stimulated a great dealof interest in this polymer since its discovery [6]. PVDF is asemicrystalline polymer consisting of longchain moleculeswith the repeat unit CF2CH2. It has been established forseveral years that PVDF exists in at least three crystallineforms: polar form I also known as -phase, anti-polar form II(-phase) and polar form III (-phase) [7]. The phase mostcommonly formed on solidi$cation is the anti-polar -phase.In this phase, the macromolecules are packed such that thedipoles from each molecule cancel. Consequently, -phaselamellae carry no net polarisation and are not piezoelectri-cally active. Dipole moment cancellation is conventionallyrelieved by inducing a transition to the -phase. In thin-$lmpolymers, this is achieved by mechanically stretching theplastic to convert the polymer crystallites to a piezoactivephase [8].However, at this stage the dipole alignment in the par-

tially crystalline regions are random, and there is no netdipole moment for the $lm. To bring about polarisation inthe $lm, the $lm is subjected to a strong electric $eld, whichpreferentially aligns the polar axes of the crystals along the$eld direction. It has been shown that poling $eld strengthsgreater than 1mV=cm in anti-polar -phase PVDF inducea phase transformation to a polar -phase which exhibits apiezoelectric activity comparable to that of mechanicallyoriented samples [7].

4. Piezoelectric constants

Consider an electric $eld applied to a PVDF polymer$lm poled in the transverse (two-direction) as shown inFig. 3. The plastic responds to the component of the electric$eld, E2, parallel to the direction of polarisation. The $eldE2 produces strains both in the direction of the $eld andtransverse to it, as follows:

S1 = d21E2; S2 = d22E2; S3 = d23E2; (1)

where the dij are the piezoelectric coeKcients of the thin$lm. For an isotropic unoriented piezoelectric polymer poledalong the two-direction, the lamellae maintain a randomorientation in the plane normal to the poling direction.Hence, its piezoelectric properties would be the same in

A. Bhatti et al. / Optics & Laser Technology 33 (2001) 145151 147

Fig. 3. Transversely polarised thin $lm polymer.

Fig. 4. Schematic structure of a D-$bre antenna showing dipole orientationof PVDF polymer jacket.

both transverse (1 and 3) directions. The two piezoelectricconstants that are of most interest in this case are the d21 andd23 constants, where the $rst subscript indicates directionof electric $eld and the second subscript indicates the direc-tion of the strain. Piezoelectric polymers have been used ina variety of applications such as in ultrasonic transducers,resonators, hydrophones, sensors and actuators their uniquecharacteristics o@er a number of advantages including [9]

Ease of integration into existing structures. Easily controlled by voltage. Low-weight and low-power requirements. Low-$eld linearity and high bandwidth.

5. D- bre antenna

The mechanism of operation for the D-$bre antenna asshown in Fig. 4 is a dynamic mechanical stressing of theD-$bre which occurs when the PVDF coating responds toan incoming RF electric $eld. The electric $eld in turn gen-erates a longitudinal acoustic wave within the PVDF jacketdue to the converse piezoelectric e@ect. As the acoustic wavetravels back and forth across the jacket an acoustic standingwave is produced causing the piezoelectric jacket to com-press and expand in a single transverse direction (along thedirection of the dipole orientation as shown in Fig. 4) andalso axially, inducing axial strains and asymmetric radialstrains in the D-$bre.

The phase of the lightwave propagating through theD-$bre is de$ned as

= L= konL; (2)

where is the wave propagation constant, ko is thefree-space optical wave number, n is the e@ective index ofrefraction for the guided mode and L is the D-$bre length.In the presence of an acoustic strain $eld, the D-$bre

is subject to modulating e@ects, an optical phase shift Moccurs in the light beam and is given by

M= konML+ koLMn: (3)

In Eq. (3), ML, the change in length can be replaced byLS3 where S3 is the axial strain along the longitudinal axisof the D-$bre. The second term is the change in refractiveindex due to the photoelastic e@ect and is computed fromthe index ellipsoid:

M(1n2

)i=

6j=1

PijSj; (4)

where Pij denotes the photoelastic coeKcients and Sj is theinduced strain in the D-$bre core. Under the approximationni n [8]:

