Ensambles en modelos paramétricos de vivienda

31

In the presence o f nonlinearity and dispersion a constant waveform can be self-modulated, a phenomenon known as modulation instability (MI), initially investigated by Hasegawa [HAS70]. In the region o f anomalous dispersion (D>0) M I has been shown to result in a break-up o f continuous wave (CW) pulses into a train o f ultrashort pulses. Fig. 2.11 shows the calculated PRBS waveform at lOGbit/s as a function o f distance for a link o f 100 exactly post-compensated spans o f 80km using low dispersion fibre (/?2= -Ips^/km). After 80 spans with 20mW launch power a fast oscillation is visible on the pulse on the right hand side increasing its magnitude in subsequent spans. At the same time the onset o f MI on the left pulse can be observed after «=100 spans. M I normally becomes relevant for long distances Z>5000km, however, this distance can be reduced to less than 500km in the presence o f ASE noise seeding the M I process [SAU97].

100 n=100 a.

20

0

Fig. 2.11 left; D istortion due to modulation instability (M l) as a function o f distance, n: num ber o f post­ com pensated spans, y02=-lps^/km, 10Gbit/s PRBS, N RZ format, 20m W launch power, no ASE, rig h t: oscillation due to MI after n=100

2.2.6 Solitons

There are two principal approaches to overcome the limitations due to nonlinearity and dispersion: in the first, which can be called ‘linear’, chromatic dispersion and fibre nonlinearity are considered to be detrimental factors while in the second the nonlinear and the dispersive effects are counterbalanced. Nonlinear effects can be used to improve the transmission characteristics o f optical communication systems resulting in nonlinearity- supported transmission. One important example is the use o f solitons in optical fibre initially predicted by Hasegawa and Tappert [HAS73]. Solitons describe a special solution o f the

Chapter 2: Theory o f optical fibre transmission 32

NLSE found using the inverse scattering method [TAY90]. For the first time, solitons were experimentally observed in optical fibre by M ollenauer in 1980 [MOL80] using a mode- locked laser at 1.5pm. In the case o f anomalous dispersion (D>0) SPM can compensate for the pulse broadening due to dispersion. Solitons maintain their pulse shape during transmission and are thus very attractive for long-haul transmission. The envelope amplitude o f the solitons is described by a hyperbolic secant

^ ( 0 , t) = ^ s e c h { t / r j (2.22) where the required peak power for the soliton is given by

f (2.23)

XT','

where Tfwhm describes the width o f the first order (fundamental) soliton pulse. Soliton transmission over a link o f standard fibre has been demonstrated [CHR93b] but this requires a high launch power, e.g. 27mW for 7i)=40ps and ,l=1550nm. This power level can be further reduced in DSF since, due to the reduced dispersion, less SPM induced chirp is needed to counteract the dispersive broadening. Pulses o f different shape evolve during transmission to a stable sech^ form. Solitons strictly exist only for œ=0. In the presence o f fibre loss the influence o f SPM reduces as the pulse propagates over the fibre and dispersion broadens the pulses. For narrow pulse width {Tfwhi^ Ips) dispersion-decreasing fibre (DDF) can be used which has a distance-dependent local dispersion following the loss profile o f the fibre [MOS97]. This allows to counteract pulse broadening by balancing dispersion and nonlinearity at all points along the fibre according to equation (2.23). Periodic amplification after each fibre span overcomes loss and, if a constant dispersion is used, results in stable pulses referred to as ‘average solitons’ [BL091]. For these pulses, SPM dominates at the beginning o f each span and GVD at the end offsets the effects o f nonlinearity.

A fundamental lim it to soliton transmission is ASE introduced by the EDFAs in the link resulting in small variations o f amplitude and phase o f the solitons. The amplitude fluctuation leads to variation in the pulse width according to (2.23) whilst the phase fluctuation leads to a random change o f the soliton frequency converted into timing jitter by the GVD. This effect introduces timing jitter known as Gordon-Haus jitter [GOR86]. It can be reduced by using optical filters to remove the ASE or periodic dispersion compensation creating dispersion managed (DM) solitons [DOR96, SUZ95]. Dispersion managed solitons were also transmitted with 8 W DM channels at 20Gbit/s over 4000km [MOR99]. The first implementation o f commercial fiber-optical networks based on DM soliton has recently been reported in [ROB98].

Chapter 2: Theory o f optical fibre transmission 33

For transmission o f soliton-like pulses it is necessary to use the retum-to-zero (RZ) format. RZ pulses have a well defined shape, independent o f the bit-pattem as shown schematically in Fig. 2.12. In contrast to the pattern-dependent pulse length found in NRZ systems, all RZ pulses are affected in the same way by nonlinearity and dispersion. However, for a given bit- rate, RZ pulses are shorter than the bit-period since they return to zero within each bit slot. At lOGbit/s the pulse width is typically lOOps for the isolated ‘one’ in NRZ and less than 5Ops in RZ. The transmission performance for RZ and NRZ has been compared in experiments [CAS99] and theory [ENN96, FOR97] by several authors. Recently, it was also shown that nonlinear effects such as intra-channel XPM (DCPM) and intra-channel FW M (IFWM) are relevant for single channel RZ transmission at 40Gbit/s [ESS99, KILOO]. This is due to the temporal overlap o f the chirped frequency components o f neighbouring RZ pulses during transmission over dispersive fibre. IFWM and IXPM between the different frequency components results in shadow pulses and jitter, respectively.

In this thesis, experiments investigating XPM distortion o f NRZ signals were used to analyse the transmission impairments due to nonlinearities (chapter 4 and 5) whilst RZ signals were used to investigate improved transmission by all-optical regeneration (chapter 6).

bit sequence

1 0 1 0 0 1 1 0 1 1 0 1 0 0 1 1 0 1

Chapter 2: Theory o f optical fibre transmission 34