1. Optik 123 (2012) 860–862
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Optik
journal homepage: www.elsevier.de/ijleo
Numerical ray tracing through a modified cladding fiber optic segment sensors
Radhi M. Chyad∗
, Mohd Zubir Mat Jafri, Kussay N. Mutter, Kamarulazizi Ibrahim
School of Physics, Universiti Sains Malaysia, 11800 Penang, Malaysia
a r t i c l e i n f o
Article history:
Received 2 January 2011
Accepted 10 June 2011
Keywords:
Fiber optic
Unclad fiber sensors
Chemical fiber sensors
Biosensor
a b s t r a c t
By using 3-D geometric optics, the effect of a modified cladding on the transmission of light through
optical fiber is investigated. Analysis of the light transmission of the optical fiber as function of the
modified cladding refraction index and length are presented for various input illumination focused and
compared with 3-D ray theory. Applications to chemical sensors are also discussed.
The intensity of light signal transmitted through an optical fiber, which its cladding over a finite length
is removed, is used as a sensor of refractive of liquids, in which the fiber is immersed. The transmitted light
intensity is measured as a function of liquid refractive index for different lengths of the unclad section of
the fiber and at each unclad length its sensitivity to change in refractive index of liquid is presented.
© 2011 Elsevier GmbH. All rights reserved.
1. Introduction
During the last decades, optical fiber has extended its applica-
bility to a wide number of displaces, being communications and
sensors two of the most important ones. There are several rea-
sons that explain this success, permits to multiplex many signals,
presents low losses, light weight and its diameter is of the order of
only one hundred microns in standard optical fiber [1].
The use of optical fiber in transducer systems for the measure-
ment or sensing of physical parameters has attracted considerable
research interest. Such sensors are useful for industrial and medi-
cal applications [2]. Kopera and Tekippe [3] proposed to build such
a fiber sensor by replacing a short section of the original fiber’s
cladding with a modified cladding, whose index of refraction is
sensitive to the temperature. As long as the refractive index of this
material is lower than the core’s refractive index, there exists an
illumination cone of bound rays for which light is guided in the
fiber with no loss. However, if at a certain temperature, the mate-
rial index of refraction becomes higher than of the core, most of
light will be extracted out of the core and the transmitted intensity
will sharply decrease [4].
In this work light transmission of the modified fiber under vari-
ous illumination conditions such as focused and defocused incident
beam, effect of the measured and analyzed by a new approach.
∗ Corresponding author.
E-mail addresses: rmc.zd09@student.usm.my (R.M. Chyad), mjafri@usm.my
(M.Z.M. Jafri), kussaynm@yahoo.com (K.N. Mutter), kamarl@usm.my (K. Ibrahim).
2. Research methodology
Optical fibers transmit light on the basis of the principle of total
internal reflection (TIR), when this phenomenon occur the light rays
are guided through the core of the fiber with very little loss to the
surrounding. The optical fiber is formed by a core with refractive
index n1 and cladding with refractive index n2. When a ray of light
strikes the boundary interface between these transparent medium
of different refractive index, and the angle of incidence is larger
than the critical angle, defined by the Snell’s law, it will be totally
internally reflected and propagated through the fiber. Optical fiber
has a refractive index distribution given by:
n(r) = no 1 − 2
r 2
1/2
(1)
Since the size of the core is large compared with the optical
wavelength, the analysis of light transmission through a modified
cladding can be accurately handled using geometrical optics. The
ray domain governs the geometry of ray propagation through fiber,
these ray can be bound, tunneling or refracting depending on the
˜ˇ − ˜l values, these are two parameters constant a longer any ray
particular ray path and determine the ray behavior in weakly guid-
ing fibers.
For step index fiber [5]:
Tunneling rays 0 ≤
˜ˇ
no
≤ 1 −
Bound rays 1 − ≤
˜ˇ
no
≤ 1
For graded index fibers [6]:
0030-4026/$ – see front matter © 2011 Elsevier GmbH. All rights reserved.
doi:10.1016/j.ijleo.2011.06.054

2. R.M. Chyad et al. / Optik 123 (2012) 860–862 861
Fig. 1. Reflection and refraction at the fiber face polar coordinators (r, ˚) define the
position of Q, and the projection of the ray path onto the enfaced makes angle
with azimuthally direction at Q.
Tunneling ray 1 − 2 ≤
˜ˇ
no
≤ 1 −
Bound rays 1 − ≤
˜ˇ
no
≤ 1
Where no is the core refractive index at the core center and is the
refractive index difference between the core and the cladding.
When a ray enters the modified cladding section, either Âz < Âc,
and the ray remains guided, or Âz < Âc, and the ray is only partially
reflected from the core cladding boundary, Âz is the angle between
the ray and the fiber axis inside the fiber, and Âc is the critical angle
for which a ray is still bound, see in Fig. 1.
Âc = cos−1 nmoc1
nco
(2)
As long as the illuminating cone of light is cylindrically sym-
metric around the following analysis we shall concentrate on
meridional rays.