M(1n2

)i=2Mni

n3: (5)

Using Eq. (4), and neglecting shear strains (S4 = S5 = S6 =0) we can now obtain the changes in the three principalrefractive indices:

Mn1

Mn2

Mn3

Mn4

Mn5

Mn6

=n3

2

P11S1 + P12S2 + P12S3

P12S1 + P11S2 + P12S3

P12S1 + P12S2 + P11S3

0

0

0

: (6)

Light propagating in the z-direction is polarised along thetransverse directions, hence Eq. (6) reduces to

Mn1 =n3

2(P11S1 + P12S2 + P12S3);

Mn2 =n3

2(P12S1 + P11S2 + P12S3); (7)

where S1; S2 and S3 are the strains in the transverseand axial directions, respectively, substituting Eq. (7) intoEq. (3) we get

M1 = konL{S3 n

2

2(P11S1 + P12S2 + P12S3)

};

M2 = konL{S3 n

2

2(P12S1 + P11S2 + P12S3)

}: (8)

148 A. Bhatti et al. / Optics & Laser Technology 33 (2001) 145151

With the non-uniform strain distribution in the D-$bre coresuch that S1 = S2, the induced optical birefringence B is de-$ned as

B=M1 M2 = kon3LP44(S1 S2); (9)where

P44 =(P11 P12)

2:

The natural geometrical birefringence produced by theasymmetric shape of the D-$bre cladding enables the polari-sation state of the lightwave to be preserved as it propagatesthrough the $bre core. Thus, by aligning one of principalaxes parallel to the plane of dipole orientation yields a purephase modulation [8]. Hence, Eq. (8) can be reduced to

M1 = konL{S3 n

2

2[P11S1 + P12S2 + P12S3]

}: (10)

6. Finite element analysis

The matrix form of the constitutive equations relatingmechanical and electrical quantities in a linear piezoelectricmaterial are used to derive the FE model:

S= sET+ dE; (11)

D= dT + UTE; (12)

where prime denotes a transposed vector or matrix. S andT are the mechanical strain and stress vectors; E and D arethe electric $eld vector and the electric displacement vector;sE; UT and d are the elastic compliance matrix at constantelectric $eld, dielectric permittivity matrix at constant stress,and piezoelectric constant matrix, respectively.Eqs. (11) and (12) can be written out in full as follows:

S1

S2

S3

S4

S5

S6

D1

D2

D3

=

sE11 sE12 s

E13 s

E14 s

E15 s

E16 d11 d21 d31

sE21 sE22 s

E23 s

E24 s

E25 s

E26 d12 d22 d32

sE31 sE32 s

E33 s

E34 s

E35 s

E36 d13 d23 d33

sE41 sE42 s

E43 s

E44 s

E45 s

E46 d14 d24 d34

sE51 sE52 s

E53 s

E54 s

E55 s

E56 d15 d25 d35

sE61 sE62 s

E63 s

E64 s

E65 s

E66 d16 d26 d36

d11 d12 d13 d14 d15 d16 T11 T12

T13

d21 d22 d23 d24 d25 d26 T21 T22

T23

d31 d32 d33 d34 d35 d36 T31 T32

T33

T1

T2

T3

T4

T5

T6

E1

E2

E3

:

(13)

The elastic behaviour of piezoelectric media is governed byNewtons second law,

(@=@x; @=@y; @=@z)T =@2g@t2

; (14)

where is the density of the piezoelectric medium and whereg= [uvw]T is the mechanical displacement vector along the

x-, y- and z-axis. The mechanical strain vector S is relatedto the mechanical displacement vector g by

S= Bg; (15)

where

B=

@=@x 0 0

0 @=@y 0

0 0 @=@z

@=@y @=@x 0

0 @=@z @=@y

@=@z 0 @=@x

:

The electrical behaviour of piezoelectric media is describedby Maxwells equations, upon the assumptions that thepiezoelectric material is an insulating material and that no3ow of charge occurs inside the media, which gives

(@=@x; @=@y; @=@z)D = 0 (16)

The electric $eld E is then related to the potential by

E=[@@x

;@@y

;@@z

]: (17)

A linear piezoelectric material may be completely mod-elled by Eqs. (11)(17). These di@erential equations canthen be solved by applying the appropriate mechanical (dis-placement and forces) and electrical (potential and charge)boundary conditions.

