Effect of panda-type single polarization fiber with?89mm ring on its spectral bandwidth

GAO Yaming,HAN Zhihui,LUO Ruifang,SHA Hongtao,LI Ruichen

(46 Research Institute of China Electronic Science and Technology Group Co.LTD.,Tianjin 300220,China)

Abstract: The waterfall line of signal,when transmitted by single polarization fiber,could be obviously narrowed and the stability will be greatly improved,which can improve the fidelity of optical signal and the measurement accuracy of FOG.The position of spectral bandwidth of single polarized optical fibers is related to the ring diameter,and ?89mm ring is the standard measurement state of single polarized optical fibers.Comparative test and analysis are conducted on two groups of panda-type SP fibers (0.133 and 0.11 numerical apertures,respectively) under flat state and wound ?89mm ring state,which show that the spectral bandwidth formed by two degenerate fundamental-mode cut-off wavelengths of LP01 mode,λCY and λCX,has changed.The average spectral bandwidth narrowing rates of the two groups of fibers are 22.22% and 30.15%respectively,and the average spectral bandwidth downshifts are -54 nm and -76 nm,respectively.The optical mechanism of the change is analyzed,which demonstrates that the combination of bending birefringence,bending stress and numerical aperture are the causes of the above phenomena.

Key words: single polarization fiber; spectral bandwidth; SP fiber ring; fiber polarizer

Single polarization fiber (SP) is a new type of optical fiber which has emerged in recent years.Its main and potential applications include fiber polarizer,fiber optic gyroscope sensing coil,resonant optical fiber gyroscope[1-3],fiber laser[4],fiber optic sensor,and high fidelity optical signal transmission medium,etc.The inherent characteristics of SP fiber make it become a kind of sensing fiber with unique advantages in some aspects[5].Due to the absence of inter-mode crosstalk,the waterfall line of signal transmitted by SP fiber is narrowed obviously and the stability is greatly improved[6],which are beneficial to the improvement of optical signal fidelity[7],FOG stability and measurement accuracy[8].Because the spectral bandwidth,extinction ratio,loss and other parameters of SP fiber are related to the diameter of the winding ring,the SP fiber is usually winded into a?89 mm ring state as the standard measurement state,so the measured parameters of the fiber are comparable.Therefore,it is very important to study the performance changes of SP fibers in the ring state of ?89mm.At present,the SP fibers in foreign companies are tie-type and elliptical cladding structure,while the SP fiber we developed is panda type.

Unlike the polarization maintaining (PM) fiber that supports two orthogonal polarization modes,a SP fiber guides one polarization mode (HE11X) only while the other polarization mode (HE11Y) is eliminated.Its physical meaning can be expressed very vividly by formula (1)[5].By designing the operating wavelengthλbetween the two cut-off wavelengths of the two modesλCYandλCX,HE11Xand HE11Ymode become the guided and radiation modes,respectively.

Whereais core radius,NAXandNAYare the numerical aperture of two orthogonal polarization modes respectively,VCYandVCXare normalized frequencies of two orthogonal polarization modes respectively.When a SP fiber is in flat and ring states respectively,its performance has a series of large changes.Under some conditions,these changes will lead to serious deterioration of SP fiber performance and even make it lose its original SP characteristics.So far SP fiber parameters are usually tested in ?89 mm ring state in market,so it is necessary to study the parameters when it is in coil state.

1 Test

We contrastively measured several batches of pandatype SP fiber samples (26 pieces),which are divided into two groups.The numerical aperture in group-1 fiber is greater than 0.13,and the fiber sample number is 9.Their numerical aperture range is 0.131～0.145,the average numerical aperture is 0.133.The numerical aperture in group-2 fiber is less than 0.13,and the fiber sample number is 17.Their numerical aperture range is 0.101～0.119,and the average numerical aperture is 0.11.In the contrastive test,the length of each SP fiber sample is all 5 m.Firstly,a series of parameters of the SP fibers were measured respectively when they are in flat state and in ?89 mm ring state,which include cut-off wavelengthsλCYandλCX,spectral bandwidth ΔλC(λCX-λCY) and ΔλCW(λCX-λCY)Wformed from two degenerate modes (HE11Xand HE11Y),spectral bandwidth narrowing rate (ΔλC-ΔλCX)/ΔλC,the changes of two degenerate mode cut-off wavelengths ΔλCYand ΔλCX,the downshift of cut-off wavelengths (ΔλCY+ΔλCX)/2 and their respective numerical aperture.Their average statistics of two groups of SP fibers are listed in Table 1,and Figure 1 displays the test results vividly.

