Applied Physics Express 2 (2009) 046502

Polarization Beat Length Distribution Measurement in Single-Mode Optical Fibers
with Brillouin Optical Correlation-Domain Reflectometry
Yosuke Mizuno, Zuyuan He, and Kazuo Hotate
Department of Electrical Engineering and Information Systems, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-8656, Japan
Received February 25, 2009; accepted March 11, 2009; published online April 3, 2009
The polarization beat length distribution along a single-mode optical fiber (SMF) is measured with a Brillouin optical correlation-domainreflectometry. The beat lengths of SMFs wound on mandrels with radii 10.0, 7.4, and 3.1 cm were measured to be 25.4, 12.1, and 2.56 m,
respectively, which agreed well with the theoretical calculations. A distributed measurement was also successfully performed using an SMF
comprising two sections with different mandrel radii. # 2009 The Japan Society of Applied Physics
DOI: 10.1143/APEX.2.046502

or high-speed ﬁber-optic communication systems,
such as those with transmission rate of 40 Gbps andabove, polarization mode dispersion (PMD), that is,the diﬀerential group delay (DGD) between the twopolarization mode propagation in the single-mode ﬁber(SMF), is one of the most serious eﬀects that reduce thetransmission capacity of the ﬁbers. Therefore, the knowledgeof DGD is of high interest. Various methods have been used
for the PMD measurement,1) but these methods give us nodistributed information about DGD along the ﬁber but only
the overall DGD of the link. A simple method based onRayleigh reﬂectometry using polarized light, which is calledpolarization-sensitive optical time-domain reﬂectometry(POTDR), has been proposed,2) and demonstrated its
potential to measure local birefringence (the beat length)
over a long distance, but with low spatial resolution and longintegration time.3) The beat length measurements with very
high resolution have been achieved by polarization-sensitive
optical frequency-domain reﬂectometry (POFDR),4) but overa short distance. Recently, as an alternative approach, thepolarization dependence of stimulated Brillouin scattering(SBS) has been used to measure the beat length distribution
along the ﬁber.5,6) One of the methods is based on Brillouin
optical correlation-domain analysis (BOCDA),7) and has
obtained a spatial resolution as high as 2.7 cm.5) However,these methods need to access both ends of the ﬁber under
test (FUT), which is often not feasible in long-range
application, and cannot work completely when the FUT
has even one breakage point. In most long-range practicalapplications, one-end access reﬂectometries are morefavorable.
In this paper, we propose a new method to measure thedistribution of beat length based on Brillouin opticalcorrelation-domain reﬂectometry (BOCDR),8,9) which wasoriginally proposed to measure the distribution of strain and/or temperature along an FUT by controlling the interferenceof continuous lightwaves. The method shows unique features
such as one-end access, random access to measuring
positions, high spatial resolution, and high speed measurement. In our previous experiments, 13-mm spatial resolution
and 50-Hz sampling rate were simultaneously achieved withthe measurement accuracy of 100 ",9) which can beimproved, for example, to 50 " by 5-times averaging.
The experimental setup of BOCDR is shown in Fig. 1.
The Stokes light due to the spontaneous Brillouin scatteringof the pump light in the FUT is heterodyned with theFFig. 1. Experimental setup of BOCDR system: AC, alternating
current; DAQ, data acquisition; DC, direct current; DFB-LD,distributed-feedback laser diode; EDFA, erbium-doped fiber
amplifier; ESA, electrical spectrum analyzer; FUT, fiber under test;
GPIB, general-purpose interface bus; PC, polarization controller; PD,
photo-diode.

reference light (self-heterodyne scheme). In order to get thedistribution of the Stokes light along the FUT, the pumplight and the reference light are sinusoidally frequencymodulated, producing periodical correlation peaks along theFUT. The measurement range of BOCDR, that is, theinterval of the correlation peaks is given bydm ¼

Vg;
2fm

ð1Þ

where Vg is the group velocity of light and fm the modulation
frequency. We limit the length of the FUT shorter than dm toinclude only one non-0th correlation peak (where the 0thpeak is deﬁned at the position of zero optical-path
diﬀerence), so that the Stokes light scattered at thecorrelation peak position can be detected. The position ofthe correlation peak can be moved along the FUT bychanging fm . Hence, the distribution of the Stokes light canbe obtained by controlling fm . The spatial resolution z isgiven byz ¼

Vg B;2fm fð2Þ

where B is the intrinsic linewidth of the Brillouin gain
spectrum (BGS), and f is the modulation amplitude of thelight source, which is limited to a half of the Brillouinfrequency shift (BFS), i.e., about 5.4 GHz in BOCDR with046502-1# 2009 The Japan Society of Applied Physics

