Measurement method for profiling the residual stress and the strain-optic coefficient of an optical fiber
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Measurement method for profiling the residual
stress and the strain-optic coefficient of an
optical fiber
Yongwoo Park, Tae-Jung Ahn, Yune Hyoun Kim, Won-Taek Han, Un-Chul Paek, and
Dug Young Kim
A method, believed novel, is demonstrated for determining the strain-optic coefficient profile as well as
the residual-stress profile of an optical fiber by use of a modified polariscope combined with a fiber-
elongation apparatus. Measurement results of the residual-stress and the strain-optic coefficient pro-
files for Ge-doped and Er–Ge–Al-doped optical fibers are demonstrated with this method. © 2002
Optical Society of America
OCIS codes: 060.2270, 060.2280, 060.2290, 060.2300, 060.2400.
1. Introduction pensable for understanding these mechanisms and
The measurement of residual-stress distribution in their respective contributions to the fabrication of
an optical fiber has been drawing much attention for fiber gratings.
the past few years because the changes of the resid- A standard method for determination of the
ual stress in a fiber provide a good explanation of the residual-stress profile of a transparent material is to
underlying mechanisms of refractive-index changes use a polariscope, which is constructed of a fixed po-
by UV or CO2 laser irradiation in fiber-grating fabri- larizer, a quarter-wave plate, and an analyzer.5,6 A
cation processes. The fundamental mechanism re- polariscope is not considered to be sufficient for de-
sponsible for fiber Bragg grating formation is not termining the stress profile of an optical fiber because
clearly understood yet. Molar refractivity, stress re- of low measurement accuracy and spatial resolution
lief, and structural deformation are three major pro- that are due to image or wave-front distortions, beam
cesses that are believed to cause refractive-index deflections in an optical fiber, nonuniform back-
changes in fiber-grating fabrication processes. It ground birefringences, and so on. Several measure-
has been found recently that the analysis of the ments of the stress profile of an optical fiber have
residual-stress change can give a good account of the been demonstrated after various modifications were
densification effect induced by UV irradiation, which made for enhancement of measurement accuracy and
is one of the dominant processes responsible for the resolution by use of a half-shade method and adap-
permanent refractive-index changes in silica glass- tation of other complicated optical imaging sys-
es.1,2 Also, the physical mechanism of the fabrica- tems.7,8 However, the stress profile of a fiber is also
tion process of a long-period fiber grating with CO2 directly related to the strain-optic coefficient profile of
laser exposure has been explained lately by the de- the fiber, although previous methods were not able to
velopment of the relief of residual stress in a fiber.3,4 measure these two different profiles independently.
The stress measurement of an optical fiber is indis- In general, the photoelastic coefficient does not vary
significantly with the change of the composition or
the concentration of a dopant in an optical fiber.
However, it can be much changed with a change in
The authors are with the Department of Information and Com- the concentration of some oxides of Al, Ti, B, and so
munications, Kwangju Institute of Science and Technology, 1
on.9 The optical fibers doped with such oxides might
Oryong-Dong, Buk-gu, Kwang-ju 500-712, Korea. Y. Park’s
e-mail address is ywpark@cactus.kjist.ac.kr. be applicable to the index profile control of an optical
Received 14 February 2001; revised manuscript received 9 Au- fiber by adjustment of the external pulling tension in
gust 2001. a fiber-drawing process. Additionally, photoelastic
0003-6935兾02兾010021-06$15.00兾0 behavior in optical fibers with different dopants can
© 2002 Optical Society of America give us much information about the acousto-optic ef-
1 January 2002 兾 Vol. 41, No. 1 兾 APPLIED OPTICS 21Fig. 2. Schematic diagrams of two phase-retardation measure-
ment setups: 共a兲 new setup in which a rotating polarizer and a
quarter-wave plate are used, 共b兲 setup in which a variable phase
compensator is used.
