Interactions of Differential Phase-Shift Keying (DPSK) Dispersion-Managed (DM) Solitons Fiber Links with Lumped In-Line Filters

Transcription

1 MAYTEEVARUNYOO AND ROEKSABUTR: INTERACTIONS OF DIFFERENTIAL PHASE-SHIFT KEYING (DPSK) Interactions of Differential Phase-Shift Keying (DPSK) Dispersion-Managed (DM) Solitons Fiber Links with Lumped In-Line Filters Thawatchai Mayteevarunyoo, Non-member and Athikom Roeksabutr, Member ABSTRACT We formulate a model for investigating the transmission of date coded in the differential-phase-shiftkeying (DPSK) format by soliton streams in the model of the dispersion-managed (DM) fiber link with in-line filters. First, we consider the transmission of the simplest two- and three-soliton strings. Summarizing results of systematic simulations, we identify a range 1.55 S 1.95, which provides for the optimal transmission regime (which is defined as that in which the bit-error-rate, BER, is kept below an acceptable limit, for a fixed large transmission distance). 1. INTRODUCTION The differential phase-shift keying (DPSK) format of encoding data into a stream of return-to-zero (RZ) pulses has been known for a while. Recently, this format has attracted renewed interest, as it was demonstrated, theoretically [1] and experimentally [2], that it may be more efficient than the ordinary on-offkeying (OOK) format, in high-bit-rate long-haul and ultralong-haul transmission. The most promising and stable implementation of the RZ pulses is provided by solitons in dispersionmanaged (DM) fiber links [3]. It is well known that, while the DM technique provides for effective suppression of noise-induced jitter of solitons, and of cross-talk between them in adjacent channels in WDM (wavelength-division-multiplexed) schemes, the most serious issue complicating the implementation of the DM is the interaction between solitons inside a given channel [4]. This problem imposes an essential restriction on the DM scheme, suggesting to use its relatively weak version [5]. In this paper, we investigate the transmission of DPSK coded data by soliton streams in the model of the DM fiber link with lumped in-line filters. We first considered elementary two- and three-soliton strings. It will be concluded that a relatively small value of the DM strength S provides for the minimization of interaction effects in the presence of in-line filters (which is qualitatively similar to what was concluded, in other contexts, in Refs. [5]). EL5R4: Manuscript received on March 1, 24 ; revised on July 1, 24. The authors are with Department of Telecommunication Engineering, Mahanakorn University of Technology, Bangkok, 153, Thailand. athikom@mut.ac.th 2. THE MODEL We consider the system corresponding to the scheme shown in Fig. 1. The evolution of the en- D(z) D n D D a L amp L map D a : anomalous fiber D n : normal fiber Amplifier Fig.1: A schematic diagram of the dispersionmanaged link with in-line filters and amplifiers. velope amplitude u(z, t) of the electromagnetic field along the propagation distance z in one channel of the DM fiber link, with lumped filters and amplifiers, is governed by the well-known perturbed nonlinear Schrödinger equation. In dimensionless units, it takes the form [7] i u z + 1 ( ) 2 D (z) 2 u G t 2 + u 2 u = i 8.69 α 2 t 2 u. (1) where α and G are, respectively, the filter strength and an excess gain to compensate for the filter loss, which is measured in db. D (z) represents the periodically varying dispersion. 3. NUMERICAL RESULTS 3. 1 Two-soliton strings Proceeding to simulations, we first examine the effect of guiding filters on the interaction between two identical DM solitons with different values of the initial phase shifts between them ( θ =, π/4, π/2, 3π/4, and π), neglecting the ASE noise [n(z, t) = in Eq. (1)]. To this aim, we launch two chirp-free Gaussian pulses with the width t FWHM = ps and energies.2 pj (which correspond to the standard value of the fiber s nonlinearity, 1.4 W 1 km 1 ), Filter

