Further analysis will focus upon the -/+D SF scheme (negative follow ed by positive GV D fibre) and in particular the initial distance within such a fibre link where the eye-opening penalty first decreases, i.e. is negative.
Num erical simulation of nonlinear fibre transm ission allows the use of hypothetical fibre param eter values to aid understanding o f the physical processes occurring within the fibre. The fibre dispersion param eter was therefore increased from 4ps/nm /km up to 100 ps/nm /km - unrealistic values of GVD for a D SF but helpful to understand the perform ance o f the D SF dispersion m anaged schem e. As previously dem onstrated in Figure 5.5 the am ount of eye-opening increased as the GV D was increased from 0.5 to 4 ps/nm /km . W hen increased beyond this value the EoP continued to fall reaching a m inim um near -1.5dB as the G V D magnitude approached 32ps/nm /km , show n in Figure 5.6 where = 6mW . Up to 16ps/nm /km the EoPs fall then rise sm oothly as a function o f distance w hereas for GVD values from 20 to 32 ps/nm /km the EoP at each span plots an evolves irregularly. distance (km) 800 200 400 600 1000 1200 1400 1600 0.00 -0.25 -0.50 Dispersion (ps/nm/km) -0.75 -1.00 K 32 -1.50
Figure 5.6 Negative EoP evolution with distance for the - / 4 - D S F configuration
with increasing dispersion, Pp^^^ = 6m W .
To try and quantify these observations the system will be exam ined in term s of the characteristic lengths of the system . The input pow er was set at 6m W in the above sim ulations which translates into a nonlinear length of = 77.0 km using equation (3.2) and at 10 Gb/s the dispersion length is given as = 1562.5/D^., where D^. is the GVD in
ps/nm/km. If the dispersion length is set to equal the nonlinear length the required dispersion is 20.3ps/nm/km. This corresponds to the GVD value at which the eye- opening penalty (a) reaches its minimum value, (b) is negative over the largest distance, 1450km and (c) gives the longest 3dB EoP distance. Figures 5.7 and 5.8 plot the 1 and 3 dB EoP distances and the maximum eye-opening against the ratio of dispersion length to nonlinear length, respectively. The maximum eye-opening was obtained over a range of
values o f close to but the longest 3dB distance was achieved when =
From Figure 5.8, the graph for fixed input power can be separated into two regions:
where the dispersion length is small (large dispersion) and dispersion dominates
the 3dB transmission distance which decreases as dispersion increases and where the
dispersion is small and the 3dB transmission distance reaches a limit of 2050km
as dispersion decreases. 2750 2250 1750 S 1250 750 250 a 0.1 4 -A.4" 'A* - - - A - - IdB distance - 3dB distance --- f— 1. 0 10. 0 VLNL(Ppeak=6mW) 1 0 0 . 0
Figure 5.7 1 and 3 dB FoP transmission distances versus the ratio of
dispersion to nonlinear lengths with = 6mW for various magnitudes of
10.00
.00
0.10
0.01
10.0 100.0
Figure 5.8 Maximum EoP versus ratio of dispersive to nonlinear lengths in
the -/+DSF configuration with 6mW for various magnitudes of
dispersion.
5 . 3 .3 D is c u s s io n
It has emerged from analysis that the position o f negative and positive GVD sections of DSF, or the dispersion map, in an amplified span plays an important role in the evolution o f the eye-opening penalty of an optical signal. By positioning the D SF with negative dispersion first in the span, immediately follow ing the am plifier, improved transm ission performance in terms of eye-opening penalty was achieved. Longer distances w ere reached compared to a span which had positive-then-negative dispersion when the absolute value o f the dispersion rose above 1 ps/nm /km . Below this value the benefit of G V D positioning was less significant.
