Dispersion Compensation In Optical Communication-A Review

Dispersion is defined as the phenomenon in an optical fiber whereby light photons arrive at a distant point in the different phase then they entered the fiber. Dispersion causes signal distortion that ultimately limits the bandwidth and usable length of the fiber cable. Therefore dispersion compensation (management) becomes an essential part to study in optical communication for better transmission. In this paper we have reviewed the various techniques (schemes) that are used for dispersion compensation. General Terms Dispersion Compensation Schemes (techniques), Dispersion, Dispersion Compensation. Indexing terms Dispersion Compensation Schemes, Dispersion, High Speed Optical Communication System. INTRODUCTION Dispersion is defined as the phenomenon in an optical fiber whereby light photons arrive at a distant point in the different phase then they entered the fiber. Dispersion causes signal distortion that ultimately limits the bandwidth and usable length of the fiber cable. Dispersion compensation is used to avoid the chromatic dispersion of optical element. This goal can be achieved by avoiding excessive temporal broadening of the pulse or the distortion of signals. Dispersion compensation is an important issue for fiber –optic links. Strong dispersive broadening of modulated signal can occur in cases with higher data rates. Without dispersion compensation, each signal would be broadened so much that it would strongly overlap with a number of neighboured symbols. Even for moderate broadening, significant inter-symbol interference can strongly distort the detected signal. Therefore, it is essential to compensate the dispersion before detecting the signal. DISPERSION COMPENSATION SCHEMES 1) Precompensation Scheme:-To avoid the effect of dispersion this scheme modifies the characteristics of input pulses at the transmitter before they are sent into the fiber link. Precompensation techniques are:a) Prechirp Technique. b) Novel Coding Technique. a) Prechirp Technique:It modifies the characteristics of input pulse before sending into the fiber link. If input pulse is Gaussian then by prechirping (chainging amplitude) the amplitude of this pulse is given by [1]2 0 0 1 (0, ) exp 2 iC t A t A T                 where C is the chirp parameter. A suitably chirped pulse ( 2  C<0) can propagate over longer distances before it broadens outside its allocated bit slot. Assuming pulse broadening factor is tolerable by 2 then the transmission distance is given by:-


INTRODUCTION
Dispersion is defined as -the phenomenon in an optical fiber whereby light photons arrive at a distant point in the different phase then they entered the fiber. Dispersion causes signal distortion that ultimately limits the bandwidth and usable length of the fiber cable. Dispersion compensation is used to avoid the chromatic dispersion of optical element. This goal can be achieved by avoiding excessive temporal broadening of the pulse or the distortion of signals. Dispersion compensation is an important issue for fiber -optic links. Strong dispersive broadening of modulated signal can occur in cases with higher data rates. Without dispersion compensation, each signal would be broadened so much that it would strongly overlap with a number of neighboured symbols. Even for moderate broadening, significant inter-symbol interference can strongly distort the detected signal. Therefore, it is essential to compensate the dispersion before detecting the signal.

