Analysis of the intrachannel nonlinear effects in optical fiber communication systems Текст научной статьи по специальности «Электротехника, электронная техника, информационные технологии»

ANALYSIS OF THE INTRACHANNEL NONLINEAR EFFECTS IN OPTICAL FIBER COMMUNICATION SYSTEMS

DOI 10.24411/2072-8735-2018-10217

Eduard L. Portnov,

MTUCI, Moscow, Russia

Keywords: nonlinear effect, intrachannel cross-phase Rabenandrasana Jocelin, modulation, intrachannel four-wave mixing, chromatic

Toliara, Madagascar, [email protected] dispersion, input power.

Due to the growing demand in Telecommunications and Triple play services must to increase bandwidth and transmission rate. Optical Telecommunication Fiber is an excellence transmission medium through high bandwidth and its low loss. However, with increasing the transmission rate, nonlinear effects is one of the key limiting factors on the transmission of signals over an optical fiber, in particular the nonlinear Kerr effects, especially in the presence of chromatic dispersion and polarization mode dispersion. The importance of nonlinear effects depends on a large of fiber signal and system parameters. Nonlinear effects degrade signal quality as the launched signal power is increased. The article gives a detailed of analysis of intrachannel nonlinear effect such as intrachannel cross-phase modulation and intrachannel four-wave mixing. We used the nonlinear Schrodinger equation to understand the cause of intrachannel nonlinearity. And we proposed the method for the mitigation of these effects in optical transmission systems.

Information about authors:

Eduard L. Portnov, Associate professor of MTUCI, Moscow, Russia Rabenandrasana Jocelin, graduate student MTUCI, Toliara, Madagascar

Для цитирования:

Портнов Э.Л., Рабенандрасана Ж. Анализ внутриканальных нелинейных эффектов в волоконно-оптических системах передачи // T-Comm: Телекоммуникации и транспорт. 2019. Том 13. №1. С. 66-69.

For citation:

Portnov E.L., Rabenandrasana J. (2019). Analysis of the intrachannel nonlinear effects in optical fiber communication systems. T-Comm, vol. 13, no.1, pр. 66-69.

In optical fiber communication systems, linear impairments arc the liber loss, chromatic dispersion (CD) and polarization mode dispersion (PMD), The Kerr поп linearity and scattering effects are the main nonlinear impairments for optical communication systems. Unlike 10 Gb/s optical transmissions systems where the nonlinear effects are due to interchannel interactions in high-speed systems (at 40 Gb/s and above), the major nonlinear penalties because of intrachannel interactions such us inlraehannel cross-phase modulation (IX PM) and intrachannel four-wave mixing (IFWM) [ 1 ]. IXPM designates the phase modulation of one symbol proportionally to the power proiile of neighboring symbols. IFWM designates a power exchange between different symbols which occurs when three regularly-spaced frequencies from three difTerent symbols interact to generate energy at a four frequency, every lime all three frequencies coexist within the same small time slot [3], [5J.The importance of these effects increases when the signal rates increases as shown in Fig, 1. These effects occur due to the nonlinear interaction between overlapping ultra-short pulses (widths 25 ps and less) with the same channel. Intrachannel nonlinear effects lead to an increase of timing jitter, amplitude jitter and noise in the channel [2].

Modulation format (OOK)

—"v,-^

NRZ

RZ

Spectra) efficiency (bit/s/Hz) 0.025 0.1 0.4

ll M , рТГ

tn ll

2.5 10 40

Bit rate per channel (Gb/s)

160

Fig. 1, Significance of interchannel and intrachannel nonlinear impairments in WDM systems of different of per-ehannel bit-rates and OOK modulation for different types of optical fiber SSMF and NZDF [3]

To understand the cause of intrachannel nonlinearity, we use the nonlinear Schrodinger equation (NLSE) which describes the propagation of optical signal through the transmission medium

8z 2 dt 2 n 1

(1)

where Z is the propagation distance along the liber, relative time T = t-z/vy gives a frame of reference moving at the group velocity E(z,J) is the complex field amplitude of pulse, « ¡s the attenuation coefficient of the fiber, p, is the group velocity dispersion (GVD), y is the nonlinearity coefficient giving rise to Kerr effect nonlinearities, namely, self-phase modulation (SPM), cross-phase modulation (XPM), and four-wave mixing (FWM).

