This document summarizes an investigation into optimizing the duty cycle of input pulses in an undercompensated optical fiber link. The link consists of 5 loops, each with 50km of standard single mode fiber followed by dispersion compensating fiber. Simulation was performed for duty cycles of 25%, 33%, 50%, 66% and 75% and reductions in compensating fiber length from 1.0-1.4%. Results show that higher duty cycles permit greater reductions in compensating fiber length while maintaining reliable communication, but require higher input powers. A 50% duty cycle provided the maximum 1.35% permissible reduction in compensating fiber length.

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Investigation of Optimal Duty-Cycle for GVD Undercompensated
Optical Link
Vinita Tiwari1, P Vignan2, Rahul Vyas3, Vinod Kumar Chaubey4
Department of Electrical and Electronics Engineering, BITS Pilani
Pilani, Rajasthan, 333031, India
1vinita@bits.pilani-pilani.ac.in
ABSTRACT: This paper investigates the optimal duty-cycle of input pulse subjected to GVD
induced degradation in an undercompensated 300 Km optical link comprising of 5 loops of
SMF followed by DCF for a data rate of 40 Gbps. Analysis has been carried out for different duty
cycles in a GVD undercompensated optical link by employing 1.0%, 1.1%, 1.2%, 1.25%, 1.3%,
1.35% and 1.4% reduction in DCF length, where 10Km DCF is required for perfect
compensation of GVD that accumulates in 50 Km SMF in each loop. Such fiber link is simulated
for duty cycles of 25%, 33%, 50%, 66% and 75%. Peak power is increased to also observe the
degradation due to nonlinear effect in this optical channel. Investigation reports the
permissible reduction in DCF length for a duty-cycle that optimizes performance in an
undercompensated link.
KEYWORDS: GVD, Duty-cycle, Q-factor, SMF, DCF, Undercompensation
I.
INTRODUCTION
Since 1980 fiber-optic communication systems are being deployed across the globe and have
truly revolutionized the technology behind telecommunications. It was possible to transmit
optically encoded information over long distances by the use of intermediate repeaters. The
first generation of lightwave systems operated near 0.8μm and had repeater spacing of up to
10 Km. Second generation lightwave systems allowed considerable increase in repeater
spacing by operating in the wavelength region near 1.33μm, where fiber loss is typically
0.5dB/km. Repeater spacing was further increased in third generation of lightwave systems by
shifting the operating wavelength to 1.55μm where silica fiber offers minimum loss of
0.2dB/Km [1]. With the advent of optical amplifiers like EDFA, fiber losses are no longer a
major limiting factor in optical communication links. This new operating wavelength has made
dispersion a major limiting factor as standard silica fibers have a large dispersion near 1.55μm.
These optical amplifiers had successfully overcome the drawbacks of opto-electro-optical
conversions with electronic regenerators and hence, allowed much higher data rate. Optical
amplifiers have solved the attenuation issue but have worsened the degradation caused by
accumulation of dispersion over multiple amplifiers [2, 3]. Duty-cycle of the input pulse is also
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B K Birla Institute of Engineering & Technology (BKBIET), Pilani, India
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2. International Journal of Electronics and Communication Engineering & Technology (IJECET),
ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online), Special Issue (November, 2013), © IAEME
one of the important design criteria as it plays a significant role in deciding the optimum
balance between fiber nonlinearities and dispersion [4, 5].
Thus in order to increase the system capacity, Group Velocity Dispersion (GVD) need to fully
compensated. Various dispersion compensation methods are being used like Fiber Bragg
Grating (FBG), Optical Phase Conjugation (OPC), Reverse Dispersion Fiber (RDF) and Negative
Dispersion Fiber (NDF) to compensate fiber dispersion in an optical link. Amongst all the above
mentioned schemes of GVD compensation, it has been found that use of dispersion
compensating fibers (DCFs) is very convenient and practical [6-9].
