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First investigation of XPM: The work on XPM followed the discovery o f SPM in optical fibres [ST078]. As early as 1980 it was predicted that Raman spectra o f ultra-short pulses would be broadened by XPM [GER80]. The investigation o f the physical nature o f XPM involved the use o f ffee-space optics, and a fibre o f a few metres length represented the nonlinear medium. The first experimental confirmation o f the XPM effect in the time domain is reported in [CHR84] using 2 lasers at /l=1.54pm and 1.3pm with Im W coupled into 15m o f standard fibre. The wide wavelength spacing resulted in a significant w alk-off o f the 50ps- pulses o f over the short fibre. The phase shift was only qualitatively analysed using an interferometer. In [ISL87] this work was extended investigating the phase change as a function o f pulse walk-off. The nonlinear phase shift was also investigated in the spectral domain [ALF87]. This experiment used a single laser emitting modelocked pulses (25ps) at 532nm. In the 10m o f SSMF both Raman (appendix E) and XPM effects occurred. The Stokes pulse at longer wavelength broadened due to a combination o f Raman amplification

C hapter 3: Cross-phase m odulation - literature review 54 [THIOOb] XPM I M / D D s y s t e m s (section 3.3) C o h e r e n t s y s t e m s (section 3.2) D i s p e rs i o n c o m p e n s a t e d li nk s [ C H I 9 6 ] P um p-probe experim ents (section 3.4) An al y tic a l c a lc u la tio n s (ch ap ter 2) Ph y si ca l p r o p e rt i e s (section 3.1) T ransm ission experim ents (XPM penalty ) M u l t i - c h a n n e l [ M A R 9 1 ] , X P M in P S K s y s t e m [ N 0 R 9 1 ] , A S K s y s t e m s [ W A N 9 7 ]

In te n s ity d isto rtio n : F r e q u e n c y d o m a in [ B E L 9 8 , C A R 9 9 ] T im e d o m a in [ S H T 9 8 ]

Overview: Investigation o f cross-phase modulation (XPM)

First X P M e x p e r im e n t: [ C H R 8 4 ] , X P M a n d G V D : [ A G R 8 9 ] , X P M p u l s e c o m p r e s s i o n : [ S C H 8 7 ] , X P M sw it c h in g : [ U C H 9 8 ] , X P M w a v e l e n g t h co n v e rte r: [M 1 K 9 7 ], X P M i n N O L M : [ B L O 9 0 ] , X P M im p a c t o n sp e c t ru m : [ W A N 9 4 ] Firs t m e a s u r e m e n t [ R A P 9 7 ] , F r e q u e n c y r e s p o n s e o f X P M [H U 19 9], for N Z D S F [ S A U 9 7 ] , W a l k - o f f [SHTOO], R e s i d u a l d i s p e rs i o n , d ista n c e [THI991, F ie ld e x p e r i m e n t o v e r S S M F ITHIOOl, Bit-ra te , p u l s e sh a p e , AA, D ITHI981 M u l t i - c h a n n e l [ M A R 9 4 ] , X P M for p r e - a n d p o s t - c o m p e n - sa tio n [ H A Y 9 7 b , B I G 9 9 ] , C o m p a r i s o n X P M - F W M p e n a ltie s [ T E N 9 9 ] , X P M p e n a l t y for D S F [ K IK 9 6 ] , L o n g ha u l u s i n g D S F [P1L99], X P M r e s o n a n c e s [ N E L 9 9 ] , H ig h l a u n c h p o w e r [ O G A 9 6 ] , D i s t a n c e d e p e n d e n t F a b r y -P e r o t [M 1 K 9 9 ] , X P M s u p p r e s s i o n [ B E L 9 9 ] Fig.3.1 O v e r v i e w o f c h a p t e r st r u c t u r e , k e y r e fe r e n c e s for X P M a n d o w n c o n t r i b u t i o n s [ T H E . . ]

and additional XPM phase modulation induced by the fundamental pulse. This broadening was found to be larger than for the Raman effect alone. The total spectral broadening due to SPM and XPM was later measured with a high resolution diffraction grating and the results were compared with theory in [WAN94]. However, the peak power of the pulses was 2W and the fibre length of Im extremely short. Further experimental work on XPM is presented in [ALF86, WAN90, LOU91], using picosecond laser sources providing single pulses o f high peak power in the order o f watts. These measurements, even though at 1064nm outside the telecommunication windows, showed intensity variation of the spectrum due to XPM. In summary, at this early stage o f investigation XPM experiments were limited to short fibre length and high pulse powers o f the available lasers.

Theoretical work investigating the XPM effect started in 1984 with a paper of Chraplyvy et al. [CHR84b]. The magnitude o f phase noise due to SPM and XPM was calculated as a function o f power variation ct/>. The RMS phase fluctuation for SPM and XPM was shown to

Chapter 3: Cross-phase modulation - literature review 55

increase by a factor o f 2 for XPM. In this work the first investigation o f XPM as a function o f channel number was reported. An A/^-channel W DM system was considered and it was concluded that cr^ increases with VvV. However, the results for XPM phase noise were not related to intensity noise. The XPM phase noise was also analysed in [BL094] and the perturbation o f a coherent CW signal due to a co-propagating intensity m odulated pump was calculated. It was concluded that XPM phase noise increases the overall quantum noise in the system. However, these results were not experimentally verified.

