300 CHAPTER 7. DISPERSION MANAGEMENT
a compact device by using semiconductor waveguides since the supermodes of two
coupled waveguides exhibit a large amount of GVD that is also tunable [80].
7.7 Optical Phase Conjugation
Although the use of optical phase conjugation (OPC) for dispersion compensation was
proposed in 1979 [81], it was only in 1993 that the OPC technique was implemented
experimentally; it has attracted considerable attention since then [82]–[103]. In con-
trast with other optical schemes discussed in this chapter, the OPC is a nonlinear optical
technique. This section describes the principle behind it and discusses its implementa-
tion in practical lightwave systems.
7.7.1 Principle of Operation
The simplest way to understand how OPC can compensate the GVD is to take the
complex conjugate of Eq. (7.1.3) and obtain
∂A∗
∂z−
iβ 2
2∂^2 A∗
∂t^2−
β 3
6∂^3 A∗
∂t^3= 0. (7.7.1)
A comparison of Eqs. (7.1.3) and (7.7.1) shows that the phase-conjugated fieldA∗prop-
agates with the sign reversed for the GVD parameterβ 2. This observation suggests im-
mediately that, if the optical field is phase-conjugated in the middle of the fiber link, the
dispersion acquired over the first half will be exactly compensated in the second-half
section of the link. Since theβ 3 term does not change sign on phase conjugation, OPC
cannot compensate for the third-order dispersion. In fact, it is easy to show, by keeping
the higher-order terms in the Taylor expansion in Eq. (2.4.4), that OPC compensates
for all even-order dispersion terms while leaving the odd-order terms unaffected.
The effectiveness of midspan OPC for dispersion compensation can also be verified
by using Eq. (7.1.4). The optical field just before OPC is obtained by usingz=L/ 2
in this equation. The propagation of the phase-conjugated fieldA∗in the second-half
section then yields
A∗(L,t)=1
2 π∫∞−∞A ̃∗
(
L
2
,ω)
exp(
i
4
β 2 Lω^2 −iωt)
dω, (7.7.2)whereA ̃∗(L/ 2 ,ω)is the Fourier transform ofA∗(L/ 2 ,t)and is given by
A ̃∗(L/ 2 ,ω)=A ̃∗( 0 ,−ω)exp(−iω^2 β 2 L/ 4 ). (7.7.3)By substituting Eq. (7.7.3) in Eq. (7.7.2), one finds thatA(L,t)=A∗( 0 ,t). Thus, except
for a phase reversal induced by the OPC, the input field is completely recovered, and
the pulse shape is restored to its input form. Since the signal spectrum after OPC
becomes the mirror image of the input spectrum, the OPC technique is also referred to
asmidspan spectral inversion.