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Wavelength Evolution of Fiber Bragg Gratings
Fabricated From Hydrogen-Loaded OpticalFiber During Annealing
Yuji Masuda, Mitsuo Nakamura, Chisa Komatsu, Keio Fujita, Makoto Yamauchi, Masanori Kimura, Yasuo Mizutani,
Susumu Kimura, Yoshifumi Suzaki, Member, IEEE, Takashi Yokouchi, Kiyoshi Nakagawa, Senior Member, IEEE,and Seiki Ejima

Abstract—The shift in the central wavelength of fiber Bragg
gratings (FBGs) during annealing of hydrogen-loaded opticalfiber exposed to ultraviolet (UV) laser irradiation through aphase mask is studied and shown to be caused by thermal
diffusion of hydrogen out of the fiber for both short-period andlong-period FBGs. Reloading FBGs with hydrogen followed bya second annealing cycle without exposing the fiber to the UV
laser reproduces the details of the wavelength evolution observed
during first annealing following UV irradiation. This shows thatthe wavelength shift of the grating during annealing is determinedby diffusion of hydrogen gas out of the optical fiber for both
short-period and long-period FBGs.
Index Terms—Annealing, Bragg grating, diffusion, excimer
laser, hydrogen, long-period fiber Bragg grating (FBG), opticalfiber, short-period fiber Bragg grating (FBG), silica, ultraviolet(UV) photosensitivity.

I. INTRODUCTIONI

T has been noticed that the central wavelength of fiber Bragg
gratings (FBGs) fabricated by exposing hydrogen loaded optical fiber to ultraviolet (UV) laser irradiation drifts to shorter
wavelengths by about 0.5–1 nm over a period ranging from a
few to several weeks when it is not heat-treated [1]. This wavelength shift exceeds or is comparable to the channel separation employed in telecommunications systems, about 0.78 or
0.39 nm for 100- and 50-GHz dense-wavelength-division-multiplexing (DWDM) systems, respectively. The wavelength canbe stabilized if the FBG is processed by annealing. However,design becomes more complicated because a wavelength offset
must be included. The wavelength shift is problematic not only
for telecom applications, but also for other applications, andgood control is needed. In long-period FBGs (LP-FBG), theshift is about two orders of magnitude greater than in short-period FBGs (SP-FBG) and can be as much as several tens ofManuscript received August 25, 2003; revised December 2, 2003.
Y. Masuda, K. Fujita, Y. Suzaki, T. Yokouchi, K. Nakagawa, and S. Ejima
are with Faculty of Engineering, Kagawa University, 2217-20 Kagawa, Japan(e-mail: ejima@eng.kagawa-u.ac.jp).
M. Nakamura was with the Faculty of Engineering, Kagawa University,
2217-20 Kagawa, Japan. He is now with the Graduate School of Engineering,Osaka University, Osaka 565-0871, Japan.
C. Komatsu was with the Faculty of Engineering, Kagawa University,
2217-20 Kagawa, Japan. She is now with Fujitsu Kochi Systems Engineering,Ltd., Kochi, Japan.
M. Yamauchi, M. Kimura, Y. Mizutani, and S. Kimura are with Shinko Electric Wire Company, Ltd., 1298-12 Shido, Kagawa, Japan.
Digital Object Identifier 10.1109/JLT.2004.825784