Appl. Phys. Express 2 (2009) 046502

Y. Mizuno et al.

standard SMF at 1550-nm wavelength.8) In BOCDR, thepeak power P of the BGS observed by the electricalspectrum analyzer (ESA) is given as:
P ¼ hEref  E Stokes i;

ð3Þ

where Eref and EStokes are the electrical ﬁelds of thereference light and the Stokes light, respectively, at theheterodyne receiver,  is a proportionality coeﬃcient, andh  i stands for time-averaging operation. When fm ischanged to perform a distributed measurement, Eref is kept
constant but EStokes changes according to the birefringence
distribution along the FUT. As a consequence, P varies
reﬂecting the distribution of the birefringence. Thus, bymeasuring the distribution of the peak power P of the BGS
by use of BOCDR, we can obtain distributed information ofbirefringence and estimate the distribution of polarization
beat length. Here, due to roundtrip of backscattered Stokes
light, the beat length LB is obtained as twice as the observed
spatial period of P variation.10)
The experimental setup is shown in Fig. 1. A distributedfeedback laser diode (DFB-LD) at frequency f0 (1552 nm)
was used as a light source, and a sinusoidal frequency
modulation was applied to generate a correlation peak within
an FUT. The output from the LD was divided into two lightbeams by a coupler. One of the beams was directly used as
the reference light of self-heterodyne detection, after passing
a 2-km delay ﬁber for controlling the order of the correlation
peak, an Er-doped ﬁber ampliﬁer (EDFA) for enhancing theheterodyne beat signal, and an optical ﬁlter composed ofﬁber Bragg grating (FBG) with a 3-dB bandwidth of about
10 GHz for suppressing the ampliﬁed spontaneous emission(ASE) noise. The other beam was injected into the FUT as
the pump light, after being ampliﬁed by a high-power EDFA
to 28 dBm. The weak Stokes light at frequency f0  fB
backscattered from the FUT was ampliﬁed again by anEDFA. An optical ﬁlter was inserted after the EDFA in orderto suppress the Rayleigh scattering from the FUT atfrequency f0 . The optical beat signal of the reference lightand the Stokes light was converted by balanced photodiodes(PDs) to an electrical signal. After 15-dB ampliﬁcation froman electrical pre-ampliﬁer, the signal was monitored by anESA.
A 1-km SMF was employed as an FUT, which was wound
on a mandrel with radius R ¼ 10:0 cm to induce birefringence intentionally. One end of the FUT was spliced to acirculator, and the other end was kept open. The sampling
rate was set to about 20 Hz, which is higher than that ofPOTDR.3) The 400-m position from the circulator wasdeﬁned as the relative position 0 m. A measurement of theBGS peak power was performed at every 1 m from therelative position 0 to 100 m. The modulation frequency fm
was changed from 98.19 to 103.09 kHz, and the modulation
amplitude f was set to 5.4 GHz, which corresponds to thespatial resolution z of about 1.8 m and the measurement
range dm of about 1 km by eqs. (1) and (2). The measured
distribution of the Stokes light is shown in Fig. 2, whereperiodical ﬂuctuation was observed. In order to estimate its
spatial period, the power spectral density (PSD) wascalculated using fast Fourier transformation (FFT), and isshown in Fig. 3. The peak of the PSD appeared at 0.079/m,
which corresponds to the spatial period of 12.7 m. Therefore,

Fig. 2. Measured distribution of the BGS peak power when themandrel radius R was 10.0 cm.

Fig. 3. Calculated PSD of the BGS peak power distribution in log
scale when the mandrel radius R was 10.0 cm. The inset shows thesame graph in linear scale.

LB was calculated to be 25.4 m. The same measurements
were performed in the cases of R ¼ 7:4 cm and R ¼ 3:1 cm
with z ¼ 55 cm and z ¼ 25 cm, resulting in LB ¼ 12:1 m
and LB ¼ 2:56 m, respectively.
In theory, the beat length LB (m) can be calculated as11)
LB ðmÞ ¼

4R2;
n3 pð1 þ Þr 2

ð4Þ

where  (m) is the wavelength of the light, R (cm) theradius of the mandrel, n the refractive index, p the strainoptical coeﬃcient,  the Poisson’s ratio, and r (m) theradius of the ﬁber cladding. Figure 4 depicts the measured
and theoretical beat length against the mandrel radius. The
theoretical values were calculated by inserting into eq. (4)parameters:  ¼ 1:55 m, n ¼ 1:46, p ¼ 0:15,  ¼ 0:17,12)
and r ¼ 63 m. The experimental results seem to agree wellwith the theory, although some discrepancy exists. This isthought to have come from the following three factors: (i)The number of sampling points of the PSD is not suﬃcient.
(ii) When a long optical ﬁber is wound on a mandrel, small
strain will remain. As a consequence, the BGS shifts toward
the upper frequency, and so the detected power changes even
if the polarization state does not change. (iii) Someparameters such as p and , which are diﬃcult to measure,
may slightly vary among ﬁbers, and their accurate values are
unknown.

