40 gbs and 4x40 gbs TDMWDM standard fiber transmission

2276 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 17, NO. 11, NOVEMBER 1999 40 Gb/s and 4 40 Gb/s TDM/WDM Standard Fiber Transmission C. M. Weinert, R. Ludwig, W. Pieper, H. G. Weber, D. Breuer, K. Petermann, and F. K¨uppers Abstract—We investigate the possibilities of 40 and 4 40 Gb/s time division multiplexing wavelength division multiplexing (TDM/WDM) return-to-zero (RZ) transmission over embedded standard single-mode fibers (SMF) at a transmission wavelength of 1.55 m both experimentally and theoretically. Dispersion of the SMF is compensated by a dispersion compensating fiber (DCF). Transmission over a span of 150 km of SMF in the single- channel case and of 100 km SMF in the multichannel case are reported. Numerical calculations are employed to investigate the possibility of cascading the spans both for single-channel and multichannel transmission. For single-channel transmission, it is shown that optimum performance is achieved with postcom- pensation of the DCF. The input power at the SMF and DCF input have to be chosen carefully. For four channel transmission, the performance is mainly limited by residual dispersion in the outermost wavelength channels. It is shown numerically that improvement is achieved by employing the newest type DCF which also compensates the dispersion slope of the SMF. For a WDM channel separation of 2 nm no significant additional degradation due to cross-phase modulation (XPM) or four-wave mixing is observed. Index Terms—Fiber transmission, optical communication, op- tical dispersion management, time division multiplexing (TDM) transmission, wavelength division multiplexing (WDM) transmis- sion. I. INTRODUCTION N EW challenges to modern telecommunications such as an expanded internet and broadband distributive and inter- active services demand for growing transmission capacities. Increasing the bandwidth can be either done by providing more channels in a wavelength division mutliplexing (WDM) system or by enhancing the bit rate of already existing channels using time division multiplexing (TDM) or by a combination of both. Capacity upgrading by TDM offers some advantages for network operators in view of economic efficiency. This is due to reduced network management efforts and because already installed single-band erbium-doped fiber amplifiers (EDFA’s) do not have to be replaced by broad-band amplifiers as used in the latest generation of WDM systems. Manuscript received February 16, 1999; revised July 19, 1999. C. M. Weinert, R. Ludwig, W. Pieper, and H. G. Weber are with Heinrich- Hertz-Institut f¨ur Nachrichtentechnik Berlin GmbH, Berlin D-10587 Germany (e-mail: weinert@hhi.de). D. Breuer and K. Petermann are with the Institut f¨ur Hochfrequen- ztechnik, Technische Universit ¨ at Berlin, Berlin D10587 Germany (e-mail: breuer@sun6hft.ee.TU-Berlin.de). F. K ¨ uppers is with Deutsche Telekom, Technologiezentrum Darmstadt D- 64307 Germany (e-mail: franko.kueppers@telekom.de). Publisher Item Identifier S 0733-8724(99)08023-8. Whereas 10 Gb/s TDM systems are already commercially available, even in WDM configurations with up to 32 channels, 40 Gb/s TDM transmission is still subject to research and development. A lot of work has already been done including impressive laboratory demonstrations like 40 Gb/s soliton transmission over 70 000 km in a dispersion shifted fiber (DSF) loop [1], 8 40 Gb/s [2] and 4 40 Gb/s [3] TDM/WDM transmission over standard single-mode fiber (SMF), and 30 40 Gb/s WDM transmission over 85 km of nonzero dispersion fiber (NZDF) [4]. In this work we will concentrate on transmission over SMF which is still the basis of most fiber optic networks all over the world. Fundamental investigations have demonstrated the useful- ness of SMF for single-channel 40 Gb/s transmission experi- mentally [5], also compared to DSF and NZDF [6]. Numerical [7] and theoretical [8] studies gave first ideas about the design of an appropriate passive dispersion management scheme for upgrading the existing SMF fiber basis. Also the choice of the appropriate modulation format [return-to-zero (RZ) instead of nonreturn-to-zero (NRZ)] has been clarified [9], [10]. The increasing interest of network operators in 40 Gb/s TDM transmission is demonstrated by recent field trials which have taken place in Japan (NTT) [11], [12] and Europe (British Telecom [13] and Deutsche Telekom [14]). In particular, the field trials of Deutsche Telekom focussed on practical problems a network operator will face when high speed optical systems are operated on a fiber base which was not intended for carrying 40 Gb/s single-channel signals when installed more than ten