iC t A t A T
         where C is the chirp parameter.
A suitably chirped pulse ( 2  C<0) can propagate over longer distances before it broadens outside its allocated bit slot.
Assuming pulse broadening factor is tolerable by 2 then the transmission distance is given by:- This scheme is known as dispersion-supported transmission. Because of fiber dispersion FSK signal is converted into the amplitude modulated signal .At the receiver side this signal is decoded using an electrical integrator with decision device [13].
If the system is properly designed then FSK technique is used for longer distance transmission with better performance [14].
The transmission distance can also be increased by using Duobinary Coding. Dispersive effects are reduced for smaller bandwidth signal. And Duobinary Coding reduces the signal bandwidth by 50% [15]. Therefore it increases the transmission distance. Two successive bits in the digital bit stream summed to form a three level duobinary code at half bit rate. 1+1=2; 0+0=0; 0+1=1; 1+0=1 At the reciever side phase information is used to distinguish the two. By using duobinary coding in optical communication system instead of using binary coding then 10Gbps signal was transmitted over 30km to 40 km [16]. Also by duobinary coding with an external modulator (frequency chirp with C>0 ) then 10Gbps signal was transmitted over 160km of a standard fiber [16].
c) Nonlinear Prechirp Techniques:-In this technique transmitter output is amplified by using a semiconductor optical amplifier (SOA). SOA operates in gain saturation region. Due to gain saturation region time dependent variation takes place in carrier density, which chirps the amplified pulse. SOA not amplifies the input pulse but also chirp (chirp parameter C>0) it. Due to this chirp, the input pulse is compressed in the fiber with 2  <0. An input pulse of 40-ps is compressed to 23-ps and it can propagate over 18 km of standard fiber [17]. This technique is used for transmitting a 16-Gb/s signal, obtained from a mode-locked external cavity semiconductor laser, over 70km of fiber [18]. This technique is used for simultaneous compensation of fiber loses and GVD if SOAs are used as in-line amplifiers [19]. A nonlinear medium is also used to prechirp the pulse by self phase modulation of pulse.
SPM Induced Prechirping -It uses self phase modulation for chirping the pulse. In it transmitter output is passed through a fiber of suitable length before passing into the fiber link. The input signal at the fiber input is given by [1]- where P(t) is the power of pulse, m L is the length of nonlinear medium,  is the nonlinear parameter.
In case of Gaussian pulse Then equation (1) can be written as:- is the chirp parameter, C is positive and suitable for dispersion compensation.
Transmission fiber itself is used for chirping the pulse because  >0 for silica fiber. This technique was used in 1986 [20]. 2) Postcompensation Technique:-This technique is used to manage the GVD at the receiver side .It uses an electronic technique at the receiver side. It is an easy technique for dispersion compensation with the use of heterodyne receiver for signal detection. Heterodyne receiver first converts data (optical signal) into microwave signal, it preserves both amplitude and phase information. A microwave filter cancels the effects of GVD. This technique has a great importance for dispersion compensation in coherent light wave system [21]. A 31.5cm long microstrip line is used for dispersion equalization [22]. By using this 8-Gbps signal was transmitted over 188 km of standard fiber having dispersion of 18.5ps/km-nm. To avoid the GVD of light wave system using fiber length of 4900km having bit rate 2.5Gbps microstrip lines were used [23]. If the phase information of the optical signal is lost then it is difficult to avoid the effect of GVD in this technique. An optoelectronic equalization technique is also used to compensate the GVD which is based on transversal filter [24]. In this technique power splitter used at the receiver splits the received signal into several branches. Fiber optic delay line introduces delays in different branches. A variable-sensitivity photodetector converts the optical signal of each branch into photocurrent and the summed photocurrent is used by the decision circuit. The transmission distance of light wave system operating at 5Gbps is extended by a factor 3 by using this technique.

3) Dispersion
Compensating Fibers:-The precompensation and postcompensation scheme extends the transmission distance of dispersion limited system by a factor of 2 and these schemes are not suitable to avoid the GVD dispersion of long hall system [1]. To avoid these limitations a special kind of fiber is used, known as Dispersion Compensating Fiber (DCF). The dispersion compensating fiber uses an all-optical technique , fiber based solution to compensate the fiber GVD completely if the average optical power kept low enough that the non-linear effect insibe the optical fibers are negligible.
Process of dispersion compensation by DCF-Let us take an example in which each optical pulse propagates through two fiber segment, the second segment is DCF. Optical power after the each fiber section is given by- The pulse recover its original shape at the end of DCF if 2  phase term vanishes for DCF. Therefore condition for dispersion compensation is The equation (2)  L should be as small as possible. This is possible only when DCF has a large negative value of 2 D .
DCF module (6-8 km) with optical amplifiers spaced apart by 60-80 km is used to upgrade the old light wave system of standard fiber [1] .The DCF compensates GVD and amplifier removes the fiber loses. But this scheme has two problems. 1) insertion losses of a DCF module typically exceed 5 dB. 2) DCFs have small mode diameter therefore effective mode area is only 20 2 m  . DCF has large optical intensity at the given input power due to this nonlinear effects increase [25].
The problems of DCF is solved by using two mode fiber (V  2.5) such that higher-order is near cutoff. The loss of these fiber is same as of single-mode fiber but dispersion parameter D for higher order mode has large negative value [26]- [29]. Two -mode DCF requires a mode-conversion device. Mode-conversion device converts the energy from fundamental mode to higher-order mode. All -fiber devices are used used for mode -conversion. Mode conversion devices use a twomode fiber with a fiber grating. Fiber grating provides the coupling betweem two modes. Grating period Two-mode DCF design with two long period gratings. First grating transfers power to higher mode and second mode transfers power back into fundamental mode. Measured dispersion characteristics of such a 2-km-long DCF shows that parameter D has a value of -420ps/(km-nm) near 1550 nm. This feature allow it to use for broadband dispersion compensation [29].