Fig. 1. Ray trajectory across an optical-fiber cross section.
fect in optical fibers and various other applications and a fiber preform was proposed by Chu and Whit-
for which this effect is used. The measurement tech- bread.5 They used a tightly focused, linearly polar-
nique to obtain the strain-optic coefficient profile in ized He–Ne laser beam passing through a fiber
an optical fiber has not, to our knowledge, been re- transversely, with its polarization direction rotated
ported yet, but strain-optic coefficients for bulk-type at 45° with respect to the fiber axis. Because of the
glasses have been investigated already.10,11 stress-induced birefringence of the fiber, the laser
In this paper, a simple and comprehensive mea- beam becomes elliptically polarized after it passes
surement method is proposed and demonstrated for through a fiber, and then it becomes linearly polar-
measuring the strain-optic coefficient profile as well ized again by a quarter-wave plate whose optical axis
as the residual-stress profile of an optical fiber. The is also oriented at 45° with respect to the fiber axis.
strain-optic coefficient profile of an optical fiber is The output polarization direction is measured by ro-
measured for the first time by introduction of a spe- tation of an analyzer after the quarter-wave plate.
cially designed fiber-elongation apparatus. Signifi- The angle between the input and the output polar-
cant improvements in measurement time and ization directions is proportional to the stress-
accuracy are obtained when an analog CCD camera induced phase retardation. The stress profile of a
and a framegrabber are used instead of a scanning fiber is obtained by a scan of the laser beam across the
photodiode. It is possible for us to position an ana- fiber cross section. Although an index-matching liq-
lyzer very close to a test fiber because we use a fixed uid is used, this measurement method suffers from
analyzer instead of a rotating one. This makes it beam deflections when the incident beam passes
possible for us to achieve a high spatial resolution. through the core region of a fiber. The spatial res-
Diffraction and interference effects are effectively olution of this method is limited by the size and the
suppressed by an incoherent imaging system in our Rayleigh range of a focused laser beam and is typi-
setup. cally larger than 1 m.
An alternative approach for measuring the stress
2. Theory profile of a fiber is by use of an incoherent imaging
An optical transverse measurement method is com- system combined with a polariscope.7,8 A fixed
monly used for determining the residual-stress pro- quarter-wave plate and a rotatable analyzer are lo-
file of a cylindrically symmetric structure such as an cated after a high-power imaging lens because the
optical fiber or a fiber preform.5– 8 Figure 1 shows working distance of the imaging lens is normally
the light-propagation trajectory across a fiber cross shorter than the occupied space of both of these com-
section. The propagation direction x of linearly po- ponents. The uniformity and the flatness errors of
larized incoming light is transverse to the fiber axis z. the quarter-wave plate associated with a high-N.A.
The residual stress in a glass optical fiber results in imaging lens are major problems of this setup.
birefringence induced by the photoelastic effect, Noises on the image when a dust-contaminated ana-
which can be expressed as lyzer is rotated are another significant source of error
for this system.
n z ⫺ n y ⫽ C共 z ⫺ y兲, (1) To overcome these problems we developed a new
type of measurement setup for obtaining the stress-
where nz, ny and z, y are the indices of refraction induced phase retardation for an optical fiber. The
and the residual stresses along the z and the y direc- idea of this method is illustrated in Fig. 2共b兲. A
tions, respectively, and C is the photoelastic coeffi- collimated laser beam is passed through a fiber trans-
cient. Because of this birefringence, two versely, as shown in Fig. 1. A polarizer and an an-
orthogonally polarized light components along the z alyzer are used, with their polarization axes adjusted
and the y directions experience a relative phase re- to be perpendicular to each other. A fiber and a
tardation as they pass through a fiber sample. A bril- variable phase compensator are placed between the
liant method for measuring the stress profile of a fiber polarizer and the analyzer. When the angle be-
22 APPLIED OPTICS 兾 Vol. 41, No. 1 兾 1 January 2002tween the fiber axis and the polarizer is 45°, the
transmitted intensity I共 y兲 as a function of the trans-
verse distance y from the center of the fiber can be
written as
I共 y兲 ⫽ I 0 sin2关⌽共 y兲兾2兴, (2)
where I0 is the input intensity and ⌽共 y兲 is the relative
phase retardation between the parallel and the per-
pendicular components of the transmitted light with
respect to the fiber axis. It is shown that the relative
phase retardation ⌽共 y兲 of the light trajectory shown
in Fig. 1 for a circularly symmetric fiber can be ex-
pected only by its axial stress profile z共r兲.12 Assum-
ing that the photoelastic coefficient is constant and
the radial stress vanishes at r ⱖ c, we can write the
total phase retardation as
兰
2C 冑c2⫺y2
⌽共 y兲 ⫽ zdx ⫹ ␦
⫺ 冑c2⫺y2
⬅ ␦ 0共 y兲 ⫹ ␦, (3)
where ␦0 is by the residual stress z, ␦ is by the phase
compensator, C is the photoelastic coefficient, is the
wavelength of light, and c is the fiber radius. Here,
the phase retardation by only the residual stress ␦0 is
defined as
4C
兰冑 z共r兲
c
␦ 0共 y兲 ⬅ rdr. (4)
y
r2 ⫺ y2
If we control the external phase-retardation term ␦ by
adjusting the phase compensator such that the trans-
mitted intensity becomes minimum, then we have Fig. 3. 共a兲 Perspective view of the Poincaré sphere for visualizing
␦共 y兲 ⫽ ⫺␦0共 y兲 by Eqs. 共2兲 and 共3兲. As the structure of the trajectories of the polarization state of the input beam for the
a fiber is axially symmetric, we can obtain the radial- experimental setup shown in Figs. 2共a兲 and 2共b兲, 共b兲 side view of the
stress profile of a fiber z共r兲 by converting Eq. 共4兲 by polarization state trajectories on the Poincaré sphere seen from the
using the Abel transformation5: positive y direction.