To show the problem more clearly,we supplied 4 measurement pictures in Figure 2,which are the actual spectral measurement curves of two typical panda-type SP fiber samples A and B[9-10].The lengths of the fiber samples are all 5 m,the numerical aperture of SP fiber A displayed in Figure 2(a) is 0.129,and the numerical aperture of SP fiber B displayed in Figure 2(b) is 0.107.Comparing the statistical data in Table 1 with that in Figure 2 for SP fiber A and B,it can illustrate clearly the statistical conclusion in Table 1.

Tab.1 Two groups' test results of SP fiber samples

Fig.1 Schematic diagram of two groups' test results of SP fibers

Fig.2 Actual spectral measurement curves of two panda-type SP fibers

2 Test results and discussion

2.1 Test results

By analyzing the statistical test data of the two groups of panda-type SP fiber in Table 1,we can draw the following conclusions：

(1) The spectral bandwidth of a panda type SP fiber in ?89mm ring state becomes narrower than that in flat state.For group-1's SP fibers,the average spectral bandwidth changed from ΔλC=126nm to ΔλCW=98 nm,and the average narrowing rate of spectral bandwidth is(126 nm-98 nm)/126 nm=22.22%.While for group-2's SP fibers,the average spectral bandwidth changed from ΔλC′=136 nm to ΔλCW′=95 nm,and the average narrowing rate of the spectral bandwidth is (136 nm-95 nm)/136 nm=30.15%.

(2) The cut-off wavelength position of spectral bandwidth of SP fiber in ?89 mm ring state appears significantly lower than that in flat state.For group-1's and group-2's SP fibers,both the cut-off wavelengths of the two fundamental modesλCYandλCXmoved to the short wave-length side.For group-1,the average moving amounts are ΔλCY= -40 nm and ΔλCX=-68 nm respectively,and the average downshift is (-40-68)/2= -54 nm.For group-2,the average moving amounts are ΔλCY′=-55 nm and ΔλCX′ = -96 nm respectively,and the average downshift is (-55-97)/2= -76 nm.

(3) Comparing the testing parameters of two groups of SP fibers,we found a common characteristic,i.e.as the SP fiber is in ?89 mm ring state,the downshift ofλCXis larger (In group 1,ΔλCX= -68 nm; In group 2,ΔλCX′ =-96 nm.Average value is -82 nm) than that ofλCY(In group 1,ΔλCY= -40 nm; In group 2,ΔλCY′= -55 nm.Average value is -47.5 nm).

(4) The experimental results show that some parameter changes are smaller for group-1's SP fibers with larger numerical aperture,as they were wound into ?89 mm rings.These changes include the average narrowing rate of spectral bandwidth,the changes ofλCYandλCX,and the average downshift of spectral bandwidth.

2.2 Discussion

When the optical fiber is in the bending state,the geometric deformation and stress formed in the fiber will produce bending birefringence.The resulting optical fast axis is in the curved plane,and theoretical analysis about this aspect is not very clear[11].What will happen on panda-type SP fiber in bending state? We shall discuss and analyze about that in terms of the SP fiber testing statistical average data.

2.2.1 Discussion about spectral bandwidth changing to narrow

The stress applied by two stress applying parts(SAP) around the core of panda type SP fiber is far greater than that of PM fiber[9].Only in this way can the cut-off wavelengths of the two degenerate fundamental modes be fully separated,and the high birefringence can be achieved through designing SP fiber structure.