To study the interactions between pulses within the channel, the Held in the Eq. (1) can be decomposed as sum of L field of individual pulses

/=1

(2)

where где Е/ represents the fth pulse centered /=/;. NLSE Eq. (1) can be rewritten, after substitution excluding effect of the second-order ofGVD (Д), as 11 ], [4]

1 =<> £ VA-

ô2E,

и i & 2 ' 2dt2

(3)

iii-i

The different terms on the right-hand of Eq. (3) corresponds to various nonlinear intrachannel effects as follows. The case l~k = m corresponds to SPM, the case / - m &k or k = m I it is IXPM, and the case or l = k.± m we

have IFWM.

Assuming a sequence of only three pulses, such that E=EI+E1 + EJ, Eq. (3) reduces to the following coupled

NLSE:

(4)

(6)

дE, a

d2E,

—^ + -£•,+- Я —~ = iy

dz 2 3 2- a2

The first term on the right-hand side of Eqs. (4) - (6) represents the SPM, whereas the next two terms describe the modulation of the phase of a given pulse by the neighboring pulses, that is, the IXPM effect. The last term corresponds to IFWM.

hitrachanncl cross-phase modulation

IXPM is the phase modulation of pulse by another pulse the same channel |5J. To describe the fundamental characteristics of the IXPM, we consider two isolated bits, we neglect ( £", = 0 ) and we receive:

ô2E,

(8)

Obviously, as noted, the last term in the above equations describes IXPM. The consequence of this phenomenon leads to timing jitter as shown in (Fig. 2).

1-CiMS-piwe modulation oui of

twwerlawmg pulses .

' > I

Fig. 2. Intrachannel cross-phase modulation across one span [3, 6]

Intrachannel four-wave mixing

IFWM — designates a power exchange between symbols which occurs when three regularly-spaced frequencies from the different symbols interact to generate energy at a fourth frequency. This interaction leads to the appearance of pulse ghost and amplitude fluctuation.

J.Four-wave mil Ing oil ol

trree overlapping su fees

20 T

» SFM alone, low find h dûpinion ПЬrrf

- S I'M • IX"?M high dispersion Til]pr

- SPM+IXFM, Im» dfopersinn lïbti

Input |><".- ■ i | liBn.l

Fig. 4, Influence of SPM and IXPM on transmission systems with low and high dispersion libel's

SPM + IXPM

C^O—0 SFM + IFWM

2 16 [apuï pontr I (lBm I

2 4 6 Input po*t*r (dBm)

Fig. 5. Influence of IFWM on transmission systems with: a) low dispersion fiber and b) high dispersion fiber

When we take into consideration the influence of all effects, we see Fig. 5 that the nonlinear threshold of the transmission with high dispersion liber is weaker than of the transmission on low dispersion fiber. However, the IFWM is all the more penalizing as the dispersion is important

As observed, both IXPM and IFWM can have a significant impact on the performance of quasilinear systems, in particular, the change in Q-factor. As a consequence, it is more important to find possible methods for the mitigation of these effects.

The method for the minimization of the intrachannel effects

The magnitude of the IXPM can be reduced by controlling the relation between the pulse width, to, and the pulse separation, tB, which is equal to the inverse of the bit rate, R. Besides, the influence IXPM can be suppressed using a symmetric dispersion map. For more details on the symmetric dispersion map, the interested reader is referred [2,4J.

Both these effects (IXPM an IXPM) can be reduced considerably by chromatic pre-compensation optimization. Killcy has shown that Fq. (9) can be used to calculate the optimum span pre-compensation to minimize these effects.

CD

N*CD■ CD.

Fig. 3. Intrachannel four-wave mixing across one span

Below, we consider the result of simulation on the dependence of 0-factor on input power under influence of intrachannel nonlinearity with low and high dispersion fibers. Fig. 4 shows, when only SPM is simulated, there is almost no degradation due to non-linear effects at the power levels considered, regardless of the line liber taken into account. The degradations due to intrachannel nonlinear effects therefore come mainly from IXPM and IFWM [7]. The impact of IXPM is more important on low dispersion libers than on high dispersion fibers.

pre-DC M

In

a„

l+exp(-a0 L^j

(9>

where: CD

pre-DC'M

■ pre-compensation DCM value,ps/nm

CD - span residual dispersion,/js/ww

CDc - fiber dispersion coefficient,ps/(nmfon)

N — number of span, assuming all spans are the same length

L — fiber of span length, km

a., - fiber attenuation constant, km'1.

ft»-

Opt

Ri.

Fig. 6. A typical optical fiber transmission system TF = Transmission fiber, DCF = Dispersion compensation liber

And also, exists another method for the mitigation of nonlinear impairment, it is called digital back propagation (DBP), which the nonlinear Schrodinger equation is solved for a virtual fiber whose sings of dispersion, loss and nonlinear coefficients are opposite those of transmission fiber, for more details we can see in [4], section 11.