⫺
兰冑 d␦ 0兾dy
c
z共r兲 ⫽ dy. (5)
2 2C r
y2 ⫺ r2 axis, and a left-hand circularly polarized state. The
linearly polarized light by a polarizer shown in Fig.
To control the external phase retardation ␦, a Babinet 2共b兲 becomes elliptically polarized just in front of the
or a Bereck compensator can be used. These de- fiber sample when it passes through a variable phase
vices, however, are expensive and difficult to be con- compensator. This process is represented by the
trolled by a computer. Figure 2共a兲 shows a new dashed trajectory in Fig. 3. It starts from S2, it ro-
setup that gives the same results of Fig. 2共b兲 without tates upward with respect to the O S 1 axis by the
use of a phase compensator. We simply replace a amount of phase retardation ␦, and it ends up at Q.
fixed polarizer and a phase compensator with a ro- In Fig. 2共a兲, the polarization state of light in front of
tating polarizer and a fixed quarter-wave plate ad- the fiber sample can become exactly the same as that
justed to 45° with respect to the fiber axis. Here the in Fig. 2共b兲 by a fixed quarter-wave plate and a ro-
light source must be randomly polarized such that tating polarizer. The trajectory of the polarization
the throughput of a polarizer should be constant, re- state on the Poincaré sphere for this process is illus-
gardless of the rotation angle of the polarizer. trated by the solid curve in Fig. 3. P is a point on the
Figure 3共a兲 is a three-dimensional view of the Poin- sphere rotated from S1 toward S2 by the amount 2,
caré sphere that compares the evolution of polariza- where is the angle between the fast axis of the
tion states for the setup shown in Figs. 2共a兲 and 2共b兲. polarizer and the fiber axis. As the fast axis of the
S1, S2, and S3 are points on the sphere that represent quarter-wave plate is 45° off from the fiber axis in
three distinct polarization states: a linearly polar- Fig. 2共a兲, the quarter-wave plate rotates any point on
ized state parallel to the horizontal axis, a linearly the Poincaré sphere by 90° with respect to the O S 2
polarized state at 45° with respect to the horizontal axis. When the polarizer in Fig. 2共a兲 is rotated prop-
1 January 2002 兾 Vol. 41, No. 1 兾 APPLIED OPTICS 23erly, the position of P on the Poincaré sphere can be strain effect ⑀z. For a given externally applied
properly adjusted such that it coincides with Q when strain, we can always adjust the phase compensator
it is rotated by 90° by the quarter-wave plate. in Fig. 2共b兲 or the angle of the polarizer in Fig. 2共a兲
Therefore we can make any elliptic polarization state such that the throughput becomes minimum. If we
made by the variable phase compensator in Fig. 2共b兲 denote the phase retardation by the compensator as
by adjusting the angle of the polarizer shown in Fig. ␦i 共 y兲 when the throughput is minimum for a given
2共a兲. Figure 3共b兲 is the side view of the Poincaré externally applied strain ⑀zi, we have
sphere seen from the right-hand side of the sphere in
Fig. 3共a兲. From the two trajectories on the Poincaré W共 y兲⑀ zi ⫹ ␦ 0共 y兲 ⫹ ␦ i 共 y兲 ⫽ 0, i ⫽ 1,2, (8)
sphere, we have
where W共 y兲 is the integrated strain-optic coefficient
␦ ⫽ 90° ⫺ 2. (6) when light passes through a fiber transversely, as
shown in Fig. 1. If ␦1共 y兲 and ␦2共 y兲 are two data sets
We can obtain the stress-induced phase retardation
of phase retardation for two different external strain
of a sample fiber ␦0 by searching a minimum intensity
values ⑀z1 and ⑀z2, we can eliminate the residual
point while rotating the polarizer for each transverse
stress-induced phase-retardation term ␦0共 y兲 in Eq.
