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ACTA ELECTROTEHNICA
Analysis of inherent perturbations
modeling on optical fibers
Titus E. CRIȘAN, Andrei CĂTINEAN, Septimiu CRIȘAN, Bogdan
ȚEBREAN
Faculty of Electrical Engineering, Technical University of Cluj-Napoca
Abstract: The purpose of this project is to analyze the inherent and induced effects of the perturbations that result in losses of the
polarization state on the fiber to measure how much the transmission data is affected. When twisting, applying stress to or bending
the fiber optics, performance will be affected due to the appearance of the birefringence phenomenon. The simulations have been
done on single mode and multimode optical fiber. We induced the birefringence phenomenon by bending the fiber at different radii
of curvature and by inducing an inherent perturbation of manufacturer, as an elliptical shape of the core. The software used for
simulations was Comsol Multiphysics®.
Keywords: Fiber optics, birefringence, Comsol Multiphysics®, polarization state
1.
INTRODUCTION
In this paper we analyzed the effects of the
inherent and induced perturbations over the
transmission data along the optical fiber. The
birefringence phenomenon is an inherent or induced
phenomenon and the main cause which affects the
maintaining of the polarization state. When losing the
polarization state, the performances of the fiber optics
diminish.
A polarization state of a wave is a superposition
result of two partial waves with certain phase shift and
certain amplitude ratio. The general polarization state
of the wave is the elliptical one. Special cases are the
circular birefringence and the linear birefringence. [7]
We analyze the factors which induce the linear
birefringence, avoiding twisting the fiber optic.
Twisting the fiber induces circular birefringence,
which is the most undesirable effect. [7]
Using Comsol Multiphysics® we simulated an
elliptical shape of the fiber core, an inherent
perturbation caused by bad manufacturing. The values
of ellipticity are 0%, 5% and 10%.
We used single mode classical fiber with
cylindrical core. For the simulations the 1550nm and
1310nm wavelengths were chosen.
In order to have a reference point, the simulations
have been made with a perfect straight fiber, then with
an elliptical shape of the core.
For the simulations, the parameters of the axes
core were set to 5.2µm for the 1310nm wavelength,
4.6µm for the 1550nm wavelength and 62.5µm for the
fiber cladding.
The simulations results were discussed and
compared to demonstrate the effects of the
birefringence on the quality of data transmissions.
2.
THEORETICAL BACKGROUND
For the fiber optics mathematical formalism, the
light can be treated as an electromagnetic wave. [4]
An electromagnetic wave is described by an electric
field intensity vector E, which propagates in the
direction of the z axis of the orthogonal coordinate
system. The wave is a superposition of two partial
waves with mutually orthogonal linear polarization
and identical frequency. [7]
E = Ex + E y ,
(1)
Where:
E x ( z , t ) = E 0, x cos(kz − ωt + Φ x ) , (2)
E y ( z , t ) = E 0, y cos(kz − ωt + Φ y ) , (3)
xyz are the orthogonal coordinate system and Ex,
Ey are the vectors of electric field intensity. E0,x , E0,x
represent the wave amplitudes and ϕx , ϕy are phases of
the wave. [6]
The birefringence represents the difference
between the propagation waves and is the significant
factor which affects the performance of the fiber optic.
The birefringence is inherent or induced in noncircular cores, caused by applying stress, twisting or
bending the fiber, in the presence of a longitudinal
magnetic field or the presence of a metal in the
vicinity of the fiber core.
© 2014 – Mediamira Science Publisher. All rights reserved
Volume 55, Number 1-2, 2014
•
The ratio amplitude E0,x , E0,x and the phase shift
Δϕ = ϕx - ϕy determine the polarization state of the
resulting wave.
If E0,x = E0,x and Δϕ = ±π/2 the resulting wave has
a circular polarization. The E vector traces a circle.
Depending on the phase difference, plus or minus, the
polarized wave is either right or left handed.
•
•
3.