years ago. One problem is polarization mode dispersion (PMD) but system manufacturers have realized this and first solutions like an automatic PMD compensation in 40 Gb/s optical transmission systems are proposed [15]. The present state of 40 Gb/s SMF transmission (theory, numerical simulation, laboratory experiments and field trials for single-channel multispan transmission and first laboratory experiments for multichannel single-span transmission) let it appear advisable to do the next step forward toward mul- tichannel multispan transmission which will be investigated here based on our previous work. The focus will be on chromatic dispersion management schemes taking into account the newest types of dispersion compensating fibers. II. T HEORY Neglecting effects of polarization and scattering effects like stimulated Raman scattering and stimulated Brillouin scattering, propagation of optical pulses in fibers is described 0733–8724/99$10.00  1999 IEEE WEINERT et al.: 40 Gb/s AND 4 40 Gb/s TDM/WDM STANDARD FIBER TRANSMISSION 2277 by the scalar nonlinear Schr¨odinger’s equation (NLSE) for the complex pulse envelope A [16], [17] (1) with (2) and denotes the transformation to a frame of reference moving with the group velocity . The first two terms on the right-hand side of (1) describe chromatic dispersion. The dispersion parameters and result from expansion of ( ) around the center frequency and describe dispersion effects up to third order. Fiber dispersion is usually given by the dispersion and the dispersion slope . For high bitrate transmission chromatic dispersion is one of the main limiting factors because dispersion induced pulse broadening decreases the signal to noise ratio. The increase in pulse width can be estimated from the analytical expression of broadening of isolated Gaussian pulses which is also a good approximation for sech 2 pulses [16]. Since chromatic dispersion of the SMF is large at 1.55 m( ps(nmkm) 1 ) it is necessary to compensate dispersion. As discussed in Section I we will treat compensation schemes with DCF’s. The DCF has a negative and can therefore compensate the dispersion of the SMF. However, the particular DCF used in the transmission exper- iments (hereafter denoted DCF1) can only partly compensate the slope of dispersion . This means that zero dispersion can be achieved for one wavelength channel only whereas at other wavelength channels a residual dispersion remains. This residual dispersion severely limits the bandwidth of WDM transmission. Fiber loss is described by (given in dB/km) in the third term on the right hand side of (1). The last term on the right hand-side of (1) describes fiber nonlinearity. It is proportional to the pulse intensity. ,as defined in (2), is the nonlinear coefficient related to the nonlinear refractive index , the effective fiber core area , and the velocity of light . The nonlinear effects included in the NLSE are self-phase modulation (SPM), cross-phase modulation (XPM), and four-wave mixing (FWM). Single channel transmission is affected by SPM only whereas in multichannel transmission the combined effects of SPM, XPM, and FWM lead to signal degradation. Since SPM affects the optical wave via its interaction with chromatic dispersion partial cancellation of the nonlinear fiber degradation can be achieved by using appropriate dispersion schemes [18]. FWM, on the other hand, is expected to be negligible because the large dispersion value in each span prevents the phase matching condition which is necessary for FWM to become effective [17]. The NLSE will be solved numerically using the well known split-step fast Fourier transform (FFT) algorithm [16]. Simu- lations were done for a PRBS of length using sech 2 pulses of 4 ps FWHM. The amplifier noise was modeled as white noise created by a Gaussian random generator and added to the optical field amplitude at the output of each amplifier. TABLE I P ARAMETERS FOR THE SMF AND DCF USED FOR NUMERICAL SIMULATION OF THE EXPERIMENTS SMF DCF1 DCF2 Fiber attenuation (dB/km) 0.22 0.5 0.5 Dispersion D @ 1.551 m (ps/(km nm)) 16.4 –90.7 –100 Dispersion slope S @ 1.551 m (ps/(km nm 2 )) 0.06 –0.23 –0.34 Nonlinear refractive index ( /W) 2.6 2.6 2.6 Effective core area ( m 2 ) 80 30 30 The receiver was modeled by an optical filter with a measured bandwidth of 125 GHz for single-channel transmission and of 87.5 GHz for multichannel transmission. The photodiode is modeled as a square law detector followed by an electrical low pass filter. In Table I, we list the parameters for the fiber span including two different DCF’s. DCF1 was used in the experiment. DCF2 is a new fiber which became available very recently. Therefore it was only