Performance evaluation and analysis of four waves mixing in DWDM optical communications

Optical nonlinearities give rise to many ubiquitous effects in optical fibres ’. These effects are interesting in themselves and can be detrimental in optical communication. In the Dense Wave length division multiplexing system (DWDM) the nonlinear effects plays important role .DWDM system offers component reliability, system availability and system margin. DWDM system carries different channels. Hence power level carried by fiber increases which generates nonlinear effect such as SPM , XPM, SRS, SBS and FWM. Four wave mixing (FWM) is one of the most troubling issues. The FWM gives crosstalk in DWDM system whose channel spacing is narrow. Wavelength exchanging enables data swapping between two different wavelengths simultaneously. These phenomena have been used in many applications in Wavelength Division Multiplexing (WDM) optical networks such as, wavelength conversion, wavelength sampling, optical 3R, optical interconnects and optical add-drop multiplexing.

ii. INTRODUCTION FWM (Four Wave Mixing) or Four Photon Mixing (FPM) is the process whereby optical power from one channel in a multi-channel system is spilled over into adjacent channels.Three waves mix together to produce the fourth wave which may coincide with the original channel or may not be coinciding [1][2][3][4][5][6][7][8].
Equation (1) shows the formula for the generation of FWM interfering term.
Equation (2) shows the total no. of interfering terms.iii.

Effects of FWM
Four wave mixing (FWM) is one of the most troubling issues.Three signals combine to form a fourth spurious or mixing component, hence the name four waves mixing.Spurious components cause following problems [16][17][18][19][20]: Interference between wanted signal(cross) It generates additional noise and degrades system performance Power is lost from wanted signals into unwanted spurious signals FWM can be substantially reduced or perhaps completely eliminated through the following steps [18][19][20].In a multi wavelength system like DWDM, three waves mix together and produces the fourth wave given by Equation (3).

( )
Equ.3 [16] Where n is the refractive index λ & c are the wavelength and speed of the light respectively.
X is the electric susceptibility.
D is the degeneracy factor which is 3 for Two tone and 6 for Three tone mixing.
is the Four wave mixing efficiency (inversely proportional to Dispersion).

iv. FWM FOR EQUAL AND UNEQUAL CHANNEL SPACING
From Figure 2, it is inferred that when the inter channel spacing is equal means then the FWM power falls on the original signals such that it will induce crosstalk.To  The FWM effect is described as [12] : ( ) In order to fulfill the coupling conditions, the four frequencies must be commensurate in a manner of Combining three waves, a fourth wave can be generated and the four wave signals are written as [12]: Where is the slowly varying envelope amplitude of the optical field with frequency is the fiber loss coefficient and Depending on the state of polarization of the waves, the parameter C=2 for parallel polarization and C= 2/3 for orthogonal polarization.The propagation mismatch constant ( ) ( )

EFFECT OF DISPERSION ON FWM
The dispersion in the fiber produces the phase mismatch and hence the interfering terms may get reduced.The simulation of the layout in the optsim software gives the power of the FWM terms for various no. of channels [20][21][22].The dispersion in the fiber could be set from 0 ps/nm/km to any value [15,16,20 ].

vi. Minimization of FWM Effects
Traditional non-multiplexed systems have used dispersion shifted fiber at 1550nm to reduce chromatic dispersion.Unfortunately operating at the dispersion minimum increases the level of FWM.Conventional fiber (dispersion minimum at 1330 nm) suffers less from FWM but chromatic dispersion rises .Solution is to use "Non-Zero Dispersion Shifted Fiber" (NZ DSF), a compromise between DSF and conventional fiber (NDSF, Non-DSF).ITU-T standard is G.655 for non-zero dispersion shifted single mode fibers.By using unequal spacing between DWDM channels effect of FWM decreases [14][15][16][22][23][24][25].

viii. RSULTS AND DISCUSSION
By varying the dispersion from 0 to 4 ps/nm/km we observed effect of dispersion on FWM by Optisystem 7.And also effect equal and unequal spacing on FWM is observed.These effects are shown in following figs [15] .

ix. CONCLUSION
FWM leads to interchannel crosstalk in DWDM systems.It generates additional noise and degrades system performance.By using non zero dispersion shifted fiber i.e. fiber having 4 ps/nm/km and using unequal spacing among channels FWM effect can be reduced.As Unequal channel spacing could simultaneously reduce non linearities [FWM & SRS], it may result in better performance reduced BER arising out of more OSNR. x.


Newly formed FWM productsMay fall on the original signal (cannot be filtered out).May not fall on the original signal (can be filtered out).Spurious components are created, causing • Interference • Degradation of signals • Cross talkFour-wave mixing transfers' energy from a strong pump wave to two waves up shifted and downshifted in frequency from the pump frequency ω1[8][9][10][11][12][13][14].If only the pump wave is incident at the fibre, and the phase matching condition is satisfied, the Stokes and anti-Stokes waves at the frequencies ω3 and ω4 can be generated from noise.On the other hand, if a weak signal at ω3 is also launched into the fibre together with the pump, the signal is amplified while a new wave at ω4 is generated simultaneously.The gain responsible for such amplification is called the parametric gain[4,[12][13][14][15][16].
(a) Individual channel power reduction (b) Increased dispersion (Phase Mismatch) (c) Increased channel spacing.
avoid this, unequally spaced channels are used.Fabrizio (1995) has analysed the FWM for different bandwidth expansion factors and demonstrated the reduction in overlapping of interfering FWM terms with the original channels for the unequal channel spacing [16-20].

Fig. 4 :
Fig.4: The spectrum at the fiber end

Table 4 .
1 FWM Vs No. of Channels for the Dispersion of 0 ps/nm/km

Table 2 .
The Matlab programs are executed and the interfering terms are Table2.Comparison of Interfering Terms.The numbers inside the cells of the table are obtained by counting the coinciding terms for each channel from the results of execution of Matlab program.