nanometers. In order to make use of the excellent characteristics of FBGs, in particular their sharp spectral response, we needto understand the mechanism of the wavelength shift and to beable to control it accurately.
The wavelength shift certainly depends on the processes used
to fabricate an FBG. Numerous studies have been made of theorigin of the UV photosensitivity, including the color centermodel [2], photoelastic model [3], [4], and so forth. These theories are quite complex, and it appears that the photosensitivity
may be determined by several different mechanisms, rather thanby a single mechanism.
Before an optical fiber is exposed to a UV laser, it isusually loaded with hydrogen gas in order to increase its
UV photosensitivity [5], and it is annealed after imprinting
an FBG to stabilize its reflectivity and central wavelength.
For the annealing process, Erdogan [6] has developed anempirical theory to describe how the reflectivity of the FBG
decreases during annealing for fibers without hydrogen loadingin accordance with a power law model based on electron
detrapping by annealing from broadly distributed traps which
capture electrons by UV absorption. Baker et al. [7] have shownthat for hydrogen-loaded fibers, the spectral evolution deviatesfrom Erdogan’s power law model, and they have proposed alog-time model. The deviation appears to take place in theearly stage of annealing. Erdogan’s theory has been extended
to other fibers in the search for thermally stable FBGs, such as
boron-doped fibers, tin-doped fibers, and fluorine-doped fibers[8]–[10]. The fibers used in these studies were without hydrogenloading or such that hydrogen gas was completely removed byleaving them for several days at ambient temperature. There,
the central wavelength varies by 0.1–0.2 nm or less.
For fibers loaded with hydrogen, the central wavelength of an
FBG without annealing has been reported to evolve gradually toshorter wavelengths by about 0.7 nm, much more than for those
without hydrogen at room temperature, owing to out-diffusionof hydrogen from the fiber over a long time, ranging from a few
to several hundred hours [1], [11].
Malo et al. [1] have interpreted their results in terms ofhydrogen molecules that are dissociated by UV irradiation
and react with dopant Ge to form Ge–OH bonds in the fiber
core; hence, the hydrogen molecules are depleted there. In thecladding, where Ge is absent, the dissociated hydrogen simply
recombines and refills the fiber core by inward diffusion. Thisin-diffusion increases the central wavelength for several hours

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MASUDA et al.: WAVELENGTH EVOLUTION OF FBGs FABRICATED FROM HYDROGEN-LOADED OPTICAL FIBER DURING ANNEALING

after UV exposure. After that, outward diffusion from thebulk causes a decrease in the central wavelength over a few toseveral hundred hours at room temperature. Thus, the central
wavelength initially increases and then decreases. They havefurther shown that, when the FBG is reloaded with hydrogengas, the central wavelength simply decreases without showing
the upswing, confirming the absence of hydrogen depletion andin-diffusion without UV exposure.
Swart et al. [12], [13] have done an experiment tracking thechange in the refractive index based on interferometry with two
FBGs in high-pressure hydrogen up to 100 atm at 40–90 C. By
loading hydrogen gas and evacuating the gas, they have determined the diffusivity and solubility of hydrogen gas molecules
into and out of the fiber silica glass.
Bakhti et al. [14] have studied the wavelength evolution of
LP-FBGs at room temperature in a fashion similar to that ofMalo et al. [1] for SP-FBGs. After UV exposure, hydrogenout-diffusion from the cladding initially decreases the refractive index for higher order cladding modes, which increases thecentral wavelength, and later the out-diffusion from the bulk remode, thereby causing anduces the refractive index of
upswing in the central wavelength similar to that in SP-FBGs.
Increasing evidence exists that the wavelength shift is causedby the diffusion of hydrogen out of the fiber. In order to obtaindefinitive evidence, we have performed a series of experimentson the evolution of the wavelength during the annealing process
at several different annealing temperatures for both short-period and long-period FBGs. The data for both SP-FBGs and
LP-FBGs agree well with theoretical predictions for different
annealing temperatures and for different hydrogen-loading pressures. To the best of the authors’ knowledge, no such combined observations have been reported previously for SP-FBG
and LP-FBG. We have also determined the minimum annealing
time for different annealing temperatures required to stabilize
the central wavelength of FBGs. In order to confirm that theevolution is due to hydrogen out-diffusion, we have reloaded an
FBG with hydrogen and annealed it a second time. Here, theevolution of the central wavelength was essentially the same asthat observed following the original first annealing; hence, thewavelength shift is certainly controlled by hydrogen out-diffusion. These data are used to determine the change in the refractive index of the optical fiber owing to hydrogen loading.
II. EXPERIMENTS
In this experiment, we loaded hydrogen gas into asingle-mode optical fiber (Corning SMF-28) at 100-atm
pressure and room temperature for ten days and stored it in afreezer at about 50 C for one day to two weeks before using
it. We fabricated an SP-FBG by removing the coating resin andexposing the bare fiber to a KrF 248-nm excimer laser througha phase mask. The laser fluence is 280 mJ/cm pulse at theposition of the fiber, and the laser was run at a repetition rateof 20 Hz for 2.5 min. The grating period of the phase mask
is 1073.63 nm, and the effective-refractive index
of thefiber is about 1.446. The central wavelength of the SP-FBG
1552.5 nm,
is expected to be
is grating pitch of the SP-FBG. The length of the
where

935

Fig. 1. Evolution of the transmission spectrum of an SP-FBG during
annealing.

