Xiaoqi Liu, Yange Liu,and Zhi Wang

AFFILIATIONS Tianjin Key Laboratory of Optoelectronic Sensor and Sensing Network Technology,Institute of Modern Optics,Nankai University,Tianjin 300350,China

ABSTRACT A fibe twist sensor using a Sagnac interferometer incorporating a tapered polarization-maintaining fibe (PMF) is proposed.The transmission properties of the sensor are investigated both theoretically and experimentally.Given the optoelastic effect,which depends on fibe geometry,the modal and group birefringences of the PMF can be controlled by applying different twist angles.The spectral wavelength shifts,free spectral ranges,and transmission losses of the original,microtapered,and etched PMFs were compared.Notably,the interference dips for the etched PMF move in opposite directions.As a result,the proposed PMF-based sensor could have multiparameter sensing applications.

KEYWORDS Fiber-optic,Fiber-optic sensor,Polarization-maintaining,Twist sensor

I.INTRODUCTION

Sagnac interferometers (SIs) have attracted considerable interest because of their various advantages,such as independence of the polarization of input light,controllable free spectral range(FSR),immunity to electromagnetic interference,and high sensitivity.1–3Geometrical birefringence is an important parameter that determines the sensitivities of SIs.With the development of fibe fabrication technology,various SI-based sensor structures with asymmetric fibers including selectively infiltrate photonic crystal fibers4,5rectangular silica microfibers6and microtapered polarizationmaintaining fiber (PMFs),1have been investigated for the measurement of temperature,pressure,refractive index,and twist.1,4–7The sensitivities of SIs can be significantl improved8by appropriately controlling the geometrical birefringence based on a predesigned fibe cross-sectional geometry,such as the asymmetrical fiel distribution of the core mode,because of the strong evanescent fiel effect.1

Recently,a variety of low-cost,low-transmission-loss,and robust fiber-opti SI twist sensors based on all-solid asymmetric fiber have been proposed.9–12The waist diameter of the solid-core fibe can be easily reduced by tapering or etching,thereby improving sensitivity.7,13However,for conventional SI-based twist sensors,all interference dips move toward the same direction,with similar sensitivities to variations in torsion angle.

In this paper,PMF-based fiber-opti twist sensors with different waist taper shapes are proposed.The influenc of torsion angle on the transmission spectral characteristics of the original,microtapered,and etched PMF-based SIs is studied both experimentally and theoretically.The sensitivity of the PMF-based fiber-opti twist sensors is improved significantl compared with the sensitivities of −0.37 nm/(rad/m),−1.01 nm/(rad/m),and 2.2 nm/(rad/m) that have been achieved with standard single-mode fiber-base sensing structures.14,15The sensitivity can be increased by decreasing the fibe diameter,which eliminates the need to change the shape of the taper,to a helical shape,for example Ref.16.Furthermore,the whole structure is more solid and more easily fabricated.Finally,this work investigates the transmission loss and FSR at spectral notches in response to changes in twist rate.

FIG.1.(a)Schematic of the experiment setup for the SI-based twist sensing system.(b)Original PMF.(c)Microtapered PMF.(d)Etched PMF.

II.EXPERIMENTAL PRINCIPLE AND DEVICE FABRICATION

A schematic of the experimental setup for the SI-based PMF twist sensing system is shown in Fig.1(a).A supercontinuum broadband source(BBS)was employed to provide a broadband light output that was launched into the SI loop.An optical spectrum analyzer(OSA,Yokogawa AQ6370C)with an operating wavelength range 600–1700 nm and a resolution of 0.5 nm was used to monitor the spectral interference fringes,and a polarization controller was used to optimize the interference spectral pattern.The cross-section of the conventional PANDA-type PMF used in the experiment,fabricated by the 46th Institute,CETC,China,is shown in Fig.1(b).There are three different regions:a germanium-doped core,two boron-doped stress regions,and silica cladding.To investigate the effect of the waist taper shape of PMFs on twist sensitivity,the original PMF with waist diameter 124μm,a microtapered PMF with waist diameter 80μm,and an etched PMF with waist diameter 97μm were selected,as shown in Figs.1(b)-1(d).The total length of each PMF was 8.0 cm,and the length of the microtapered or etched segment was approximately 1.0 cm.The two ends of each PMF were spliced between two single-mode fiber (SMF-28e,Corning,Inc.)to construct the sensor head.One side of the sensor was clamped by a fibe holder,and the other end was mounted at the center of the rotator with an embedded engraved dial to apply twist to the PMF.7The distance between the two fibe holders was 28 cm.An 8 g weight was attached after the rotator to maintain the tight stretch of the fiber

