21.3 QUANTUM THEORY OF FOUR-WAVE MIXING
IN OPTICAL FIBER
Four-wave mixing has long been studied, especially in the context of isotropic
materials, e.g., optical fibers [25, 32]. Generally speaking, it is a photon–photon
scattering process, during which two photons from a relatively high-intensity beam,
called pump, scatter through the third-order nonlinearity (
(3)
) of the material (silica
glass in the case of optical fibers) to generate two daughter photons, called signal
and idler photons, respectively. The frequencies of the daughter photons are
symmetrically displaced from the pump frequency, satisfying the energy conserva-
tion relation !
s
þ !
i
= 2!
p
,where!
j
( j = p, s, i) denotes the pump/signal/idler
frequency, respectively. They are predominan ...