SIMULATION OF DISPERSION COMPENSATION IN TRANSMISSION
SYSTEMS BASED CHIRP FIBER BRAGG GRATING AND SYMMETRICAL
COMPENSATION METHOD
H. Taslim1 and S. Shahi2*
1
Biophotonics and laser in dentistry research center (BLDRC), Islamic Azad University,
Khorasgan (Isfahan) Branch, Arghavanieh, Isfahan, Iran.
1
Hossein.Taslim@yahoo.com
biophotonics@khuisf.ac.ir
2*
Abstract. One of the basic causes of function limitations in optical transmission is
dispersion that is the phenomenon in which the phase velocity of a wave depends on its
frequency. Waveguides as an optical fiber are highly dispersive due to their geometry
for optical frequencies widely used in modern telecommunications systems. The rate at
which data can be transported on a single fiber is limited by pulse broadening due to
chromatic/material dispersion among other phenomena as well as group velocity,
waveguide and modal dispersion. Hence, in thispaper, we introduce the Chirp Fiber
Bragg Grating as a key component and dispersion compensation fibers (DCFs) that both
employed in symmetrical compensation method for compensate the dispertion in WDM
system. By simulating transmission system can find the best numerical quantity of
parameters for optimum outputs and its effect on improving gained information in the
receiver that compare by different compensation components.
Keywords: Chirp Fiber Bragg Grating, Dispersion Compensation, Symmetrical
Dispersion Compensation method.
1. Introduction
Over the past 20 years, two major product revolutions have taken place due to the
growth of the photonics, opto-electronics and the fiber optic communication industries.
The fiber optic communication industry has literally revolutionized the
telecommunication industry by providing higher performance, more reliable
telecommunication links with ever decreasing bandwidth cost [1].
Waveguide optical fiber is a di-electric cylinder in which the information on optic
waves transfer. The main structure of optical fiber includes core & clad. The clad guides
the light in core using total internal reflection method passing the fiber. Light will be
affected by some factors such as attenuation, destruction or dispersion. This paper focus
on dispersion in optical waveguides as a fiber and simulation of random dispersion
compensation. According to the kind of fibers, there are two kinds of dispersion:
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Mode dispersion and chromatic dispersion.
Telecommunication systems modulates the intensity of a light source in order to
transmit information. Information is modulated and sent as a series of pulses
representing binary encoded data. Data can be transmitted with few errors, as long as
these pulses travel through the fiber without changing their shape. But usually, as they
travel along the fiber, the pulses start to spread, loosing their original shape and overlap
each other and so becoming indistinguishable at the receiver input. Dispersion is the
general term applied to this cause. Dispersion was initially a problem when multimode
step-index fiber, the first optical fibers, were introduced. Multimode graded-index fiber
improved the situation, but even when they are well graded there are severe limitations
to the information capacity of multimode fibers. It was single-mode fiber that
eliminated multipath dispersion and left only intramodal dispersion and polarization
mode dispersion to be dealt with by engineers. Intramodal dispersion may occur in
multimode and single-mode index fibers, and represents the fact that different colors or
wavelengths travel at different speeds, even within the same mode. Pulse broadening
due to material dispersion results from the wavelength-dependent index of refraction in
the bulk material, which makes up the fiber, as seen in Figure 1.[2].
Figure 1. Refractive index of pure fused silica[2].
The use of erbium doped fiber amplifiers (EDFA) in optical communication systems
has made chromatic dispersion, the most significant limitation for the transmission
performance since EDFAs compensate for he transmission losses. dispersion
compensating fibers (DCF) and bulk type dispersion compensators have been widely
used to compensate for the chromatic dispersion. In addition, the amount of
compensation is wavelength dependent and can only be perfectly achieved in a
relatively narrow band. Chirped fiber Bragg grating (FBG) has also been proposed
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recently for chromatic dispersion compensation and is recognized as a perfect
alternative do DCF. Recently, symmetrical compensation is also suggested to random
dispersion compensation fibers that more introduce in next parts[3].
2. Chirp Fiber Bragg Grating
Photosensitivity of optical fiber was discovered at the Canadian cammunication
research center in 1978 by Ken Hill [4]. Fiber Bragg gratings are spectral filters
fabricated within segments of optical fiber. Like any other diffraction grating, they rely
on the Bragg Effect (constructive interference from a diffraction grating) to reflect light
over a narrow wavelength range and transmit all other wavelengths, but they also can be
designed to have more complex spectral responses. Many uses exist for FBGs in today’s
fiber communications systems that although they are complex to design, but we will
briefly describe their properties. When an optical fiber is exposed to ultraviolet light, the
fiber’s refractive index is changed; if the fiber is then heated or annealed for a few
hours, the index changes can become permanent which this phenomenon is called
photosensitivity. In germanium-doped single-mode fibers, the index differences
between 10-3and 10-5 have been obtained. Using this effect, periodic diffraction gratings
can be written in the core of an optical fiber. This was first achieved by interference
between light propagating along the fiber and its own reflection from the fiber endface;
this is known as the internal writing technique and the resulting gratings are known as
Hill gratings. Gratings can also be written in the fiber core by irradiating the fiber
through a phase mask with a periodic structure. These techniques can be used to write
FBGs in the fiber core; such gratings reflect light in a narrow bandwidth centered
around the Bragg wavelength,  B , which is given by
 B  2neff 
(2.1)
Where  (Fig 2) is the spatial period, or pitch of the periodic index variations and neff is
the effective refractive index for light propagating in the fiber core [5-6].
