FWM Suppression Techniques

The FW M process has been found to be a severe limitation to both single and multiple channel system s operating at or about the zero dispersion w avelength. Despite being the best location for a single channel to eliminate dispersion, the use o f optical amplifiers instead of regenerational repeaters and the addition of channels for increased capacity has m eant that the FW M effect is dom inant. To allow an increase in the num ber o f channels within such system s, yet keep the degradation due to FW M to a m inim um , som e m ethod of FW M suppression is required.

4 . 5 . 1 . 1 U n eq u al C h a n n e l S p acin g

The m ost effective suppression o f the effects of FW M is the use o f unequal channel spacing in WDM system s. First suggested by W aarts and Braun [16], and fully developed by Forghieri et al. [17] the method borrow s from a technique used in radio system s to reduce the effect intermodulation interference [18]. The principle behind the / technique is quite simple. Firstly consider a uniform frequency spaced WDM system , the FW M products within the system bandwidth will necessarily fall on the existing channels causing not only channel pow er depletion but an element of channel crosstalk. If the frequency separation of any tw o channels is assigned differently from any other pair of channels then no FW M products will be generated at any o f the original channel frequencies. The unequally spaced channels experience pow er depletion due to FW M but not channel crosstalk. Referring back to the schematic of Figure 2.6(b) o f Chapter 2, which show s the simple case of 3 unequally spaced channels - none of the 9 mixing products fall upon the original signal locations.

To assign channels to the appropriate unequally spaced frequencies the available optical bandw idth is first split into n- slots of width Af. With the condition that no tw o slot pairs can have the same difference value and that the minimum channel spacing Af^= nAf, the channel locations (slot num bers) are then found such that the total num ber o f slots is m inim ised to keep the required system bandwidth at a m inimum . The problem of finding the optim al channel locations has required an exhaustive com puter search [17] or, with the constraint that the total num ber of channels equals (p+1) where p is a prime num ber less than 37, by an algebraic m ethod [19]. In either case, a lower bound on the optimum bandw idth of the unequally spaced system can be simply obtained from the requirement that each channel is separated by at least n slots and have distinct slot num bers.

a

B. .. >

n Beq (4.4)

w here B^^=(N-J) Af^ is the optical bandw idth of an equally spaced W D M system [17]. After propagation through the fibre the optical filter/dem ultiplexer m ust be able to pass the

signal located at slot but reject any FW M pow er in the neighbouring slots. The

frequency stability o f the transmitted channels becomes important: with some frequency jitter present on the input signals the FW M power will experience frequency deviations up to three tim es as great, inferred from equation (2.39) and reasoned in [20], hence the slot size, Af, m ust be large enough such that the influence of any jitter is negligible. To attain this requirem ent the frequency stability should be on the order of Af/10 with A f > I B p. {Bp

the bit-rate) and the m inim um channel spacing of the order 105^. The resulting m inimum num ber o f slots betw een channels is 5 [17]. For a ten channel system the bandw idth needed is 1.8 tim es greater than an equally spaced system using these values and equation (4.4). Increasing the num ber of slots n within the system bandwidth w ould reduce the bandw idth factor but places tighter constraints on the frequency stability and filter characteristics (larger n for the same bandwidth gives smaller slot w idths). F or the conventional configuration the num ber of mixing products landing upon the existing frequencies reaches 30 (by the m ethod given in Section 2.4.3.3) for the central channels w hereas none appear at channel locations with unequal spacings [21]. This is graphically illustrated in Figure 4.3 w here the arrows locate the channel positions.

35 30 25 o Q. O) 20 c ;>< 5 o 15 1 1 10 z Equal Spacing M I I I I f I I I 35 30 1 25 2 0. O) 20 .Ê :e 2 o 15 1 1 10 z Unequal Spacing 1---1---1---r . 1 1 : 1 t : t : t;.. . 1 1 -I : I 1000 Channel Frequency (GH z) (a) (b)

Figure 4.3 Number of mixing products generated by the FWM effect within the system bandwidth for (a) equally and (b) unequally spaced channels. The arrows point to the channel locations. From [21].

The same authors and co-workers subsequently experimentally dem onstrated the ability of

the technique to suppress the deleterious effects of FWM with the transm ission of 8

unequally spaced lOGb/s channels [22]. The slot size was set at 25G Hz and the minimum channel spacing was 125GHz (Inm ). The m axim um pow er budget was found to increase by a factor o f 5 (7dB) compared to the conventionally spaced system. This allows a higher SN R or greater distances to be achieved. The channel performance w as degraded at higher pow ers due to channel pow er depletion as the pow er extracted to create the FW M products became significant. More recent experimental results successfully transmitted 10 unequally spaced lOGb/s channels over 1200km of D SF using a slightly narrow er slot size o f 20Ghz [23], but with the same minimum num ber o f slots between any tw o channels, 5, i.e. Af^= lOOGHz. In the former experiment, as a com parison, the total system bandw idth was kept constant for both equal and unequal channels spacing - and still the unequal channel spacing out-performed the conventional system (with larger channel spacing). The latter experiment had a system bandw idth o f 13nm taking advantage of the w ider and flatter bandwidth available from the particular E D F A ’s used.

This highly effective method of reducing the impact of FW M is very useful in fibre systems where FW M is the dominant nonlinearity, i.e. in D SF with the WDM channels located near the zero dispersion wavelength. For a given system bandw idth (due to, say, amplifier constraints) the bandwidth expansion factor can be reduced if the minimum num ber of slots between channels is increased (slot size reduced). The trade-off being that the frequency stability of the channels m ust be higher and the filters/demultiplexers narrower. If devices with such improved performance are feasible then for a large num ber of channels, a large number o f slots is desirable, see equation (4.1). For a small number of channels a larger bandwidth expansion may be acceptable in return for less stringent criteria on the stability and filter performance (lower minimum slot num ber). These considerations make the prospect of utilising unequal spacing more profitable. It m ust be borne in mind that the expansion o f bandwidth will also affect the degree to w hich the system is influenced by SRS. From the expression for total pow er-bandw idth, equation (2.57), it is straightforward to find that doubling the system bandw idth will result in halving the limit of maximum allowable pow er per channel.