II.
THEORY
The use of DCF provides an all-optical technique which is able to compensate fiber dispersion
completely provided the average optical power is maintained low enough that the degradation
due to nonlinear phenomena in optical fiber can be neglected. Assuming that the fiber behaves
in linear regime the pulse propagation Eq. can be written as
A i 2  2 A  3  3 A


0
z
2 t 2
6 t 3
(1)
Where, A is the pulse envelop amplitude. The effect of third order dispersion modeled by β3
can be neglected when |β2 | exceeds 0.1 ps2/km. Neglecting β3, the solution to Eq. (1) becomes
A( z , t ) 
1
2



1
Ã(o, ) exp(  2 z 2  it ) d
2
(2)
Ã(0,ω) in Eq. (2) is the Fourier transform of A(0,t). Consider the situation where optical pulse
propagates through two different fiber segments, one segment of single mode fiber (SMF)
followed by a segment of DCF. Using Eq. (2) consecutively for both the fiber sections, we obtain
A( L, t ) 
1
2



1
Ã(o, ) exp[  2 ( 21L1   22 L2 )  it ]d
2
(3)
Where, L = L1+L2 and β2i is the GVD parameter for the optical fiber section of length Li.
For GVD to be compensated perfectly the pulse should be able to recover its initial shape after
L distance, so the phase term in Eq. (3) should vanish. So, putting the ω2 phase term in Eq. (3)
to be zero, the condition that ensures perfect compensation of GVD is
β21 L1 + β22 L2 = 0 i.e. D1L1 + D2L2 = 0
(4)
L2 in Eq. (4) provides the required length of DCF segment for perfect compensation and is
given by
L2 = - (D1/D2) L1
(5)
It is practically possible for DCF to have a large negative value of dispersion parameter D2, so L2
in Eq. (5) can be considered as small as possible [10, 11]. DCF with large negative value affects
the cost budget of an optical link. The nonlinear refractive index coefficient (n2) of the DCF is
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3. International Journal of Electronics and Communication Engineering & Technology (IJECET),
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higher than that of the SMF because of its smaller effective area. Thus, the nonlinear
phenomena, which are dependent on (n2/Aeff), are more prominent in DCF than in SMF [11].
Hence selection of optimum length of DCF remains a challenging problem in a single span of
fiber (SMF + DCF) where dispersion need to be compensated to the extent that it offers an
reliable communication and also manage to keep the nonlinear effects to cause a minimal
degradation
III.
PERFORMANCE MEASURE
To investigate upon the length of DCF that can provide us with some savings in DCF while
maintaining reliable communication, we have considered different pulse widths that optimize
and recommend certain level of under- compensation.
A reliable communication in optical domain requires a minimum bit error rate (BER) of 10-9.
This implies that the quality factor (Q-factor) should be maintained over 6. In this paper BER
has been estimated using semi-analytic BER evaluation method and BER-equivalent Q factor
has been considered for all analysis. So, throughout this paper Q-factor of 6 has been
considered as reference and the performances of various parameters are evaluated based on
Q-factor.
IV.
SYSTEM DESCRIPTION AND RESULT
A fiber loop consisting of 50 Km SMF followed by 10 Km DCF has been considered for
simulation. This is the length of DCF segment obtained from Eq. (5) to completely compensate
fiber dispersion of 50 Km SMF. Simulative analysis has been performed using commercial
package OptSimTM .Fig 1 shows the simulation setup of 40Gbps optical channel to investigate
optimum pulse width i.e. duty cycle of RZ pulses in a GVD undercompensated 300 Km link
made up of 5 fiber loops. For DCF lengths lesser than 10 Km GVD is not compensated perfectly,
hence, uncompensated dispersion keeps on accumulating which finally limits the transmission
in such fiber link.
