Nonlinear Fiber Optics - 4 ed. Agrawal

416 Chapter 10. Four-Wave Mixing
Figure 10.23: Noise spectrum under minimum-noise conditions. Horizontal line shows the
quantum-noise level. Reduced noise around 45 and 55 MHz is a manifestation of squeezing in
optical fibers occurring as a result of FWM. (After Ref. [141]; c○1986 APS.)
the fiber in a liquid-helium bath. Indeed, a 12.5% reduction in the quantum-noise level
was observed in a 1986 experiment in which a 647-nm CW pump beam was propagated
through a 114-m-long fiber [141]. SBS was suppressed by modulating the pump beam
at 748 MHz, a frequency much larger than the Brillouin-gain bandwidth. Figure 10.23
shows the observed noise spectrum when the local oscillator phase is set to record the
minimum noise (two large peaks are due to guided acoustic waves). Squeezing occurs
in the spectral bands located around 45 and 55 MHz. During the 1990s, several
other types of squeezing was realized, even though FWM was not always the nonlinear
process employed [139].
Much attention has focused in recent years on optical sources that emit photon pairs
exhibiting quantum correlations because such photon pairs can be used for applications
related to quantum communication, quantum cryptography, and quantum computing
[142]–[152]. The nonlinear process of FWM occurring inside optical fibers provides a
simple way to generate correlated photon pairs within a single spatial mode. Although
one can employ the single-pump FOPA configuration in which a weak signal beam
is launched into the optical fiber with a strong pump, it is more practical to launch
the pump alone and employ the spontaneous FWM process to generate the correlated
signal and photons from quantum noise. In both cases, the correlated photons are
emitted at different frequencies satisfying the FWM condition ω 3 + ω 4 = 2ω 1 , where
ω 1 is the pump frequency. If it is desirable to have a source that emits correlated photon
pairs at the same frequency, one may employ the dual-pump configuration in which the
nondegenerate FWM process is used to produce the signal and idler photons such that
Eq. (10.1.7) is satisfied. When an optical filter centered at the mid frequency of the two
pumps is placed at the fiber output, the correlated photons have the same frequency
such that ω 3 = ω 4 = 1 2 (ω 1 + ω 2 ).
It was observed in several experiments that the quality of the photon-pair source