3(c), three transmission zeros are really excited using the intro-duced cross-coupling section and help us to create an upper-stopband as we expect.

4. EXPERIMENT VERIFICATION

In this work, the interdigital coupled lines with enhanced couplingdegree are used in filter design instead of the parallel coupled lines.As exhibited in [3] and [8], this interdigital coupled-line approachcan improve its wideband performance due to its tightened cou-pling degree. Following the work done in Section 3, an UWBbandpass filter with the cross-coupling embedded MMR is fabri-cated, and its photograph with all the dimensions are shown inFigure 4(a). Figures 4(b) and 4(c) depict the predicted and mea-sured frequency responses of S21 and S11 magnitudes as well asgroup delay. They are found in good agreement with each other,and so the actual realization of the preferred UWB passband andextended upper-stopband are well confirmed in experiment. FromFigure 4(b) it can be observed that three transmission zeros aresimulated upper-stopband and the measured upper-stopband isnow extended up to 20 GHz with an insertion loss higher than 10dB. The measured insertion loss is found to be 0.8 dB at the centerfrequency of the desired UWB passband. The 3-dB passbandcovers the range of 2.3–10.0 GHz with a fractional bandwidth of125%. The designed passband is slightly shifted from the desiredUWB band, e.g., 3.1–10.6 GHz. However, the design approachand theorem is proved to be true and this frequency shifted can beadjusted by circuit parameters. Moreover, the rejection skirt nearthe cutoff frequencies are sharpened to a great extent against theMMR-based UWB filters in [1] and [3], and the group delay isvery flat over the passband.

5. CONCLUSIONS

In this work, two types of the shunt short-circuited stub MMRstructures are proposed and characterized for designing of twoalternative UWB bandpass filters. Using even- and odd-modeanalysis, the proposed MMR structure can not only realize thedesired UWB passband but also create a wide upper-stopband dueto the excitation of three transmission zeros by a cross-coupledsection. An UWB bandpass filter is then designed to exhibit itsattractive sharper rejection skirts and extended upper-stopband.Finally, an UWB bandpass filter is fabricated and measured toverify the predicted UWB in-band and out-of-band performancesin experiment.

REFERENCES

1. L. Zhu, S. Sun, and W. Menzel, Ultra-wideband (UWB) bandpass filtersusing multiple-mode resonator, IEEE Microwave Wireless ComponLett 15 (2005), 796–798.

2. K.M. Shum, W.T. Luk, C.H. Chan, and Q. Xue, A UWB bandpass filterwith two transmission zeros using a single stub with CMRC, IEEEMicrowave Wireless Compon Lett 17 (2007), 43–45.

3. S.W. Wong and L. Zhu, EBG-embedded multiple-mode resonator forUWB bandpass filter with improved upper-stopband performance, IEEEMicrowave Wireless Compon Lett 17 (2007), 421–423.

4. S.W. Wong and L. Zhu, Ultra-wide bandpass filters with sharpenedroll-off skirts, extended upper-stopband and controllable notch-band,Microwave Opt Technol Lett 50 (2008), 2958–2961.

5. H. Shaman and J.S. Hong, Novel ultra-wideband (UWB) bandpass filter(BPF) with pairs of transmission zeroes, IEEE Microwave WirelessCompon Lett 17 (2007), 121–123.

6. M.-Y. Hsieh and S.-M. Wang, Compact and wideband microstrip band-stop filter, IEEE Microwave Wireless Compon Lett 15 (2005), 472–474.

7. H. Shaman and J.S. Hong, Wideband bandstop filter with cross-cou-pling, IEEE Trans Microwave Theory Tech 55 (2007), 1780–1785.

8. G.L. Zysman and A.K. Johnson, Coupled transmission line networks inan inhomogeneous dielectric medium, IEEE Trans Microwave TheoryTech 17 (1969), 753–759.

9. C. Nguyen and K. Chang, On the analysis and design of spurlinebandstop filters, IEEE Trans Microwave Theory Tech 33 (1985), 1416–1421.

© 2009 Wiley Periodicals, Inc.