The mode birefringenceBof SP fiber is expressed in formula (2)：

WhereBGis the geometric birefringence of the fiber caused by the geometric distortion of the fiber core;BSis the stress birefringence caused by the two internal SAP beside the fiber core; andBWis the bending birefringence caused by the bending stress of the fiber.To simplify the discussion,we assume that the geometrical birefringenceBGof SP fiber is zero in this paper.

When the fiber is in the bending state,the bending stressσXWandσYWalong the fiber core axis ofXandYare expressed in formula (3) and (4) respectively,and the bending stress difference ΔσWbetween the two axes is expressed in formula (5),and bending birefringenceBWis expressed in formula (6).

WhereC1=R2E/ρ2,C0=(1-2γ)/(1-γ);Ris fiber cladding radius;Eis Young's modulus;ρis curvature radius;γis Poisson's ratio; andηbis 0.093 (coefficient factor of fused silica).According to formula (5) and (6),it is obvious that both bending stress difference and bending stress birefringence of SP fiber increase with the decrease of the curvature's radius.

When a panda-type SP fiber is wound into a ?89 mm ring,the bending stress and bending birefringence are inevitably be produced.Furthermore the test's average data in Table 1 show that the spectral bandwidth of the SP fiber becomes narrow,which means that the attached bending stress and the bending birefringence offset the intrinsic stress and intrinsic birefringence respectively,while these intrinsic ones are all produced from SAP.Finally this leads mode birefringenceBof the panda-type SP fiber become small.Moreover this also means that the spectral bandwidth of the SP fiber changes towards the spectral bandwidth of PM fiber,which has smaller birefringence.

2.2.2 Discussion on spectral bandwidth shifting to short wavelength side

We know that the cut-off wavelength of the second order mode LP11moves to short wavelength when normal single mode (SM) fiber is in sufficient curvature state,but the fundamental mode LP01is not affected according to waveguide theory,because the fundamental mode of SM fiber will not be cut-off,and the transmission constant of SM fiber is forever betweenk0n1andk0n2.However,the actual optical fiber is not the case.In Figure 3,the curvature radius of the ordinary SM fiber is 7.5 mm and 5 mm respectively.The bending loss of theoretical calculation and experimental measurement vary with the radius of curvature.When the radius of curvature is reduced,the loss of LP01mode in SM fiber increases rapidly.Furthermore it becomes larger with the increase of the wavelength,and theoretical and experimental results are fitted very good[11].If the radius of optical fiber ring is further reduced,it can completely lead to the cut-off of the fundamental mode.

Fig.3 Comparison on theoretical and experimental values of normal SM fiber bending loss with wavelength increasing

A normal SM fiber supports two modes with orthogonal polarizations (LP01mode).Then what is the effect on the SP fiber cutoff wavelengths as it is wound into a?89 mm ring ? From the test results of group-1's and-2's panda-type SP fiber in Table 1,not only the fundamental mode (LP01) of the SP fiber is cut-off,but also its two cut-off wavelengths of the degenerate fundamental modeλCYandλCXmove to short wavelength side with the SP fiber bending.Although the numerical aperture sizes of group-1's and -2's SP fibers are different,but their movements are similar,as shown in Figure 2.From macroscopic view,this is similar to the experimental results of SM optical fiber,and the only difference is the cut-off modes of SM fiber and the SP fiber are LP11and HE11Ymode,respectively.

The characteristic of the SP fiber is that the cut-off wavelengths of two degenerate modes HE11Xand HE11Yin LP01mode split[12].When the SP fiber is wound into a?89 mm ring,the two cut-off wavelengths (HE11Xand HE11Y) are affected by bending stress and bending birefringence,which are related to the curvature's radiusρ.If the operating wavelengthλis lower than the two cut-off wavelengths,that is,the two degenerate modes are all guided modes (equivalent to SM fiber LP01mode's transmission),referencing to normal single optical fiber coiling loss calculation formula,the calculation of lossαRXandαRYfor each unit length of the two modes (XandYaxial linear polarization modes) is calculated by formula (7) and (8) respectively：

WhereVXandUXare respectively the normalized frequency and the normalized transverse propagation constant of theXaxial polarization mode (HE11Xmode);VYandUYare respectively the normalized frequency and the normalized transverse propagation constant of theYaxial polarization mode (HE11Ymode);K1X(VX) andK1Y(VY)are the Bessel functions of the virtual variables of the two modes,respectively; ΔnXand ΔnYare the effective refractive index difference of the core alongXandYaxis respectively;ais the core radius of the SP fiber; andn2is the refractive index of the cladding.

