Japanese Journal of Applied Physics
Vol. 45, No. 6A, 2006, pp. 5035–5038#2006 The Japan Society of Applied Physics

Eﬀect of Spherical Aberration on Fabrication of Fiber Bragg Gratings
Yoshifumi S UZAKI, Jun-pei M OHRI, Keisuke NAKAYAMAy, Maki A NDOz, Kenji S AKAMOTO,
Makoto Y AMAUCHI1 , Yasuo M IZUTANI1 , Takashi Y OKOUCHI and Seiki E JIMA
Department of Advanced Material Science, Faculty of Engineering, Kagawa University,
2217-20 Hayashi-cho, Takamatsu 761-0396, Japan1Shinko Electric Wire Co., Ltd., 1298-12 Shido, Sanuki, Kagawa 769-2101, Japan(Received February 13, 2006; accepted March 15, 2006; published online June 8, 2006)

Cylindrical convex lenses are commonly used in fabricating ﬁber Bragg gratings (FBGs) by the phase mask method toincrease the energy ﬂuence of UV laser light and thereby enhance FBG productivity. We have found that lens aberrations canaﬀect the eﬃciency of FBG fabrication by this method. Comparisons of the experimental measurements of FBG transmission
minimum as a function of ﬁber position during irradiation by focussed excimer laser light with ray tracing calculations
demonstrate the eﬀect of spherical aberration, particularly for lenses with shorter focal lengths.
[DOI: 10.1143/JJAP.45.5035]
KEYWORDS: fiber Bragg grating, optical fiber, lens, aberration

1.

Introduction

Because ﬁber Bragg gratings (FBGs) have very sharp,
narrow-band reﬂection spectra, they are well suited for
applications involving narrow-band optical signals, such as
optical ﬁlters in optical telecommunication systems, ﬁber
laser cavities, and various types of ﬁber sensors.
FBGs, which have a periodic structure of the refractive
index inside the optical ﬁber in the longitudinal direction,
are commonly fabricated by exposing the optical ﬁber to UV
laser light. Because the grating period is very short, on theorder of 0.5 mm, irradiation is normally carried out in theinterference patterns of UV laser light so that these patterns
are transprinted into the optical ﬁbers.
There are two standard methods for generating theseinterference patterns: the two-beam interference method andthe phase mask method.1) In the ﬁrst method, an interference
pattern is formed by splitting the incident UV laser beam
into two, deﬂecting the two beams with mirrors and letting
them cross each other. The second method uses a phasemask grating; that is, a UV laser beam incident onto thephase mask is diﬀracted into þ1st and 1st order beams thatinterfere with each other within a short distance from thephase mask, typically less than 1 mm. The optical ﬁber isplaced very close to or in contact with the mask. Although
the two-beam interference method has the advantage ofallowing FBG production with diﬀerent grating periods
simply by controlling the crossing angle of the two beams,
the phase mask method is more common, presumably
because of high reproducibility in FBG fabrication owing
to the fact that the optical ﬁber is positioned very close tothe mask.
To enhance the eﬃciency of FBG fabrication by the phasemask method, it is customary to increase the ﬂuence of theincident UV laser light by inserting a plano-convex lens andplacing the optical ﬁber near its focal point. We have foundthat the optimum position for the optical ﬁber is not on theoptical axis of the plano-convex lens, contrary to our initialE-mail address: suzaki@eng.kagawa-u.ac.jp
Present address: MicroCraft, Inc., 630-2 Tanaka, Okayama 700-0951,
Japan.
z
Present address: Aoi Electronics Co., Ltd., 455-1, Kohzai Minamimachi,
Takamatsu 761-8014, Japan.
yBeam
expanderMirror

KrF excimer
laser

3
Stop
Cylindrical lens
Phase mask
Optical fiberFig. 1. Illustration of FBG fabrication by phase mask method.

expectation. Instead, higher eﬃciency was obtained byshifting the ﬁber away from the optical axis of the lens. Withthe aid of detailed experiments and ray tracing calculations,
we demonstrate that this higher eﬃciency is explained by thespherical aberration of the plano-convex lens that produces ahigher energy ﬂuence oﬀ axis.
2.