2 5 ECTI TRANSACTIONS ON ELECTRICAL ENG., ELECTRONICS, AND COMMUNICATIONS VOL.2, NO.2 AUGUST 24 and the initial separation T = 45 ps (it corresponding to the bit rate of 22 Gb/s). To measure the strength of the interaction between the solitons, we first define the position of the center of a given pulse as t p = t u 2 dt u 2 dt. (2) The integration in this expression extends to the region that does not include the other pulse. Next, we define the collision length, as a propagation distance after which the temporal shift of each soliton, t t p t [t is the initial value of the position, as defined in Eq. (2)], see Fig. 2, exceeds half of its FWHM width = 217 GHz Initial soliton t 4 3 Shifted soliton 2 1 Fig.2: The definition of the soliton s shift induced by the interaction between them Figure 3 shows the collision length versus the DM map strength S, as found from direct simulations of Eq. (1) for different values of the filter s bandwidths. The excess gain is also varied, so that to keep the relation G/8.69 =.825 α. The comparison of the panels and in Fig. 3 clearly shows that, in the case of the in-phase solitons, there is a value, S 1.65, at which the collision length diverges, unless the filtering is too strong, while for the out-of-phase solitons such a single value of S cannot be identified. In other words, the interaction between the in-phase solitons effectively switches off at this value of S. As a further illustration of this property, in Fig. 4 we display the collision distance for the pair of in-phase solitons versus the filtering bandwidth for different fixed values of S. In practical terms, Fig. 3 shows that the collision length for the in-phase solitons exceeds 4, km, in the case of the weak DM, 1.2 S 2.1, (3) provided that sufficiently narrow-band guiding filters are used (while the interaction imposes a severe limit Fig.3: The collision length for the pair of in-phase and out-of-phase solitons as a function of the DM strength for different bandwidths of the guiding filters. on the transmission, distance, z < 3, km, in the absence of filters). It is relevant to mention that increase of the collision length for in-phase DM solitons in the presence of lumped narrow-bandwidth filters was earlier demonstrated in Ref. [6]. For the out-ofphase solitons with θ = π, Fig. 3 shows that, within the interval of 1.55 S 2 (4) [somewhat narrower than the one (3) for the in-phase soliton pair], the appropriately selected filters secure the collision length in excess of 4, km. The results of the simulations of the two-soliton string can be presented in a different way, convenient to applications, if one sets a condition that the propagation distance, after passing which the temporal shift of each soliton attains the size of t FWHM /4

3 MAYTEEVARUNYOO AND ROEKSABUTR: INTERACTIONS OF DIFFERENTIAL PHASE-SHIFT KEYING (DPSK) [htb] S = 1.1 S = 1.65 S = 2.52 GHz. Contrary to this, for θ = π the necessary restriction relaxes with the increase of S; however, as both cases of θ = and π are equally possible in the soliton stream, one must select the stringiest condition, i.e., narrowest filtering bandwidth for given S. Note that θ = and π determine one and the same in a small subinterval, 1.3 < S < 1.5. The above (GHz) 4 3 Fig.4: The collision length of the in-phase solitons as a function of the filter s bandwidth, for different map strengths. 2 1 (which is still quite acceptable), must exceed a certain large value, which we set to be 6, km (GHz) θ = θ = π/4 θ = π/2 θ = 3π/4 θ = π Fig.5: The filter s bandwidth,, which is necessary to keep the interaction-induced temporal shifts of the two solitons smaller than t FWHM /4 within the propagation distance of 6 km, vs. the DMmap strength S, for different values of phase difference, θ. In Fig. 5 we display the filter s bandwidths,, which is necessary to secure this condition, as a function of the DM map strength S, for different initial phase shifts θ. The curves terminate at points where the condition can no longer be met, therefore Fig. 5 also shows intervals of values of the map strength S within which the condition holds; as is seen, the interval is narrow for θ = π/2 and 3π/4, while for θ =, π/4, and π it is considerably wider. Notice that the nearly constant value of for θ = in the range of 1.3 < S < 2.16 complies with Fig. 3, where a virtually infinite collision length is observed in this range of S for the in-phase soliton pair, provided that the filtering bandwidth shrinks to Fig.6: The collision length for the three-soliton strings versus the DM map strength for different. The panels and pertain to the strings of the -- and -π- types, respectively. consideration was focused on the shift of the solitons positions due to the interaction. As the final objective is to analyze the stability of the DPSK coding scheme, it is also necessary to monitor the change of the phase difference between the solitons. Without showing details, which are of minor interest, we mention that, in all the cases, the perturbation-induced change of the phase difference remains definitely smaller than π/8 within the collision length defined above.