When operating wavelength is between the two cut-off wavelengthsλCYandλCXof degenerate modes HE11Xand HE11Y,the fiber has SP fiber properties ,and the HE11Ymode is in the cut-off state.At this timeUY=V′Y,and the HE11Xis still in the conduction state.The formula(7) has no big changes,andUX＞VX.As for formula (8),it can be simplified into formula (13)：Comparing formula (7) and (13),we can see that bothαRXandα′RYincrease with the decrease of the curvature radius of the SP fiber,butαRY′ increases sharply with the decrease of the radius[10],which means HE11Ymode is in cut-off state and its light energy is radiating out of the fiber core,but the HE11Xmode is still in conduction state though its loss is rising.No matter the increase ofαRX,

αRYorαRY′,it is indicated that the cut-off wavelengths of the two degenerate modes move to the short wavelength side,so the spectral bandwidth is moved to the short wavelength side as a whole.

2.2.3 Discussion about ΔλCX＞ΔλCY caused by bending

But Tsarevitch Vasilii set the point of his sword against her breast and said: Listen, Helen the Beautiful! Thou art now in our hands. We shall bring thee to our little father, Tsar Vyslav, and thou shalt tell him that we, and not Tsarevitch Ivan, found the Fire Bird, and won the Horse with the Golden Mane and thine own lovely self. If thou dost not swear by all holy things to say this, then this instant will we put thee to death! And the beautiful Tsar s daughter, frightened by their threats, swore that she would speak as they commanded.

SAP are placed on both sides of the core of pandatype SP fiber,which makes additional refractive index Δn1XSand Δn1YSalong the two directions ofXandYaxis on fiber core,and Δn1XS＞Δn1YS.Referencing the Δnformula of polarization maintaining optical fiber ,we can express them by formula (14) and (15).The birefringence produced by this is called stress applying birefringenceBs.

Wheren1is the refractive index of the SP fiber core,Eis the Young modulus,γis the Poisson's ratio,P12andP11indicate the photoelastic coefficients along theXandYaxis respectively,P0is the photoelastic coefficient of ordinary SM fiber core (no SAP),ΔσXSis the stress difference before and after the stress is applied at the SP fiber core along theXaxis direction,and ΔσYSis the stress difference before and after the stress is applied at the SP fiber core along theYaxis direction.

The stress applying birefringenceBsof panda type SP fiber is expressed in formula (16)：Where △nseffis the effective refractive index difference between two axial directions (alongXandY) generated by SAP.The differences of refractive index Δn1XSand Δn1YSalong the two axial directions ofXandYare caused by the exerted stress difference themselves,and the numerical aperture's increased values along the two axial directions ofXandYare different,as shown in formula (17) and (18).When the SP fiber is wound into a?89 mm ring,the bending stress difference ΔσWand the bending birefringenceBWare introduced to the SP fiber.Joint the applying stress and bending stress,the complex effect causes the difference of the numerical aperture of the SP fiber alongXandYaxis,which is represented byNAX′ andNAY′ respectively in formula (19) and (20).Meanwhile,the wavelength position of the single polarization window leads to the difference of the normalized frequencyVCX′ andVCY′ ofXandYpolarization modes.we can knowVCX′ ＞VCY′ in terms of optical fiber mode cut-off theory,and these factors ultimately lead to the cut-off wavelength changes (ΔλCXand ΔλCY) of the two fundamental modes,which are different and are expressed in formulas (21) and (22).