Experimental Methods

Our experimental setup is illustrated schematically inFig. 1.2) The excimer laser (Lamda Physik, COMPex-102)
delivers up to 240 mJ/pulse at 248 nm with a pulse widthof 25 ns at repetition rates of 1– 20 Hz. The 8  24 mm2
rectangular output beam is shaped by a 7  7 mm2 stop toselect a higher quality uniform portion of the beam. Thislimits the energy to 60 mJ. After passing through a 3 beam
expander, the beam is deﬂected downward by a mirror andfocused by a plano-convex cylindrical lens. A phase mask ismounted in front of the nominal focus of the lens. A bare
optical ﬁber is placed underneath the phase mask at adistance of less than 0.5 mm. We have used two diﬀerent
plano-convex cylindrical lenses (Sigma Koki, fused silica
cylindrical lenses F100 and F200), with focal lengthsof 87.9 mm (F100) and 176.9 mm (F200), as shown in
Figs. 2(a) and 2(b), respectively. The lens parameters are
given in Table I. Focal length is deﬁned in the table by its

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Jpn. J. Appl. Phys., Vol. 45, No. 6A (2006)

KrF excimer laser light

156.2
82.5

87.9

176.9

5.44
Phasemask

(a)

20.7

220

Energy density

15

1210

8

54Transmission
minimum

0-0.450-0.3-0.15

0Energy density (mJ/mm )(b) F200 cylindrical lensTransmission minimum(dB)(a) F100 cylindrical lensY. SUZAKI et al.

0.15

0.30.45

Position of optical fiber (mm)Optical fiber(b)Table I. Lens parameters (unit: mm).
Lens type

F100F200

Focal length

87.9

176.9

Lens thickness

5.0

5.0

Curvature radius

46.0

92.0

4

5

Energy density
43.2

3

2.4
1.6

2
1

Transmission
minimum

0.8
00-1.5 -1.2 -0.9 -0.6 -0.3

0

0.3

0.6

0.9

1.2

Energy density (mJ/mm 2)

Transmission minimum(dB)

Fig. 2. Optical arrangements of two cylindrical lenses F100 (a) andF200 (b).

1.5

Position of optical fiber (mm)distance from the lens back surface. The beam is focussed in
the direction perpendicular to the optical ﬁber, i.e., in theright-left direction in the plane of Fig. 2. The 21 mm widthof the beam as it is incident on the cylindrical lens is reduced
to 1– 2.5 mm at the position of the optical ﬁber. The opticalﬁber is mounted 5.4 mm in front of the focal point in
Fig. 2(a) and 20.7 mm in Fig. 2(b).
The optical ﬁber used here is a standard single mode ﬁber(Corning SMF-28), with core and cladding diameters of 8.3and 125 mm, respectively. Prior to the experiment, the ﬁber
was kept under 10 MPa hydrogen gas for ten days forhydrogen loading to increase its sensitivity to UV light. The
resin coating of the ﬁber was removed and the ﬁber was
ultrasonically cleaned just before it was placed underneaththe phase mask. The grating period p of the phase mask is1070.3 nm giving the grating pitch  ¼ p=2 in the ﬁbercore; hence, using the eﬀective refractive index of theoptical ﬁber neff ¼ 1:446, the FBG central wavelength isexpected to be 0 ¼ 2neff  ¼ 2neff p=2  1547 nm.
During FBG fabrication using the shorter-focal-length
lens (F100), we noticed that the eﬃciency of FBG formationis very sensitive to the ﬁber position relative to the opticalaxis, in contrast to our initial expectation that the highest
eﬃciency should be obtained on the optical axis. Suspectingthat this phenomenon might be a lens aberration eﬀect, we
carefully shifted the position of the optical ﬁber away fromthe optical axis of the lens and studied how the eﬃciency ofFBG formation depends on the ﬁber position. We deﬁne theeﬃciency of FBG formation by the transmission minimum
attained after a given duration of exposure to the laser lightfor quantitative comparison.
We normally monitor FBG formation by injecting abroadband light signal from an ampliﬁed spontaneousemission (ASE) source (Thorlabs ASE-7701-AP) and byanalyzing the signal transmitted through the FBG using an
optical spectrum analyzer (Advantest Q8384).

Fig. 3. Transmission minimum of FBGs generated using two diﬀerent
lenses plotted against shift of optical ﬁber perpendicular to optical axis oflens. The solid lines are ray tracing calculations of the distribution of theenergy ﬂuence for the corresponding lenses: (a) F100; (b) F200.

By exposing the optical ﬁber to the excimer laser light for
30 s, we measured FBG transmission minimum from theoptical spectrum. The dependence of transmission minimumon the position of the optical ﬁber relative to the optical axisof the plano-convex lens is shown by the solid circles inFigs. 3(a) and 3(b), for which the lens conﬁgurations
correspond to Figs. 2(a) and 2(b), respectively. The positional dependence for the shorter-focal-length lens [F100,Fig. 3(a)] varies strongly, particularly toward the edge ofthe beam, whereas for the longer-focal-length lens (F200),
this dependence is almost uniform. Note that the diameter ofthe optical ﬁber is 0.125 mm. The solid curves are energy
ﬂuence distributions obtained from the ray tracing calculations discussed in the next section.
3.