References

1. Djordjevie I.V. and Vasic B. (2006). Constrained coding Techniques for the suppressions of intrachannel Nonlinear Effects in Highspeed Optical Transmission. J, Liglmv. TechnoI., vol.24, no. I, pp. 411* 416, Jan. 2006.

2. Bob Chomycz. (2009/ Planning fiber optical fiber networks. M с ©raw-Hill.

3. Kaminow ¡.P., Li T., Willner A.E. (2008). Optical Fiber Telecommunications VB. Systems and Networks. N.Y.: Academic.

4. Ferre ira Mario F.S. (2011). Nonlinear effects in optical fibers. John Wiley & Sons. 1 loboken. New Jersey.

5. Shiva Kumar, M. Jamel Deen. (2014). Fiber optic communications. Fundamentals and Applications. John Wiley & Sons.

6. Portnov E.L. (2018). Fiber optics in telecommunications. Moscow: Hot line - Telecom. 392 p. (in Russian)

1. Mathieu !.. (2007). Stitch' of advanced technologies for optimization of optical transmissions systems multiplexed in wavelength at 40 Gb/s. Paris XI.

АНАЛИЗ ВНУТРИКАНАЛЬНЫХ НЕЛИНЕЙНЫХ ЭФФЕКТОВ В ВОЛОКОННО-ОПТИЧЕСКИХ СИСТЕМАХ ПЕРЕДАЧИ

Портнов Эдуард Львович, МТУСИ, Москва, Россия Рабенандрасана Жослен, г. Тулиара, Мадагаскар, [email protected]

Аннотация

Из-за роста потребностей в телекоммуникационных и мультисервисных услугах, необходимо увеличить полосу пропускания и скорость передачи. Оптическое волокно представляет собой превосходную среду передачи сигналов по оптическому волокну благодаря высокой полосой пропускания и низким потерям. Однако, при увеличении скорости передачи, нелинейные эффекты являются одним из ключевых ограничивающих факторов на передачу сигналов по оптическому волокну, в частности нелинейные эффекты керровского типа, тем более при наличии хроматической и поляризационной модовой дисперсий. Нелинейные эффекты ухудшают качество сигнала при увеличении вводимой мощности. В отличие от оптических систем передачи со скоростью 10 Гбит/с, где нелинейные эффекты обусловлены межканальными взаимодействиями в высокоскоростных системах передачи со скоростью 40 Гбит/с и выше, основные нелинейные эффекты вызваны внутриканальными взаимодействиями, такими как SPM, IXPM (внутриканальная фазовая кросс-модуляция), IFWM (внутриканальное четырехволновое). Рассматривается влияние IXPM и IFWM. Дается детальный анализ внутриканальных нелинейных эффектов, таких как внутриканальная кросс-фазовая модуляция (IXPM) и внутриканальное четырехволновое смешение (IFWM). Мы использовали нелинейное уравнение Шредингера (NLSE), чтобы понять причину внутриканальной нелинейности. И мы предложили метод уменьшения этих эффектов в волоконно-оптических системах передачи.

Ключевые слова: нелинейные эффекты, внутриканальная фазовая кросс-модуляция, внутриканальное четырехволновое смешение, хроматическая дисперсия, входная мощность.

Литература

1. Djordjevic I.V. and Vasic B. Constrained coding Techniques for the suppressions of intrachannel Nonlinear Effects in High-Speed Optical Transmission // J. Lightw. Technol. Mol.24, no. 1, pp. 411-416, Jan. 2006.

2. Bob Chomycz. Planning fiber optical fiber networks. Mc Graw-Hill. 2009.

3. Kaminow I.P., Li T., Willner A.E. Optical Fiber Telecommunications VB. Systems and Networks. N.Y.: Academic, 2008.

4. Ferreira Mario F.S. Nonlinear effects in optical fibers. John Wiley & Sons, Hoboken, New Jersey. 2011.

5. Shiva Kumar, M. Jamel Deen. Fiber optic communications. Fundamentals and Applications. John Wiley & Sons. 2014.

6. Портнов Э.Л. Волоконная оптика в телекоммуникациях. Учебное пособие для вызов / Под ред. Ю. Н. Чернышова. М.: Горячая линия - Телеком, 2018. 392 с.

7. Mathieu L. Etude de technologies avanc?es pour l'optimization des systems de transmission optique multiplex?s en longueur d'onde au d?but de 40 Gib/s. Paris XI, 2007.

Информация об авторах

Портнов Эдуард Львович, профессор МТУСИ, Москва, Россия Рабенандрасана Жослен, аспирант МТУСИ, г. Тулиара, Мадагаскар

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