Improving Signal Strength Through Higher-Order Dispersion And Phase Modulation for nCRZ Modulation

Improving Signal Strength Through Higher-Order Dispersion And Phase Modulation for nCRZ Modulation

*Rupanjali Banerjee, **Manjit Singh, ***Kuldeep Sharma

*M.Tech (ECE), R.I.E.T. Phagwara, **Asstt. Proff. M.Tech (ECE), GNDU (RC), ***Jalandhar,

***HOD M.Tech (ECE), R.I.E.T. Phagwara

Abstract

Fiber nonlinearity and dispersion are among those factors that play a significant role in degrading the performance of a system. Modulation format may be suggested as a way out in this regard whereby a signal can be transmitted over a long distance thereby improving the performance of a system. Considering one particular optical format that will help in this manner is a tough job to do. Thus it has inspired us to go deep through the root to study the various aspects of Wave-Division Multiplexing System (WDM) or more precisely Optical WDM (OWDM) or Dense WDM (DWDM). In this short version, we have analysed how the performance of an optical system changes when higher order dispersion effects are compensated along with phase modulation. Here based on our some results, we have graphically explained the impact of higher order dispersion on our modulation format. For different values of phase modulation, graphical representation shows a significant change in the signal strength of the system.

Keywords- nCRZ, RZ Modulation Format, GVD, SPM, SSMF.

1. Introduction

   With the emerging technology, the need for proper transmission of signal, without any disruption has effectively increased. [1] Now with the help of a phase modulator at the transmitter side, it has become almost

   possible to form a narrower signal spectrum of Return- to-Zero (RZ) pulses. Thus enabling the increment of spectral efficiency to a much higher level. With this effort it has also been observed that the nonlinear tolerance which plays an important role in signal transmission is increased to a great extent. The chirping of the RZ signal is realized by a phase modulation and the higher order harmonics are suppressed by significantly choosing an optimal value of the phase modulation index.[2], [3]. This makes the signal spectrum formed with only two side bands and a carrier component, which causes less spectral broadening of the signal. The Novel Chirped RZ (nCRZ) spectrum is narrower by a factor of 2 when compared to that of a conventional RZ signal, while the carrier peak possesses equal amplitude as the peaks of both side bands. Thus the nCRZ modulation has an increased dispersion tolerance and the signal form reduces Self- Phase Modulation-Group-Velocity Dispersion (SPM- GVD) impairment in Standard Single Mode Fiber (SSMF) based transmission systems when compared to RZ modulation. [4]. in this paper we have evaluated the effect on output electric field in the presence of higher order dispersion and for various values of phase modulation index. [5].

   1.1Basic Description of nCRZ Modulation

   The generation of alternate chirped RZ pulses can also be done by using a much more modified modulation format named Novel Chirped Modulation Format. By using a phase modulator at the transmitter end it is

   possible to achieve a much narrower signal spectrum of RZ pulses. This enhances to produce higher spectral efficiency and an increased nonlinear tolerance. [6] The light of the continuous wave (CW) pump is modulated externally in a LiNbO3 MZM with a RZ encoded electrical signal. The 40 GB/s RZ optical pulses are additionally phase-modulated in a phase modulator (PM). It is then driven by a sine-clock signal at half the

   bit-rate. [8] This leads to a spectral form which is

   due to dispersion as shown in figure 2. There are generally two sources of dispersion: [13]

   Material Dispersion is caused by the wavelength dependence of silicas refractive index. It comes from a frequency-dependent response of a material to waves. In single mode fiber amount of pulse spreading caused by material dispersion per unit length is given by [14]:-

   t

   compact in nature. It also provides a better

   m D

   ()

   (1.1)

   concentration of the signal spectrum around the wavelength of the carrier. Thus the signal spectrum

   L( ps / Km) m

   formed here is quite similar to that of alternate chirped

   Where, tm is material dispersion Dm

   is material

   RZ pulses but there lies significant differences between the two: the chirping of the RZ signal is realized by a phase modulation and the higher harmonics are suppressed by choosing an optimal value of phase modulation index. [9], [10]. This enables a signal spectrum with only two side bands and a carrier component that causes less broadening of the signal. Moreover in nCRZ, no additional optical filtering has to be at the transmitter side. [11], [12]. The basic description of this method is illustrated below with a block diagram as given in figure 1.

   dispersion parameter and L is fiber length, is spectral width of the source.

