Volume 2, Issue 6, June 2017 International Journal of Innovative Science and Research Technology

ISSN No: - 2456 - 2165

Analysis and Simulation of Coaxial Bragg Fiber Using

Toolbox
Prof. Amit Kumar Poonam Yadav
Dept. of Electronics and Communication Dept. of Electronics and Communication
Krishna Institue of Engineering & Technology Krishna Institue of Engineering & Technology
Ghaziabad (U.P), India Ghaziabad (U.P), India

Abstractin this paperIn this thesis, the propagation Consist of Bragg bers [8, 9] have attracted increasing
characteristic plays an extremely very important role in optical importance over the past time because of their unique
fiber communication system. We have given the information of property.
various fibers which are available in communication system.
Further, after using the two different methods (Exact solution Attention on the performance of photonic crystal fibers as
and TMM). We have computed the propagation characteristic of useful components or devices as an alternate of a
Bragg fiber. transmission medium. Photonic crystal fibers applications
in ber lters, ber sensors, ber lasers, and dispersion
KeywordsOptical fiber, Photoniccrystalber; Braggber. advantage have been well considered [10, 11]. Bragg bers
have in recent times received much attention for their
I. INTRODUCTION motivating dispersion and modal properties and for
advances in manufacture techniques [12]. Bragg fiber
Optic fibers communication is a communication that uses light containing of a core bounded by alternating layers of small
pulses to transfer information from one point to another through and great refractive index was first projected in [13]. Light
an optical fiber. The information transmitted is essentially digital is narrowed in the core by one dimensional photonic band
information generated by telephone systems. The optical fibers gap. Bragg fiber is a beautiful knowledge, but it is relatively
are dielectric cylindrical waveguide made from low-loss difficult to fabricate a Bragg fiber with square technique. It
materials, usually silicon dioxide. The core of the waveguide has was more than 20 years later that first actual Bragg fiber is
a refractive index a little higher than that of the outer medium fabricated in MIT [14]. Which was composed of alternating
(cladding), that light pulses is guided along the axis of the fiber layers of PES? A silica core Bragg fiber is fabricated by
by total internal reflection [1]. The optical communication sputtering Si and SiO2 on the other hand on silica fiber [15],
systems is optical communication systems a very high degree of but the fiber length in only 20 cm, because the Si layers in
complexity. The normally includes multiple signal channels, cladding contains the drawing of fiber. An air-silica Bragg
different topologies, nonlinear devices, and non-Gaussian noise fiber design was recommended which was a cylindrically
sources, is highly complex and labor-intensive. Advanced symmetric fiber with a high-index core (silica) enclosed by
software tools make the design and analysis of these systems alternating layers of silica and air, dispersion properties of
quick and efficient [2]. The growing demand for commercial this air-silica Bragg fiber was discussed. It was impossible
software for optical communication systems has led to the to arrange for structural support to this air-silica fiber, which
availability of a number of different software solutions. More made this design unrealizable. A Bragg fiber can also be
popular of these the optic system software as we noted in [3, 4]. calculated to a single guided mode without azimuthal
dependence (TE or TM). In difference with the fundamental
mode in conventional fiber which is always all the more
degenerate, these guided Bragg fiber modes are really single
mode. Therefore, many undesirable polarization dependent
effects can be completely reduced in Bragg fiber [16].
Figure1.1: Optical fiber

The Bragg fiber grating (FBG) [5] and extensive period grating
[6] two of the most significant ber lters and ber sensor
have been well advanced due to their advantages together with
compression and ber compatibility and numbers of
applications. The photonic crystal bers (PCFs) [7] which also

Figure 1.2: Bragg fibe

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Volume 2, Issue 6, June 2017 International Journal of Innovative Science and Research Technology
ISSN No: - 2456 - 2165

II. EXACT SOLUTION FOR STEP INDEX FIBERS In individual, we will study a fiber with a low index core then
the alternating low and high index cladding. The geometry of
We will achieve the modal fields and the corresponding this structure is drawn in Fig. 1.3. The index profile is then given
propagation numbers for step index fiber for which the refractive by
index variation is a fiber it is possible to achieve rigorous
solutions of the vector equations. The most practical fibers used
, 0 <
in communication are weakly guiding relative refractive index
, < (4)
difference (1 2 )/1 1 and in such a case the radial part
n(r) = , <
of the transverse element of the electric field satisfies the
n, <
following
, <
1 ((1)12 ) 1 1 (()12 )
(1 )12 = 2 ; = We income the z axis as the course of transmission, thus that
((1)12 ) (()12 )
every field factor has the form
(, , , ) = (, ) () (5)
(1)

1 ((1)12 ) 1 1 (()12 )
Where can be , , , , , Is the angular frequency and
(1 )12 = 2 ; =0 (2) is the Spread constant.
0 ((1)12 ) 0 (()12 )