used in the numerical simulation. DCF2 nearly perfectly compensates both and . The calculated quantities which we compare with experi- ment, are the pulse width of the RZ pulses and the eye closure penalty. The pulse width is determined by averaging over the individual pulse widths of the bit sequence. The eye closure penalty is evaluated from the eye closure at the receiver for the complete transmission path as compared to back-to-back eye closure. III. E XPERIMENTAL A. Single-Channel 40 Gb/s Transmission The schematic of the experimental set-up is depicted in Fig. 1. The data transmitter comprises a tunable mode-locked laser, operating at 10 GHz repetition rate [19]. The pulse train is intensity modulated with a pseudorandom bit sequence (PRBS) of length or using an external modulator. The 10 Gb/s optical data signal is sequentially bit interleaved by a fiber delay-line multiplexer. In the multiplexer, the bit sequences were shifted against each other by bit periods ( = 2, 4) in order to ensure a PRBS, 40 Gb/s single-polarization (no polarization multiplexing) data signal. The pulsewidth of the transform-limited pulses is 4 ps with a sech 2 pulse shape. The 40 Gb/s signal is then transmitted over 150 km SMF. The overall link dispersion is compensated to zero for the signal wavelength of nm by using 27 km of DCF1 (see Table I). The DCF is placed either at the transmitter (precompensation) or at the receiver (postcompensation). The optical power launched into the DCF is always low (<5 dBm) to ensure operation in the linear transmission regime. At the receiver a SLALOM- based configuration is used as an optical demultiplexer [20]. Fig. 2 shows measured bit error rates for two word lengths and for the two different compensation schemes. An error- free transmission (BER = 10 9 ) was achieved with receiver sensitivities of 27 dBm for PRBS . For PRBS there was an additional penalty of 1 dB for both compensation schemes which we attributed to the system electronics. The measurements of the four TDM channels showed identical 2278 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 17, NO. 11, NOVEMBER 1999 Fig. 1. Experimental setup for transmission of one WDM channel. (a) (b) Fig. 2. Measured bit error rates for the transmission of one WDM channel. (a) Precompensation and (b) postcompensation. results. Therefore, in Fig. 2 only one channel is depicted. The receiver sensitivity in Fig. 3 refers to 40 Gb/s. The received power was measured at the end of the transmission line before the power was coupled either into the optical demultiplexer in the precompensation scheme or into the input of the postcompensation scheme. In the precompensation scheme the launched signal power into the SMF was 11 dBm. In the postcompensation scheme a signal power of 14 dBm Fig. 3. Bit error measurements using the postcompensation scheme in the one channel experiment. was launched into the fiber. In the following we describe measurements with PRBS = only in order to compare these results with calculations in the subsequent sections. Fig. 3 shows bit error ratio measurements with various optical input powers into the 150 km SMF in the postcompensation scheme. Similar measurements were also performed in the precompensation scheme. From these results we evaluated the system penalty versus the input power, which is discussed and compared with theoretical results in Section IV. B. 4 40 Gb/s TDM/WDM Transmission The experimental setup is shown in Fig. 4. The four WDM channels to were generated by two modelocked semi- conductor lasers (FWHM 1.3 ps) and with the use of spectral slicing technique based on an arrayed waveguide grating (AWG). The AWG has a channel spacing of 2 nm and a FWHM of 0.9 nm. Using this technique, optical pulses (FWHM 4.0 ps) at four different wavelengths to with a wavelength spacing of 2 nm were obtained. The four pulse trains were coupled together into one intensity modulator (10 Gb/s, PRBS and ). Each of the four 10 Gb/s data signals was then multiplexed four times by the same fiber delay-line multiplexer as described in Section III-A. WEINERT et al.: 40 Gb/s AND 4 40 Gb/s TDM/WDM STANDARD FIBER TRANSMISSION 2279 Fig. 4. Experimental setup for transmission of four WDM channels. Fig. 5. Optical spectra of the four WDM channels each with 40 Gb/s. Also, the measured pulse widths at the input of the demultiplexer are shown. Finally, we obtained four 40 Gb/s OTDM single-polarization WDM channels at wavelengths to . All four WDM channels carry the same data pattern. Without dispersion, the interchannel interference would be maximum because the data then travel synchronously. The large local dispersion causes a walk-off between the pulses of different