Operaciones unitarias

In a linear system the dispersion com pensation can be placed anywhere within the fibre link, e.g. before the transm ission fibre, at the receiver or anywhere in between because the linear effect is additive and completely reversible (with the appropriate com pensator supplying the reverse amount of GVD and GVD slope). The intensity dependence o f the nonlinearity in lossy fibre means that any distortion of the optical pulses due to nonlinearity and the following interaction with dispersion along the fibre will not simply be reversed with a dispersion compensating element because the intensity level and therefore nonlinearity will have changed. The position o f the dispersion compensation may therefore influence a channel’s performance and with repeated am plified spans the location and length of the com pensation interval becomes important. If chosen incorrectly dispersion or nonlinearity may accumulate on the signal such that the original transmission is unrecoverable. The types o f com pensation schemes proposed and dem onstrated with regard to position and am ount of compensation with in a link are now discussed.

The amplified span length and the compensation interval are not necessarily equal. In [10] and [73] the compensation interval was o f the order of 1000km of D SF so that the amplifier spacing was necessarily smaller than the com pensation interval. In other D SF experiments the compensation length was equal to the amplifier span [36], [74]. Since D SF can have very small values of dispersion, ID^I < 1 ps/nm /km , the accumulation of dispersion is very low, becoming appreciable only after significant transm ission distances. The compensation interval could therefore encom pass many amplifier spans given the longer dispersion length. The utilisation of non-zero D SF (N Z-DSF) with higher dispersion, LD^I ~ 2-4ps/nm /km , requires greater consideration o f the compensation interval since the accumulating dispersion rises faster. W hen compensating SM F with DCF the compensation interval may need to be reduced to less than a few spans since the build-up o f dispersion within SM F is rapid.

-

[r

(a)

Tx - T ^ >7 ^MïyH ^ ^ - /dCfZ Rx

( ii) T^

-^^^^>VSMFj^CFy^ ^ ^

-/sMF^CFy^ ^ ^ ^

-

( iii) T , - -

(b)

Figure 4.4 Schematic displaying possible dispersion intervals for (a) pre- and (b) post- compensation: (i) per link (ii) per span (iii) before/after several spans.

The length of com pensation interval was exam ined in [75] com paring compensation (a) at the receiver (b) before every amplifier (i.e. per span) or (c) after several spans, see schem atic of Figure 4.4, with transmission fibre dispersion in the normal region ranging from -0 .1 to - 1 0 ps/nm/km (i.e. DSF). The performance o f a channel was assessed in term s o f the eye-opening penalty introduced by the same authors in a previous w ork [2]. W ith the compensation lumped at the receiver there was found to be an optimum range of com pensation, not necessarily 100% linear com pensation, which reduced as the transm ission distance increased. At 100% com pensation the IdB eye-penalty transm ission distances could be summarised as

^dB ~

H

(4.7)

for IDJ < lOps/nm/km, which is a factor 4.5 times larger than the same system w ithout com pensation given by equation (4.2), i.e. it is governed by the interaction o f SPM and GVD. Larger dispersion values were found not achieve distances beyond those given by equation (4.2).

If com pensated every span, 100% compensation was found to achieve the greatest transm ission distances and were governed by the interaction o f second order GVD and

SPM , proportional to given by equation (4.3). If over-com pensated, i.e.

positive dispersion accumulates, the eye-pattem (i.e. pulse behaviour) appeared as if the pulses were travelling through anomalous dispersion with the behaviour poorer as a result: the pulse shapes distorting in an irregular fashion rather than additional broadening associated with pulses in nonlinear fibre with negative dispersion.

The final scheme placed the compensator after several amplified spans of dispersive fibre. Tw o regimes become apparent: short compensation intervals, less than the dispersion length, L^, of the transm ission fibre, the transmission distances were governed by the interaction of 2""* order GVD and SPM and for longer com pensation intervals, greater than the dispersion length, L^, the transm ission distance was greatly reduced being inversely proportional to the compensation interval,

^ crit ~

/

(4-8)

Dividing these two regimes is a critical interval determined by the dispersion, dispersion slope and the power of the transmitted channel given as

(4.9)

Below the critical interval the best transm ission lengths given by equation (4.9) were achieved. Larger compensation intervals resulted in transm ission lengths given by equation (4.3).

Introducing noise in the form of ASE at each amplifier was found to have little effect upon the achievable IdB eye-closure distances for fibre dispersion greater than 3ps/nm/km because any interaction between signal and noise from FW M was strongly suppressed, and the eye was closed due to nonlinearity between the signals and imperfect dispersion com pensation.

The results give an indication of the processes governing dispersion compensated transm ission, specifically for normal dispersion D SF but are limited in application to

system s such as SM F which has high and anomalous dispersion. The second limitation w as their assum ption that the compensator is both a linear element, correcting all linear dispersion (including dispersion slope) and adds no loss to the fibre link or span. For D C F fibre the loss is significant at 0.6dB/km , has a larger nonlinear coefficient than the transm ission fibre due to it’s smaller effective area and may or may not com pensate for the transm ission fib re’s dispersion slope.