In the Sagnac loop,the 3 dB coupler splits the input light into two counterpropagating beams and then recombines them at the output port of the coupler,resulting in spectral interference due to the phase difference between the two polarization modes guided in the PMF.17With the insertion loss of the 3 dB coupler neglected,the spectral transmittanceTof the Sagnac loop is given approximately by a periodic function of the wavelength:18

FIG.2.(a)Transmission spectral characteristics of the original PMF-based SI for torsion angles ranging from 0° to 90° .(b)Interference dip wavelength shift as a function of torsion angle.(c)FSR as a function of torsion angle for the original PMF-based SI.

whereB=nslow−nfastis the modal birefringence of the PMF,Lis the length of the PMF used in the fibe loop,andλis the operating wavelength.When a certain twist is applied to a PMF,the torsional stress fiel has an effect on the effective refractive index of the PMF.The variations in the effective refractive index can be described by the photoelastic coefficient along the fast and slow axes.19Thus,the modal birefringence of the PMF,B,can be expressed as

wheregslowandgfastare the photoelastic coefficient along the slow and fast axes,respectively,andtis the twist rate define by the variation in the torsion rate per unit length.Interference dips appear at the wavelengths at which the following phase-matching condition is satisfied

wheremis an integer,B1is the birefringence of the microtapered or etched PMF,L1is the length of the microtapered or etched segment of the PMF,andB2andL2are the birefringence and length of the remaining segment of the PMF.Furthermore,since obviouslyL1=L−L2,the phase-matching condition for interference dips can be rewritten as

FIG.3.(a)Transmission spectral characteristics of the microtapered PMF-based SI for torsion angles ranging from 0° to 90° .(b)Interference dip wavelength shift as a function of torsion angle.(c)FSR as a function of torsion angle for the microtapered PMF-based SI.

Differentiating both sides of Eq.(4)with respect totgives

Taking account of the group birefringence formula

Eq.(5)can be rewritten as

whereBg1is the group birefringence of the microtapered or etched PMF andBg2is the birefringence of the remaining segment of the original PMF.

The interference dips will move toward longer-and shorterwavelength regions when dλ/dt>0 and dλ/dt<0,respectively.If dλ/dt=0,the dip will not shift,regardless of any change in torsion angle.

Taking account of the presence of a microtapered or etched PMF segment and the original segment in our proposed SI loop,the FSR can be written as1,6,11,15

where Δn1is the effective refractive index variation of the microtapered or etched PMF,and Δn2is the effective refractive index change of the remaining PMF segment.

III.EXPERIMENTAL RESULTS AND DISCUSSION

Figures 2(a) and 3(a) show the interference spectra of the original and microtapered PMFs,respectively.As twist is applied,periodic refractive index modulation occurs and causes a shift in the interference wavelength.When the fibe diameter is tapered,a portion of the core mode is coupled to the cladding,thus forming a cladding mode.Moreover,as twist stress is applied to the cross-section of the fiber the two original polarization modes will be coupled,leading to polarization interference.16As shown in Figs.2(b) and 3(b),the wavelength shift of both the original and microtapered PMFs can be nonlinearly fitte using a sinusoidal function for an anticlockwise (ACW) torsion angle range of 0° to −180° and a clockwise (CW) torsion angle range of 0° to 180° .The maximum sensitivities of the microtapered PMF are 6.99 nm/(rad/m) and −6.03 nm/(rad/m) in the ACW and CW ranges,respectively,which are nearly twice as high as those of the original PMF.Similar spectral responses can be seen in Figs.2(c)and 3(c).

