1.

Introduction

Today, as the bit rate and the transmission distance of optical fiber communication systems continue to increase, the signal distortion caused by polarization mode dispersion (PMD) in optical fiber channels is becoming a major limitation of system performance improvement. The use of optical PMD compensators (OPMDCs) is effective to reduce the system degrading effects caused by PMD.^{1, 2, 3} The design of OPMDCs is mainly based on launching the signal into the principal state of polarization (PSP) or a cascade of polarization controllers (PCs) and differential group delay (DGD) elements.^{1, 2, 3} PSP launch and the OPMDCs with one PC and one fixed or variable DGD element are typical first-order OPMDCs which can only compensate the PMD to first order.^{2, 3} A cascade of more than one PC and one fixed or variable DGD element compose typical higher-order OPMDCs which can compensate PMD to second order or even higher order.^{2, 3, 4} All the compensators mentioned above require feedback signals to control the PCs and the variable DGD segments. Especially for the typical higher-order OPMDCs, a very complex software algorithm for the feedback control must be used to correlate the several composed sections to achieve the optimum compensation effects.^{2, 3, 4} In fact the compensators always tend to get trapped in suboptima and cannot always ensure a better performance than the first-order OPMDCs.³

We demonstrate a new higher-order optical compensator to compensate first-order and higher-order PMD effectively. It just requires one more DGD element and one more PC compared with the first-order OPMDCs using adjustable DGD element.³ And the optimum working condition can be easier to track than the typical higher-order OPMDCs mentioned above. By an advised control method, the compensation scheme can always have better efficiency than the first-order optical compensators.

2.

Principle of the Proposed Higher-order Optical Compensator

2.1.

Proposed Higher-order OPMDC Model

The frequency-dependent PMD vector can be defined in terms of a Taylor expansion in angular frequency $\omega$ .² Second-order PMD is decided by the change of DGD with wavelength and the rotation of PSPs with frequency (PSP depolarization).² The frequency-dependent eigenvector of the transmission matrix of the PMD dominated fiber channel tends to process at a nearly constant PSP depolarization rate within a certain limited bandwidth.^{2, 5} Based on this theory, we propose the new higher-order OPMDC. The transmission matrix of the proposed compensator can be described by Jones matrix as:

$$U_{\mathit{com}}\left(\omega \right)=\left(\begin{array}{cc}\exp (-\frac{j\omega {\tau }_2}{2})& 0\\ 0& \exp \left(\frac{j\omega {\tau }_2}{2}\right)\end{array}\right)R_2^{-1}\left({\theta }_2\right)\left(\begin{array}{cc}\exp (-\frac{j\omega {\tau }_1}{2})& 0\\ 0& \exp \left(\frac{j\omega {\tau }_1}{2}\right)\end{array}\right)R_2\left({\theta }_2\right)R_1\left({\theta }_1\right),$$

where $\omega$ is the deviation from the central carrier angular frequency ${\omega }_0$ . The compensator is depicted in Fig. 1. This compensator has two adjustable DGD elements ${\tau }_1,{\tau }_2$ , which are both decided by PSP depolarization rate $p_{\omega }$ and DGD $\Delta \tau$ in the optical fiber channel. The relations are: ${\tau }_1={(p_{\omega }^2+\Delta {\tau }^2)}^{1∕2},{\tau }_2=p_{\omega }$ . $R_1\left({\theta }_1\right)$ is the transmission matrix of $PC1$ , which is used to transform the optical fiber channel output PSPs to linear polarization states. $R_2\left({\theta }_2\right)$ and $R_2^{-1}\left({\theta }_2\right)$ are transmission matrices of $PC2$ and $\overline{PC2}$ , which make opposite transformation. The control information of $\overline{PC2}$ can be completely obtained from the setting of $PC2$ . And ${\theta }_2=(1∕2)\mathrm{arctg}(p_{\omega }∕\Delta \tau )$ . The two delay sections both have a polarization splitter and a polarization combiner before and after the variable delay. The PMD vector of the proposed compensator realizes procession at the constant PSP depolarization rate. So the PSP depolarization caused by higher-order PMD can be compensated effectively within a certain bandwidth.^{2, 5}

Fig. 1

Sketch map of the proposed higher-order optical compensator.

3.

Efficiency Analysis of the Proposed Higher-order Compensator

The efficiency of our proposed higher-order optical compensator is proved by the comparison with the higher-order compensation scheme of Shtaif ⁶ which has the same degree of freedom (DOF) with the proposed compensation scheme but different design theory. Like our compensation scheme, the adjustable PCs and DGD elements of the referenced compensator are also related with each other to ensure a better performance than the first-order OPMDCs all the time.⁶ The Jones transmission matrix of the higher-order optical compensator of Shtaif is⁶:

Fig. 2

Outage probability as a function of input power penalty with the higher-order optical compensator of Shtaif (circles), with our proposed higher-order optical compensator (squares) and without compensation (triangles) for average $\mathrm{DGD}=10.2\mathrm{ps}$ . Outage: $\mathit{BER}>{10}^{-12}$ .

We also give the states of polarization (SOPs) variation of output optical signals on a Poincaré sphere without compensation and with first-order or the proposed higher-order PMD compensation in Fig. 3. Our aim is to qualify our proposed compensator’s capacity of reducing the PSP depolarization effects. The capacity is also an important quality for higher-order PMD compensators.^{2, 6} The bandwidth of simulated samples sweeps from $-40\text{to}40\mathrm{GHz}$ supposing that ${\omega }_0=0$ . In order to keep the comparison fair and creditable, here the first-order compensator with adjustable DGD element³ just matches the fiber channel PMD at the carrier frequency, and the parameters setting of the proposed higher-order compensator is unchanged. We set the power splitting of the launched input SOP $\gamma$ to be 0.5. Then first-order and higher-order PMD effects both lead to the pulse distortion. In Fig. 3, first-order and our proposed higher-order compensator can both work to improve the system performance. And our scheme is more effective to reduce depolarization effects caused by higher-order PMD effects. The SOPs of output signals compensated by the proposed compensation scheme (circles) nearly maintain the same place on the Poincaré sphere and this good result can be obtained from arbitrary optical fiber channel realization in our simulations.

Fig. 3

SOPs of output signals without compensation, with first-order compensator using adjustable DGD element,³ and with proposed higher-order compensator on Poincaré sphere.

4.

Conclusions

In this paper, a new optical compensation scheme for higher-order PMD effects is proposed. The control algorithm for this compensation scheme is easier and more stable than the commonly used higher-order optical compensators. And a control method is advised to ensure the proposed scheme provides better performance than the first-order compensation. The efficiency is proved by numerical calculations.