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The presence of a transversal electical field.
If the fiber is subjected to a powerful
transversal electrical field, the birefringence
is induced in the fiber through the Kerr
electro-optic effect.
Twisting the fiber results in circular
birefringence proportional with the twisting
ratio. The coefficient of proportionality of
the silica fiber optic is ≈ 0.146.
The presence of a longitudinal magnetic
field. If the fiber optic is subjected to a
longitudinal magnetic field, an additional
circular birefringence is induced through the
magneto-optic effect called the Faraday
effect.
SIMULATIONS RESULTS
Fig. 2 – Left handed ellipticaly polarized wave [2]
The first step of simulations was to determine the
optical power, the polarizations component vector
evolution in ideal conditions, without induced
birefringence phenomenon. The second step of
simulations was to determine the optical power loss by
creating the birefringence phenomenon when inducing
the ellipticity of the core.
The wavelengths choosen for the simulations
where 1310nm and 1550nm. The value of attenuation
is minimum, 0.33 dB/km for the 1310nm wavelength
and 0.19dB/km for the 1550nm wavelength. The
optical fiber used was single mode with the refractive
index of the core 1.4677 for 1310nm, 1.4682 for
1550nm and 1.4615 for the cladding.
The boundary conditions established through
Comsol Multiphysics® were: the material of the fiber
core and cladding is silica glass, the Poisson ratio
0.17, Young module E=73.1e9 [Pa], the length of the
fiber is 2cm, the value of the ellipticity was set to 0%,
5% and 10% for the fiber. In Figure 3 is presented the
mesh pattern established for the simulations, analyzing
on the entire length of fiber the wave propagation and
its properties.
Factors that induce birefringence on the fiber are
the following:
• Elliptical shape of the core due to bad
manufacturing of the optical fiber.
• The presence of mechanical stress on the
fiber, resulting in local variations of the
refractive index of the core through the optoelastic effect.
• Bending the fiber induces a mechanical
birefringence by creating an asymmetry in
the refractive index profile. When the fiber is
bent, the superior part is strained and the
lower part is compressed.
Fig. 3 – The mesh pattern for simulations
Fig. 1 – Right handed circular polarized wave [1]
If Δϕ ≠0, ±π/2 or E0,x ≠ E0,x the resulting wave
has a elliptical polarization. The E vector traces an
ellipse. Depending on the phase difference, plus or
minus, the polarized wave is either right or left
handed.
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ACTA ELECTROTEHNICA
3.1. Simulations on 1310nm wavelength
The first model was set as a reference model for
the wavelength of 1310nm. The radius of the fiber
core is 5.2µm and 62.5µm for the fiber cladding. The
refractive index of the core is 1.4677 and 1.4615 for
the fiber cladding.
The parameters of the axes are 5.2µm for the
major axes and 4.9µm for the minor axes.
Figure 4 represents the polarization state of the
light propagated over the optical fiber in ideal
conditions, without external perturbations. In ideal
situations, the polarization state is the same over the
entire length of the fiber.
Fig. 6 – Polarization norm for 5% ellipticity
Figure 6 represents the polarization state of the
light propagated over the optical fiber with an
elliptical shape of the core, as a result of bad
manufacturing.
In ideal conditions the polarization state was the
same on the entire length of the fiber. In the case of an
elliptical shape of the core the performance of optical
fibers diminish resulting in loss of the polarization
state and optical power.
Fig. 4 – Polarization norm for 1310nm in ideal conditions
We can observe the light stabilized along the
entire length of the fiber. From the calculations done
by the software COMSOL®, it provided us the average
of the polarization norm which is equal to 1.33E07(C/m2).
Figure 5 represents the total power dissipation
density on the fiber. COMSOL® provided the average
which is equal to 6.97E-07.
Fig. 7 – Total power dissipation density for 5% ellipticity
Fig. 5 – Total power dissipation density for 1310nm in ideal
conditions
The next step of the simulations is inducing a 5%
elliptical shape of the core for analyzing and
comparing the resulting polarization states.