wavelength channels and thus the interchannel interaction is reduced and averaged out. We therefore expect no change when using nonidentical modulation in the WDM channels. The 4 40 Gb/s data signal was then transmitted over 100 km of SMF. The dispersion compensating fiber (17.5 km of DCF1) was placed at the receiver. Behind the DCF a tunable optical filter (FWHM 2 nm) was used to select one of the four 40 Gb/s WDM channels. Note, that no individual dispersion compensation of the WDM channels was applied. Fig. 5 shows the optical spectra of all four WDM channels at the output of the transmission line. The width (FWHM) of the optical pulses at the input of the demultiplexer (SLALOM) varied between 4.5 and 8 ps depending on how close a channel was with respect to the optimum wavelength for dispersion compensation. This optimum wavelength was chosen to be at about 1551 nm. A comparison of the measured pulse Fig. 6. Measured bit error rates for the four WDM channels. width with the calculated pulse broadening over the fiber span verified the total fiber dispersion and its slope. The selected channel was then demultiplexed in the time domain as already described in Fig. 1. The SLALOM demultiplexer has a small polarization dependence which may lead to reduced contrast ratio for separation of the different TDM channels. Therefore, for each WDM channel, polarization was adjusted for minimum BER before the BER curve was measured measurement. Fig. 6 shows the BER-measurements on each of the four WDM channels. The measurements of the four TDM channels showed identical results. Therefore, in Fig. 6 only one channel is depicted. The received power was measured at the output of the 100 km transmission line. The data presented were taken for a PRBS of length to allow for a comparison with simulations. However, the performance exhibited small dependence ( 1 dB) for pattern lengths up to similar to the results in Fig. 2. From the error ratio performance of the system, both before and after the transmission, we can see that the transmission penalty (BER 10 9 ) is about 3 dB. This penalty was attributed to the dependence of the demultiplexer on the pulse width. The demultiplexer had an optimum performance for pulse width less than 4 ps. Similar to the investigations in Section III-A, the penalty was investigated versus the optical power at the input of the SMF. As compared to single-channel transmission no additional penalty due to nonlinear effects was obtained for four channel transmission with a total fiber coupled input power up to 20 dBm. IV. N UMERICAL SIMULATION AND DISCUSSION A. Single-Channel Single-Span Transmission For the theoretical analysis the setup depicted in Fig. 1 was assumed. According to Fig. 1 the 40 Gb/s signal was transmitted over 150 km SMF. At the transmission wavelength of 1548 nm the accumulated SMF dispersion was completely compensated by the 27 km of DCF1 (see Table I) which was either placed at the receiver (postcompensation) or at the transmitter (precompensation). The input pulse width of the sech 2 pulses was 4.3 ps. In the numerical calculations a PRBS pattern of length was chosen to allow a comparison be- 2280 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 17, NO. 11, NOVEMBER 1999 Fig. 7. System penalty for 150-km SMF transmission against average fiber (SMF) input power for pre- and postcompensation scheme. tween the experimental and theoretical results. As shown in the experimental part it was verified that a pattern length of did not cause a significant change. Both compensation schemes pre- and postcompensation were investigated. Fig. 7 shows the penalty against the average fiber input power for the two different compensation schemes assuming complete dispersion compensation. For the experimental data the penalty was extracted from the BER curve for postcompensation as shown in Fig. 3 with respect to back-to-back for a BER of 10 9 . A similar BER extraction was used for precompensation. As shown in Fig. 7 a good agreement between experimental and theoretical data is achieved. An EDFA noise figure of 6 dB was assumed. At low fiber input powers, the system performance is hampered due to a low signal-to-noise ratio (SNR) and at high input powers, the system performance is degraded due to the increasing impact of nonlinear self-phase modulation. In the postcompensation scheme the system penalty increases strongly for fiber input powers exceeding 16 dBm, whereas in the precompensation scheme the penalty increases already at power levels exceeding 13 dBm. In the linear regime for low fiber input powers there is no difference between pre- and postcompensation. Fig. 8 shows the eye-diagrams for both compensation