FBG is 15.5 mm. A weak tension of 80 gf was applied to theoptical fiber for secure mounting during laser irradiation [15].
An LP-FBG was made by exposing the same -loaded fiber
to the same KrF excimer laser through multiple slits in thinstainless steel with 50% opening factor and a 540- m period.
The laser irradiation conditions were the same as for SP-FBG
fabrication, i.e., 280 mJ/cm pulse at the position of the fiberand 20-Hz repetition rate. The fiber holder, together with themultiple slits, was moved against the laser beam in the longitudinal direction of the fiber. The beam spot size was 16 mm indiameter, and the total length of the LP-FBG was 40 mm. Eachslit was irradiated by the laser for a total of 45 s.
The fabricated FBGs were placed in an annealing oven andsplice-connected to an in situ monitoring optical circuit within
10 min after exposure to the laser. The oven was set at theexperimental annealing temperature beforehand. We define thein the data below as the time when the UV
start timelaser irradiation was completed. The spectral evolution of thesignal transmitted through the FBG was monitored for about
100 h by injecting the wide-band signal light from an amplified
spontaneous emission (ASE) source.
A. Wavelength Evolution of SP-FBG
Fig. 1 shows spectra of the light transmitted through the
SP-FBG at the end of the UV exposureand after 80 hof annealing at 140 C. The trajectory of the transmission
minimum is also shown there. The initial central wavelengthis 1552.0 nm, slightly shorter than that expected from therelation
1552.5 nm. The central
wavelength reaches its maximum value after 15 min anddecreases to a stable value after 6 h.
The time evolutions of the transmission minimum and peakcentral wavelength are shown in Fig. 2(a) and (b), respectively,
for annealing temperatures 50, 100, 140, and 200 C. The shift
in the central wavelengthis taken to be the difference froma reference that is taken just after the FBG is placed in the oven.

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Fig. 3. Change in the central wavelength of an LP-FBG during annealing.

however, was reproducible and is shown in Fig. 3, where the, the difference from the reference taken
shift is defined as
immediately after the FBG was placed in the oven. The LP-FBG
77 nm, or about two orders of
has a wavelength shift
0.7 nm .
magnitude greater than that for the SP-FBG
C. Comparison With the

Diffusion Theory

The diffusion of molecular hydrogen is described by the diffusion equation(1)

Fig. 2. (a) Transmission minimum and (b) change in the central wavelengthof an SP-FBG during annealing.

Theapproaches a stable value after a certain annealing time,
but the transmission minimum continues to decrease.
The temperature of the annealing oven was set before the
FBG was placed in it but does drop temporarily because the door
is opened; however, the temperature recovers after about 15 min,according to thermocouple measurements. The upswing of thecentral wavelength in Fig. 2(b) is partly due to the temperaturedependence of the shift in the FBG wavelength, which is about
0.01 nm C. It also appears to be partly due to the hydrogen
depletion by UV laser irradiation followed by in-diffusion as
described in [1].
B. Wavelength Evolution of LP-FBG
The time evolution of the central wavelength of the LP-FBG
is shown in Fig. 3. Normally an LP-FBG manifests several
spectral modes. We have tracked themode. The mode
number is determined in the following way. By fabricating
many LP-FBGs with different slit periods and monitoring theirspectra through injecting a wide-band signal, 1450 1610 nm,
from the ASE light source (Thorlabs ASE-7701-AP), we haveidentified the spectrum of the shortest wavelength mode asin accordance with Fig. 1 of [16] and have confirmed thatthe mode we have tracked is. The slit period was varied
in intervals of 30
50 m over the range of 540
690 m
using two sets of multiple slits with 540- and 600- m periods
and additional periods were obtained by tilting these two slits.
The central wavelength of the LP-FBG was 1530 nm for aslit period of 540 m. Unlike the SP-FBG, the transmission
minimum was very sensitive to how the fiber is mounted in
the annealing oven. The behavior of the central wavelength,

is the hydrogen concentration. The diffusion coeffiwherecient for hydrogen in silica glass is given by Lemaire [17] ascm

s40.19 kJ/mol

(2)