7. FEA simulation

The basic concept of the FE method is that a continuum(the total structure) can be modelled analytically by its sub-divisions into regions (FEs), in each of which the behaviouris described by a separate set of assumed functions repre-senting the stresses or displacements in that region. FEA iscomposed of several stages: Fig. 5 gives a brief overviewof the necessary steps involved in a typical FEA computa-tion. Pre-processing involves the preparation of data, suchas geometry construction, mesh generation, material proper-ties and load=boundary conditions. The processing stage iswhere the main analysis takes place whereby for each FE,the physical process is approximated by mathematical func-tions. Finally, the post-processing stage deals with the pre-sentation of results. A complete FEA is a logical interactionof the three stages.The commercial software package, AbaqusJ was used

to carry out the FE modelling of the D-$bre antenna,shown in Fig. 4. This package is a general purpose;production-oriented FE program capable of addressing abroad range of engineering problems. The advanced piezo-electric capabilities within this package make it an idealtool to analyse the acoustooptic interaction taking placewithin a piezoelectric polymer coated optical $bre. The

A. Bhatti et al. / Optics & Laser Technology 33 (2001) 145151 149

Fig. 5. Finite element code implementation.

modelling approach used in AbaqusJ is best described bythe 3ow chart in Fig. 5.A D-shaped optical $bre with a d-distance (3at surface=

core distance) of 7m, core diameter of 4m, claddingdiameter of 125m and carrying 20m thick piezo-electric coating was modelled by using three-dimensionalFEA. Mechanical and electrical boundary conditionsemployed within the model assumed a stress-free sur-face at coating-air interface, continuity of stresses atD-$bre=coating interface and continuity of displacements atD-$bre=coating interface. In addition, application of 30Vpotential di@erence to piezoelectric coating was simulatedwhilst the average axial force was assumed to be zero.The mesh in Fig. 6 represents a symmetrical cross-sectionof the D-$bre=jacket composite. Each region representingthe D-$bre core, cladding and piezo-jacket was meshedseparately by using appropriate linear brick elements. Themodelling thus created 70,000 elements for a 10 cm lengthof coated D-$bre. Table 1 shows the material propertiesused to de$ne the D-$bre=jacket composite [7].Steady-state dynamic response analysis was employed to

compute the axial- and radial-strain distribution within theglass D-$bre resulting from the converse piezoelectric e@ect.This procedure is used when the steady-state response of asystem is required as it undergoes excitation by harmonicloading at a given frequency. Such analysis is usually done asa frequency sweep by applying the loading (AC voltage) ata series of di@erent frequencies and recording the response.The solution provides the peak amplitudes and phase re-

lationships of the solution variables (strain, displacements,etc.) as a function of frequency. Once the strain coeKcientsare known, the optical phase shift resulting from both thechange in $bre length and refractive index can be calculatedusing Eq. (2). Linear dynamic analysis is computationallyinexpensive and can provide useful insight into the dynamic

Fig. 6. Finite element mesh representing symmetrical cross-section of theD-shaped optical $bre with PVDF coating.

behaviour of a system. Execution times are dependent onmodel size and preferred analysis choice. For a 10 cm lengthof coated D-$bre de$ned using 70,000 elements the calcu-lation time to complete the three-dimensional analysis wasapproximately one hour using a Hewlett Packard (HP 700)workstation.

