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Optik 123 (2012) 860– 862

Contents lists available at ScienceDirect

Optik

j o ur nal homepage: www.elsev ier .de / i j leo

umerical ray tracing through a modified cladding fiber optic segment sensors

adhi M. Chyad ∗, Mohd Zubir Mat Jafri, Kussay N. Mutter, Kamarulazizi Ibrahimchool of Physics, Universiti Sains Malaysia, 11800 Penang, Malaysia

r t i c l e i n f o

rticle history:eceived 2 January 2011ccepted 10 June 2011

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 throughoptical fiber is investigated. Analysis of the light transmission of the optical fiber as function of themodified cladding refraction index and length are presented for various input illumination focused and

eywords:iber opticnclad fiber sensorshemical fiber sensors

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 lightintensity is measured as a function of liquid refractive index for different lengths of the unclad section ofthe fiber and at each unclad length its sensitivity to change in refractive index of liquid is presented.

© 2011 Elsevier GmbH. All rights reserved.

iosensor

. Introduction

During the last decades, optical fiber has extended its applica-ility to a wide number of displaces, being communications andensors two of the most important ones. There are several rea-ons that explain this success, permits to multiplex many signals,resents low losses, light weight and its diameter is of the order ofnly one hundred microns in standard optical fiber [1].

The use of optical fiber in transducer systems for the measure-ent or sensing of physical parameters has attracted considerable

esearch interest. Such sensors are useful for industrial and medi-al applications [2]. Kopera and Tekippe [3] proposed to build such

fiber sensor by replacing a short section of the original fiber’sladding with a modified cladding, whose index of refraction isensitive to the temperature. As long as the refractive index of thisaterial is lower than the core’s refractive index, there exists an

llumination cone of bound rays for which light is guided in theber with no loss. However, if at a certain temperature, the mate-ial index of refraction becomes higher than of the core, most ofight will be extracted out of the core and the transmitted intensity

ill sharply decrease [4].In this work light transmission of the modified fiber under vari-

us illumination conditions such as focused and defocused incidenteam, 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).

030-4026/$ – see front matter © 2011 Elsevier GmbH. All rights reserved.oi:10.1016/j.ijleo.2011.06.054

2. Research methodology

Optical fibers transmit light on the basis of the principle of totalinternal reflection (TIR), when this phenomenon occur the light raysare guided through the core of the fiber with very little loss to thesurrounding. The optical fiber is formed by a core with refractiveindex n1 and cladding with refractive index n2. When a ray of lightstrikes the boundary interface between these transparent mediumof different refractive index, and the angle of incidence is largerthan the critical angle, defined by the Snell’s law, it will be totallyinternally reflected and propagated through the fiber. Optical fiberhas 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 opticalwavelength, the analysis of light transmission through a modifiedcladding can be accurately handled using geometrical optics. Theray domain governs the geometry of ray propagation through fiber,these ray can be bound, tunneling or refracting depending on the˜̌

− l̃ values, these are two parameters constant a longer any rayparticular ray path and determine the ray behavior in weakly guid-ing fibers.

For step index fiber [5]:

Tunneling rays 0 ≤ ˜̌no

≤ 1 − �

Bound rays 1 − � ≤ ˜̌no

≤ 1

For graded index fibers [6]:

R.M. Chyad et al. / Optik 123 (2012) 860– 862 861

Fig. 1. Reflection and refraction at the fiber face polar coordinators (r, ˚) define thepw

Wr

artf

�

mm

mNtsptNt⟨[c

vcZ[

aai

Modified length (mm)302520151050

Rel

ativ

e ra

tio p

ower

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6nmclad = 1.468nmclad = 1.525nmclad = 1.591nmclad = 1.450nmclad = 1.448nmclad = 1.443

osition of Q, and the projection of the ray path onto the enfaced makes angle ith azimuthally direction at Q.

Tunneling ray 1 − 2� ≤ ˜̌no

≤ 1 − �

Bound rays 1 − � ≤ ˜̌no

≤ 1

here no is the core refractive index at the core center and � is theefractive index difference between the core and the cladding.

When a ray enters the modified cladding section, either �z < �c,nd the ray remains guided, or �z < �c, and the ray is only partiallyeflected from the core cladding boundary, �z is the angle betweenhe ray and the fiber axis inside the fiber, and �c is the critical angleor which a ray is still bound, see in Fig. 1.

c = cos−1[nmoc1nco

](2)

As long as the illuminating cone of light is cylindrically sym-etric around the following analysis we shall concentrate oneridional rays.The number of reflection (i.e. core–cladding encounters) in a

odified cladding region of length Lo is determined by the relation = Lo/Zp, where Zp is the path length between reflections, and by

he initial conditions in which a ray enters the modified claddingection, see in Fig. 2. While the initial conditions are not known ariori, the number of reflection must be an integer. We have choseno treat the fractional part of N in statistical terms, if a ray suffers

reflections, an effective reflection coefficient can be defined inerms 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 reflectionoefficient.

