Nonlinear Fiber Optics - 4 ed. Agrawal

412 Chapter 10. Four-Wave Mixing
mentioned, FOPAs can be employed for signal amplification, phase conjugation, and
wavelength conversion. In addition to these, FWM can be useful for applications such
as optical sampling, channel demultiplexing, pulse generation, and high-speed optical
switching [66]. It can also be used for reducing quantum noise through squeezing, and
for generating photon pairs that are quantum-correlated. This section focuses on a few
such applications.
10.6.1 Parametric Oscillators
Perhaps, the simplest application of the parametric gain is to use it for making a laser
by placing the fiber inside an optical cavity and pumping it with a single pump source.
Since no signal beam is launched, the signal and idler waves are created initially from
noise through spontaneous modulation instability (or FWM) at frequencies dictated by
the phase-matching condition; the two are subsequently amplified through stimulated
FWM. As a result, the laser emits the signal and idler beams simultaneously at frequencies
that are located symmetrically on opposite sides of the pump frequency. Such
lasers are called parametric oscillators; the term four-photon laser is also sometimes
used. They were made soon after FWM was realized inside an optical fiber. As early
as 1980, a parametric oscillator pumped at 1.06 μm exhibited a conversion efficiency
of 25% [112]. In a 1987 experiment [113], a parametric oscillator emitted 1.15-μm
pulses of about 65-ps duration when it was pumped with 100-ps pulses obtained from
a mode-locked, Q-switched, Nd:YAG laser. Synchronous pumping was realized by
adjusting the cavity length such that each laser pulse overlapped with the next pump
pulse after one round trip.
A new kind of parametric oscillator, called the modulation-instability laser can
be made by pumping optical fibers in the anomalous-dispersion region. As seen in
Section 10.3.2, modulation instability can be interpreted in terms of a FWM process
that is phase-matched by the SPM. Such a laser was first made in 1988 by pumping
a fiber-ring cavity (length ∼100 m) synchronously with a mode-locked color-center
laser (pulse width ∼10 ps) operating in the 1.5-μm wavelength region [114]. For a
250-m ring, the laser reached threshold at a peak pump power of 13.5 W. Such a laser
generated the signal and idler bands with a frequency shift of about 2 THz, a value
in agreement with the theory of Section 5.1. The use of vector modulation instability
(see Section 6.4) makes it possible to operate a parametric oscillator in the visible
region [115].
A modulation-instability laser is different from a conventional parametric oscillator
in the sense that it can convert a CW pump into a train of short optical pulses (rather
than generating a tunable CW signal). This objective was realized in 1999 by pumping
a 115-m-long ring cavity with a CW laser (a DFB fiber laser). The SBS process was
suppressed by modulating the pump phase. The laser reached threshold at a pump
power of about 80 mW and emitted a pulse train at the 58-GHz repetition rate when
pumped beyond its threshold [116]. The spectrum exhibited multiple peaks, separated
by 58 GHz, that were generated through a cascaded FWM process.
A parametric oscillator, tunable over a 40-nm range centered at the pump wavelength
of 1539 nm, was realized in a 1999 experiment [117]. This laser employed a
nonlinear Sagnac interferometer (with a loop length of 105 m) as a FOPA that was