Four Wave Mixing (FWM)

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					Four Wave Mixing (FWM)
          Spring 2004 EE290F
                 Xiaoxue Zhao
Contents

Origin of FWM
Effect on WDM systems
Solutions
 Polarization Allocation
 Unequal Channel Spacing
 Dispersion Management
Origin of FWM [1]

Third order nonlinearity

             PNL   0  3   EEE

Energy Conservation
            4  1  2  3

Momentum Conservation—phase matching
             4  1   2   3
Origin of FWM—Phase Matching [2]
 Phase mismatch:
 k   F   k   i   j   2 i  k  j  k 
 FWM efficiency:
     1  exp[  ik L            k  1,  F  1
                               2

F 
            ik L                k  1,  F  0
 Coherencelength :
        2
 Lcoh                  L  Lcoh
        k m
Effects on WDM Systems [2]

Channel spacing and fiber dispersion are
 small enough
Effects on WDM Systems [3]
 Nonlinear Crosstalk

                        N channels f ijk  f i  f j  f k

                          N  N  1 mixing products
                        1 2
                        2


                            equally spacing,
                            product terms fall
                            at channel frequency
                            Coherent interference
Effects on WDM Systems [4]

Bit pattern




Power Depletion
Effects on WDM Systems—Solutions

Polarization Allocation
Unequal spacing
Dispersion management
Polarization Allocation [5]
Polarization Allocation [5]
Polarization Allocation [5]




   Add polarization filter at the receiver end
Unequal Channel Spacing [6]
Unequal Channel Spacing [6]
Dispersion-Management [4]

No dispersion-zero point
Total accumulated dispersion near zero
Dispersion Management [7]
Dispersion map for dispersion-
 compensating fiber (DCF)




Small core area
New Type of Fibers
Large effective area fiber
Nonzero dispersion shifted fiber (NZ-DSF)

                                          large-effective-area fiber (red)
                                           suppressed four-wave mixing
                                          crosstalk to -22.5 dB, compared to
                                           -19.0 dB for NZ-DSF
                                           fiber (blue).




http://www.corning.com/opticalfiber/products__services/reprints/r1083.asp
References
  [1] G.Agrawal “Nonlinear Fiber Optics”, 3rd edition
  [2] G Agrawal “Fiber-Optics Communication Systems” 3rd edition
  [3] Nori Sibata, Ralf Braun and Robert Waarts, IEEE J.
   Quantum Electron. QE23, 1205, 1987
  [4] Ivan Kaminow and Thomas Koch, OFT IIIA
  [5] C. Mahon, L. Olofsson, E. Bodtker, G. Jacobsen, IEEE
   Photon. Tech. Lett. 8,575, 1996
  [6] F. Forghieri, R. Tkach, A. Chroplyvy, J. Lightwave Tech, 13,
   889 1995
  [7] R. Tkach, R. Derosier and et. al, IEEE Photon. Tech. Lett. 7,
   1369, 1995

				
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