Simulation has been carried out for RZ pulses of different duty cycles like 25%, 33%, 50%, 66%
and 75%. A fiber loop shown in Fig. 1 consists of a SMF segment followed by a fixed gain EDFA,
a DCF segment and another fixed gain EDFA. The 50 Km length SMF has the following
specifications: attenuation loss of 0.2dB/km, dispersion and dispersion slope of 0.2ps/km-nm
and 0.08ps/nm2-km at 1550nm respectively, effective area of 93 μm2 and refractive index of
3x10-20 m2/W. EDFA_1 provides a gain of 10 dB and has a noise figure of 6 dB. DCF segment
with the following specifications has been considered for simulation. It has attenuation loss of
0.5dB/km, dispersion and dispersion slope of -80ps/km-nm and 0.08ps/nm2-km at 1550nm
respectively, effective area of 23 μm2 and refractive index of 3x10-20 m2/W. EDFA_2 follows the
DCF segment and provides a gain of 5 dB with a noise figure of 6dB.
Mach Zehnder Modulator (MZM) having an extinction ratio of 30 dB is used to modulate an
optical laser having 10 MHz linewidth. Optical Bessel filter of 160 GHz bandwidth centered at
1550 nm precedes the PIN photo detector which has a responsivity of 0.8 A/W, dark current of
10 nA and thermal noise of 1x10-24 W/Hz. A low pass Bessel electrical filter then provides
filtered output data to a BER estimator for performance measurement.
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4. International Journal of Electronics and Communication Engineering & Technology (IJECET),
ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online), Special Issue (November, 2013), © IAEME
Fig. 1: Layout for 40Gbps link to study SPM effect
In the present work, to investigate the under-compensation effect we have considered 1.0%,
1.1%, 1.2%, 1.25%, 1.3%, 1.35% and 1.4% reduction in DCF length, where 10Km DCF is
required for perfect compensation in each loop. Simulation has been carried out for duty cycles
of 25%, 33%, 50%, 66% and 75% for each of the under-compensation scenario mentioned
above. Effect of pulse width on system performance where GVD is not perfectly compensated
has been simulated and analyzed. Reduction in length of DCF though causes uncompensated
GVD to be accumulated over multiple spans of fiber loop; it has lessened the nonlinear effect to
some extent owing to shorter DCF segment in order to provide some benefit towards
sustaining degradation due to nonlinearities.
Fig. 2 shows the system performance for RZ pulses having different duty cycles with increasing
input power in a channel (5 spans of 50 Km SMF + 10 Km DCF) where GVD is fully
compensated. It is observed that the degradation due to nonlinear effects is the major limiting
factor in such links where dispersive effects are nullified. Pulse with 25% duty-cycle is least
affected by nonlinear effect whereas the pulse with 75% duty-cycle has encountered severe
degradation as the peak power increased.
Fig. 2: Q-Factor vs. Peak Power for perfect compensation of GVD
Fig. 3-7 reports the performance in an undercompensated optical link where uncompensated
GVD accumulated over multiple loops becomes a major limiting factor. As DCF is subjected to
more nonlinearities than SMF, a reduction in DCF length will eventually lower the nonlinear
effect in the optical channel.
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5. International Journal of Electronics and Communication Engineering & Technology (IJECET),
ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online), Special Issue (November, 2013), © IAEME
Fig. 3: Q-Factor vs. Peak Power for duty cycle of 25%
It can be interpreted from Fig. 3 that 25% duty cycle pulse permits only 1.0% reduction in DCF
length for minimum required source power of 3mW.
Fig. 4: Q-Factor vs. Peak Power for duty cycle of 33%
Fig. 4 shows that 33% duty cycle pulse can provide reliable communication even with 9.875
Km DCF in place of 10 Km DCF. This results in a saving of 1.25% DCF length but at the same
time the minimum required peak power increases with increase in duty-cycle.