XPM and GVD: The temporal and spectral phenomena based on XPM were systematically investigated in a fundamental paper by Agrawal [AGR89]. It was studied in simulations how GVD and nonlinearity affect single pulses both in the time and frequency domains. This work gave a significant contribution to the understanding o f the physical nature o f XPM providing analytical expressions and description o f phenomena resulting from the interaction o f XPM and dispersion. The paper is divided into 2 main parts: in the first part, the case o f low GVD was considered and the phase shift and shown in equation (2.18), was derived. XPM resulted in spectral broadening due to nonlinear chirp while the magnitude o f the broadening was shown to depend on the relative time delay between the 2 interacting pulses [ISL87]. In the second part, the interaction o f XPM and GVD was considered. GVD influences the XPM process via the walk-off and PM-IM conversion. As a result, the shape o f the probe pulse becomes asymmetric, broadens and develops internal structure. These features were discussed in separate papers in more detail and are discussed in the following paragraph. A pulse compression mechanism for low intensity probe pulses was also proposed. As there is negligible SPM affecting the probe the nonlinear chirp must be introduced by XPM. It is reported that by using pump pulses wider than the probe and by careful adjustment o f the relative delay linear chirp could be introduced on the probe necessary for GVD assisted pulse compression. Unlike the case o f solitons discussed in section 2.2.6 pulse compression could be extended into the normal dispersion regime.

XPM and pulse shape: M any effects originating from SPM and GVD were also observed for multi-channel operation where XPM and GVD interact, such as modulation instability (MI, section 2.2.5), solitary waves [TRI88], self-focusing [ALF89] and ultrashort pulse generation [KOR98]. The required nonlinear chirp for these effects was introduced by a second channel. Therefore, MI could be observed in the normal dispersion regime where no MI is observed in presence o f SPM alone [AGR89c]. Additional experiments investigated MI between 2 modes in a normally dispersive bimodal fibre [MIL97]. The relative walk-off between the lowest two modes is determined by the signal wavelength relative to Xq o f the fibre. A limitation o f this

Chapter 3: Cross-phase modulation - literature review 56

work was that in order to enable multimode operation the operating wavelength had to be in the visible region below the cut-off wavelength o f 790nm requiring several watts launch power. A more general description o f XPM between modes in an optical fibre is given in [BOA95]. The optical wave breaking due to GVD and XPM was investigated in [AGR89b]. It results in an oscillation o f the pulse intensity near the pulse edges due to interference o f chirp components. Unlike SPM-induced wave-breaking, it is only observed at one side due to asymmetry introduced by the channel walk-off. The nonlinear pulse compression discussed above was investigated in [SCH87], [JAS88] and subsequently in [SOU96] where a technique is described using XPM compression and Raman amplification. XPM -induced pulse compression was also observed between different pulse components o f a biréfringent fibre [ROT90, DRU90].

XPM switching: Optical switching taking advantage o f the XPM -induced phase shift has been shown for wavelength conversion, regeneration and demultiplexing. This area is potentially one o f the most important applications o f the XPM effect. The switching process can be achieved by wavelength shifting which is a result o f X PM chirp as investigated in several experiments and simulations [ALF89, FEL98]. It is possible to compensate Raman induced frequency shift by XPM chirp [SCH88] although this might not be practical for a large channel number. For short fibre with negligible SRS the wavelength shift o f the probe channel was investigated as a function o f delay between femto-second pulses in the pump and probe to demonstrate femto-second switching [BOY94]. XPM chirp between orthogonally polarised waves was used to generate a frequency modulated laser beam where XPM was induced by a copropagating intensity-modulated component in polarisation maintaining fibre [MAT97]. The advantage o f this all-optical modulation technique over EAM modulators is the high achievable pulse power o f a few kW and short duration which is only determined by the pump pulses. The XPM induced wavelength shift can also be used for wavelength routing where the intensity dependent transmission coefficient is a result o f XPM between the different pulse components in a biréfringent fibre [KIV93, RAM 97]. Recently, XPM-induced wavelength shift was used to demonstrate the error-free operation o f an OTDM-WDM converter based on a demultiplexer with multiple output channels (MOXIC) [UCH98]. A lOOGbit/s OTDM stream was demultiplexed using a train o f chirped clock pulses with each pulse linearly down-shifted in frequency. The clock pulse temporally overlaps with all data pulses o f a given OTDM bit-slot during propagation over 3km o f DSF. Therefore, each data channel introduces XPM at a given time compensating in this particular time slot the copropagating pre-chirped clock pulse. Due to the pre-chirp o f clock pulses this time slot corresponds to a unique wavelength.

Chapter 3: Cross-phase modulation - literature review 57

Another important application o f XPM-induced switching is the nonlinear optical loop mirror (NOLM) [DOR88] which can be used for demultiplexing and pulse format conversion [BLO90, LEE96]. In addition to optical fibres, the XPM effect was also studied in waveguides [FON97] and in semiconductor optical amplifiers (SOA). The phase shift due to XPM in SOAs is utilised in all-optical wavelength converters operating in a M ach-Zehnder interferometeric configuration [MAR95, LAC96]. The advantage over optical fibre are the high nonlinearity and small dimensions o f SOAs. Although slower than Kerr nonlinearities on optical fibre, operation up to 40Gbit/s has been demonstrated [MIK97]. All-optical regenerators based on XPM switching in SOAs are described separately in chapter 6.

In summary, the early experiments only investigated the physical nature o f XPM. This has led to the development o f key techniques using the XPM -induced nonlinearity, such as XPM- based optical switching. Theoretical work included the investigation o f pulses affected by XPM and dispersion and led to the study o f many XPM -related phenomena. However, the expected impairment to multiwavelength optical transmission had not been analysed.