From waveguide the transverse field components can be expert

in terms of and
III. TRANSFER MATRIX METHO

We will present a matrix method near the compute the mode

features as well as the power flux of radially stratified fibers. = ( + )(6)
2 2
The simple idea is to replace the boundary conditions by a
matrix equation. Thus, each cladding interface is characterized
= 2 ( )(7) = (
2 2 2
by a matrix. The intro diction of this 4 X 4 matrix greatly
simplifies the analysis. )(8)

= ( + )(9)
2 2

(r,) (, )

2 + (2 2 )] { } = 0(10)

2
Where 2 = 2 is the right angles operative.
2

The common solution can be written

= [A (kr) + B (kr)] cos( + )(11)

Hz = [C (kr) + D (kr)] cos( + ) (12)

Where A, B, C, D, are numbers, l is an integer, and

Fig.1.3: Bragg fiber
K= (2 2 )1/2 (13)
We study a fiber by the index profile given by
We at present study the boundary conditions at a common clad-
0<r<1 ding interface at r = p. The result of the wave equation is taken
n(r) = , < r<+1 (3) as
v= 1, 2, 3...

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Volume 2, Issue 6, June 2017 International Journal of Innovative Science and Research Technology
ISSN No: - 2456 - 2165
= [ 1 (1 r) + 1 (1 r)] cos( + 1 ), r< Where up to date numbers the products with respect to their own
disagreement. This equation has to be satisfied for all. From
= [ 2 (2 r) + 2 (2 r)] cos( + 2 ), r> (14) (21) and (22)
1 1
Or ( 2) [1 (1 ) + 1 (1 )] ( 2 )[2 (2 ) + 2 (2 )]
1 2

= [1 (1 r) + 1 (1 r)] cos( + 1 ), r< (24)

( 1)[1 (1 ) + 1 (1 )] ( 2)[2 (2 ) + 2 p)]
1 2
= [ 2 (2 r) + 2 (2 )] cos( + 2 ), r> (15) (25)
In case1 2 . Thus we complete from (23)-(25) that

Where sin( + ) = cos( + )(26)

= [( /)2 - 2 )1/2 i= 1, 2. (16)
Or
The state line conditions at r = p are that , , , are

constant at the interface. Thus a 44 matrix can be start which = (27)
2
relates1 , 1, 1 , 1 to2 , 2 , 2 , 2 Continuity of and Eq. (9)
1 1
2 1 ( [1 (1 p) +1 (1 p)]sin( + )- 1 [1 (1 ) +
12
2 1 (1 )[cos( + )]
( ) = M ( 1) (17) 1
2 1 = 2 ( [ 2 ( 2 ) + 2 ( 2 )] sin( + ) -
2
2 1 2
2 [2 (2 ) + 2 (2 p)]cos( + )(28)

1.1 Derivation of M
From (26) or (27) we categorize the waves into two types:
In relations of fields (14) and (15) the stability of gives
1. = [ (kr) + (kr)] cos
[A ( 1 p) + 1 (1 )] cos( + 1 ) = [ 2 ( 2 p) +
2 (2 p)]cos( + 2 ) (18) = [C (kr) + D (kr)] sin (29)

This equation has to be content for all which denotes 2. = [A (kr) + B (kr)] sin (30)

1 = 2 (19) = [C (kr) + D (kr)] cos

They also from the continuity of The state line conditions for these two classifications

1 = 2 (20) 1 (1 p) +1 (1 p) + 0 + 0 = (1 2), (31)

Thus permanence of 1
1 (1 ) +
1
1 (1 ) +

1 (1 p) +

1 (1 p)
1 1 12 12

1 (1 ) + 1 (1 ) = 2 (2 ) + 2 (2 )(21) = (1 2) ,
(32)

1 (1 ) + 1 (1 ) = 2 (2 ) + 2 (2 )(22) 0 + 0 + 1 (1p) +1 (1 ) = (1 2), (33)

1
In relations of the field (14), (15) and (7), the stability of 1 (1 p) + 1 (1 p ) + 1 (1 ) +
12 12 1
gives 1
1 (1 ) = (1 2), (34)
1
1 1
( [1 (1 p) +1 (1 p)]sin( + )- 1 [1 (1 ) +
12
1 (1 )[cos( + ) There are of the same kind equations except that the coefficient
1
= 2 ( [ 2 ( 2 ) + 2 ( 2 )] sin( + ) - 2 is replaced by 2 .Equations (31)-(34) can be written as a
2 1 1
2
2 [2 (2 ) + 2 (2 p)]cos( + )(23) matrix equation.

