In recent years, the RZ-DPSK format has attracted much attention and become a promising format in long-haul high-speed optical communication systems [29] due to its superior sensitivity, higher nonlinear tolerance and higher spectral efficiency, compared with the traditional OOK format. However, because optical DPSK signal carries binary data on its phase domain, DPSK systems are limited by both AN and PN. Therefore, either PN or AN must be prevented from being accumulated to expand the reach of DPSK systems. Spectral inversion by phase conjugation [51][52] and post nonlinear phase-shift compensators [53][54] can reduce accumulated nonlinear PN. Although in-line filtering is a simple means of constraining PN by the stabilization of amplitude [55][56], in-line regenerators for DPSK signals are needed to manage either AN or PN and to further expand the transmission distance. Unfortunately, most of the all-optical regeneration schemes for the OOK format [15]-[17] are not suitable for the DPSK format, because these regenerators will distort its phase information. Phase-preserving amplitude regeneration has been proposed to reduce AN of DPSK signals but not to affect the phase of DPSK signals much [19][20]. While the amplitude of DPSK signals is managed by these phase-preserving regenerators, the nonlinear PN induced by nonlinear signal-noise beating can be reduced simultaneously [20]. However, existent PN will keep being accumulated due
independently, phase is a relative parameter. Hence, a reference beam is needed to identify and regenerate phase information. A PSA which requires a coherent reference beam can eliminate both AN and PN simultaneously [18]. Unfortunately, if such a phase-locked coherent beam can be obtained practically, coherent-detection BPSK signals would have been adopted, instead of direct-detection DPSK signals. Another approach is to convert a DPSK signal to OOK signals (DB and AMI), and then convert the amplitude information of these signals to the phase of a probe beam [57][58]. The PN is suppressed due to nonlinear phase-to-intensity conversion in a DI [57] or amplitude regeneration of OOK signals [58]. However, because the amplitude data of these OOK signals are the differential code of phase data of the DPSK signal, the regenerative DPSK signal carries different data from original DPSK signal, and this should be avoided by precoding the data at the transmitter. Additionally, while the number of this kind of regenerators in the transmission is n, the precoding times must be n + 1.
In fact, since the DPSK signals are demodulated by a DI, what influences received signals is differential PN, instead of PN itself. Consequently, not only reducing PN, but also increasing the correlation between PN of neighboring pulses can improve signal performance. In the following sections, a novel PNA which can average the PN of adjacent pulses will be introduced. Both decreasing PN and increasing the correlation of PN of adjacent bits can be achieved simultaneously by averaging PN. Furthermore, the effects of PN averaging on linear and nonlinear PN are also investigated.
4.2 Concept and realization of phase noise averaging
The function of a PNA is to average the PN of one bit with that of its adjacent bit.
Figure 4.1 presents a simple concept in the realization of a PNA. Based on an assumption
that all signals have a constant amplitude, E0, each bit of the DPSK signals can be represented as, En = snE0exp(jϑn), where sn = ±1 corresponds to a zero or π phase shift and ϑn is the PN of the n-th pulse. After one bit delay, if the logic of the delay data sequence can be modified to be equivalent to that of the original DPSK data, as shown in Fig. 4.1, then the sum of this modified signals and the original signals can be written as,
En0 = 2snE0cos
µϑn− ϑn−1 2
¶
× ejϑn+ϑn−12 . (4.1)
Therefore, the output field will have original information and contain averaged PN and minor AN converted from the differential PN. If ϑnand ϑn−1can be treated as independent noise with the same variance, σ2, from Eq. (4.1), the variance of the output PN, (ϑn+ ϑn−1)/2, is σ2/2. However, after demodulation via a DI, the received signals are influenced by the differential PN, ∆ϑn= ϑn− ϑn−1, not by the PN itself. Furthermore, the variance of the original differential PN is 2σ2, and the differential PN becomes (ϑn − ϑn−2)/2 with the variance of σ2/2 after this PNA is applied. Accordingly, the PNA can increase the correlation between the PN of neighboring bits and reduce the differential PN. The assumption of uncorrelated PN is not always correct for nonlinear PN, although linear PN of neighboring pulses caused by ASE noise can be treated as iid random variables.
Therefore, how the PN averaging affects PN and differential PN should be investigated after understanding the characteristics of various PN.
Moreover, since the PN after an ideal PNA can be also written as,
ϑ0n = 1 2
·µ1 0
¶ ϑn+
µ1 1
¶ ϑn−1
¸ ,
the PN passing through PNAs twice becomes,
- - - - -
: 0 phase shift : phase noise
Figure 4.1: Concept of a PNA
= 1
where the identity of binomial coefficients, ¡n+1
k
processing, the PN after N PNAs is,
ϑ(N )n = 1
showing the multiple PN averaging effect.
Before discussing the types of PN and their properties, how to realize a PNA will be given in the following in advance. Figure. 4.2 shows the setup of a PNA, which is made up by a PSA. Considering only a PSA, in which a coherent pump beam, Ep, and a signal beam, Es, are launched, the output field of the PSA is [18],
Es0 = ejφ0(Escos φnl− Epsin φnl) , (4.3)
R+ R E
pE
sE'
sFigure 4.2: Setup of a PNA where
φ0 = jαL
2 + γLeff(|Es|2+ |Ep|2)
2 , (4.4)
φnl = γLeff|Es||Ep| sin (φs− φp) ; (4.5)
γ is the nonlinear coefficient of the HNLF; α denotes the fiber loss; L is the fiber length;
Leff is the effective fiber length, and φs and φp are the phases of signal and pump beams, respectively. Eq. (4.3) clearly reveals that the weighting term of Ep can modify its logic information to be identical with the data of the signal beam. Hence, the basic idea of phase regeneration is let the pump power much larger than signal power, and the output field is approximately proportional to Epsin φnl, which implies the phase modulation of the coherent pump field is either 0 or π. Figure. 4.3 shows the results of Eq. (4.3), where
|Ep|2/|Es|2 = 13 dB and γL|Ep|2 = π/2, and it is obvious that the PSA works as a phase limiter.
The main difference between the proposed PNA and the conventional PSA is that a challenging phase-locking pump beam is not needed. The pump beam is replaced
−1 −0.5 0 0.5 1
−30
−20
−10 0