POLARIMETRIC MULTILONGITUDINAL-MODE DISTRIBUTED BRAGGREFLECTOR FIBER LASER SENSORFOR STRAIN MEASUREMENT

Hao Zhang,1 Jianhua Luo,2 Bo Liu,1 Shuangxia Wang,2

Chenglai Jia,2 and Xiurong Ma3

1 Institute of Modern Optics, Nankai University, Tianjin 300071, China;Corresponding author: haozhang@nankai.edu.cn2 College of Information Technical Science, Nankai University, Tianjin300071, China3 School of Electronics Information Engineering, Tianjin University ofTechnology, Tianjin 300191, China

Received 7 February 2009

ABSTRACT: A polarimetric multilongitudinal-mode distributed Braggreflector fiber laser sensor is proposed and experimentally demon-strated. We have theoretically analyzed the mode beat mechanism of thislaser sensor, which is verified by the experimental observation, and itsapplication in strain measurement has also been studied. Experimentalresults indicate that both of the longitudinal mode beat (LMB) and bire-fringence-induced polarization mode beat signals have linear strain de-pendence, and the coefficients of determination reach 0.9991 and0.9908, respectively. One possible way to improve the sensitivity ofLMB-based sensing has been investigated as well. © 2009 Wiley Peri-odicals, Inc. Microwave Opt Technol Lett 51: 2559–2563, 2009;Published online in Wiley InterScience (www.interscience.wiley.com).DOI 10.1002/mop.24671

Key words: fiber-optic sensor; polarimetric fiber laser sensor; distrib-uted Bragg reflector (DBR); beat frequency demodulation

1. INTRODUCTION

Due to its good reliability, electro-magnetic immunity, compactsize, and high sensitivity, fiber Bragg grating (FBG) has become adistinguished component in the field of fiber-optic sensing tech-nology. In recent years, FBG-based sensors have been widelyapplied for the measurement of various physical parameters, in-cluding temperature [1, 2], strain [3, 4], pressure [5, 6], vibration[7], etc. The uprising of fiber laser technology makes it possiblethat fiber laser itself could be utilized as the active fiber sensor.With FBGs as the cavity reflectors, laser gain accumulates to ahigh level before stable laser output is yielded. In this case,FBG-based fiber laser sensors would offer higher accuracy andhigher signal noise ratio (SNR) compared with conventional pas-sive FBG sensors, which makes active FBG laser sensors espe-cially suitable for long-distance and high accuracy sensing appli-cations. According to the operation principle, fiber laser sensorscould be categorized into wavelength-encoding and polarimetricfiber laser sensors. For the former, physical measurands could beconverted into wavelength information, and by monitoring theshift of laser wavelength, sensing information could be acquired.And for the latter, polarimetric fiber lasers sensors require twoorthogonal polarization modes to generate polarization mode beat(PMB) as the sensing signal. The change of physical measurands

DOI 10.1002/mop MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 51, No. 11, November 2009 2559

will induce the shift of the laser beat frequency. Thus by trackingdown the laser beat frequency in the radiation frequency (RF)domain, the variation of environmental physical parameters couldbe measured. As expensive absolute wavelength measurement isavoided, polarimetric fiber laser sensors have attracted consider-able interest in the past decade [8–11]. In 2008, Zhang et al.reported a single-longitudinal-mode polarimetric distributed Braggreflector (DBR) fiber laser based on PMB demodulation for lateralforce measurement [12]. Since fiber-birefringence-induced PMBsignal is highly sensitive to the environmental perturbations, thiskind of DBR fiber laser has the application potential in the mea-surement of various physical measurands. However, to ensuresingle-longitudinal-mode operation and avoid the extra connectionloss between FBG and EDF, a pair of FBG with high reflectivitywas directly inscribed in a section of �2 cm EDF in their design.In addition, to establish effective laser oscillation, highly concen-trated erbium-doped fibers are indispensable to maintain a suffi-cient gain level and FBGs with high reflectivity are also requiredto ensure adequate feedback. Moreover, the effective sensinglength is limited by the �cm cavity length, as it would be ratherdifficult to apply lateral force or strain on the EDF without affect-ing the FBGs. For sensing applications, the multilongitudinal-mode DBR fiber laser has a few advantages over its single-longitudinal-mode counterpart. Firstly, it is fairly easy to fabricatea multilongitudinal-mode fiber laser with commercially availableEDF and it is unnecessary to inscribe FBGs in the EDF. Further-more, with longer cavity length, the multilongitudinal-mode fiberlaser would provide much higher laser power, and hence higherSNR, which makes it more suitable for long-distance sensingapplications. Thirdly, the multilongitudinal-mode fiber laser is ableto provide more frequency information, which could be moreflexibly exploited for sensor demodulation.