where
8.31 J/K/mol is the gas constant, and the temperature is in . The solution on the axis for outward diffusion incylindrical geometry is conveniently given by Crank [18] as(3)where is the radius of the optical fiber, 62.5 m and is timeafter the onset of diffusion from a fully loaded sample.
The experimental data of Fig. 2(b) for an SP-FBG and of
Fig. 3 for an LP-FBG are compared with this theory in Fig. 4.
in Figs. 4(a) and (b) are taken with
The wavelength shifts
respect to the stable wavelength toward the end of annealing,
and data points within about 15 min after annealing have been
removed since the oven temperature is not stabilized at thosetimes, as explained previously. For the same reason that theout-diffusion effectively starts after 15 min, the theoreticalcurves in Fig. 4(c) are shifted to later times by 15 min. Since
the diffusion coefficient given by (2) is 405, 92, 26, and 3.5
times greater than the value at room temperature (22 C) for annealing temperatures of 200, 140, 100, and 50 C, respectively,
the out-diffusion process effectively takes place after the oventemperature has returned to its steady state, and the error causedby the 15-min shift in the theoretical curves should be small. The
amount of wavelength shift
was 0.7 nm for the SP-FBG
and 77 nm for the LP-FBG at any of the annealing temperatures in Fig. 4(a) and (b), respectively. The behaviors offorMASUDA et al.: WAVELENGTH EVOLUTION OF FBGs FABRICATED FROM HYDROGEN-LOADED OPTICAL FIBER DURING ANNEALING

937

Fig. 5. Annealing time as a function of the reciprocal of the annealing
temperature required for stabilization of the central wavelength. Open circles
are for SP-FBG, and filled circles are for LP-FBG.

can be calculated by setting (3) equal to 5%. This means thatcan be determined experimentallythe diffusion coefficientby combining this relation with (4). The resulting coefficientiscm

33.87 kJ/mol(5)

in good agreement with (2), Lemaire’s formula [17].
E. Dependence of

1Fig. 4. Evolution of the central wavelength shift  during annealing for(a) SP-FBG and (b) LP-FBG. Curve (c) is the on-axis hydrogen concentrationin the fiber calculated using diffusion theory.

both SP-FBGs and LP-FBGs are nearly identical to Fig. 4(c) for
the theoretically expected outward diffusion of hydrogen gas.
D. Minimum Annealing Time
From the standpoint of practical applications, it is very
useful to know how many hours of annealing are needed tolet hydrogen gas diffuse out of an optical fiber in order toachieve a stable central wavelength. The time required to driveout 95% of the hydrogen, i.e., the time for the wavelength
shift to reach 95% of the total
is plotted in Fig. 5 as afunction of the reciprocal of the annealing temperature. There,
the open circles correspond to data for the SP-FBG, and thefilled circles correspond to that for the LP-FBG. Both havenearly identical dependences on temperature, and a fitting a
curve for both gives(4)
For annealing times longer than this, the hydrogen is nearly all
driven out by diffusion from the fiber. Theoretically, this timeon Loading Pressure

In order to confirm further that the wavelength shiftofthe FBGs is due to diffusion of hydrogen out of the optical fiber,
we have conducted experiments in which the hydrogen-loadingpressure is changed from 100 to 50 and 10 atm. The resulting
evolution of the central wavelength during annealing at 140 C
is shown in Fig. 6(a) and (b) for SP-FBGs and LP-FBGs,
respectively. Data for the case without hydrogen loading are
included. In this case, although the transmission minimum wasvery low at around 1 dB because of poor UV photosensitivity
owing to the lack of hydrogen, the spectrum is clearly visible,
and the central wavelength did not shift during the entire
annealing time. The corresponding theoretical curve is that for
140 C in Fig. 4(c). As expected theoretically, the total
does increase with loading pressure as shown in Fig. 6(c) and(d) for the SP-FBG and LP-FBG, respectively. These curves
show some deviation from linearity unlike our expectation ofa linear dependence.
F. Change in the Refractive Index Caused by Hydrogen
Experimental data, especially those in Figs. 4 and 6, demonstrate clearly that the evolution of the central wavelength of
FBGs during annealing is defined by the out-diffusion of hydrogen from the optical fiber. The question then arises as tohow much the refractive index of the fiber changes as a result of the annealing. For SP-FBGs, this can be analyzed using, and the formula for the modulation
is given
by
(6)

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1

Fig. 6. Variation in the change in the central wavelength  for different hydrogen-loading pressures: evolution during annealing for (a) SP-FBG and (b) LP-FBG;
and (c) and (d) are the total shift  for SP-FBG and LP-FBG, respectively.