schemes after 150-km SMF transmission at an average fiber input power of 16 dBm. To show the principle difference of the two compensation schemes and to avoid burdening the interpretation by amplifier noise, we used the eye-diagrams of the theoretical study neglecting the amplifier noise. The eye-diagrams in Fig. 8 show that signal distortions in the precompensation scheme arise mainly due to strong bit- pattern dependent variations of the pulse peak power. In the postcompensation scheme, however, the signal distortions at 16 dBm are significantly lower and a penalty of about 2 dB is achieved. A mixed compensation scheme with 1/3 precompensation and 2/3 postcompensation and vice versa was also investigated. No improvement of a split compensation scheme was achieved in this case. Since for NZDF a significant difference in the spectra for pre- and postcompensation has already been observed [21] we also monitored the spectrum after 150 km SMF transmission for both transmission schemes. However, in contrast to NZDF the spectra were almost (a) (b) Fig. 8. Theoretical eye-diagrams after 150 km SMF fiber at 16 dBm for pre- and postcompensation. (a) Precompensation and (b) postcompensation. identical. We attribute this to the high local dispersion of the SMF. Due to the high chromatic dispersion of the SMF a large phase mismatch between the different frequency components occurs. This leads to a reduced influence of SPM in the SMF compared to the influence of SPM in the NZDF. The system behavior in the precompensation scheme may be explained as follows: in the precompensation scheme the data signal is at first transmitted over the DCF. Due to the reduced power in this fiber the signal is mainly affected by chromatic dispersion. This causes severe pattern dependent dispersive waveform distortions. If this signal is now launched into the SMF the nonlinearity in this fiber causes strong signal distortions of the already perturbed pattern. This leads to large variations in the peak power at the end of the transmission line. Simulation showed that these distortions are not caused by higher order dispersion ( ). To investigate the optimum compensation ratio and the dis- persion tolerance for 40 Gb/s RZ single-channel transmission Fig. 9 shows the penalty versus the residual link dispersion for SMF transmission for the postcompensation scheme for two different input powers. For both fiber input powers 10 and 16 dBm the optimal system performance occurred for complete dispersion compensation. The penalty shows a symmetrical behavior around zero average dispersion like in a linear transmission scheme indicating that at high power levels no optimization due to under-compensation is feasible. A similar WEINERT et al.: 40 Gb/s AND 4 40 Gb/s TDM/WDM STANDARD FIBER TRANSMISSION 2281 Fig. 9. Penalty against residual dispersion for 150 km SMF transmission for the postcompensation scheme for different fiber input powers. Fig. 10. Investigated compensation schemes for cascaded span transmission. behavior has been reported for RZ transmission at 10 Gb/s [9]. The dispersion tolerance for 1 dB penalty at an input power of 10 dBm is about 15 ps/nm corresponding to a SMF length of about 1 km. B. Single-Channel Cascaded Span Transmission To investigate the potential of cascading single-channel 40 Gb/s transmission over multiple spans we performed nu- merical calculations using different dispersion compensation schemes. In this study we considered a postcompensation, a symmetrical compensation, and an alternating compensation scheme as depicted in Fig. 10. Particularly for 10 Gb/s RZ transmission the symmetrical and alternating schemes showed superior performance compared to pure postcompensation [22]. Precompensation was not considered, since already in single-span transmission it was less effective than postcom- pensation. The amplifier spacing was reduced to 100 km. In all compensation schemes DCF1 was considered to be operated in the linear regime. Fig. 11 shows the calculated penalty against Fig. 11. Penalty after 300-km SMF transmission against fiber input power for post-, symmetrical, and alternating compensation scheme. the average fiber input power for the three compensation schemes for three spans corresponding to 300 km SMF. For low input power all schemes show almost identical behavior. The performance is limited by the amplified spontaneous emission noise. For higher input powers there is only a differ- ence of about 0.5 dB between the post- and the alternating- compensation scheme. The penalty is about 1.3 to 1.8 dB for a fiber input power of 12 dBm. In the symmetrical compensation scheme, however, the penalty increases significantly at power