In this article, we have theoretically analyzed the mode beatmechanism of a multilongitudinal-mode DBR fiber laser sensor,and its application for strain measurement has also been investi-gated. Experimental results indicate that this laser sensor couldoperate in two modes, i.e. strain measurement could be achievedbased on either the longitudinal mode beat (LMB) between differ-ent longitudinal modes or the birefringence-induced PMB. More-over, the possibility of improving the sensitivity has also beeninvestigated.

2. OPERATION PRINCIPLE

The basic configuration of the proposed multilongitudinal-modeDBR fiber laser sensor is shown in Figure 1.

A 980 nm laser diode (LD) serves as the pump source. About22.5 cm EDF (absorption coefficient: 15.2dB/m at 979 nm; nu-merical aperture: 0.22) with a pair of FBGs are utilized to form theFabry-Perot cavity. In order to avoid the possible influence offorward remnant 980 nm on the beat signal, backward monitoring

is adopted. Fiber tip A is processed to avoid reflection, and also toeliminate the backward reflection, an optical isolator (ISO) isplaced at the signal port of the wavelength division multiplexer(WDM). In our experiment, a 3dB coupler is employed to separatethe backward laser light. One portion of the backward laser istransmitted to an optical spectrum analyzer for real-time lasermonitoring, and the other portion is converted into electrical signaland then transmitted to a RF spectrum analyzer for beat frequencydemodulation. The EDF is pasted along the central axis of auniform-strength cantilever beam (UCB) and by changing thedeflection of its free end, strain could be applied.

As different orders of longitudinal modes with intracavitybirefringence-induced mode splitting exist simultaneously, laserbeat frequency in a multilongitudinal fiber laser originates from theintracavity-birefringence-induced PMB and the LMB between dif-ferent orders of longitudinal modes as well. Firstly, let us considerthe intracavity-birefringence-induced mode splitting. According tothe laser principle, the laser frequency of a certain longitudinalmode v is determined by:

v �cq

2nl(1)

where c is the light velocity in vacuum, n is the effective refractiveindex of the fiber core, l represents the cavity length, and q refersto the order number. Considering the fiber inherent birefringence,the two orthogonal polarization modes would experience slightsplitting, and hence the laser frequency corresponding to the x andy polarization modes could be expressed as:

vx �cq

2nxl,vy �

cq

2nyl(2)

where nx and ny represent the refractive indices corresponding to xand y polarization modes, respectively. Therefore, the PMB fre-quency induced by the intracavity birefringence is:

vPMB � vx � vy ��ny � nx�cq

2nxnyl(3)

Considering �n � nx���n,�n � ny���n, the above expressioncould be modified as:

vPMB �Bv

n(4)

where B refers to the intracavity birefringence �B � ny � nx�.Hereby, for each longitudinal mode, we have a mode splittingdescribed by formula (4).

Figure 1 Schematic diagram of the active strain sensor based on a multilongitudinal-mode erbium-doped fiber laser

2560 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 51, No. 11, November 2009 DOI 10.1002/mop

For simplicity, let us consider two adjacent longitudinal modeswith birefringence-induced splitting, as illustrated in Figure 2. Dueto the fiber birefringence, either mode has slight mode splitting.v1� and v2� represent the relatively lower frequencies in either ofthe two adjacent longitudinal modes, respectively, and v1� and v2�

stand for the higher frequencies, respectively. If the differencebetween v1 and v2 relative to the original frequency of v1 or v2 isnegligible, (as the mode order number q is normally quite large,this assumption is appropriate for most single-wavelength fiberlasers), mode beat of the fiber laser could be attributed to fourfactors: the PMB frequency between v1� and v1�, v2� and v2� isBv