Where Δn1XWand Δn1YWare additional changes in the refractive index of the fiber core along the two optical axis,ΔNAX′ and ΔNAY′ are the additional changes in the numerical aperture of the two degenerate modes,ΔVCX′and ΔVCY′ are additional changes in the normalized frequency of two degenerate modes,and they are all caused by the SP fiber bending.

Because the cut-off wavelength of HE11Xmode moves to short wavelength in ?89 mm ring state,that is,λCXis closer to the operating wavelength (1053 nm),so ΔVCX′ should be negative,making (VCX+ΔVCX′) less,but generallyVCX+ΔVCX′ is still larger thanVCY.To simplify the problem and ignore the effect of ΔVCX′,formula (21)is simplified.

Because the HE11Ymode is the cut-off mode,ΔVCY=0,and ΔλCYare only related to the ΔN′AY.Because the optical axis is random when the SP fiber is wound into the ?89 mm ring,we can assume Δn1XW=Δn1YWin formula (19) and (20),and compare two formulas,we can get ΔNAX′＞ΔNAY′.

We can also explain this from another view.In terms of the above discussion,we can see that the spectral bandwidth of the panda-type SP fiber wound into the?89 mm ring tends to be narrower,which shows the bending stressσWand attached birefringenceBWweakened the influence of inherent applied stress and the intrinsic stress birefringence of the SP fiber.Moreover,it can be seen in formula (5) and (6) that the increase intensity of ΔσWandBWincreases rapidly as the bending radius decreases.Therefore,ΔλCXSand ΔλCYS,produced by the inherent applied stress,will decrease under the negative effect of bending stress and bending birefringence,and the larger amplitude should be ΔλCXS.As ΔλCXSis more influenced by inherent stress,it is more strongly influenced by the negative effect of bending,and finally it shows the test result of ΔλCX＞ΔλCY.

2.2.4 Discussion on the SP fiber performance with different NA

By comparing and analyzing the test data of the SP fiber in flat and ?89 mm ring states respectively,we can draw a conclusion that the spectral bandwidth of group-1's SP fibers with larger numerical aperture has less narrowing rate change and downward shift amount to the short wavelength side,and less downward shift amount of ΔλCXand ΔλCYthan those of group-2's SP fibers with smaller numerical aperture[13].

Fig.4 is a simulation diagram of the stress field distribution on a SP fiber section.It can be seen that the applied stress is concentrated around its core area[14].In the same bending state,it is confined to the core where concentrated the most light energy of group-1's SP fibers with larger numerical apertureNA,i.e.the stress concentration area,as shown in Fig.5(a).The effect of the additional bending stress is smaller for group-1's SP fiber,so they are smaller than the narrowing rate and the downward shift amount of the spectral bandwidth and the changes of the two cut-off wavelengths of the fundamental mode ΔλCXand ΔλCY.While for group-2's SP fiber with smaller numerical apertureNA,the most light energy is not propagated in the core when it is in the same bending state,and the mode field leaves the stress concentration area,as shown in Fig.5(b).So the effect of the bending attached additional stress is larger.Finally this leads to larger change of the narrowing rate,the downshift of the spectral bandwidth,and the shift of the cut-off wavelengths of the two fundamental modes ΔλCXand ΔλCY.

Fig.4 Simulation diagram of stress distribution in SP fiber

Fig.5 Schematic diagram of mode field deviating from cores of group-1 and -2 of SP fiber in bending state

3 Conclusion

After winding panda-type SP fiber into ?89 mm ring,the spectral bandwidth becomes narrower,and it moves to short wavelength side simultaneously,and the unequal changes of the cut-off wavelength of two degenerate fundamental modes ΔλCXand ΔλCYare caused.These changes are related to the numerical aperture of the SP fiber,and the influence of 89mm ring state on the fiber with larger numerical aperture is small.The laws of these panda-type SP fibers have important practical significance for making SP fiber polarizer and FOG sensitive coil,especially for its potential use in resonant optical fiber gyroscope.