These considerations are important since the ray under goesery little reflection in the modified cladding region. Using (3) itan be shown that the ratio of the output power in the fiber at

= Lo(Pbr(Lo)) to the power at Z = 0(Pbr(0)) (i.e. the input power) is8,9]:

Pbr(Lo)Pbr(0)

=∫ 2�odϕ

∫ �or dr

∫ 2�od�

∫ �max

oI(r, �o, ϕ, �ϕ)

⟨R⟩

sin �o d�o∫ 2�odϕ

∫ �or dr

∫ 2�od�ϕ

∫ �max

oI(r, �o, ϕ, �ϕ) sin �o d�o

(4)

The �max is the largest angle, in air, between an input bound ray

nd the fiber axis, as determined either by the fiber’s numericalperture or by the input distribution of rays I(r, �, �, ��) is the inputntensity distribution in air.

Fig. 2. Optical fiber with a modified cladding segment.

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, onlymeridian rays are excited, and the intensity distribution is given by[9,10]:

I =

⎧⎨⎩

ı(r)f 2P1

2�r cos3 �ofor 0 ≤ �o < sin−1[NAlens]

0 for sin−1[NAlens] ≤ �o ≤ �

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 unitarea in the collimated beam. If “sin−1 [NAlens] < �c” then from Eqs.(4) and (5), the ratio of the output power in the fiber at Z = Lo to thepower at Z = 0 is:

Pbr(Lo)Pbr(o)

=2∫ sin−1(NAlens)

o(R)[sin �o/ cos3 �o] d�

tg2(sin−1 [NAlens])(6)

and N is given by:

N = Lo

2� cos g{sin−1 [sin (�o)/ncore]}(7)

3. Result and discussion

When studying the transmission of light rays in the step-indexfiber, the refractive index of core (ncore = 1.460), and the diame-ter of fiber core (a = 100 �m). The solve equation (6) by numericalanalysis with use Simpson’s rule. Using 3-D geometric optics fortransmission light in incorporating modified cladding segments isget us two cases depending on the different refractive index (�)between refractive index of core (ncore) and the refractive index ofmodified 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 thelength of modified cladding region reach into decay do not reachto saturation stage, as well as the power is very low level becausethe refractive of fiber core less than the refractive index of modifiedcladding, means that does not take the condition of wave guide orthe condition of total internal reflection, but all rays have partiallyreflection 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 assensors.

Case 2: when the refractive index of modified cladding region

less than refractive index of fiber core (nmclad < ncore). Shows thecurves (4–6) in Fig. 3 the behavior of relative ratio power withmodified cladding length, the relative ratio power reach to satu-ration after short length of modified cladding region. The reason

8 ptik 1

ipf

4

tsdc

uaettsaa

[1983.

62 R.M. Chyad et al. / O

s the numerical aperture of new material to determine the levelower as the saturation, in this case to get many element sensorsor differential applications.

. Conclusions

We have analyzed the effect of a modified cladding region onhe optical fiber transmission. It was shown that a three dimen-ional ray theory, which takes into account the input intensityistribution, as well as a proper choice of the effective number ofore–cladding encounters [10,11].

Now that the transmission of the modified cladding fiber isnderstood with respect to its dependence on the refractive indexnd length of the modified cladding, and also with respect torrors in the input conditions, this type of system can be advan-ageously used a temperature sensor, having the ability to transmit

he temperature dependent intensity a long distance from the mea-urement point, using the fiber itself. The results of this study can belso applied to the sensing of the other physical parameters, whichffect the refractive index of a suitable modified cladding.

[

23 (2012) 860– 862

References

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[3] P.M. Kopera, V.J. Tekippe, Transmission of optical fiber with short section ofmodified cladding, Opt. News 7 (1981) 44.

[4] T.A. AL-Jumailly, R.M. Chyad, Fiber sensors incorporating modified claddingsegments military engineering college in Iraq, 1992.

[5] C. Pask, Generalized parameters for tunneling ray attenuation in optical fiber,J. Opt. Soc. Am. 68 (1978) 110–116.

[6] A. Ankiewicez, C. Pask, Geometric optics approach to light acceptance andpropagation in graded index fiber, Opt. Quantum Elect. 9 (1977).

[7] M. Gottlieb, G. Brandt, Temperature sensing in optical fibers uses cladding andjacket loss effects, Appl. Opt. 20 (1981) 3867.

[8] M. Born, E. Wolf, Program on Principle of Optics, London, 1970.[9] T.A. Al-Jumailly, Examination of optical fiber inhomgeneties and their effect in

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