levels exceeding 9 dBm. The eye closes due to variation of the peak power like in the pure precompensation scheme in single- span transmission. We attribute the superior performance of the post- and alternating compensation scheme to the fact that in both compensation schemes the first fiber part is of SMF fiber (like in pure postcompensation), whereas in the symmetrical scheme the first fiber part is of DCF type (precompensation). C. Multichannel Cascaded Span 40 Gb/s Transmission We first show the calculated results for the 4 40 Gb/s transmission over 100 km of SMF with postcompensation by 17.5 km SMF [3]. In order to compare the measured results with experiment, we first look at the pulse broadening in the four channels at 1547, 1549, 1551, and 1553 nm which will be labeled channels 1, 2, 3, and 4, respectively. For the average SMF input power of 10 mW and using the values for the fiber nonlinearity and for the dispersion (DCF1) as given in Table I the calculated values of the pulse width (FWHM) are 8.5, 6.2, 4.5, and 6.2 ps, respectively, which compare very well with the measured pulse widths given in Fig. 6. For the calculation the dispersion zero was placed at 1551 nm. The eye-diagrams of the four channels are shown in Fig. 12. Because of the dispersion zero at 1551 nm channels 2 and 4 are very similar whereas channel 1 shows the largest eye closure penalty due to the large pulse broadening. The pulse broadening of the four channels are mainly due to residual dispersion. This can be shown by a simple estimate of pulse broadening of channel 1 which is 4nm away from the dispersion zero. Using the values given in Table I the sum of the residual dispersion in channel 1 amounts to ps/nm. Using the well known pulse broadening formula [16], the pulse broadens from 2282 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 17, NO. 11, NOVEMBER 1999 Fig. 12. Calculated eye-diagrams for channel 1 to 4 of the 4 40 Gb/s single-span transmission. The FWHM of the pulses averaged over the bits is given as parameter. to 8.8 ps at the end of the fiber span which is close to the measured pulse width. The effects of FWM were tested numerically by launching power into three channels only and monitoring the effect of FWM in the fourth channel. The simulations showed that no noticable FWM products appear in the fourth channel. This was expected because of the phase mismatch due to the dispersion map and because of large channel spacing. We also investigated possible signal degradation due to XPM numerically by comparing the eye-diagram of channel 2 of the 4 40 Gb/s system with the eye-diagram of a single channel at the same wavelength. We chose identical bit patterns and parallel polarization for all channels. The large local dispersion leads to a walk-off between pulses in different channels. Consequently we see no difference in XPM crosstalk if the bit strings are delayed or changed between the channels. Comparison of the average pulse width and the eye closure penalty showed no difference between the four channel and the single-channel case. In order to test the cascadability of 4 40 Gb/s transmission we perform numerical simulations of the repeated span with 100 km SMF postcompensated by 17.5 km DCF1. However, we now minimize residual dispersion in the outer wavelength channels by choosing the dispersion zero at 1549 nm and the four channels at 1546, 1548, 1550, and 1552 nm. In Fig. 13, we depict the eye-diagrams for the inner channel at 1548 nm and the outer channel at 1546 nm for one and three cascaded spans. The eye-diagrams of the channels at 1550 and 1552 nm are not shown since they are essentially the same as the ones at 1548 and 1546 nm, respectively. This reflects the symmetry with respect to the dispersion zero. From Fig. 13, it is seen that the outer channel 1 at 1546 nm shows the largest degradation. This degradation of the eye comes from pulse broadening which limits transmission to two or maximum three cascades. As seen from comparison (a) (b) Fig. 13. Calculated eye-diagrams for the 4 40 Gb/s transmission span cascaded one to four times: (a) for channel 1 at 1546 nm and (b) for channel 2 at 1548 nm. Fig. 14. Calculated eye closure penalty versus SMF input power for channel 1 (1546 nm) after three cascaded spans solid: line—compensation with DCF1 used in the single-span experiment, dashed line—compensation with DCF2, and dotted line—compensation with DCF1 plus individual channel dispersion compensation at the receiver. with the inner channel, this broadening is caused by the residual dispersion due to the imperfect compensation of the dispersion slope. In order to verify this, we show in Fig. 14 the calculated eye closure penalties