1

where is transmission and the FBG length. The grating pitch
is half of the phase mask period which is 1073.63 nm, andis 15.5 mm. The effective-refractive index
can be calculated
fromusing the experimentally observed wavelength, and the grating modulation
can be calculated from(6) using measured transmission . These are summarized inTable I for the case of 140 C annealing.
The grating modulation
contributes to the refractive
index by its average value. However, its difference between
before and after annealing,is negligibly small compared with the difference of the effective
refractive index,. The fact that the refractive index has decreased by this amount, owing tooutward diffusion of hydrogen during annealing, means thatthe refractive index has already been increased by hydrogenloading to 100 atm before the FBG was fabricated by exposing
it to the UV laser. This interpretation suggests that, if an FBG
that has been annealed once is reloaded with hydrogen, thenthe central wavelength should recover the value it had before
the first annealing. In addition, if it is subsequently annealed
again, then the should evolve in the same way as during thefirst annealing. A reloading experiment of this sort is described
next.
G. Reloading Experiment
In order to test this expectation, we have reloaded hydrogen in
an LP-FBG at the same loading pressure for the same number ofdays and have annealed the sample in the same way as during
the first annealing, without exposing it again to the UV laser.
An LP-FBG was chosen for this test because it has a much

TABLE ICHANGES OF REFRACTIVE INDEX n AND MODULATION INDEX n
BEFORE AND AFTER THE ANNEALING FOR 140 C ANNEALING OF SP-FBG

1largerso that it provides better resolution than an SP-FBG.
Fig. 7(a) shows the evolution of the central wavelength during
the first annealing and Fig. 7(b) the time evolution during asecond annealing for two LP-FBGs. The fiber coating resin wasremoved before exposure to the UV laser and was reapplied
after the first annealing. Hydrogen reloading and the second annealing were carried out on the recoated LP-FBG. The time evolution of the central wavelength in the second annealing cycle
reproduced that in the first annealing cycle nearly identically,
thereby proving that the evolution of the central wavelength iscaused entirely by diffusion of hydrogen out of the optical fiber.
The first data point in Fig. 7(a) was taken at the end of UV irradiation, and, analogously, the initial data point in Fig. 7(b)was taken before the start of the second annealing cycle. The
LP-FBG was recoated within about 2 h after it was taken outof the oven. In this series of experiments, hydrogen gas was
loaded at 90 atm, instead of the 100 atm used for Fig. 3, and thehydrogen-loaded fiber was processed to UV exposure within acouple of days, instead of the week or two in the case of theMASUDA et al.: WAVELENGTH EVOLUTION OF FBGs FABRICATED FROM HYDROGEN-LOADED OPTICAL FIBER DURING ANNEALING

939

Fig. 7. Evolution of the central wavelength of an LP-FBG with hydrogen reloading: (a) is for the first annealing and (b) for a second annealing after hydrogen
reloading.

data of Fig. 3. These differences seem to have yielded a shift of
60 nm, which is less than the 77-nm shift of Fig. 3. The transmission minimum is sensitive to how the fiber has been heldin the oven which is indicative of some sensitivity to the weakbending and applied stresses; however, the central wavelength
was quite reproducible. The data of Fig. 7 confirm that the evolution of the is the result of the diffusion of hydrogen out of
the fiber.
III. DISCUSSION
The physics model of Malo et al. [1] for the depletion of hydrogen molecules by UV laser irradiation followed by in-diffusion of hydrogen to the core of the fiber from surrounding
cladding, appears to be very likely. This will cause the central
wavelength to increase initially and decrease later. In their experiment, at room temperature, the upswing occurred in the first
4 5 h. For the annealing temperatures of our study up to 200 C,
it should take place at much earlier times. The time
can beestimated from the simple relation
using the diffusion coefficient given by (2) and taking the diffusion path
length as the fiber core diameterm. This crude estimate of the time
for room temperature 20 C gives 5 h,
in agreement with their experiment. For our annealing temperatures 140 and 200 C as in Fig. 2,
is 2.6 and 0.6 min,respectively. Although it is not clear for 50 C for whichis 1.1 h, the increases of the wavelength within 10 15 min for
140 and 200 C seen in Fig. 2 are very likely to be caused byinward diffusion. However, because of uncertainties in the oventemperature in the first 15 min, we do not think our data can resolve the process well.
According to the hypothesis of Malo et al. [1], the wavelength
should shift to shorter values in real time during pulsed irradiation with the UV laser as depletion of hydrogen molecules in thefiber core proceeds. The growth of the grating during this stage,i.e., the increase of, of course, raises background value
by the averaged amount of the modulation, but its magnitude is much smaller than the decrease of
caused by thedepletion, probably by the magnitude of the ratio
toin Table I which is; hence,the shift of the wavelength to shorter values is to be expected.
Unlike this expectation, however, we observe a shift to longer