   Wave Guide Dispersion occurs because the light signal is guided by a structure i.e. optical fiber. It usually occurs when the speed of a wave in a waveguide like an optical fiber depends on its frequency for geometric reasons, independent of any frequency dependence of the materials from which it is constructed. The information pulse is distributed in core and cladding. The pulse spreading per unit length is given by [14]:-

   twg

   D ()

   L( ps / Km) wg

   (1.2)

   t

   Where wg is pulse broadening due to dispersion and

   Dwg

   is wave guide dispersion parameter L is the fiber

   length and

   is the spectral width of the source.

   Figure 1. Generation of 40 Gb/s nCRZ signal [8]

   1.2. Dispersion and its sources

   Dispersion may be defined as the phenomenon in which the phase velocity of a wave depends on its frequency or in other words, when the group velocity depends on the frequency. Dispersion is sometimes called as chromatic dispersion to emphasize on its wavelength dependent nature, or group velocity dispersion to emphasize on the importance of group velocity. Dispersion plays a very important role in the transmission of an optical signal. Pulse gets broadened

   Figure 2. Pulse broadening due to dispersion [15]

2. Analytical Dispersion of nCRZ Modulation The complex amplitude of the generated nCRZ pulses is given by: [8], [16], and [17]

   Here the values of F2, F3, and F4 are the higher order dispersion parameters

   EnCRZ

   PRZ

   exp i m sin2ft

   (2)

   F2

   2 L

   4 c

   (6)

   Here i is the current in amperes, m is the phase modulation index in radians, f is the clock frequency in GHz, t is the time period in seconds

   Is the second order dispersion term

   L 2 2 2

   To insert dispersion into equation number (2), we can multiply it with e jL

   F3 6 2c2

   2

   2

   (7)

   EnCRZ

   PRZ

   exp i msin2ft e jL

   Is the third order dispersion term

   (3) Similarly the value of F4

   can be taken as the fourth

   Propagation constant can be expanded in terms of

   order dispersion term

   Taylors series around 0 , then (3) can be written

   L 3

   3 3

   2 2

   as:

   d 1

   2 d

   F4 24 2 c3

   3

   6

   2 6

   (8)

   2

   2

   0 0 d 2 0 d2

   1

   3 d 1

   4

   4 d

   4 d

   …

   In order to simplify the equation (5)

   3

   3

   6 0 d3 24

   d

   0 d4

   (4)

   Let

   E

   E

   j P

   PRZ

   exp i msin2ft

   (9)

   Now as we know that

   is the group delay for

   d

   nCRZ

   2e

   RZ

   3e

   4e

   unit length and L denotes fiber length by putting the

   E jF2 t 2 F3 t3 jF4 t 4 …

   value of from equation in exp j L , we will get

   [10], [11], [12], and [17].

   (10)

   2 3 4

   EnCRZ j1 jF2 t 2 F3 t 3 jF4 t 4

   PRZ

   exp i msin2ft

   (5)

   2 e

   t 2 E2

   3

   , e

   , e

   t 3 E

   3 , and

   4 e

   t 4

   E 4 respectively.

   By using the above equation, (9) becomes

   4

   4

   4

   4

   E j P

   E jF2 E

   2 F3 E3

   E 2 cos2ft 2fE1 sin2ft

   E 2imf

   1

   1

   nCRZ

   RZ jF E

   …

   (11)

   3 2fE

   sin2ft 4 2 f 2 E cos2ft

   (16)

   Now, let us consider our original equation which is

   E 2 cos2ft 4fE1 sin2ft

   E3 2imf 4 2 f 2 E cos2ft

   given by

   EnCRZ

   PRZ

   exp i msin2ft

   To find the fourth order derivative, we get

   (17)

   3

   3

   2

   2

   It is now required to find up to fourth order derivative

   E cos2ft 2fE sin2ft

   of the above expression. From (10) it is clear that the

   2 2

   first order derivative is expressed as E1 , second order as E , third order as E and fourth order as E

   E 2imf 4fE2 sin 2ft 8 f E1 cos 2ft

   4 4 2 f 2 E cos2ft

   2 3 4 1

   respectively.