Figure 2. Schematic illustration of a fiber grating. Dark and light shaded regions
within the fiber core show periodic variations of the refractive index[6].
One of the most interesting Bragg grating structures with immediate applications in
telecommunications is the chirped Bragg grating. This type of grating has a
monotonically varying period, as illustrated schematically in Fig 3 [7].
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Chirped fiber gratings have a relatively broad stop band and were proposed for
dispersion compensation as early as 1987. The optical period neff  in a chirped grating
is not constant but changes over its length. Since the Bragg wavelength also varies
along the grating length, different frequency components of an incident optical pulse are
reflected at different points, depending on where the Bragg condition is satisfied locally.
In essence, the stop band of a chirped fiber grating results from over lapping of many
mini stop bands, each shifted as the Bragg wavelength shifts along the grating. The
resulting stop band can be as wide as a few nanometers. It is easy to understand the
operation of a chirped fiber grating from Fig 4, where the low-frequency components of
a pulse are delayed more because of increasing optical period (and the Bragg
wavelength). This situation corresponds to anomalous GVD. The same grating can also
provide normal GVD if it is flipped (or if the light is incident from the right). Thus, the
optical period neff  of the grating should decrease for it to provide normal GVD. From
this simple picture, the dispersion parameter D g of a chirped grating of length L g can be
determined by using the relation TR  D g L g  , where TR is the round-trip time inside
the grating and  is the difference in the Bragg wavelengths at the two ends of the
grating. Since TR  2neff Lg / c , the grating dispersion is given by a remarkably simple
expression,
Dg  2neff / c( )
(2-2)
Some changes happen in the chirp fiber Bragg Grating during the grating as the
Grating periodicity changes along the shaft, different wavelengths are reflected by
different grating and consequently they delay in different time interval. Final effect of a
compaction is in incident pulse which can be suitable for compensation of random
dispersion that stored in transmission link. The most important advantages of chirp fiber
Bragg grating are internal loss, nonlinear effects and low cost [8].
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Figure 3. Schematic diagram of a chirped grating with an aperiodic pitch. For
forward-propagating light as shown, long wavelengths travel further into the grating
than shorter wavelengths before being reflected. (b) Schematic diagram of a cascade of
several gratings with increasing period that are used to simulate long, chirped
gratings[7].
Figure 4. Dispersion compensation by a linearly chirped fiber grating: (a) index profile
n(z) along the grating length; (b) reflection of low and high frequencies at different
locations within the grating because of variations in the Bragg wavelength[8].
The chief problem in FBG function is Fresnel reflection which is both reflection
and refraction that happens to the light where it transfers from one one medium to
another with different refractive index (Fig 5).
Figure 5. FBG spectral behaviour[6].
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3. Dispersion Compensation Fibers (DCFs)
In recent years, there has been considerable work on dispersion-compensating fibers
(DCFs), which are being used extensively for upgrading the installed 1310 nm
optimized optical fiber links for operation at 1550 nm.
Now, in many countries, the tens of millions kilometers of CSFs already exist in the
underground ducts operating at 0  1300nm . One could increase the transmission
capacity by operating these fibers at 1550 nm and using WDM techniques in optical
amplifiers. But, there will be significant residual (positive) dispersion, too. On the other
hand, replacing these fibers by DSFs would involve huge costs. Hence, in recent years,
there has been considerable work in upgrading the installed 1310 nm optimized optical
fiber links for operation at 1550 nm. This is achieved by developing fibers with very
large negative dispersion coefficients, a few hundred meters to a kilometer, which can
be used to compensate for dispersion over tens of kilometers of the fiber in the link.
Compensation of dispersion at a wavelength around 1550 nm in a 1310 nm optimized
single-mode fiber can be achieved by specially designed fibers whose dispersion
coefficient (D) is negative and large at 1550 nm. These types of fibers are known as
DCFs. Since the DCF has to be added on to an existing fiber optic limit, it would
increase the total loss of the system and, hence, would propose problems in detection at
the end. The length of the DCF required for compensation of dispersion can be reduced
by having fibers with very large negative dispersion coefficients. Thus, there has been
considerable research effort to achieve DCFs with very large (negative) dispersion
coefficients [9]. In next parts, we consider some simulation results for reduce the
dispersion in communication links.