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Volume 2, Issue 6, June 2017 International Journal of Innovative Science and Research Technology
ISSN No: - 2456 - 2165
1 2
21
M (1, p) = ( 1) = M (2, P) ( 2) 34 = () ()- ( ) () ()
1 2 12
1 2
( ) ( ) 0 0 41 = (/2 )(1/ 1/) () ()

( ) ( ) ( ) 2 ( )
2 42 =(/2 )(1/ 1/) () () (39)

(35)
0 0 ( ) ( )
21
( ) ( ) ( ) ( ) 43 = ( ) () ()- () ()
[ 2 2 ] 12

(36) 21
44 = ( ) () ()- () ()
12

Where i = 1, 2. We sign that when l = 0, the matrix is reducible All over again we find that the transfer matrix M is block
we can have clean TE or pure TM waves when I = 0. diagonal zed when l = 0. In this example the matrix equation
(17) can be written as two single equations.
A matrix in Eq. (17) can be written as using (35),

( 2 ) = ( 1 )(40)
1
M = (2, p) M (1, p) 2 1
(37)

( 2 ) = ( 1 )(41)
If we define x =1 , = 2 , write M 2 1

11 12 13 14
21 22 23 24 The matrix method described directly above can be
M= ( ) (38) employed to gain the mode dispersion relations for several
2 31 32 33 34
41 42 43 44 conventional fibers.

IV. SIMULATION RESULTS

Using (36) and next some matrix use, the matrix elements
in (38) are found as In this section we use the above method to analyze the
propagation characteristics for a step index fiber. The Bessel
21 equation has all the information that we can obtain from our
11 = () () ( ) () () modal analysis and it gives the result of this investigation. In this
12
paper we have assume a step index fiber and consider a higher
12 = () (y) ( 21 /22 ) () () value of V (Let V=6.5 when n2 =1.45, =0.0064, a =3 m, and
lambda = approx. 0.4757 m) and plotted the LHS and RHS of
13 = (/2 )(1/ 1/) () () equation (x) in fig4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7 (for l=0, 1, 2, 3,
4).We find that there are two modes corresponding to l=0 (also
14 = (/2 )(1/ 1/) () () called LP 0X), two modes corresponding to l=1, and one mode
each corresponding to l=2, 3 and l=4.
21
21 = ( ) () () - () ()
12 Table-1.1 Cutoff frequency of various linear polarized in a step
index fiber
21
22 = ( ) () () - () ()
12
l LPxx B
LP01 0.8977
23 =(/2 )(1/ 1/) () () 0
LP02 0.4752
24 = (/2 )(1/ 1/) () ()
LP10 0.7422
1
31 =( /2 )(1/ 1/) () () LP11 0.1792
2 LP20 0.5411
32 =( /2 )(1/ 1/) () () 3 LP30 0.3003
4 LP40 0.0270
21 5 LP5x NA
33 = () () - ( ) () ()
12

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Volume 2, Issue 6, June 2017 International Journal of Innovative Science and Research Technology
ISSN No: - 2456 - 2165
The corresponding values of b are given in table-1.1. Further
using the above method we have plotted in fig 4.6 the variation
of the normalized propagation constant b with normalized
frequency V for a step index fiber corresponding to some low
order modes. From table-1.1 the smallest value of b is very close
to cutoff frequency.

Figure 1.6:Variation of the LHS (blue color) and RHS (Green

Color) in equation (1) and (2).This curve is plotted in case of l=2
and V=6.5. Also, the points of intersection represent the discrete
modes of the waveguide.

Figure 1.4:Variation of the LHS (blue color) and RHS (Green

Color) in equation (1) and (2).This curve is plotted in case of l=0
and V=6.5. Also, the points of intersection represent the discrete
modes of the waveguide.

Figure 1.7:Variation of the LHS (blue color) and RHS (Green

Color) in equation(1)and (2)This curve is plotted in case of l=3
and V=6.5. Also, the points of intersection represent the discrete
modes of the waveguide.

Figure 1.5:Variation of the LHS (blue color) and RHS (Green

Color) in equation(1) and (2)This curve is plotted in case of l=1 Figure 1.8:Variation of the LHS (blue color) and RHS (Green
and V=6.5. Also, the points of intersection represent the discrete Color) inequation (1) and (2).This curve is plotted in case of l=4
modes of the waveguide. and V=6.5. Also, the points of intersection represent the discrete
modes of the waveguide.
IJISRT17JU43 www.ijisrt.com 44
Volume 2, Issue 6, June 2017 International Journal of Innovative Science and Research Technology
ISSN No: - 2456 - 2165
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ACKNOWLEDGMENT 2004, WI1.
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This work is supported by Krishna Institute of Engineering and and Juan J. Miret, High-index-core Bragg fibers:
Technology and Faculty of Engineering, Dr. A.P.J.Abdul Kalam dispersion properties, Opt. Express 11, 1400-1405
Technical University, Lucknow. (2003)

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