4) Optical Filters:-
The limitations of DCFs is that in order to compensate the GVD over 50km of standard fiber it needs long length DCF (>5km). Due to this, link loss increases in long-haul applications. These limitations are removed by using optical filters. The pulse propagation in linear case is given by- where A is the pulse-envelope amplitude. Using fourier transform method the solution of the equation (3) is given by- GVD affects the optical signal through the spectral phase of If an optical filter has property that its transfer function cancels this phase then it will restore the signal. No optical filter has the property to compensate the GVD exactly (expect for an optical fiber).
Optical signal after the filter if this filter is placed after a fiber length L is given by- Expanding the phase of () H  in a Talyor series-   Coupled-mode equations are used to analyze the Bragg Grating and written as [52] Council for Innovative Research   . An ultraviolet Gaussian beam is used to write the apodization grating holographically [30]. The reflectivity spectrum of an apodized is 7.5-cm long grating. In some grating  varies linearly over the length. A 11-cm long grating is used to compensate the GVD acquired by a 10Gbps signal transmitted over 100 km of standard fiber [32].

5) Fiber Bragg Gratings:-Fiber
b) Chirped Fiber Gratings:-These gratings have broad stop band and are used for dispersion compensation [33].
The optical period n of chirped grating is non -uniform over its length [30]. Limitation of chirped fiber bragg grating-The main limitation of the chirped fiber bragg gratings is that they work as a reflection filter. It uses 3dB fiber coupler to separate the reflected signal from the incident one. The use of 3-dB fiber coupler increases the insertion losses. These insertion losses are reduced by using optical circulator. Low insertion losses are achieved by combining two or more fiber gratings as a transmission filter [34].

C) Chirped Mode Coupler:-A chirped mode fiber coupler is an all-fiber and it is based on the concept of chirped
distributed reasonant coupling [35]. Figure below shows the operation of two devices.  Dispersion compensation by tapered dual-core fiber. The chirp grating couples the two spatial modes of dual fiber core. The grating transfers the signal from the fundamental mode to a higher-order mode, but different frequency components travel different length before being transferred. If grating period increases along the coupler length the coupler can compensate for the fiber GVD. The signal remains propagating in the forward direction but ends up with in a higher-order mode of the coupler. The signal is reconverted back into the fundamental mode by uniform-grating convertor. If the two cores are close then transfer of energy from one core to another takes place because of evanescent-wave coupling between the modes. When the spacing between the core is linearly tapered (close), such transfer takes place at different points along the fiber, according to frequency of propagating signal. Thus, a dual core fiber with the linearly tapered core spacing can compensate for fiber GVD.

6) Optical Phase Conjuction:-
where A is the pulse-envelope amplitude. Take the complex conjugate of above equation (4) we get Comparison of above two equation shows that 2  is reversed for the phase-conjugated field. Therefore pulse shape is restored at the fiber end. The 3  term does not change sign on phase conjugation therefore OPC cannot compensate for the third-order dispersion. OPC compensates the even order dispersion terms and leaves the odd order dispersion term. Pulse spectrum just before the phase conjugator is given by And pulse spectrum after the phase conjugation is   Optical field at the end of the fiber link is given by is the Fourier transform of  * , 2

  
and is given by

  
Put this value in equation (5), we get Thus pulse shape is restored to its input form irrespective of how much pulse broadened in the first section. This technique is also known as midspan spectral inversion.

a) Self-Phase Modulation (SPM) Compensation:-
The OPC technique is different from all other dispersion compensation techniques. It can compensate both GVD and SPM simultaneously. This feature was noted in 1980s [36]. Pulse propagation in a lossy fiber is given by-  term is neglected,  is related to the fiber losses. When  =0, * A satisfies the same equation when we take the complex conjugate of equation (6) and change z to -z. Therefore midspan OPC can compensate for SPM and GVD simultaneously. Fiber losses destroy this important property of midspan OPC. The main reason for this is: SPM -induced phase shift is power dependent. Due to this much larger phase shifts are induced in the first-half of the link than the second half and OPC cannot compensate for the nonlinear effects. The pulse propagation is given by- By taking the complex conjugate of equation (4)  () Z  decrease exponentially as exp(- z) due to fiber losses, both GVD and SPM can be compensated exactly in dispersion-decreasing fiber whose GVD decreases as exp(- z).
If FBG dispersion compensation technique is compared with Optical Phase Conjugation dispersion compensation technique then Optical Phase Conjugation is best technique to reduce the dispersion in optical fiber communication [54].