coordinate position y. If 0 is the angle between the
共7兲 and obtain the integrated strain-optic coefficient
polarizer and the fiber axis when the output intensity
experimentally as
through the system in Fig. 2共a兲 becomes minimum,
the stress-induced phase retardation ␦0 becomes
⫺共90° ⫺ 20兲 because of Eqs. 共2兲 and 共3兲. We find 0 ␦ 1共 y兲 ⫺ ␦ 2共 y兲
W共 y兲 ⫽ ⫺ . (9)
by taking throughput intensity data as a function of ⑀ z1 ⫺ ⑀ z2
and fitting the acquired data with a quadratic func-
tion of for each y. We can obtain an approximate The radial distribution of the strain-optic coefficient
residual-stress profile of a fiber from Eq. 共5兲 by as- profile with respect to the radial direction for a cir-
suming a constant photoelastic coefficient C across cularly symmetric fiber P共r兲 can be obtained by use of
the cross section of a fiber. an Abel transformation:
For the measurement of the strain-optic coefficient
兰冑
profile, a fiber-elongation apparatus is combined with
⫺ c dW兾dy
the stress-induced birefringence measurement setup. P共r兲 ⫽ dy. (10)
The strain-optic coefficient of a glass material is ex- 2 2 r
y2 ⫺ r2
pected to vary with the composition and the concen-
tration of each dopant. When a fiber is pulled from By following the same procedure used to obtain Eq.
both ends, a uniform external strain instead of a 共5兲, we can easily find the expression for the residual-
uniform external stress is applied to the cross section strain profile of a fiber out of the measured phase
of a fiber. The measurement of the birefringence retardation ␦0共 y兲:
change of a fiber as a function of externally applied
strain would give information about the strain-optic
⫺
兰冑 d␦ 0兾dy
c
coefficient of the fiber. Thus we can obtain the ⑀ z共r兲 ⫽ dy. (11)
strain-optic coefficient by using a fiber-elongation ap- P共r兲2 2 r
y2 ⫺ r2
paratus combined with a stress-induced birefrin-
gence measurement setup. Here we newly define
the strain-optic coefficient P共r兲 that is the ratio be-
tween the externally applied axial strain and the
induced birefringence in a fiber. For the external
strain ⑀z ⫽ ⑀r兾 ⫽ ⑀兾, the induced birefringence can
be written as11
n 03
n z ⫺ n y ⫽ C z ⫽ 共 p 12 ⫺ p 11兲共1 ⫹ 兲⑀ z ⬅ P⑀ z, (7)
2
where is the Poisson ratio, p11 and p12 are the
Pockel’s strain-optic coefficients, and n0 is the refrac-
tive index of an isotropic silica glass before it is
stressed. The reason why we chose the strain-optic
coefficient rather than the photoelastic coefficient is
because the external pulling strain does not vary
across the cross section of a fiber, whereas the applied
tension over the fiber cross section can vary with
different Young’s moduli for core and cladding mate-
rials.6 When a sample fiber is pulled from both Fig. 4. Experimental setup for the measurement of stress and
ends, Eq. 共3兲 must be modified to include the external strain-optic coefficient profiles of an optical fiber.
24 APPLIED OPTICS 兾 Vol. 41, No. 1 兾 1 January 2002Fig. 6. 共a兲 Measured phase-retardation profiles induced by the
stresses in a Ge-doped fiber, in which the core is doped with Ge
oxides and the inner cladding is doped with P oxides and F; 共b兲
calculated axial component of the residual-stress profile; 共c兲 calcu-
lated strain-optic coefficient profile.