n; the LMB frequency between v1� and v2�, v1� and v2� turns to

bec

2nl; the LMB frequency between v1� and v2� yields

c

2nl

�Bv

n; the LMB frequency between v1� and v2� gives

c

2nl

�Bv

n. Till this stage, we have discussed all the possible mode

beats originated from two adjacent longitudinal modes. If the modebeats originated from other longitudinal modes are taken intoaccount, the above analysis should be periodically repeated andthus we have a more universal beat frequency expression for themultilongitudinal-mode fiber laser:

vB � �Bv

n,cm

2nl,cm

2nl�

Bv

n � (5)

where m is a positive integer starting from 1.According to the above analysis, possible beat frequency could

only turn up at the above positions. In our experiment, as strain isapplied on the EDF, the fiber birefringence, cavity length andrefractive index would change accordingly, which induces the shiftof laser beat frequency. And via beat-frequency-based demodula-tion, strain measurement could be achieved.

3. EXPERIMENTAL RESULTS AND DISCUSSION

In our experiment, two FBGs with matching reflection peak wave-lengths were utilized as the cavity reflectors. The output laserwavelength of this DBR fiber laser is around 1527.82 nm, asshown in Figure 3. The number of longitudinal modes is generallydetermined by the gain profile of the EDF and the mode spacing.For the proposed DBR fiber laser, the cavity length is about 37.4

cm, corresponding to the distance between the central points of thetwo FBGs. Due to its relatively longer cavity length, the DBR fiberwill no longer operate in single longitudinal mode.

From Figure 4, it is obvious that there exist a series of periodicbeat frequencies from zero frequency up to 2GHz. Since the fiberinherent birefringence is in the magnitude of 10�6, birefringence-induced PMB frequency is normally the lowest and closest to thezero frequency. As the refractive index of the fiber core is 1.467,the LMB frequency between different orders of longitudinalmodes should be about 273.39 MHz, which is in good agreementwith our experimental results. In Figure 4, it is clear that a pair of

beat frequencies with deviation ofBv

nregularly turns up on either

side of the primary LMB frequency for different orders. All of theabove experimental results indicate the validity of our theoreticalanalysis on the origin of mode beat in the multilongitudinal-modefiber laser.

A UCB with L in length and h in thickness is utilized to applystrain on the EDF. The dependence of strain � on the free enddeflection fof the UCB could be expressed as [13]:

� �hf

L2 (6)

Figure 2 Illustration of two adjacent longitudinal modes with birefrin-gence-induced mode splitting

Figure 3 Output laser spectrum of the DBR fiber laser

Figure 4 Frequency spectrum of the DBR fiber laser. [Color figure canbe viewed in the online issue, which is available at www.interscience.wiley.com]

DOI 10.1002/mop MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 51, No. 11, November 2009 2561

Thus by observing the change of deflection, we could measure thevariation of strain applied on the EDF. In Figure 5, it is apparentthat as the strain increases from �5150.552 �� to 5142.848 ��,the first order LMB frequency between different primary longitu-dinal modes linearly decreases, and the coefficient of determina-tion reaches 0.9991.

According to formula (5), the LMB frequency between differ-ent primary longitudinal modes is determined by the cavity lengthand the refractive index of the fiber core. The LMB frequency shift�vLMB could be described as:

�vLMB � �c�n

2n2l�

c�l

2nl2 � �c

2n2l��n

�l

l

��l

l�

c

2nl��l

l(7)

Define C� ��n

�as the strain dependence of refractive index, and

considering � ��l

l, the expression of LMB frequency could be

further modified as:

�vLMB � �c

2n2l� C� � � �

c

2nl� � � �

c � �C� � n�

2n2l� (8)

If the applied strain is small enough, there is approximately a linearrelationship between the shift of LMB frequency and strain, whichis describes as:

�vLMB � kLMB� (9)

where kLMB � �c � �C� � n�

2n2lis the proportional coefficient.

When strain is applied on the EDF, both of refractive index andcivility length will change accordingly. However, the refractiveindex dependence on the strain has very low negative straincoefficient of approximately �10�7/�� [14, 15], and thus in thiscase, the cavity length variation plays a major role in causing theLMB frequency shift. Therefore, the increase of strain will lead toa beat frequency shift towards lower frequency.