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6. International Journal of Electronics and Communication Engineering & Technology (IJECET),
ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online), Special Issue (November, 2013), © IAEME
Fig. 5: Q-Factor vs. Peak Power for duty cycle of 50%
As shown in Fig. 5, 50% duty cycle pulse provides reliable communication even with 9.865 Km
DCF replacing 10 Km DCF. This reports a maximum saving of 1.35% DCF length. It can also be
observed that the Q-factor optimizes at the same input power for all the observed values of
DCF length. But the range of input power that ensures reliable communication is getting
narrower as DCF of shorter length is being deployed in the link.
Fig. 6: Q-Factor vs. Peak Power for duty cycle of 66%
A similar qualitative behavior is seen in Fig. 6 for 66% duty-cycle. Here, the minimum required
power to achieve Q-factor of 6, power for maximum Q-factor and limiting power records a
lower value in comparison with those for pulses with 50% duty-cycle. This observation
becomes more prominent with percentage increase in GVD undercompensation.
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7. International Journal of Electronics and Communication Engineering & Technology (IJECET),
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Fig. 7: Q-Factor vs. Peak Power for duty cycle of 75%
It can be observed from Fig. 7 that 75% duty-cycle pulse is most severely affected by nonlinear
effects in comparison with pulses of lesser duty-cycle. It can provide reliable communication
till 1.3 % reduction in DCF length.
V.
CONCLUSION
The simulative analysis performed in this paper helps in estimating the optimal duty-cycle in a
undercompensated link design. Investigation reports that 25% duty cycle pulse permits only
1.0% reduction in DCF length while 33% duty cycle pulse can withstand till 1.25% reduction in
DCF length but at the cost of increased minimum peak power requirement for reliable
communication. Even reduction till 1.35% in DCF length is achievable for duty cycles of 50%,
66% whereas 75% duty-cycle can afford reduction only up to 1.3%. It has been observed that
minimum peak power requirement to achieve optimal Q Value decreases with increase in duty
cycle, whereas the performance degradation due to nonlinear effects become more prominent
due to increase in peak power for pulses having higher duty cycles.
ACKNOWLEDGEMENT
Authors are thankful to the Director, B.I.T.S Pilani for extending the facility in the optical
communication lab to implement the concept.
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[3]J. I. Yamada, S. Machida, and T. Kimura, “2Gb/s optical transmission experimentsat 1.3 um
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[4]C. Caspar, H.-M. Foisel, A. Gladisch, N. Hanik, F. Kuppers, R. Ludwig, A. Mattheus, W. Pieper,
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BIOGRAPHY
Vinita Tiwari was born in Pilani, Rajasthan India. She received her Master
of Engineering degree with specialization in Communication systems from
BITS-Pilani in 2009 and Bachelor of Engineering degree in Electronics &
communication from M.B.M. Engineering College Jodhpur in 2006. She is
presently working as Lecturer in the Electrical & Electronics Engineering
Department, BITS-Pilani. Her research interest includes High speed optical
communication, complex modulation schemes, network design and
simulation.
Vignan Pusunala born in Hyderabad, Andhra Pradesh, India. He received
his Bachelor of Technology degree from Vignan Institute of technology and
Science in the year of 2011. Presently he is pursuing Masters Degree from
BITS-PILANI with specialization in Communication Engineering. His area of
interest includes Optical Communication, Computer Networks and Digital
Signal Processing.
Rahul Vyas was born in Jodhpur, Rajasthan India. He received his Bechlor
of Engineering in Electronics & Communication from Marwar Engineering
College and Research Centre Jodhpur in 2009. He worked as a Lecturer in
Vyas Institute of Engineering and Technology from 2010 to 2012 in
Electronics and Communication Department. He is presently pursuing his
Masters degree with specialization in Communication Engineering from
BITS PILANI. His area of interest includes Optical Communication, Wireless
Communication, and Digital Signal Processing.
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B K Birla Institute of Engineering & Technology (BKBIET), Pilani, India
October 18-20, 2013
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