Nonlinear effects in fibre have become very important as transmission lengths, optical power levels, number of wavelengths and optical fibre data rates have increased. Intense electro- magnetic fields (light) produce nonlinear effects in any dielectric material. The waveguide
geometry that confines light to a small cross section over long fibre lengths makes nonlinear effects quite important in the design of modern communication systems which must be con- sidered in designing optical systems. Such effects include Stimulated Brillouin Scattering (SBS), Stimulated Raman Scattering (SRS), Four-Wave Mixing (FWM), Self-Phase Modu- lation (SPM), Cross-Phase Modulation (XPM) and Inter-Modulation mixing. All these non- linearities are important as they represent fundamental limiting mechanisms to the amount of data that can be transmitted on a single optical fibre.
The two most important parameters leading to fibre nonlinearities are the refractive in- dex of glass which is a function of the optical power passing through the material, and the effective area of the fibre core. The equation for the refractive index of the core in an optical fibre is [5, 7]: n= n0+ n2 P Ae f f (1.17) Where, n0 is the refractive index of the fibre core at low optical power levels, n2 is the nonlinear refractive index coefficient (2.6 × 10−20m2/W for silica fibre), P is the optical power, Ae f f is the effective area of the fibre core. The intensity dependence of the refractive
index is referred to as the Kerr-nonlinearity or Kerr-effect, which results in induced-phase shifts in the propagated signal, and hence spectral broadening.
The equation shows that by minimising the power, P, and maximising the effective area of the fibre, Ae f f, the nonlinearities introduced by the power dependence of the refractive
index are reduced.
• SBS occurs when a powerful light wave travels through a fibre and interacts with
phonons of the acoustic vibration modes in the glass. This causes a scattering mech- anism that reflects much of the light back to the source. SBS imposes an upper limit on the amount of optical power that can be usefully launched into an optical fibre. The SBS effect has a threshold optical power. When the SBS threshold is exceeded, a significant fraction of the transmitted light is redirected back toward the transmitter. This results in extra attenuation of the optical power reaching the receiver, as well as problems associated with the back reflection of the optical signal. The SBS process also introduces significant noise into the system, resulting in degraded bit error rate (BER) performance. Controlling SBS is particularly important in high-speed trans-
mission systems that employ external modulators and continuous wave (CW) laser sources. The precise threshold for the onset of the SBS effect depends on a number of system parameters including wavelength (the threshold is lower at 1550 nm than 1310 nm) and line-width of the transmitter. The SBS threshold increases proportionally as the optical sources or laser line-width increases. SBS is minimised by broadening the effective spectral width of the optical source [5, 7].
• SRS is a fibre nonlinearity similar to SBS while for SRS photons are scattered by
interaction with optical phonons, and SRS has a much higher threshold [5, 7]. This mechanism causes the transfer of power from shorter wavelength signals to longer wavelength signals. SRS is much less of a problem than SBS. Its threshold is nearly a thousand times higher than SBS. SRS is a third-order nonlinear effective susceptibility.
• FWM usually appears in fibre optic transmission systems that simultaneously carry
many wavelengths, such as DWDM systems [5, 7]. FWM is a third-order nonlinear ef- fective susceptibility , as is described with a X(3)coefficient. It can occur if at least two different frequency components propagate together in a nonlinear fibre. A refractive index modulation at the difference frequency occurs, which creates two additional fre- quency components. These cross products cause problems because they often fall near or on top of the desired signals. The magnitude of the FWM products is determined by the FWM mixing efficiency [46, 47] . Two factors strongly influence the FWM mixing efficiency. The first is the channel spacing. The mixing efficiency increases greatly as the channel spacing becomes smaller. The second factor is fibre dispersion, because the mixing efficiency is inversely proportional to the fibre dispersion, being strongest at the zero-dispersion point. In all cases, the FWM mixing efficiency is ex- pressed in dB, and more negative values are better since they indicate a lower mixing efficiency [1, 5, 34].
• SPM, like FWM, is due to the power dependency of the refractive index of the fibre
core. It interacts with the chromatic dispersion in the fibre to change the rate at which the pulse broadens as it travels down the fibre. SPM causes a frequency chirp on the rising and falling edges of an optical pulse. Increasing the fibre dispersion will increase the impact of SPM but will reduce the impact of FWM. XPM is very similar
to SPM, except that it involves two pulses of light, whereas SPM needs only one pulse. XPM causes multiple pulses travelling down the fibre to interact through their mutual effect on the refractive index of the fibre. XPM causes pulses to become distorted as they interact. Fibre designs with larger effective areas reduce XPM and all other fibre nonlinearities. Inter-modulation mixing is similar to XPM and SPM except that it causes new frequency components to appear that are cross-products of the original frequencies.