Japanese Journal of Applied Physics
Vol. 43, No. 7A, 2004, pp. 4234–4235#2004 The Japan Society of Applied Physics

Short Note

Dependence of Fiber Bragg Grating Characteristics on its Length
Maki A NDO, Makoto Y AMAUCHI1 , Keisuke N AKAYAMA, Kenji M ORIYAMA, Keio F UJITA, Yuji M ASUDA,
Masanori K IMURA1 , Yasuo M IZUTANI1 , Susumu K IMURA1 , Takashi YOKOUCHI,
Yoshifumi S UZAKI, Kiyoshi N AKAGAWA and Seiki E JIMAy
Department of Advanced Material Science, Faculty of Engineering, Kagawa University,
2217-20 Hayashi-cho, Takamatsu, Kagawa 761-0396, Japan1
Shinko Electric Wire Co., Ltd., 1298-12 Shido, Sanuki, Kagawa 769-2101, Japan(Received November 25, 2003; accepted April 1, 2004; published July 7, 2004)

A ﬁber Bragg grating (FBG) is normally made with a length of 10 to 30 mm. Depending on the application, however, a shortlength may be desired, especially in sensor applications for local detection. Under the most common fabrication conditions
using the phase mask method, we have fabricated FBGs with lengths ranging from 0.35 to 15 mm using diﬀerent excimer laser
irradiation times. Although 0.35-mm-long FBGs can be made with laser exposure times exceeding 1 h, the practical minimum
FBG length appears to be around 3 mm with exposure times in the range of 3 to 5 min. [DOI: 10.1143/JJAP.43.4234]
KEYWORDS: fiber Bragg grating, optical fiber, KrF eximer laser, phase mask, refractive index

gas by maintaining it under a high hydrogen gas pressure of
100 atm for approximately 10 days. After the hydrogenloading, we kept the ﬁber in a 70 C freezer for
approximately 5 days before using it. After removing theﬁber-coating resin and placing the bare ﬁber underneath thephase mask, we irradiated the bare ﬁber using a KrF excimer
laser (Lambda Physik COMPex-102) from the other side of
the phase mask. The energy density of the laser radiation is420 mJ/cm2 per pulse at the plane of the ﬁber,2) and the laser
was run at a repetition rate of 20 Hz. These conditions arevery typical for FBG fabrication commonly adopted inindustry. To obtain FBGs of diﬀerent lengths, we placed an
optical stop before the phase mask and changed the opening
width of the stop from 0.35 mm to 15 mm which results in
diﬀerent FBG lengths. The growth of the FBG during thepulse-to-pulse irradiation of the excimer laser has beenmonitored in situ by injecting wideband light from anampliﬁed spontaneous emission (ASE) light source (Thorlabs ASE-7701-AP) into the optical ﬁber and detecting thetransmitted light through the FBG from the other end using
an optical spectrum analyzer (Advantest Q8384).
Transmission spectra are shown in Fig. 1 for 3 min
irradiation of the laser with diﬀerent FBG lengths of 0.35,
1, 3, 5, 10 and 15 mm. Sharp spectra with deep transmission
minimums were observed for the FBGs with lengths greaterthan 3 mm, but for the 0.35- and 1-mm-long FBGs, thetransmission minimums were about 1 dB or below.
The growth of the FBG was monitored in situ up to100 min. Results are shown in the log-log plot in Fig. 2,0Transmission (dB)

Owing to the excellent characteristics of ﬁber Bragg
grating (FBG), particularly its sharp spectral response, theFBG is widely used for many applications in devices which
need accurate wavelength control such as wavelengthselecting devices in dense wavelength division multiplexing(WDM) optical telecommunication, resonators of ﬁber lasers
and many types of optical sensors. For sensor applications,1)
the spatial resolution of parameters to be detected such as
strain, load, vibration, and temperature depends on how theFBG is embedded in the structures. The parameter being
detected will be averaged over the length of the mounting
element containing the FBG. To increase the spatialresolution of the parameters, the element must be madewith its length as short as possible. Therefore, the ﬁrst
question that arises is how much the FBG itself can beshortened. The FBGs originally developed for opticaltelecommunication applications are normally made withtypical lengths of 10 to 30 mm. The purposes of the present
study are to determine the dependence of FBG characteristics on the FBG length and to ﬁnd how much the FBG canbe shortened from these typical values under the constraintsof typical fabrication conditions.
The optical signal size reﬂected from the FBG, that is, thetransmission minimum, depends on the type of application,
but it is quite common that the transmission minimum
should be less than 10 dB. We have studied experimentally
how the transmission minimum depends on the FBG length
under the most commonly adopted fabrication conditions byexposing a single-mode ﬁber to an excimer laser using thephase mask method. Our result shows that the FBG length isinversely proportional to the exposure time of excimer laser
irradiation for a given transmission minimum. Although theFBG with a length as short as 0.35 mm can be made with an
exposure time longer than 1 h, 3 mm appears to be a practicalminimum FBG length, when exposure to the laser irradiationin the range of 3 to 5 min is considered.
Under the commonly adopted fabrication conditions, wefabricated FBGs of diﬀerent lengths. The optical ﬁber weused was a standard single-mode ﬁber (Corning SMF-28).
Prior to the fabrication, the ﬁber was loaded with hydrogen-10-20-30

