design optimization of chirped fbg as a dispersion compensator
TRANSCRIPT
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Design optimization of chirped FBG as a dispersion
compensator
D. Aneesh1, A.Vishnu Vardhanan
2, and R.Gangopadhyay
3
Dept. of Electronics and Electrical Communication Engineering
Indian Institute of Technology, Kharagpur
E-mail: [email protected], [email protected], [email protected]
Abstract:Chirped fiber Bragg grating (FBG) provides an
attractive solution for low cost dispersion compensation
in a fiber optic transmission system. The present work
carries out the design optimization of a chirped FBG in
respect of chirp bandwidth and apodisation profile in
achieving optimum dispersion compensation in a
40Gbps optical transmission link for differentmodulation formats.
1. Introduction:Linearly chirped fiber Bragg gratings are commonly usedfor dispersion compensation in 10Gbps optical transmission
systems. The availability of mass production techniques and
low cost has made this device very attractive for dispersion
compensation. Even in higher bit rates such as 40Gbps case
they are also found to be very effective.
The performance of a chirped FBG is controlled by several
parameters such as the length of the grating used for
compensation, chirp bandwidth, apodisation profile, acindex modulation depth and the number of uniform steps in
the grating. Several studies are carried out to optimizedesign procedure for dispersion compensating chirped FBG.
The critical parameters for the design of a chirped FBG used
as dispersion compensator are the grating length, chirped
bandwidth and the apodisation profile. Conventional
approach for choosing the length of the grating ( Lg ) basedon the knowledge of the signal bandwidth and amount of
the fiber dispersion to be compensated. Such a procedure
needs adhoc trial of fixing the length of the grating to be2Lg, 3Lg etc in order to achieve the best performance.
However this approach does also consider how different
modulation formats may require the FBG lengthoptimization.
The present procedure determines the choice of the FBG
length based on appropriate selection of chirped bandwidth
containing a desired level of signal energy Ethdepending on
the performance optimization required. It is known thatoptimization of apodisation profile has a distinctive role in
ensuring minimum delay ripple across the gratingbandwidth. As per current literature the symmetric tanh
apodisation is claimed to be the best apodisation profile. In
the present study we show that further design optimizationcan be effected if one uses asymmetric tanh apodisation.
.
2. Design Procedure Optimization
and SimulationA number of parameters are involved in the design of a fiber
Bragg grating. The design of chirped FBG for dispersion
compensation requires proper choice of various gratingrelated parameters. The following steps are involved in the
design.
1) Calculate the grating length as
=
nBDLL fg
2
2
(1)
Lf is the length of the fiber, D is the fiber dispersion
parameter (ps/nm/km), B is the signal bandwidth, is the
central wavelength and n is the effective refractive index.
2) For a given length Lg the number of uniform sections ischosen to be 60 or higher. The grating simulation is carried
out by transfer matrix approach [6] for an adequately chosenvalue of the chirp bandwidth, neff=1.45, ac modulation index
at optimized value 1.2x10 -4 an and appropriate apodisation
profile (tanh) to maintain a desired accuracy and the
performance targets.
3) For a chosen value of the chirped bandwidth it is further
necessary to optimize the grating length to be 2Lg, 3Lg etc.
in order to achieve the optimum result.
It may be noted that the above choice of length also varies
depending on the signal modulation used. This may beappreciated referring to Table 1 which shows that for the
eye opening penalty (EOP) of 0.2 dB for the dispersion
compensated 40Gbps signal at the output of the grating, the
grating length differs depending on the value of the chirp
bandwidth and the modulation format. The above designprocedure suffers because the choice of chirp bandwidth
does not actually take into account the detailed nature of the
signal spectrum.
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Table1: FBG parameters for an EOP of 0.2 dB for different
modulation formats:
ModulationFormat Length(cm)
ChirpBandwidth(nm)
NRZ 10.00 0.8
21.00 1.6
RZ 20.30 1.6
26.30 2.0CSRZ 10.29 0.8
20.68 1.6
2.1 Present Design approachIn this design we tried to optimize the design in
terms of the length of the grating, chirp bandwidth and
apodisation. For all other parameters standard values are
adopted. DC index modulation of zero and AC indexmodulation of 1.2x10 -4 are taken for all the cases. Number
of steps in the calculation of grating is chosen to be 100.
Length optimization:The choice of Lg can be simplified by taking B in (1) as the
chirp bandwidth of the dispersion compensator. The
interdependence of parameters in the past design andambiguity can be removed by this method.
In order to find out the amount of chirped bandwidth neededfor effective compensation we consider the bandwidth
containing energy above a certain threshold. For example
Table2 shows the energy content in a specified bandwidthfor different modulation format. Based on the required EOP
one can choose the signal bandwidth containing energy
greater than the threshold. Based on this value of chirp
bandwidth the grating length is calculated using (1).
The above approach is used for the simulation based designof the chirped FBG for dispersion compensation. In the
simulation a PN sequence of length 26-1 at 40Gbps isgenerated which is used to produce a modulated signal
(NRZ, RZ and CSRZ) from the Mach Zahnder modulator.
The output from Mach Zahnder modulator is coupled to a
single mode fiber (D=16ps/nm/Km). The received output isfiltered by an optical Bessel filter (3dB
bandwidth=160GHz) and after photo detection is filtered by
an electrical filter (3dB bandwidth= 28GHz). Split step
Fourier method is used to simulate the propagation through
the fiber and transfer matrix method [6] is used forsimulation of the Bragg grating.