wavelengths by the amount of 0.08 nm momentarily, coincident
in time with laser pulse in SP-FBGs, which is caused, we believe, by the temperature increase of the fiber heated by the UV
laser pulse [19]. The LP-FBG also did not show the shift. It
is not clear to us whether this is due to the opto-lastic effectcaused by the release of dilating pressure of dissolved hydrogenmolecules.
For an LP-FBG, Bakhti et al. [14] obtained an upswing of thecentral wavelength very similar to that in SP-FBG by Malo et
al. [1], but for a different reason. The central wavelength of an
LP-FBG is given by
(7)
where
and
are the effective refractive indexes ofthe fundamental modeand cladding mode
, respectively. The index
is defined by the cladding. Whenhydrogen out-diffuses from the outer portion of the fiber, i.e.,the cladding
decreases and, consequently,
increases.
As the hydrogen continues to diffuse out from the bulk offiber, bothanddecrease and decreases, thus giving
an upswing in . This interpretation predicts larger upswing
for uniformly loaded fiber and a weaker one for partiallyout-diffused fiber. Our data in Fig. 3 do not show any upswing,
but the data for hydrogen reloading in Fig. 7 appear to show
an upswing both after UV exposure and after reloading. The
data in Fig. 3 have been taken using fibers stored in a freezer
for about a week at about
after hydrogen loading,whereas the data in Fig. 7 were taken within a couple of days.
Therefore the LP-FBG of Fig. 7 had hydrogen more uniformly
loaded over the fiber cross section than that of Fig. 3, and theirinterpretation regarding the upswing in seems to apply to ourdata qualitatively.
Although our annealing data for the evolution of central FBG
wavelength have some uncertainties early in time for about 15
minutes because of increasing oven temperature and the initial
upswing as described above, the majority of data extending from15 minutes to 100 hours are well described by the out-diffusion
theory for both SP-FBG’s and LP-FBG’s.
Recently an interesting experiment was done by Viswanathan
et al. [20] showing that hydrogen loading can be done using dilute hydrogen gas mixed with other gases such as Ar,,

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and. In their experiment, they have shown that the refractive index increases linearly with loading hydrogen pressure. In
our experiment, as shown in Fig. 6(c) and (d), the dependence
deviated from linearity unlike their result. This difference is notwell understood at the moment.
Several recent reports show that the UV photo sensitivity canbe enhanced by blank exposure to UV laser light that is, pre-sensitization [21]–[23]. Effective imprinting of FBG at later times
has been demonstrated in such fibers with weaker degradation of
the transmission minimum during high temperature annealing
than in the case of hydrogen loaded fiber. They also manifest
little shift of the central wavelength, typically less than 0.1 nm,
because of the absence of hydrogen gas. Ref. [23] shows thatpre-sensitization can be effective even with a cheap UV lamp.
This is certainly very attractive for FBG fabrication when theoffset in the central wavelength does not have to be predicted.
IV. CONCLUSION
The evolution of the central wavelength of FBGs during
annealing has been experimentally proven to be caused bydiffusion of hydrogen gas out of the optical fiber, which has
been loaded with hydrogen before being exposed to UV laser
light. The time evolution has been examined for both SP-FBG
and LP-FBG. When an FBG is reloaded with hydrogen andreannealed, but without re-exposure to a UV laser, the evolutionof the central wavelength during re-annealing is the same asthat seen in the first annealing; therefore, the evolution isclearly determined by the diffusion of hydrogen out of the
optical fiber.
A formula (4) for the minimum number of hours of annealing
required to drive the hydrogen out of the fiber that is consistent with theoretical model of hydrogen out-diffusion has been
derived.
ACKNOWLEDGMENT
The authors would like to thank the referee for kind advice
pointing out two articles [14] and [20] of which the authors were
not aware at the time of manuscript submission. The authors
also wish to thank Prof. K. Saito of Toyota Institute of Technology for his suggestion of reloading the experiment (Fig. 7)
for stronger evidence of hydrogen out-diffusion from opticalfiber. Finally, the authors also thank Dr. D. H. McNeill for his
careful proofreading of the manuscript.
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MASUDA et al.: WAVELENGTH EVOLUTION OF FBGs FABRICATED FROM HYDROGEN-LOADED OPTICAL FIBER DURING ANNEALING