As there exist a series of periodic LMB frequencies in the RFdomain, the LMB frequencies other than the first order one could

also be utilized for beat frequency demodulation. Assume �v1 isthe shift of the first order LMB frequency and N is the mode ordernumber. The shifted LMB frequency turns to be v1 � �v1. Sincethe Nth order LMB frequency is always N times as that of the firstorder, the Nth order LMB frequency should be N�v1 � �v�. Andtherefore, the Nth order LMB frequency shift is N�v1, which is Ntimes as that of the first order one. This is to say if the laser poweris high enough, higher order LMB signals could be exploited forthe improvement of laser sensitivity. To confirm this analysis, wehave experimentally observed the shift of the first order and thirdorder LMB frequencies with the same strain variation. From Fig-ure 6, it can be seen that for the same strain variation, the thirdorder LMB frequency decreases by 1.3 MHz, which is about 3.1times as the 0.42 MHz shift of the first order LMB frequency. Thisis in good agreement with our above analysis.

The strain response of birefringence-induced PMB frequencyhas also been experimentally studied. From Figure 7, it is apparentthat as strain increases from 0 to 5139.424 ��, birefringence-induced PMB frequency increases as well. There is basically alinear relationship between them, and the coefficient of determi-nation reaches 0.9908. Since strain is applied along the fiber axis,the fiber birefringence will not be much affected. According to

Figure 5 First order LMB frequency between different primary longi-tudinal modes as a function of strain

Figure 6 Comparison of first order (a) and third order (b) LMB fre-quency spectra under the same strain variation. [Color figure can be viewedin the online issue, which is available at www.interscience.wiley.com]

2562 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 51, No. 11, November 2009 DOI 10.1002/mop

formula (4) and neglecting the variation of fiber birefringence,refractive index should be the primary factor that affects the shiftof PMB frequency. As strain applied on the EDF increases, therefractive index of the fiber core decreases, causing a PMB fre-quency shift towards higher frequency, as expressed by:

�vPMB � �Bv

n2 �n � �Bv

n2 ��n

�l

l

��l

l� �

Bv

n2 � C� � � (10)

If strain is small enough, the PMB frequency shift should have anapproximately linear dependence on strain, which can be describedas:

�vPMB � kPMB � � (11)

where kPMB � �BvC�

n2 is the proportional coefficient. Therefore, as

the strain increases, the PMB frequency will experience a shifttowards longer frequency.

4. CONCLUSION

In summary, we have investigated the characteristics of a polari-metric multilongitudinal-mode DBR fiber laser in the RF domain.The mode beat mechanism of this laser has been theoreticallyanalyzed and validated by our experimental observation. Experi-mental results show that we could achieve strain measurement viaeither LMB-based or PMB-based demodulation. The good linear-ity for both of the above operation modes reveals the great poten-tial of this DBR fiber laser for strain measurement. One possibleway to improve the laser sensitivity has also been discussed withexperimental proof. It should be noted that our work in this articleis just a preliminary demonstration of the multilongitudinal-modeDBR fiber laser for strain measurement. Since the multilongitudi-nal-mode fiber laser has a good variety of frequency information,different beat frequencies could be used for the sensing of differentphysical measurands. In this sense, it is possible to realize simul-taneous measurement of various physical parameters. Our nextwork would be focused on the improvement of its sensing perfor-mance and its applications in the simultaneous measurement ofdifferent physical measurands. The proposed multilongitudinal

DBR fiber laser with simpler fabrication technique, high SNR, andmore available frequency information is expected to be promisingin future sensing applications.

ACKNOWLEDGMENTS

This work was jointly supported by the National Key NaturalScience Foundation of China under Grant No. 60736039, theTianjin Key Project of Applied and Basic Research Programsunder Grant No. 07JCZDJC06000, the Key Project of Ministry ofEducation under Grant No. 206006, the “100 Projects” of CreativeResearch for the Undergraduates of Nankai University under GrantNo. BX6-215, and the National Undergraduate Innovation Exper-iment Project under Grant No. 081005511. The authors thank Dr.Zhi Wang for his constructive suggestions and great encourage-ment.

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© 2009 Wiley Periodicals, Inc.

Figure 7 Birefringence-induced PMB frequency as a function of strain

DOI 10.1002/mop MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 51, No. 11, November 2009 2563