4 52 ECTI TRANSACTIONS ON ELECTRICAL ENG., ELECTRONICS, AND COMMUNICATIONS VOL.2, NO.2 AUGUST Three-soliton strings = 2 GHz θ = θ = π Power (mw) Time (ps) Distance π π π S = 1.1 S = 1.65 S = B (GHz) f Power (mw) Time (ps) Distance Fig.7: The collision length for the asymmetric threesoliton string of the π-- type versus the filter s bandwidth at different values of the map strength S. The next necessary step is to consider the transmission of three-soliton arrays, which may be, according to their relative-phase pattern, of three different types, --, -π-, and π--. Keeping the same definition of the collision length as introduced above for the two-soliton strings, in Fig. 6 we summarize results of systematic simulations of the three-soliton symmetric patterns, i.e., ones of the -- and -π- types. The figure shows the collision length as a function of the DM map strength for these two cases. Comparison of Figs. 4 and 2 makes it evident that the dependences for the -- and -π- three-soliton strings resemble those for the two-soliton strings of the - and -π types, respectively. For the asymmetric π-- three-soliton pattern, the results are summarized in Fig. 7, which shows, in the panel, the same characteristic, viz., the collision length vs. S, Fig.8: Typical examples of collisions in the asymmetric three-soliton string of the π-- type, at the optimum value of the DM map strength, S = 1.65, for two different values of the filter s bandwidth, = 256 GHz, and. In these two cases, either of the two substrings, - or π-, determines the collision distance. as in Fig. 6, and the panel displays the collision length as a function of the filter bandwidth for different fixed values of S. For the asymmetric string, we conclude that, as a matter of fact, the collision distance is determined by the intrinsic interaction between two solitons in either the - substring, or the π- one. In particular, the former and latter substrings play a dominant role in the cases, respectively, 265 GHz, and 186 GHz. In the intermediate case, around = 2 GHz, the - and π- pairs dominate, respectively, if S < 1.5 or S > 1.5. In Fig. 8, such two different situations are illustrated by typical examples (for S = 1.65, which was

5 MAYTEEVARUNYOO AND ROEKSABUTR: INTERACTIONS OF DIFFERENTIAL PHASE-SHIFT KEYING (DPSK) identified above as the optimum value of the DM strength), and the corresponding regions are separated by the vertical solid lines in Fig. 7. As well as in the case of the two-soliton strings, the interaction-induced changes of the phase differences between the solitons belonging to the three-soliton patterns remained negligible in all the cases studied, as along as the transmission length did not exceed the collision distance. 4. CONCLUSION In this work, we have investigated the transmission of DPSK coded data by soliton streams in the model of the DM fiber link with lumped in-line filters. We have first considered elementary two- and three-soliton strings. Eventually, we have identified a range of values of the DM map-strength S, which provides for the optimal transmission regime. Combining the results (3) and (4) obtained for the twosoliton strings, and the one for the three strings, we can identify the eventual safe-transmission interval as 1.55 S Athikom Roeksabutr graduated from King Mongkut s Institute of Technology, Ladkrabang, Bangkok, Thailand. He also got Master degree in the area of optoelectronics from Floride Institute of Technology, USA, and PhD in Optical Communication from University of New South Wales, Australia. He is currently an Associate Professor at the department of Telecommunication Engineering, Mahanakorn University of Technology, Bangkok, Thailand, where he is now surving as a Vice President and the Dean of Engineering. His research interest covers optical technology and communication sush as acoustooptic device, DWDM devices and system, nonlinear optics, fourier optics, optical image processing, etc. References [1] M. Hanna, H. Porte, J. P. Goedgebuer, and W. T. Rhodes, Electr. Lett. 37 (21) 644; J. Leibrich, C. Wree, and W. Rosenkranz, IEEE Phot. Tech. Lett. 14 (22) 155; M. Hanna, D. Boivin, P. A. Lacourt, and J. P. Goedgebuer, J. Opt. Soc. Am. 21 (24) 24. [2] C. Rasmussen, T. Fjelde, J. Bennike, F. H. Liu, S. Dey, B. Mikkelsen, P. Mamyshev, P. Serbe, P. van der Wagt, Y. Akasaka, D. Harris, D. Gapontsev, V. Ivshin, and Reeves-Hall, J. Lightwave Tech. 22 (24) 23. [3] A. Berntson, N. J. Doran, W. Forysiak, and J. H. B. Nijhof, Opt. Lett. 23 (1998) 9. [4] T. Yu, E. A. Golovchenko, A. N. Pilipetskii and C. R. Menyuk, Opt. Lett. 22 (1997) 793. [5] M. Wald, B. Malomed, and F. Lederer, Opt. Commun. 172 (1999) 31. [6] M. Matsumoto, H. Kurokawa, Y. Kodama, and A. Hasegawa, Opt. Commun. 155 (1998) 28. [7] E. Iannone, F. Matera, A. Mecozzi, and M. Settembre. Nonlinear Optical Communication Networks (John Wiley & Sons: New York, 1998). Thawatchai Mayteevarunyoo received the B.Eng degree in telecommunication engineering from Mahanakorn university of technology in 1995 and the M.S.Eng degree in optical communication from the University of New South Wales, sydney, Australia, in He is currently pursuring the Ph.D. degree from Mahanakorn university of technology, Bangkok, Thailand. His research interests are in nonlinear wave propagation, optical soliton comunication systems and Gap solitons.