4. Simulation results
The experimental setup that designed in figure 6 by optisystem software is contain of
Pseudo-Random Bit Sequence Generator, CW Laser, NRZ Pulse Generator, MachZehnder Modulator, Optical Fiber, Optical Time Domain Visualizer, Optical Amplifier,
Fiber Bragg Grating, Optical Power Meter, Eye Diagram Analyzer and Photodetector
PIN for propose the transmitter external modulated laser by using optical and electrical
visualizers. The following parameters of fiber and grating in table 1 are used also to
better simulation of transfer system
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Figure 6. Simulation of total transfer system.
Table1. Fiber Parameters
Name
Length
Attenuation
Dispersion
Dispersion Slope
Value
10 Km
0.2 dB/Km
17 ps/nm/Km
0.05 ps/nm2/Km
Table 2. FBG Parameters
Name
Frequency
Effective Index
Length
Chirp Function
Value
193.1 THz
1.45
5 mm
Linear
Linear Parameter
Apodization
Function
Tanh Parameter
0.0001  m
Tanh
2
In addition, we emloyed CW laser diode in frequency of 193.1THz and 1mW power
which is modulated by a Pseudo random bit sequence generator in 10Gbits/s by a MachZehnder modulator with extinction ratio of 30dB. The Erbiume amplifier in this system
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has gain around 6dB and can be ignored without any destractive noise which is used
only for dispersion compensation and nonlinear effects in designed system.
By simulating of transferring system (Fig 6) and depicting the Eye diagram of this
system, it can be understood that the system has a lot of dispersion and attenuations
(Figs 7- 9).
Figure 7. Eye diagram for the related design with dispersion.
Figure 8. Out put power results from the optical spectrum Analyzer.
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Figure 9. Electrical Power Meter Visulizer
The output figures demonstrated clear dispersion factor that after crossing the signal
of fiber, causes disforming the primary information. As a result, a tool should be used to
recover the dispersion and renew the primary signal shape.
Firstly, the chirp Bragg Grating is used to recover dispersion and the system is
simulated as illustrated in Figure 10.
Figure 10. Simulated system by chirp fiber Bragg grating.
By employing the chirp fiber Bragg Grating in this system, the output results of
dispersion compensation will be like as Figure 11 that the pulse figure renewed greatly
but the peak power of signal is lower than figure 8 that is a problem in system.
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Figure 11. Eye diagram for the design by using chirp grating.
In next design, we replaced the system by symmetrical dispersion compensation fiber
in transmission system that shown in Figure 17. Summerize description on Pre, Post and
symmetrical compensation by DCF and symmetrical compensation configurations are
shown in Figs. 12, 13 and 14.
Figure 12. Dispersion pre-compensation.
Figure 13. Dispersion post-compensation.
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In post compensation case, DCF is placed after SMF whereas in precompensation
case it is inserted before SMF. In symmetrical compensation case, fiber placement
follows the sequence of DCF, SMF, SMF, DCF.
Figure 14. Dispersion symmetrical compensation.
Simulation results based Q factor of received signal verses transmitted signal power
for these three schemes at 2.5 and 10 Gb/s bit rates are shown in Figs. 15 and 16. These
figures are obtained by sweeping the power from –12 dBm to 12 dBm and using the
software’s Graph Builder. From these figures, we can receive the best performance is
obtained by using symmetrical dispersion compensation. The worst case is dispersion
pre-compensation. Post-compensation gives a result as well as symmetrical
compensation. This results confirmed by the eye diagrams given in Fig. 16 [10,11].
Figure 15. Q factor verses signal power at 2.5 and 10 Gb/s bit rates for pre-, post-,
and symmetrical dispersion compensations.
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Figure 16. System performance at 2.5 and 10 Gb/s bit rates for pre-, post-, and
symmetrical dispersion compensations. The eye diagrams for these cases have been
shown for –12 and 10 dBm signal powers, respectively[10,11].
In continue, we stimulate system by symmetrical DCF as figure 17.
Figure 17. Simulated system by symmetrical DCF.
By this method, the dispersion of system can be more reduced as shown in figure 18.
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Figure 18. Eye diagram for the design by using symmetrical DCF.
Furthermore, the peak power of signal and average power increased based this design
more than 15 dBm and 2.8 dBm, respectively as proposed in figures19 and 20.
Figure 19. Optical spectrum Analyzer diagram
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Figure 20. Electrical Power Meter Visulizer.
Finally, we will survey a completed system by coupled of symmetric DCF and FBG
system that show in Fig. 21 that better output results proposed in Figs. 22- 24.
Figure 21. Simulated system by symmetrical DCF and FBG.
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Figure 22. Eye diagram for the design by using symmetrical DCF and FBG.
Figure 23. Optical spectrum Analyzer diagram.
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Figure 24. Electrical Power Meter Visulizer
CONCLUSION
Dispersion compensation in optical transmission system is an important challenging
subject. Without dispersion compensation, every pulse will become wide and overlap
with near pulse so extremely that can not be distinguished. Although the chirp FBG is
preffered in many transmission systems for supress and reduce the dispersion problem
but for achieve the optimum results despite of nonlinear effects and high cost of DCF,
employing the both components suggested.
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