for the outer channel 1 after 3 cascades with the experimentally used DCF1 (solid line) and for compensation with DCF2 (dashed line) which nearly completely compensates both and . It is found that both curves are similar in shape with a minimum in the range between 3–10 dBm per channel. However, the curve for the experimental DCF1 is shifted by about 3dB to higher penalty values compared to compensation by DCF2. It is also interesting to compare perfect dispersion com- pensation of DCF2 with the combined effects of incomplete WEINERT et al.: 40 Gb/s AND 4 40 Gb/s TDM/WDM STANDARD FIBER TRANSMISSION 2283 dispersion compensation with DCF1 plus individual dispersion compensation for each wavelength channel at the receiver. In Fig. 14 the dotted line depicts the calculated penalty of channel 1 after 3 cascaded spans of compensation with DCF1 plus compensation of the residual dispersion of this channel after the wavelength filter (e.g., by a suitable fiber grating). In the regime of low input power (linear behavior), both curves coincide whereas for an input power larger than 6 dBm the receiver compensation exhibits a slightly larger penalty. Note, however, that for three cascaded spans com- pensation of residual dispersion at the receiver is almost as good as perfect dispersion compensation with DCF2 in each span. As for the single-span transmission we investigated the effects of XPM and FWM. There are found minor pulse broad- ening effects due to XPM whereas FWM remains negligible. We also numerically investigated the effects of incomplete dispersion compensation by slight reduction of the DCF length (undercompensation). The channels which have to be im- proved are the outermost wavelength channels. Shortening the DCF in general improves the low wavelength channel but degrades the high wavelength channel. Therefore, no net improvement is achieved for multiwavelength channel transmission by undercompensation with the DCF. V. C ONCLUSION In conclusion, we reported recent achievements in fiber optic 40 Gb/s TDM/WDM transmission. Theory and results of numerical and experimental investigations were presented and discussed starting with a single-channel single-span (150 km SMF) configuration for which pre- and postcompensation schemes were compared with the result that postcompensation allows for higher input powers. The number of channels was increased to four with a channel spacing of 2 nm. For 100 km SMF no additional penalty compared to single-channel transmission could be observed. For single-channel multispan (3 100 km SMF) transmission the different compensa- tion schemes showed almost identical behavior at low signal power levels. For higher power levels post- and alternating compensation schemes showed superior system performance whereas pre- and symmetrical compensation suffers from the high nonlinear distortions in the DCF. Finally we investigated numerically a 4 40 Gb/s WDM/TDM transmission over 3 100 km SMF and found that system behavior is domi- nated by the residual chromatic dispersion of the individual WDM channels. Because of the residual chromatic disper- sion in the outer channels undercompensation schemes which are advantageous for single-channel transmission fail for the multichannel transmission. Nonlinear channel interaction like XPM and FWM were of minor importance which is due to the high local dispersion of a dispersion compensated SMF transmission line. Using the newest type of DCF which offers an appropriate dispersion slope to compensate for chromatic dispersion exactly over a broad wavelength range, every single channel of the WDM system behaves like a single-channel system with exact compensation. Similar good results for individual channel compensation at the end of the cascaded fiber span are predicted by numerical simulation . The results can be used to establish engineering rules and design tools for upgrading existing SMF based networks toward higher capacity. A CKNOWLEDGMENT The authors would like to thank Deutsche Telekom AG and the Bundesministerium f ¨ ur Bildung und Forschung for support of the work. The authors would also like to thank Lu- cent Technologies Denmark A/S for providing the dispersion compensating fiber (DCF2). R EFERENCES [1] K. Suzuki, H. 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VOL. 17, NO. 11, NOVEMBER 1999 40 Gb/s and 4 40 Gb/s TDM/WDM Standard Fiber Transmission C. M. Weinert, R. Ludwig, W. Pieper, H. G. Weber, D. Breuer, K. Petermann, and F. K¨uppers Abstract—We investigate. et al.: 40 Gb/s AND 4 40 Gb/s TDM/WDM STANDARD FIBER TRANSMISSION 2277 by the scalar nonlinear Schr¨odinger’s equation (NLSE) for the complex pulse envelope A [16], [17] (1) with (2) and denotes