The sign o f the dispersion has an important effect on the propagation of pulses in a nonlinear m edium . W ith positive (anom alous) dispersion the pulses can narrow leading to possible pulse break up w hereas in regions o f negative, or normal dispersion pulses will be excessively broadened, greater than the broadening from linear dispersion alone. In our D SF arrangem ent the first effective length o f fibre, = 14.5km {a = 0.21dB /km ) where the nonlinearity is m ost significant, is either of positive or negative dispersion. The amplified signal enters the first 25km o f fibre and becomes chirped due to the action of SPM and local dispersion. A fter 25km the pulses then enter the second fibre section with opposite sign o f GVD. In a linear medium the second order dispersion w ould be exactly com pensated at the end of each span, but the chirp im posed upon the pulses by SPM in first cannot be reversed by the SPM and dispersion further along the fibre because the
pow er level, and so nonlinear interaction, is lower. Thus at the end o f each span there is a residual pulse distortion which builds up with each span.
From the simulations results above it is apparent that positive followed by negative GVD fibre results in pulse distortions at the end of each span causing eye-closure, but with the dispersion map reversed (negative followed by positive GVD) the residual chirp translates into an initial pulse com pression, or eye-opening, until the build up of chirp is so great that the eye-penalty quickly increases. It appears that it is the dispersion sign o f the fibre at the end of the fibre span which determines w hether the eye opens or closes. This was found in the analysis in [2] where the dispersion of the final section o f fibre caused pulse com pression (final length was positive GVD) or broadening (final length w as negative GVD).
W ithin the -/+DSF configuration the dispersion or SPM dominate the pulse behaviour and channel performance. With large values of GVD it is dispersion which determines the 3dB eye-closure distance whereas for small values of GVD the nonlinearity sets this distance. N aka and Saito [3] first demonstrated the association o f the three characteristic lengths (nonlinear, second and third order dispersion lengths) to IdB eye-opening penalty transm ission distances for uncom pensated, nonlinear dispersive system s, obtaining a num ber o f simple relations between these lengths and the IdB transm ission distances depending on the regime (dispersive and/or nonlinear) in which the transm ission w as operating. They later examined compensated nonlinear system s [4], but took the com pensator to be a lumped element, with neither higher order dispersion nor nonlinearity and only considered the position of the com pensator to be at the end of each span or a num ber of spans. They found the channel distortion was minimised and transm ission distances maximised if com pensation occurred before every amplifier (denoted by 4-/-DSF in this analysis) and the transm ission limit approached that defined by the interaction of 2nd-order GVD (dispersion slope) and SPM. Similar behaviour is dem onstrated in the D SF system although not quantitatively the same. W hen the dispersion is small,
Li/Lj^j> \, the 3dB distance approaches the limit of 2050 km independent o f the value of GVD. U sing their formula for IdB transm ission length in this regim e,
gives Lj^g= 2510km which is double the value of 1500km obtained from the IdB curve in
F igure 5.8. The results differ since the com pensator forms part o f the transm ission fibre in the above system and the com pensator’s nonlinearity is accounted for.
In practice, fibre dispersion values for D SF lie within the range ±6ps/nm /km , encom passing the “non-zero Dispersion Shifted Fibre” (N Z-DSF) w hich has been developed recently [5]. The simulation with ±4ps/nm /km is a reasonable value for this
fibre and Figure 5.9 sum m arises its perform ance in terms of the 3dB E oP transm ission distances as a function o f input pow er (from Figure 5.3). (The 3dB distances were m easured to the span num ber at which the EoP became greater than 3dB, i.e. rounded to the nearest span length of 50km ). A pow er-curve-fit gives a simple relationship between the 3dB transm ission distance (km) and input pow er (mW):
L,„„= 1 1167 />-■ “ and L„,= 12196 P-0.99 (+/-DSF) (-/-hDSF) (5.1) (5.2)
indicating the greater distances that are obtained with the -/-t-DSE dispersion map. These expressions will be useful to compare against the two other dispersion management schem es w hich follow.
10000 Q 1000 ... ... -... ' . S ----- - L : ' .... "'1 L Dispersion of 4ps/nm/km: o +/-DSF # -/+DSF 1[ ■s. I >x J 3 4 Power (mW) 7 8 9 10
Figure 5.9 Comparison of 3dB EoP Transmission distance versus input in
the two DSF configurations with fitted curves (equations (5.1) and (5.2) in the text).