Yuji Masuda received the Bachelor’s degree inapplied materials science from the Faculty ofEngineering, Kagawa University, Kagawa, Japan,
in 2003. He is currently working toward the M.Sc.
degree at the same university.

Mitsuo Nakamura received the Bachelor’s degree
in applied materials science from the Faculty ofEngineering, Kagawa University, Kagawa, Japan,
in 2003. He is currently working toward the M.Sc.
degree in materials science at the Graduate Schoolof Engineering, Osaka University, Osaka, Japan.

Chisa Komatsu received the Bachelor’s degree inapplied materials science from the Faculty of Engineering, Kagawa University, Kagawa, Japan, in 2003.
She currently works for Fujitsu Kochi Systems Engineering, Ltd., Kochi, Japan.

Keio Fujita received the Bachelor’s degree inapplied materials science from the Faculty ofEngineering, Kagawa University, Kagawa, Japan,
in 2003. He is currently working toward the M.Sc.
degree at the same university.

Makoto Yamauchi received the Bachelor’s degree in
intelligent mechanical systems engineering from theFaculty of Engineering, Kagawa University, Kagawa,Japan, in 2002.
He currently works for Shinko Electric Wire Company, Ltd., Kagawa, Japan.

Masanori Kimura was educated in control technologies at Kagawa Polytechnic College, Kagawa, Japan.
He has worked for Shinko Electric Wire Company,
Ltd., Kagawa, Japan, since 1995.

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Yasuo Mizutani received the Bachelor’s degree inapplied physics from the Engineering Department,
Tokai University, Kanagawa, Japan, in 1986.
He has worked for Shinko Electric Wire Company,
Ltd., Kagawa, Japan, since 1986.

Susumu Kimura received the Bachelor’s degree inapplied chemistry from the Engineering Department,
Yokohama National University, Yokohama, Japan, in
1972.
He is Director of the Technology Division of
Shinko Electric Wire Company, Ltd., Kagawa,Japan.

Yoshifumi Suzaki (M’94) received the Bachelor’s
degree, the M.Sc. degree in precision engineering,and the Dr.Eng. degree from Osaka University,
Osaka, Japan, in 1985, 1987, and 1995, respectively.
He was Associate Professor at Takamatsu National College of Technology from 1987 to 2000.
Since 2000, he has been an Associate Professor
in the Faculty of Engineering, Kagawa University,
Kagawa, Japan.

Takashi Yokouchi received the Bachelor’s degree
in law from the Law Department, Hosei University,
Tokyo, Japan, in 1986.
He is currently on the technical staff of the Facultyof Engineering, Kagawa University, Kagawa, Japan.

Kiyoshi Nakagawa (S’69–M’82–SM’91) received the M.Sc. degree in law
from the Graduate School of Science and Technology, Kobe University, Kobe,
Japan, in 1986.
He has been an Associate Professor at the Faculty of Engineering, Kagawa
University, Kagawa, Japan, since 2001.

Seiki Ejima received the M.Sc. degree in telecommunications from Waseda University, Tokyo, Japan,
in 1970 and the Ph.D. degree in plasma physics from
Columbia University, New York, in 1973.
He worked on nuclear fusion research from 1974
to 1987 at General Atomic Company, San Diego, CA,
and on electronics material research and development
at Shin-Etsu Chemicals Company, Ltd., from 1987
to 2000. Since 2000, he has been a Professor in the
Faculty of Engineering, Kagawa University, Kagawa,Japan.