TheoryThe optical geometry for our calculations is shown inFig. 4. We shall derive the equation of the ray that enters thelens, with the angle of incidence in , at position #1 and exits
the lens with the exit angle out at position #2. At position #1,we havex1 ¼ R  D  R cos in ; y1 ¼ R sin insin innL¼:sin Lnair
The equation for the line from #1 to #2 isy  y1
¼  tanðin  L Þ;x  x1

ð1Þ
ð2Þ

ð3Þ

where R is the radius of curvature of the lens surface andD is the thickness of the lens. L is the angle of refraction
at position #1. Here, nL and nair are the refractive indices of5036

Jpn. J. Appl. Phys., Vol. 45, No. 6A (2006)

Y. SUZAKI et al.

yθ inθ in - θ L

#1#2

θ out

θLy1y2

DO
x1x
R

Fig. 4. Illustration of geometry for ray tracing calculations in plano-convex cylindrical lens.

x2 ¼ 0;y2 ¼ x1 tanðin  L Þ þ y1y  y2
¼  tan out ;xsinðin  L Þ nair¼sin outnL

Distance from y-axis (mm)the lens and air, respectively. At the exit position #2, weobtain similar equations, i.e.,ð4Þð5Þ

and¼ x tan out þ x1 tanðin  L Þ þ y1 :

ð6ÞSubstituting x1 by eq. (1), the equation for the exiting raybecomesy ¼ x tan outþ ðR  D  R cos in Þ tanðin  L Þ þ y1 :

ð7ÞUsing the above equations, we have traced the paths ofparaxial rays incident on the lens with a step size of 1 mm
across our beam width. The results are shown in Fig. 5 near
the focal point. The lens parameters are those given inTable I, and the refractive index of the lens nL is taken to be
1.508 equal to that for silica glass at the wavelength of theKrF excimer laser (248 nm). The eﬀect of aberration isclearly evident for the shorter-focal-length (F100) lens[Fig. 5(a)], whereas it is negligible for the longer-focallength (F200) lens [Fig. 5(b)].
The distribution of the energy ﬂuence of the laser light
can also be calculated from the equations discussed aboveasE3 ðyÞ ¼ E1 y1:
y3

ð8Þ

Assuming a uniform distribution of the energy ﬂuence of
the incident laser light incident on the lens (position #1), i.e.,
E1 , the distribution E3 ðyÞ beyond the lens can be obtained at
any point by determining the paths of a set of rays separated
by the small, ﬁxed step size y1 at position #1 in the same
way as in Fig. 5 and using eq. (8). The calculated results
for the two lenses used in our experiments are shown by theFocal point

0.4
0.2
0-0.2
-0.4

Position of optical fiber-0.6
80Distance from y-axis (mm)y ¼ x tan out þ y2(a)0.68284868890(b)1.5
Focal point

10.5
0-0.5
-1

Position of optical fiber

-1.5
150

160

170

180190Distance from back surface of lens x (mm)Fig. 5. Calculated ray paths near focal point of two plano-convex
cylindrical lenses used in our experiments.

solid lines in Figs. 2(a) and 2(b). These ﬁgures show that thecalculated energy ﬂuence distributions correlate well withthe dependence of FBG transmission minimum on thedistance from the optical axis of the focussing lens. Thisconﬁrms the eﬀect of spherical aberration on the optimum
position for FBG production using these lenses.
4.

Conclusions

In the phase mask method for the fabrication of FBGs by
exposing an optical ﬁber to UV laser light, a cylindrical lensis commonly used to enhance the energy ﬂuence of the laser
light. The ﬁber is mounted near the focal point of the lens totake advantage of the higher ﬂuence. It might be expectedthat the optimum position for the optical ﬁber would be on5037

Jpn. J. Appl. Phys., Vol. 45, No. 6A (2006)

Y. SUZAKI et al.

the optical axis of the lens. On the other hand, we have foundthat the best position for FBG fabrication is somewhat
shifted from the optical axis of the focussing lens.
Experimental data on the eﬃciency of FBG fabrication(deﬁned in terms of grating transmission minimum) were ingood agreement with theoretical ray tracing calculations forthe lenses employed in these experiments, thus conﬁrming
the eﬀect of lens aberration. Thus, the eﬀect of lensaberration on FBG fabrication should be taken into account,particularly when short focal length lenses are used.

Acknowledgements
We thank Dr. H. Iwata of Takamatsu National Collegeof Technology for his kind advice about the lens aberration.
We also acknowledge Dr. D. H. McNeill for his careful
proofreading of our manuscript.
1) R. Kashyap: Fiber Bragg Grating (Academic Press, London, 1999)
p. 55.
2) M. Nakamura, C. Komatsu, Y. Masuda, K. Fujita, M. Yamauchi,
Y. Mizutani, S. Kimura, Y. Suzaki, T. Yokouchi, K. Nakagawa andS. Ejima: Jpn. J. Appl. Phys. 43 (2004) 147.

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