Nonlinear Fiber Optics - 4 ed. Agrawal

7.5. Applications of XPM 253
Figure 7.10: Schematic of a fiber gyroscope. Light from a laser is coupled through a 50%
coupler to launch counterpropagating waves in a multiturn fiber loop. The rotation-induced
phase difference is measured through a phase-sensitive detector.
between the counterpropagating waves can change Δφ by ∼1×10 −6 rad if we use γ ≈
10 W −1 /km and L ∼ 100 m. This value typically corresponds to an equivalent rotation
rate of 0.1 ◦ per hour. For this reason, XPM severely limits the sensitivity of fiber
gyroscopes unless the power levels are controlled to within 10 nW.
Several schemes can be used to mitigate the XPM problem and improve the gyroscope
performance. In one scheme, the laser power is modulated before the counterpropagating
waves are launched inside a fiber loop [97]. Because of the time dependence
of optical fields, this case is analyzed by solving Eq. (7.5.1) with the appropriate
boundary conditions [101]. The results show that the effect of nonreciprocity is reduced
drastically if modulation frequency is chosen suitably. This can be understood
physically by noting that XPM occurs only if the two pulses overlap temporally. On
a more fundamental level, XPM-induced nonreciprocity results from interference between
the counterpropagating waves. Modulation reduces the coherence between the
counterpropagating waves, thereby reducing the effectiveness of such an interference.
Indeed, the same result can also be obtained by using broadband sources with a limited
coherence time [98]–[100]. Thermal sources or light-emitting diodes have been used
for this purpose [102].
Let us consider briefly the effect of XPM on optical bistability. Any nonlinear
medium placed inside a cavity can exhibit bistability [104], and optical fibers are no
exception. If a fiber-ring cavity is used for this purpose, optical bistability can occur
irrespective of whether the beam propagates in the clockwise or counterclockwise direction.
An interesting situation occurs when the optical beams are launched in both
directions. Because of the XPM-induced coupling between the counterpropagating
beams, the device acts as two coupled bistable systems and can exhibit many new
qualitative features [85]–[87]. Although optical bistability has been observed in the
case of unidirectional propagation in a fiber-ring cavity [88], the bidirectional case has
not attracted much attention.
The XPM interaction between two counterpropagating optical pulses is generally
quite weak and can be neglected in the case of ultrashort pulses. The reason can be
understood by noting that the XPM-induced phase shift decreases even for copropagating
pulses as the relative group-velocity difference increases [see Eq. (7.4.9)]. For
counterpropagating pulses the group-velocity mismatch is so large that the two pulses
have little time to interact with each other. Nonetheless, measurable effects can occur