FBG length
0.35mm1mm
3mm
5mm
10mm-40-50
1553

15mm
1553.51554

1554.51555Wavelength (nm)Present address: Kyowa Electric Instruments Co., Ltd., 3-5-1, Chofugaoka, Chofu, Tokyo 182-8520, Japan.
yE-mail address: ejima@eng.kagawa-u.ac.jp

Fig. 1. Transmission spectra of FBGs with diﬀerent lengths. The FBGs
are all made with 3 min exposure to the excimer laser.

4234

Jpn. J. Appl. Phys., Vol. 43, No. 7A (2004)

M. ANDO et al.
0.011001mm
10Amplitude of refractive
index modulation ∆nmod

Transmission Minimum (dB)4235

FBG length15 mm
10 mm

15 mm

FBG Length0.001

0.35m3mm10mm

15mm0.0001

3 mm
1 mm

0.1

5mm

0.35 mm
0.0000100.010.1

1101
10Exposure Time (min)

100

100

Exposure Time (min)Fig. 2. Transmission minimums of FBGs with diﬀerent lengths against
exposure time to the excimer laser.

Fig. 3. Amplitude of refractive index modulation for FBGs of diﬀerentlengths.

Exposure Time (min)100

where the transmission minimum is plotted against the laser
exposure time for the FBGs with lengths of 0.35, 1, 3, 5, 10
and 15 mm. All the cases show a linear increase when theexposure time is short and deviate from linearity slightly
when the time is long.
The amplitude of the refractive index modulation nmodof the FBG is expected to be the same locally for the same
exposure time within the FBG even when its length is varied.
Using the two well-known FBG formulas3) below, nmod
can be calculated as

10Transmission
Minimum
30 dB
20 dB

110 dB
5 dB
0.10

B ¼ 2neff 1  T ¼ tanh2nmod L;
neff 2

ð1Þ
ð2Þ

where B is the Bragg wavelength, neff the eﬀectiverefractive index of the fundamental mode LP01 ,  thegrating pitch, L the FBG length and T the transmission. The
amplitude of the refractive index modulation nmod , thus
calculated for the data in Fig. 2, is shown in Fig. 3. The
values for FBGs of diﬀerent lengths are approximately thesame as expected.
Laser exposure times for a ﬁxed transmission minimum
are plotted for the data set in Fig. 2 against the FBG lengthin Fig. 4 for 5, 10, 20 and 30 dB transmission minimums.
The exposure time is approximately inversely proportional
to the FBG length. The transmission minimum diﬀers fordiﬀerent FBG applications, but normally, the values lessthan 10 dB are required. This minimum can be obtainedwith the 3-mm-long FBG by 4 min laser irradiation, butwhen the 1-mm-long FBG is used, laser irradiation takes
12 min, which is 3 times longer than that with the 3-mmlong FBG.
Based on our observations, under the standard FBG
fabrication conditions, the exposure time of the FBG to110100

FBG Length (mm)Fig. 4. Exposure time to the excimer laser and FBG lengths for diﬀerenttransmission minimums.

excimer laser irradiation for a given transmission minimum
is inversely proportional to the length of the FBG. Thetransmission minimum of 10 dB commonly required for
FBG applications is obtained with approximately 4 min
exposure to the laser for the 3-mm-long FBG. This is theshortest FBG for most practical applications under the
standard fabrication conditions.
We thank Professor W. L. Finn of Faculty of Engineering,
Kagawa University for his careful proof reading of themanuscript.

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