1.458 at room temperature. A fixed analyzer whose
axis is aligned to 45° with respect to the fiber axis is
placed just after the fiber. The gap between the
fixed analyzer and the cover glass is ⬃0.5 mm. The
thickness of the uncoated dichroic polarizer is 0.8
mm. For the strain-optic coefficient measurement,
the fiber is clamped and pulled by a stepper motor.
The magnified image of the optical fiber is detected by
a CCD camera through a 20⫻ objective lens and is
Fig. 5. Three-dimensional intensity profiles of transmitted light digitized by a framegrabber. To remove the inter-
through our experimental setup for the Er–Ge–Al-doped fiber 共a兲 ference effect between the CCD sensor and its pro-
with no external strain, 共b兲 with 0.067% external strain applied to tecting cover glass, the cover glass just in front of the
the fiber. CCD camera is removed. Line-scanned data are ac-
quired more than 30 times for each angle position of
the rotating polarizer, and these averaged data are
It should be noted that the strain-optic coefficient is fitted with a quadratic function of to obtain ␦0共 y兲.
not assumed to be constant over the cross section of a
fiber to obtain the residual-strain profile ⑀z共r兲. 4. Results
We measured the residual-stress and the strain-optic
3. Experimental Setup coefficient profiles of a Ge-doped fiber and an Er–Ge–
The schematic drawing of our experimental setup is Al-doped fiber. Two data sets were taken for these
shown in Fig. 4. A 7-mW He–Ne laser with random measurements: one is without any external strain
polarization is used as a light source. As a coherent 共0% strain兲 and the other is with 0.067% external
imaging system exhibits a ringing effect at a sharp strain applied to these fibers. The length of both
edge of an object because of diffraction, a diffuser is fibers is 15 cm. Figure 5 shows a series of line-
used to make the setup an incoherent imaging sys- scanned intensity profiles of transmitted light
tem. An unwanted speckle pattern on the image is through our experimental setup for the Er–Ge–Al-
effectively eliminated when the diffuser is rotated doped fiber. The angle of the polarizer in our lin-
extremely fast during measurement. The scattered ear birefringence device shown in Fig. 2共a兲 is varied
light from the rotating diffuser is collected by a col- for each line-scan data set. The three-dimensional
limating lens. The collected beam is incident upon a intensity profile shown in Fig. 5共a兲 is obtained when
vertically arranged linear bifringence setup through the fiber is not pulled. Figure 5共b兲 is obtained when
an Al-coated mirror. Because we use a randomly the fiber is pulled by 0.067% of its original length.
polarized laser source, birefringence of the mirror can Figure 6共a兲 shows the measured phase-retardation
be ignored. A rotating polarizer and a quarter-wave profiles ⌽共 y兲 induced by the stresses in the Ge-doped
plate are used as a variable phase compensator fiber. The concentration of Ge oxides in the core
whose principle of operation is described in Figs. 2共a兲 area is measured to be 5.19% in weight percent with
and 3共a兲. The light is weakly focused by a condens- an electron probe microanalyzer. The inner clad-
ing lens to an optical fiber. The fiber is immersed in ding is doped with P oxides and F. When 0.067%
an index-matching liquid whose refractive index is strain is applied to the fiber, it shows that the phase
1 January 2002 兾 Vol. 41, No. 1 兾 APPLIED OPTICS 255. Summary
In summary, we have proposed a simple measure-
ment method for profiling the residual stress and the
strain-optic coefficient distribution of an optical fiber.
Some measured stress distributions have been dem-
onstrated, and the values are close to the other pre-
viously reported results.7 In addition, we measured
the strain-optic coefficient profiles for Ge-doped and
Al–Er–Ge-doped fibers. Our results agree well with
other previously measured results for bulk-type
glasses.
This research was supported in part by Samsung
Electronics, by the Korea Science and Engineering
Foundation through the Ultra-Fast Fiber-Optic Net-
Fig. 7. 共a兲 Measured phase-retardation profiles induced by the works Research Center at Kwangju Institute of Sci-
stresses in the Er–Ge–Al-doped fiber, in which the core is doped ence and Technology, and by the Korean Ministry of
with Er, Al, and Ge oxides and the inner cladding is doped with P Education through the BK21 Program.
oxides and F: 共b兲 calculated axial component of the residual stress
profile; 共c兲 calculated strain-optic coefficient profile. References
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26 APPLIED OPTICS 兾 Vol. 41, No. 1 兾 1 January 2002You can also read