The number of reflection (i.e. core–cladding encounters) in a
modified cladding region of length Lo is determined by the relation
N = Lo/Zp, where Zp is the path length between reflections, and by
the initial conditions in which a ray enters the modified cladding
section, see in Fig. 2. While the initial conditions are not known a
priori, the number of reflection must be an integer. We have chosen
to treat the fractional part of N in statistical terms, if a ray suffers
N reflections, an effective reflection coefficient can be defined in
terms of N and R [7]:
R = (N − [N])R[N]+1
+ (1 − (N − [N]))R[N]
(3)
[N] denotes the integer part of N; R is the Fresnel intensity reflection
coefficient.
These considerations are important since the ray under goes
very little reflection in the modified cladding region. Using (3) it
can be shown that the ratio of the output power in the fiber at
Z = Lo(Pbr(Lo)) to the power at Z = 0(Pbr(0)) (i.e. the input power) is
[8,9]:
Pbr(Lo)
Pbr(0)
=
2
o
dϕ o
r dr
2
o
dÂ
Âmax
o
I(r, Âo, ϕ, Âϕ) R sin Âo dÂo
2
o
dϕ o
r dr
2
o
dÂϕ
Âmax
o
I(r, Âo, ϕ, Âϕ) sin Âo dÂo
(4)
The Âmax is the largest angle, in air, between an input bound ray
and the fiber axis, as determined either by the fiber’s numerical
aperture or by the input distribution of rays I(r, Â, , Â ) is the input
intensity distribution in air.
Fig. 2. Optical fiber with a modified cladding segment.
Modified length (mm)
302520151050
Relativeratiopower
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
nmclad
= 1.468
nmclad
= 1.525
nmclad
= 1.591
nmclad
= 1.450
nmclad
= 1.448
nmclad
= 1.443
Fig. 3. shows the relative ratio power as modified cladding length, ncore = 1.460,
a = 100 ␮m, with different refractive index of material surrounding fiber core.
2.1. Intensity distribution
If a collimated laser beam is focused onto the fiber axis, only
meridian rays are excited, and the intensity distribution is given by
[9,10]:
I =
⎧
⎨
⎩
ı(r)f 2P1
2 r cos3 Âo
for 0 ≤ Âo < sin−1
[NAlens]
0 for sin−1
[NAlens] ≤ Âo ≤
2
(5)
where f is the lens focal length, NAlens its numerical aperture, ı(r)
is the Dirac delta function, and P1 is the (uniform) power per unit
area in the collimated beam. If “sin−1 [NAlens] < Âc” then from Eqs.
(4) and (5), the ratio of the output power in the fiber at Z = Lo to the
power at Z = 0 is:
Pbr(Lo)
Pbr(o)
=
2
sin−1
(NAlens)
o
(R)[sin Âo/ cos3 Âo] dÂ
tg2(sin−1
[NAlens])
(6)
and N is given by:
N =
Lo
2 cos g{sin−1
[sin (Âo)/ncore]}
(7)
3. Result and discussion
When studying the transmission of light rays in the step-index
fiber, the refractive index of core (ncore = 1.460), and the diame-
ter of fiber core (a = 100 ␮m). The solve equation (6) by numerical
analysis with use Simpson’s rule. Using 3-D geometric optics for
transmission light in incorporating modified cladding segments is
get us two cases depending on the different refractive index ( )
between refractive index of core (ncore) and the refractive index of
modified cladding segment (nmclad).
Case 1: when the refractive index of the modified cladding big-
ger than the refractive index of core (nmclad > ncore). The curves (1–3)
in Fig. 3, shows the value changed of relative ratio power with the
length of modified cladding region reach into decay do not reach
to saturation stage, as well as the power is very low level because
the refractive of fiber core less than the refractive index of modified
cladding, means that does not take the condition of wave guide or
the condition of total internal reflection, but all rays have partially
reflection in modified segments, to get many losses for transmis-
sion power as absorption loss, scattering loss and radiation loss.
That the level of ability cannot be extracted a few benefit from it as
sensors.
Case 2: when the refractive index of modified cladding region
less than refractive index of fiber core (nmclad < ncore). Shows the
curves (4–6) in Fig. 3 the behavior of relative ratio power with
modified cladding length, the relative ratio power reach to satu-
ration after short length of modified cladding region. The reason

3. 862 R.M. Chyad et al. / Optik 123 (2012) 860–862
is the numerical aperture of new material to determine the level
power as the saturation, in this case to get many element sensors
for differential applications.
4. Conclusions
We have analyzed the effect of a modified cladding region on
the optical fiber transmission. It was shown that a three dimen-
sional ray theory, which takes into account the input intensity
distribution, as well as a proper choice of the effective number of
core–cladding encounters [10,11].
Now that the transmission of the modified cladding fiber is
understood with respect to its dependence on the refractive index
and length of the modified cladding, and also with respect to
errors in the input conditions, this type of system can be advan-
tageously used a temperature sensor, having the ability to transmit
the temperature dependent intensity a long distance from the mea-
surement point, using the fiber itself. The results of this study can be
also applied to the sensing of the other physical parameters, which
affect the refractive index of a suitable modified cladding.
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