The FWM efficiency may be measured in using a method similar to that presented in . Two tunable-wavelength laser sources, one “pump” and one “probe,” are launched into fiber in order to produce a third (degenerate) FWM signal at frequency fFWM = 2·fpump - fprobe (Fig. 1a).The probe is held at a fixed frequency while the pump is swept over the wavelength region of interest, resulting in a plot of FWM efficiency versus frequency. This process is repeated for multiple probe frequency values, with the resulting FWM efficiency plots averaged together for a composite picture of the FWM efficiency. As pointed out in , the generated FWM products can have local maxima when the pump wavelength is not equal to the fiber’s ZDW. By measuring the efficiencies at multiple probe wavelengths, the fact that a peak value will always occur at the ZDW is utilized, and the dependency on the particular probe wavelength chosen is averaged out.
Figure 1b shows that the sharpest peak in the FWM efficiency plot (red, left) corresponds precisely to the ZDW (blue, right) of the first 6 km spool in the long span. Accordingly, the second, third, and fourth highest peaks correspond well with the second, third, and fourth fiber spools in the span. Other peaks are indiscernible because signal powers are no longer high enough to generate FWM products (past the ~60 km mark), highlighting the need for a measurement technique which doesn’t average the dispersion over the entire length of the fiber.This is a compelling demonstration of the correlation existing between the ZDW of the different fiber segments, and the wavelengths and peak power of the degenerate FWM products. In a real network scenario, the distribution of ZDW shown above (blue, right) for the lab test example becomes the unknown, and therefore must be derived from the degenerate FWM spectra. This derivation is achieved with the inverse method described next.
The inverse-method calculation takes the experimentally-measured FWM data as an input and generates an equivalent distribution of ZDW values along the fiber length. The term “equivalent” is applied throughout because there can exist multiple ZDW distributions over fiber length which can yield the same FWM efficiency result. The physical distribution of the ZDWs is not as important as accurate modeling of the FWM efficiency of the span.
The experimental FWM efficiency spectrum represents the target, or “merit,” function which the search-and-optimization algorithm seeks to match. A merit function is defined as the absolute difference (or RMS value) between the target function and the calculated function. One example of a search-and-optimization routine well suited for such an application is Genetic Algorithm (GA), which can be easily implemented in e.g., MATLAB, although other search and optimization algorithms may be used.
This GA-based inverse method was run for the example given in Sec. 2 with the 112 km fiber. In the calculation of FWM products, the FWM model used in  was utilized, with the resultant degenerate FWM efficiency profile compared with the plot of FWM mixing efficiency from Fig. 1 as the basic merit function. The algorithm divided the fiber into n = 20 segments, and was seeded with an initial population of 1550.43 nm (i.e., the average measured ZDW for the full 112 km span) for all segments. The GA parameters were population size = 500, generations = 225, selection = 10%, crossover = 55%, and mutation = 35%. The set of ZDW values resulting from the optimization yields the FWM efficiency spectrum shown in Fig. 2a. The merit function was designed to emphasize matching the main “peaks” with lesser importance given to matching the regions of spectrum with low FWM efficiency.
This equivalent ZDW distribution may then be used as the fiber profile input to an S-USCA optimization tool. The tool employed here also utilizes the genetic algorithm to produce a channel plan with maximum capacity for a given channel count . By accounting for the equivalent distribution of ZDWs through the fiber, an increase in channel capacity can be realized when compared to the assumption of a single, averaged ZDW value that would be obtained from a typical in-field fiber characterization. Figure 2b depicts FWM-induced crosstalk for a per-channel launch power of -3 dBm versus number of channels for 2 cases: (1) S-USCA plan optimized for the correct equivalent ZDW distribution (○’s), and (2) one optimized using only an average ZDW value for the entire span (□’s). Supposing a system crosstalk tolerance level of -20 dB, under the assumption of a distributed ZDW (case 1), a maximum of 76 channels may be deployed. The simple assumption of an average ZDW (case 2) would in practice limit the system to 68 channels for the same level of crosstalk, and increases levels of crosstalk by as much as 4 dB above what was expected (in this case) for high channel counts. In general, penalties generated by using the wrong ZDW may be even higher depending on the specific differences in the ZDW assumed and the actual distribution of ZDWs.
the actual optimal placement of channels in the transmission band differs greatly once a distributed model of ZDWs is considered, additionally highlighting the need for a more sophisticated method of describing link dispersion than simple MPS dispersion measurement.
The work contained herein demonstrates a technique for characterizing an equivalent zero-dispersion wavelength (ZDW) distribution on fibers with ZDWs in the transmission band in order to maximize transmission capacity. The FWM efficiency of a span is measured, and an equivalent ZDW distribution is extracted from an inverse search-and-optimization numerical algorithm, which can be used to generate an S-USCA scheme for a given network. This technique may be combined with additional mitigation procedures (e.g., power pre-emphasis, Raman amplification) in order to further increase total capacity. More recent developments in high-coding gain forward error correction, electronic equalization, and coherent detection allow transmission at higher bit error ratios, up to 10-2 (SD-FEC). This, coupled with higher-order phase-modulated formats which generate less FWM than amplitude-keyed predecessors, enables significant increases in capacity when utilizing an S-USCA approach.
OFC/NFOEC: Measurement of Equivalent Zero-Dispersion Wavelength Distribution for…
Measurement of Equivalent Zero- Dispersion Wavelength Distribution for Capacity Increase in FWM-limited Networks Mark Filer and Sorin Tibuleac ADVA Optical Networking, Atlanta GA email@example.comOFC/NFOEC 2013, Anaheim CA (NW4E.4)