Optical Bit Error Rate

Chapter 2.18 - Four-Wave Mixing

2.18   FOUR-WAVE MIXING

Consider three optical frequencies, f1, f2, and f3 closely spaced (in frequency). Then,
from the interaction of the three, a fourth frequency is generated, ffwm, such that ffwm


Figure 2.18. When an optical channel operates above the zero-dispersion point, two side lobes are symmetrically generated, a phenomenon known as self-modulation or modulation instability.


Figure 2.19. Effect of excessive pulse widening on ISI and BER.


= f1 + f2 f2. This is known as four-wave mixing (FWM), or four-photon mixing
(Figure 2.20). FWM is a DWDM phenomenon.

The efficiency of FWM depends on:

  • Channel spacing
  • Power intensity of the contributing frequencies
  • Phase matching of the contributing channels
  • Chromatic dispersion of the fiber; because FWM performs best at the zero-
    dispersion wavelength, the operating point is preferably slightly above the
    zero-dispersion wavelength.
  • Refractive index
  • Fiber length
  • Higher-order polarization properties of the material (nonlinear Kerr coefficient)

Figure 2.20. Three adjacent optical frequencies, f1, f2, and f3, interact to produce a fourth frequency, ffwm, where ffwm = f1 + f2 – f3, known as four-wave mixing.


FWM may also occur with two signals at different wavelengths, if their intensity
and wavelengths are in a specific relationship. In such a case, the fiber refractive index
is modulated at the beat frequency of the two wavelengths. In this case, the
phase modulation creates two sidebands (at frequencies given by their difference)
but at a lower intensity.

FWM affects the signal-to-noise ratio and thus the bit error rate. The effects of
four-wave mixing on optical transmission and in single-mode fiber are manifested
as:

  • Cross talk, due to superposition of uncorrelated data from contributing channels;
    this is manifested as degradation of OSNR and OBER.
  • Signal-power depletion as a result of signal-power sharing among the contributing
    channels to the FWM generated channel.
  • Optical signal-to-noise degradation, due to superposition of noise and random
    data from the contributing frequencies.

As the signal input power of f1, f2, and f3 increases, or as the channel spacing decreases
(due to denser channels in the spectral band), the FWM term increases. ITU-T (G.663)
recommends that the critical optical power for FWM be greater than 10 mW, although
this depends on channel spacing. At 200 GHz channel spacing, it has been experimentally
verified that the FWM effect is drastically decreased as compared with 100 GHz or less
spacing.

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