7) Dispersion Compensation For High-Capacity System:-WDM light wave system uses a large
number of channels to handle the capacity of more than 1 Tb/s. Therefore it becomes necessary to compensate the dispersion of each channel for better transmission. Dispersion compensation by fiber grating [29]-A chirp fiber grating can have a stop band of 10nm. These gratings are used in WDM system if the number of channels are small (<10). A 6-nm-bandwidth chirped grating was used for four-channel WDM systems (each channel operating at 40Gb/s) [37]. If the WDM-signal bandwidth is much larger then a cascaded chirped grating is used in series for dispersion compensation. Each channel reflects one channel and compensates its dispersion [38]- [42]. Advantage of this technique is that the grating is tailored to match the GVD of each channel. Cascaded grating scheme for four-channel WDM system is shown in figure below.

Figure:
Cascaded Grating used for dispersion compensation in WDM system [41].
Four grating compensates the GVD of all the channels and two optical amplifiers handles the losses. The use of multiple grating becomes difficult when number of channel increases and signal bandwidth becomes more than 30nm. This problem is solved by using FP filter. This filter compensates the GVD of all the channels if all the channels are spaced apart equally and free spectral range of the filter is matched to the channel spacing. But FP filters are not be designed with large amount of dispersion. This problem is solved by using Sampled Fiber Grating [43]- [45]. This grating has multiple stop band and is easy to fabricate. These fibers are used for simultaneous compensation of fiber dispersion 750 | P a g e w w w . i j c t o n l i n e . c o m over 240 km for two 10-Gb/s channels [43]. But if the number of channels increase then it becomes more difficult to compensate the GVD of all channel simultaneously. This problem is solved by using negative-slope dispersion compensating fibers. These fibers are used for dispersion management in highly capacity WDM system with large number of channels. A broadband DCFs was used to transmit a 1-Tb/s WDM signal ( total 101 channels and and each operating at 10Gb/s) over 9000 km [46]. The highest capacity of 11-Tb/s WDM signal ( total 273 channels and and each operating at 40Gb/s) is transmitted by using reverse-dispersion fibers [47].
b) Tunable Dispersion Compensation:-It is very difficult to achieve the full GVD compensation for all channels in a WDM system. A small amount of residual dispersion always remains there. Postcompensation technique is used to avoid the residual dispersion of each channel. But this technique cannot be used for commercial WDM system because of following reasons-1) Precise amount of residual dispersion is not known in practice (dispersion variations takes place along the fiber length).
2) Dyanamic variations can accur because of temperature fluctuations. Therefore tunable dispersion compensation technique is used.

Tunable Dispersion Compensation By Stretched Fiber Grating:-
In it dispersion is tuned by stretching a nonlinearly chirped grating. Grating is placed on a mechanical stretcher and a piezoelectric transducer is used to stretch it [48]. In a chirped grating group delay is given by    The equalizing filter eliminates the oscillatory tail and reduces pulse width to 2.8 ps. Residual increase in the pulse width takes place due to PMD.
Cascaded Chirped Fiber Gratings -A nonlinearly chirped fiber grating is used to compensate the third -order dispersion [50]. Cascading of two chirped grating compensates 3  without affecting 2  .
One of the chirped grating is flipped so that the combination provides no net dispersion.

Need for PMD Compensation-
Average pulse broadening for a link of length L is given by-

 
where P D is the PMD parameter. where N is the total number of taps,  is the delay time, m C is the tap weight for mth tap. Tap weight is adjusted in a dynamic fashion to improve the system performance [52]. Conclusion:-In this paper we have reviewed the various dispersion compensation techniques (schemes). The dispersion compensating fiber (DCF) removes the limitations of precompensation and postcompensation schemes. The limitations of DCF is removed by optical filter. Fiber Bragg Grating works as an optical filter. Fiber Bragg Grating has also certain limitations. And when FBG technique is compared with Optical Phase Conjugation technique then Optical Phase Conjugation techniques becomes the best technique to reduce the dispersion in optical communication system [54]. Therefore overall Optical Phase Conjugation technique is the best technique to reduce the dispersion in optical