046502-2# 2009 The Japan Society of Applied Physics

Appl. Phys. Express 2 (2009) 046502

Y. Mizuno et al.

Fig. 4. Polarization beat length as a function of the mandrel radius.
The curve shows the theoretical values.

Fig. 6. Measured distribution of the BGS peak power. The mandrel
radii were 7.4 and 10.5 cm corresponding to the ranges of 0 – 40 and40 –100 m, respectively.

In conclusion, we have presented that the BOCDR system
can be applied to a distributed measurement of polarization
beat length in single-mode optical ﬁbers. The measurement
was successfully performed with unique features such as
one-end access, 25-cm spatial resolution, and 20-Hz
sampling rate.
Fig. 5. Structure of the FUT.

Finally, a distributed beat length measurement wasperformed using an FUT comprising two SMFs with
diﬀerent mandrel radii. The schematic structure of theFUT is shown in Fig. 5. A 200-m SMF wound on a mandrel
with radius R ¼ 10:5 cm was spliced to a 100-m SMF
wound on a mandrel with radius R ¼ 7:4 cm. The 60-m
position from the circulator was deﬁned as the relative
position 0 m, and consequently, the mandrel radius changes
at the relative position 40 m. The measurement of the BGS
peak power was performed at every 50 cm from the relative
position 0 to 100 m. The modulation frequency fm waschanged from 125.64 to 130.95 kHz, and the modulation
amplitude f was set to 5.4 GHz, which corresponds to thespatial resolution z of about 1.4 m and the measurement
range dm of about 800 m. The experimental result is shownin Fig. 6. The spatial period of the ﬂuctuation certainly
changes at the relative position 40 m. The calculated PSDs
within the range of 0 – 40 and 40 –100 m became maximal atfrequency 0.17 and 0.067/m, which correspond to the beatlengths LB of 11.76 and 29.8 m, respectively. Theirtheoretical values are 15.6 and 31.5 m, respectively. Considering the error causes discussed above, these experimental values are valid.

Acknowledgments The authors are grateful to Dr. Weiwen Zou at
the University of Tokyo, Japan, for helpful discussions and comments. Y.M.
thanks the Japan Society for the Promotion of Science (JSPS) Research
Fellowships for Young Scientists. This work was supported by a Grant-inAid for Creative Scientiﬁc Research and the Global Center of Exellence
Program from the Ministry of Education, Culture, Sports, Science andTechnology, Japan (MEXT).

1) C. D. Poole and D. L. Favin: J. Lightwave Technol. 12 (1994) 917.
2) A. J. Rogers: Appl. Opt. 20 (1981) 1060.
3) M. Wuilpart, G. Ravet, P. Megret, and M. Blondel: IEEE Photonics
Technol. Lett. 14 (2002) 1716.
4) M. Wegmuller, M. Legre, and N. Gisin: J. Lightwave Technol. 20(2002) 828.
5) Y. Yamamoto and E. Sasaoka: ECOC’2007, paper Th.10.1.3.
6) L. Thevenaz, S. F. Mafang, and M. Nikles: ECOC’2007, paper
Th.10.1.2.
7) K. Hotate and T. Hasegawa: IEICE Trans. Electron. E83-C (2000)
405.
8) Y. Mizuno, W. Zou, Z. He, and K. Hotate: Opt. Express 16 (2008)
12148.
9) Y. Mizuno, Z. He, and K. Hotate: IEEE Photonics Technol. Lett. 21(2009) 474.
10) M. Nakazawa, T. Horiguchi, M. Tokuda, and N. Uchida: IEEE
J. Quantum Electron. 17 (1981) 2326.
11) R. Ulrich, S. C. Rashleigh, and W. Eickhoﬀ: Opt. Lett. 5 (1980) 273.
12) D. E. Gray: American Institute of Physics Handbook (McGraw-Hill,New York, 1972) 3rd ed., p. 6.

046502-3# 2009 The Japan Society of Applied Physics