8. Results and discussion

To obtain the response of the D-$bre antenna to an ACelectric $eld, a frequency sweep was carried out over the

150 A. Bhatti et al. / Optics & Laser Technology 33 (2001) 145151

Table 1Elastic properties of glass together with the piezoelectric and elasticproperties of the PVDF polymer

D-9breDensity 2200 kg=m3

Core diameter 4mCladding diameter 125md-Distance 7mCore refractive index 1.46Youngs modulus 7:3 1010 N=m2Poissons ratio 0.17Optical wavelength 0:6mPockels coeKcients P11 = 0:121

P12 = 0:270

Unoriented PVDF polymerDensity 1780 kg=m3

Dielectric constant 13Youngs modulus 2:5 109 N=m2Poissons ratio 0.39Jacket thickness 20mPiezoelectric constants d21 = d23 = 6 1012 m=V

d22 = 13 1012 m=V

range of values from 1 to 800MHz as shown in Fig. 7. Inthis high-frequency region, the net axial strain tends to zeroas the wavelength of the acoustic waves propagating in theD-$bre becomes smaller than the longitudinal dimensionsof the device, hence the D-$bre response can be consideredas being axially constrained [5]. Thus, at high frequencies,the dominant contribution to the overall phase shift is onlyfrom the radial strains induced by the electric $eld.An optical-phase shift of 2:43 105 rad=(V=m) per me-

tre was calculated at 5MHz. At frequencies higher than8MHz, the response is dominated by radial resonances ofthe D-$bre=jacket composite as the acoustic wavelength be-comes comparable to the radial dimensions of the device.A large number of radial resonance peaks are observed in

Fig. 7. Finite element results showing optical phase shift as a function of the applied AC voltage frequency for a 10 cm length D-$bre coated withPVDF polymer.

the region from 8800MHz. The $rst resonance peak isat 8MHz and the last at 799MHz. Using the resultsfrom FEA, an electric-$eld-induced phase shift of 7:35 105 rad=(V=m) per metre was calculated for the coatedD-$bre. This signi$cantly larger value of phase shift com-pared to the elliptical core D-$bre with double claddinglayer can be attributed to two factors: $rstly, the circularcore D-$bre has a d-distance which is nearly half that ofthe elliptical core [2]. Secondly, the extra cladding layerfor the elliptical core D-$bre plays a major role in absorb-ing some of the strain waves as they propagate through tothe D-$bre core.Assuming that the smallest optical phase shift which

can be measured (with a detection bandwidth of 1Hz) is106 rad, the minimum detectable electric $eld for a 1 kmlength of coated circular core D-$bre can be shown to be13:6V=m. This value of electric $eld response indicatesthat the sensitivity of the D-$bre is three times greaterthan that of the conventional circular coated $bre [8]. Thetypical level of electric $eld present at the microcellularstation depending on coverage area (suburban or urban)has been shown to be around 80V=m [1013]. Hence, thehigh electric $eld sensitivity of the piezoelectrically coatedD-$bre antenna can be utilised at the microcellular stationas a means of detection and external modulation.Furthermore, since the D-$bre antenna is constructed

from totally dielectric materials it can be used to receiveRF transmissions without distorting or disturbing the $eldlines since there are no metallic components to re3ect ortransmit RF energy. This type of antenna has the potentialof wide bandwidth and electrical passivity. In addition, ito@ers other advantages over conventional antennae such asintrinsic safety in hazardous environments as well as geo-metrical 3exibility which enables its use in smart structuresystems.

A. Bhatti et al. / Optics & Laser Technology 33 (2001) 145151 151

9. Conclusions

It has been demonstrated that an all-$bre optical antennacomprising a circular core D-shaped optical $bre coatedwith a transversely poled piezoelectric material can besuccessfully modelled by using FEA techniques. The mod-elling was employed to compute the phase shift over thefrequency range from 1 to 800MHz. The FEA simulationspredict a phase shift value of 7:35105 rad=(V=m) permetre. By using the circular core (single-cladding) D-$bre asigni$cant increase in the electric-$eld-induced phase shifthas been achieved over the elliptical core (double-cladding)D-$bre. Moreover, by utilising the asymmetric propertyof the D-$bre an increase in optical-phase modulation by afactor of three compared to conventional circular $breis obtained over a wide frequency range. The geometricalstructure of the D-$bre enabling a higher degree of inter-action between the strain $eld and the propagating opticalwave o@ers a considerable advantage over conventionalcircular $bres, thus allowing construction of a far more sen-sitive device. The D-$bre antenna has potential applicationsin areas such as EMC testing where its totally dielectricproperties can be utilised within hazardous environments.In addition, the use of an optical antenna for the next gen-eration mobile RoF networks provides a convenient meansof optically generating radio signals.

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