For the microtapered PMF-based SI,the FSR in response to a variation in twist rate can be linearly fitted and the maximum sensitivities are 1.67 nm/(rad/m) and −0.78 nm/(rad/m),respectively,which are twice the values of 0.38 nm/(rad/m) and−0.36 nm/(rad/m)for the original PMF-based SI.The transmission loss at dip I,as shown in Figs.2(a) and 3(a),was also analyzed.Figure 4 indicates that the transmission loss remains unchanged in both the CW and ACW directions for the original PMF-based SI.However,for the microtapered PMF,the transmission intensity can be nonlinearly fitte using a Lorentzian function in both the CW and ACW directions,withR2=0.99.The fittin equations can be expressed as follows:

The transmission properties of the SI based on an etched PMF with an outer diameter of 97μm were also investigated.Figure 5(a)shows the transmission spectra in the CW direction.All of the interference dips moved toward shorter-wavelength regions within the 0° –180° twist range,corresponding to a 0 to −11.22 rad/m twist rate.Four interference dips,A1,B1,C1,and D1,shifted as linear functions of twist rate,as shown in Fig.5(b)and according to Eq.(7);in this case,dλ/dt<0.

As shown in Fig.6(a),for an ACW torsion angle of 0° to −70° ,interference dip A2 exhibits some degree of redshift,while interference dips C2 and D2 experience some degree of blueshift.Notably,interference dip B2 at 1438.71 nm remains unchanged despite the change in torsion angle;in this case,dλ/dt=0.Moreover,interference dips B2 and C2 nearly vanish when the torsion angle further increases to approximately −110° ,as shown in Fig.6(b).Figure 6(c)shows that at −120° ,dip A2 moves to 1424.22 nm,which is very close to the initial position of dip B2(1438.71 nm).The wavelength sensitivity of dip A2 varies from −3.49 nm/(rad/m)to −0.85 nm/(rad/m).Additionally,dips A2 and C2 both move toward B2,and the wavelength shift sensitivity of dip C2,which is 3.79 nm/(rad/m),is slightly greater than that of A2,which is −3.49 nm/(rad/m),as shown in Fig.6(d).

FIG.4. Transmission loss as a function of torsion angle for the original and microtapered PMF-based SIs.

FIG.5.(a)Transmission spectral characteristics of the SI based on the etched PMF in the CW direction for torsion angles ranging from 0° to 90° to 180° .(b)Interference dip wavelength shift as a function of torsion angle.

FIG.6.(a)–(c)Transmission spectral characteristics of the etched PMF in the ACW direction for torsion angles ranging from(a)0° to −70° ,(b)−80° to −110° ,and(c)−120° to −180° .(d)Wavelength shift in response to variations in torsion angle.

FIG.7.FSR in response to torsion angle variation for the etched PMF.

The FSR responses to the torsion angle variation for the etched PMF in the CW and ACW directions are shown in Fig.7.The transmission spectra do not change much as the torsion angle increases in the CW direction.However,as dips A1,C1,and D1 move toward dip B2,the FSRs decrease sharply with the change in torsion angle in the ACW direction.Once dips B2 and C2 have disappeared,dips A2 and D2 form a new FSR7,which significantl increases and then decreases to nearly the same value as FSR5.Therefore,FSR5 and FSR7 show inverse wavelength shifts,as shown in Fig.7.

FIG.8.Transmission response of interference dips as a function of torsion angle for the etched PMF.

Compared with Fig.4,a similar response in the ACW direction is observed in Fig.8.The transmission loss at point I2 in the ACW direction can also be fitte using a Lorentzian function as follows,withR2=0.98:

IV.CONCLUSIONS

The effects of twist on the spectral characteristics of original,microtapered,and etched PMFs incorporated in an SI have been theoretically and experimentally investigated.The interference dip wavelength shift,transmission loss,and FSR are highly sensitive to the applied torsion angle because of the distinct modal and group birefringence characteristics of PMFs with specifi waist taper shape.The interference dip wavelength shift of the tapered PMF is increased by more than 6 nm/(rad/m) compared with that of the original PMF.The wavelength shift of the etched PMF in response to variations in torsion angle can be fitte by nonlinear and linear curves in the CW and ACW directions,respectively.Furthermore,opposite wavelength shift trends appear for other interference dips in the SI based on the etched PMF.

ACKNOWLEDGMENTS

This work was supported partly by the National Natural Science Foundation of China (Grant Nos.11804171,11674177,and 61775107),partly by the Natural Science Foundation of Tianjin,China (Grant No.16JCZDJC31000),and partly by the Self-Made Experiment Teaching Instrument Project of Nankai University 2018(Grant No.2018NKZZYQ04).

The authors declare that they have no known competing finan cial interests or personal relationships that could appear to have influence the work reported in this paper.