The performance result of grating is expressed in terms ofEOP vs chirp bandwidth for different modulation formats.
As one finds from Fig. 1 that depending on the modulation
format appropriate chirp bandwidth needs to be utilized in
the design for obtaining required EOP. It is also found fromsimulation that for an EOP of 0.2 dB the required energy
threshold Eth =98%, 96% and 98% for NRZ, RZ and CSRZ
respectively.
Figure 2 also depicts the EOP performance with fiber lengthfor two different values of chirp bandwidth providing
different levels of energy for NRZ signaling format.
Table2. Energy content in a given signal bandwidth
Percentage energy in a Bandwidth
( Eth)SignalBandwidth NRZ RZ CSRZ
0.6 97.63 61.04 97.37
0.8 97.81 87.30 98.25
1 98.47 89.63 99.08
1.2 98.78 90.21 99.75
1.4 98.81 90.30 99.85
1.8 99.18 91.05 99.91
2 99.20 94.09 99.96
3 99.50 95.12 100
0
2
4
6
8
10
0 2 4
Chirp Bandwidth (nm)
EOP(dB)
NRZRZCSRZ
Fig. 1. EOP variation of EOP for different chirp
Bandwidth at 40Gbps
0
0.5
1
1.5
2
2.5
70 75 80 85 90
Fiber Length (Km)
EOP(dB)
E=95% chirpBW=0.6nm
E=99% chirpBW=1.6nm
Fig. 2. EOP performance with distance for different chirp bandwidth
providing different levels of energy for NRZ at 40Gbps
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Apodisation Optimization:Several investigations have been carried in the past out to
find out the best apodisation profile for sidelobe suppression
and improved time delay ripple performance [3] [7]. In
literature it is found that symmetric tanh is the best known
apodisation among these. We show here that further gratingimprovement can be effected if asymmetry is introduced in
the tanh apodisation profile:
( )( )
=
LzkLL
zLb
kLzL
az
xf
,2
tanh
0,2
tanh
..(2)
where a and b are tanh window parameters and k is
asymmetric apodisation parameter.
Fig. 3. Asymmetric apodisation profiles
Figure 3 shows several asymmetric apodisation profilesalong the grating length for different values of a, b and the kvalue varies in the range of 0.1 to 0.9. The impact of the
slope asymmetry on both EOP and mean time delay ripple is
shown in Figure 4. Compared to symmetric tanh profile
asymmetric tanh profile provides significant improvement
of grating performance.
0
0.2
0.4
0.6
0.8
1
0 0. 1 0 .2 0 .3 0. 4 0 .5 0. 6 0 .7 0 .8 0. 9 1
Apodisation asymmtery(k)
E
OP(dB)
0
5
10
15
20
25
Averagetim
edelay
ripple(ps)EOP
Avg.time delay
Fig4.EOPand average time delay ripple versus apodisation asymmetry for
NRZ at 40Gbps
0
0.51
1.5
2
2.5
3
3.5
4
70 75 80 85 90Fiber Length ( Km)
EOP
(dB)
tanh a=4 b=4 k=.5
tanh a=2 b=7 k=.8
Fig. 5.Comparison of EOP for asymmetric and
symmetric apodisation
3. Conclusion
A simple easy-to-use design optimization of chirped FBG asdispersion compensator is presented. In particular, the
criterion for appropriate choice of the chirp bandwidthbased on threshold energy of the signal allows the
determination of grating length automatically optimized.
The procedure also easily accommodates length
optimization for different modulation formats. Further,better length optimization can be achieved by introducing
slope asymmetry in conventional tanh apodisation resulting
in both decreased passband delay ripple and reduced EOP.
References
[1] P.Fernandez, J.C. Aguado, J.Blas, R.Duran, I.deMigfuel, J.Duran, R.M. Lorenzo and E.J. Abril,Analysis and Optimisation of the apodisation sharpness
for linearly chirped dispersion compensation gratings,IEE proc-Optoelectronics, pp-69-73, April-2004.
[2] D. Pastor, J.Capmany, D. Ortega, V. Tatay and J. Marti ,Design of apodized linearly chirped fiber grating fordispersion compensation, J.of Lightwave Technology,
pp-2581-2588, November 1996.
[3] K.Ennser, M.N. Zerva and R.I. Laming, Optimization
of apodised linearly chirped fiber grating for opticalcommunications, IEEE J. of quantum technology, pp-770-777, May 1998.
[4] K.Ennser, R I Laming and M.N. Zerva, Analysis of
40Gbps TDM-Transmission over Embedded StandardFiber Employing Chirped Fiber Grating DispersionCompensators, J.Lightwave Technology, pp 807-811
May 1998.
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[5] F. Ouellette, Dispersion cancellation using linearly
chirped Bragg grating filters in optical waveguides,Optics Letters, pp 847-849, October 1987.
[6] Raman Kashyap, Fiber Bragg Grating, Sen Deigo,Academic Press, 1999.
[7] M.N. Zervas and D.Taverner, Asymmetrically apodized
linearly chirped fiber Bragg gratings with improveddispersion characteristics, ECOC98, September 1998.