   8 3 f 3 E sin2ft

   (18)

   Since PRZ is a constant as well as a common term

   involved in all the derivatives expression, its value will be put at the expression of the fourth order derivative,

   i.e. E

   E 3 cos2ft 6fE2 sin2ft

   4 1

   4 1

   E 2imf 12 2 f 2 E cos2ft

   4 8 3 f 3 E sin2ft

   Now,

   E EnCRZ

   PRZ

   exp i msin2ft

   (12)

   Now putting PRZ in (18) we have

   (19)

   E 3 cos2ft 6fE2 sin2ft

   To find the first order derivative

   E 2imf P 12 2 f 2 E cos2ft

   4 RZ 1

   8 3 f 3 E sin2ft

   E1 expi msin2ft i m 2f cos2ft

   (13)

   (20)

   E1 i 2 m f E cos2ft

   (14)

   Putting the values of

   E2, E3 and

   E4 from (14), (16)

   and (18) in equation number (10) we have

   To find the second order derivative

   E2 2imf E1 cos2ft 2fE sin2ft

   (15)

   To find the third order derivative

   E

   2imf

   E1

   Using these values we have obtained the following dispersion parameters using equation (6), equation (7) and equation (8) respectively.

   3

   2 d 3

   jF2 cos2ft

   F 2 12.72( ps) L, F 3 0.00298( ps) L

   2fE

   d 4

   d3

   sin2ft

   F 4 5.32×105 ( ps)4 L .

   2imf

   d 4

   E

   E

   2

   cos2ft

   The modified mathematical relationship for the nCRZ modulation format in the presence of higher order

   dispersion terms is given in equation (21). Accordingly

   3

   3

   F 4fE

   1

   we have visualized the effect of higher-order dispersion compensation that has led to a quantitative change in

   sin2ft

   the strength of the signal with the signal distance

   EnCRZ j

   PRZ

   4 2 f

   2 E

   covered, as shown in the following figure (3). To be

   cos2ft

   2imf

   3

   3

   E

   cos2ft

   2

   2

   6fE

   jF4 sin2ft

   more clear, the effect of higher-order dispersion has been considered individually in our results with F3=0, F4=0 and F4=0 in figure (4) and (5) respectively. It is realized that the signal strength is found to be improved when all of the higher order dispersion parameters are considered together, as shown in figure (6). The result is not limited to only higher order dispersion compensation but also shows the effect for different

   values of phase modulation on nCRZ. Here the signal

   12 2 f 2 E

   1

   strength is plotted against with phase modulation index m=1, m=2 and m=3 in figure (7), (8) and (9)

   cos 2ft

   8 3 f 3 E

   sin2ft

   (21)

   respectively. Effect of all the phase modulation index has been shown together in figure (10) where a steady curve depicts that the signal strength enhances with distance.

   This equation can be further simplified by putting the value of higher-order derivatives in detail. Putting the different values of all the constant terms used ( i, m, f,

   PRZ

   ) in equation number (21) we will plot our

   required graphs accordingly.

3. Results and Discussion

   Here we have assumed the wavelength 1.55m , change of group delay with respect to wavelength as

   20 ps / nm.km and L denotes fiber length [18].

   Figure 3. Signal Strength is plotted against distance with F2, F3 and F4

   Figure 4. Signal Strength is plotted against distance with F2, F3=0 and F4=0.

   Figure 5. Signal Strength is plotted against distance with F2, F3 and F4=0.

   Figure 6. Signal Strength is plotted against distance with higher-order dispersion.

   Figure 7. Signal Strength is plotted against distance with m=1.

   Figure 8. Signal Strength is plotted against distance with m=2.

   Figure 9. Signal Strength is plotted against distance with m=3.

   Figure 10. Signal Strength is plotted against distance with m=1, m=2 and m=3.

4. Conclusion

   The equation number (20) presents a modified relationship for the signal strength including the higher order dispersion effect and the phase modulation for optical nCRZ based communication system. At an

   operating wavelength of 1.55 m the effect of higher

   order dispersion has been evaluated. It has been observed from the graphical representation that the signal strength is enhanced when the higher order dispersion compensation is considered together. Here we have just added dispersion compensation and phase modulation in our existing model to find out the effect of these parameters on the signal. Also to find out how these factors helps in enhancing the strength of a signal when passed over a long distance. This method can also helps in cost saving in an OFC link. Thus after making a detailed comparison between the existing model and the modified model, we can conclude that signal strength can increase as well as improve if higher order dispersion compensaion and phase modulation are equally considered for that particular signal.

5. Future Scope

The results presented in this work can be used for the future research purpose in the following areas as mentioned below:

1. The work can be extended to study the impacts of other non linearitys like Four Wave Mixing (FWM),

   Self Phase Modulation (SPM) and Cross Phase Modulation (XPM) etc.

2. The results obtained in this paper also encourage the multimedia and personnel communication applications as it requires large bandwidth.

3. Due to the Polarization Mode Dispersion (PMD) impact of data transfer at higher bit rate proper choice of PMD coefficient influences the design of todays DWDM networks. So this work can be extended in this direction also.

4. This work can also be extended for use in WDM systems.

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