Four Wave Mixing in Silicon Photonics - Optical Signal Processing by Silicon Photonics - page 99

processes, depending on whether the second-order susceptibility x (2), or the third-
order susceptibility x (3), is responsible for them.
If irradiance is high enough, vibrations at all frequencies corresponding to all
energy differences between populated states, are produced (Fig. 8.1 ).
Because χ (2) vanishes for an isotropic medium (in the dipole approximation),
the second-order processes such as second-harmonic generation should not occur
in silica fibers. Normally they do occur because of quadrupole and magnetic-
dipole effects but with relatively low conversion efficiency.
The third-order parametric processes involve nonlinear interaction among four
optical waves and include the phenomena such as FWM and third-harmonic gen-
eration [ 1 - 3 ]. The main features of FWM can be understood from the third-order
polarization term in the equation given below.
P NL = ε 0 χ ( 3 ) .EEE
where E is the electric field and P NL is the induced nonlinear polarization.
In general, FWM is polarization-dependent and considerable physical insight
is gained by first considering the scalar case in which all four fields are linearly
polarized along a principal axis of a birefringent fiber such that they maintain their
state of polarization.
Fig. 8.1 Schematic diagram
showing basis of four wave
mixing [ 3 ]