We can observe in Figure 7 the moment the light
wave enters/penetrates the fiber and the polarization
state is destabilized for the entire length of the fiber.
In the third model we induced a 10% ellipticity
shape of the core. The parameters of the axes are
5.2µm for the major axes and 4.7µm for the minor
axes.
In the case of 10% ellipticity in the shape of the
core, the loss of polarization state and optical power
are higher than of the 5% ellipticity. The average of
total power dissipation density is equal to 7.17E-06.
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63
average of the polarization norm obtained from the
calculations done by the software COMSOL® is equal
to 1.78E-09 C/m2 and -3.28E-09 W/m3 is the average
of the total power dissipation density.
Fig. 8 – Polarization norm for 10% ellipticity
Fig. 11 – Total power dissipation density for 1550nm in ideal
conditions
The next step is inducing a 5% ellipticity of the
core. The parameters are 4.6µm for the major axis and
4.4µm for the minor axis.
Fig. 9 – Total power dissipation density for 10% ellipticity
3.2. Simulations on 1550nm wavelength
Same as the simulations on 1310nm wavelength,
the first model was set as a reference model for the
wavelength of 1550nm. The radius of the fiber core is
4.6µm and 62.5µm for the fiber cladding. The
refractive index of the core is 1.4682 and 1.4615 for
the fiber cladding.
Fig. 12 – Polarization norm for 5% ellipticity
Fig. 13 – Total power dissipation density for 5% ellipticity
Fig. 10 – Polarization norm for 1550nm in ideal conditions
It the case of the 1550nm wavelength, the
polarization state of the light wave launched in the
optical fiber acts the same as in the 1310nm
wavelength. The light enters the fiber and remains
stabilized for the entire length of the fiber. The
With a 5% ellipticity of the core, the polarization
state has been altered and is destabilized along the
entire length of the fiber. The average of the
polarization norm is 2.33E-09(C/m2) and 1.33E06(W/m3) of the total power dissipation density.
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ACTA ELECTROTEHNICA
The last step is inducing a 10% ellipticity shape
of the core. The parameters of the axis are 4.6µm for
the major axis and 4.1µm for the minor axis.
the higher the values of ellipticity shape of the core,
the higher the loss of polarization state and optical
power.
To reduce the loss of the polarization state of the
light waves in the optical fiber it is necessary for a
lower attenuation of the wavelength or special
polarization maintaining optical fiber.
A low attenuation reduces the loss of the
polarization state and the need of amplifiers along the
fiber’s length to renew the transmitted signal.
Polarization maintaining fibers are specifically
manufactured with inner structures that allow
maintaining the polarization state of the wave over
long distances.
REFERENCES
Fig. 14 – Polarization norm for 10% ellipticity
1.
2.
3.
4.
5.
6.
Fig. 15 – Total power dissipation density for 10% ellipticity
7.
In the case of 10% ellipticity shape of the core,
we can observe the light wave is stabilized for the
entire length of the fiber but at a lower optical power.
This is a result of the low attenuation of the 1550nm
wavelength.
4.
CONCLUSIONS
We demonstrated how the perturbations of
manufacture, as an elliptical shape of the core, affect
the polarization state of the light wave and the optical
power.
By comparing the results of the simulations for
both wavelengths, 1310nm and 1550nm, inducing a
perturbation similar to a manufacturing flaw, as an
elliptical shape of the core, the performance and
optical power of the optical fiber are affected and
reduced. Analyzing the graphs it can be observed that
8.
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Titus E. CRIȘAN
Andrei CĂTINEAN
Septimiu CRIȘAN
Bogdan ȚEBREAN
Electrical Engineering and Measurements Department
Faculty of Electrical Engineering
Technical University of Cluj-Napoca
Str. Memorandumului nr. 28, 400114 Cluj-Napoca