1. Introduction

Polarization-mode dispersion (PMD) is one of the major limiting factors for high-speed optical communication systems [1–10]. PMD paralyses the OC-768 (40 Gb/s) and also highly degrades the OC-192 (10 Gb/s) over long fiber spans. In single-mode fiber, the polarization vector of the optical signal or pulse can be resolved into two mutually orthogonal components corresponding to the state of polarization (SOP) each called a polarization mode. Because of birefringence (though weak in fibers) these polarization modes travel at different group velocities along the fiber. The travel time difference Δτ between the two modes is called the differential group delay (DGD). In the first-order PMD, a linearly polarized input pulse has two components (SOP) along the two axes of the fiber (orthogonal to axis), called the principal states of polarization (PSPs). In first-order PMD the PSPs and DGD are independent of frequency, whereas the second- and higher-order effects are functions of frequency [1].

PMD in optical fiber arises from the modal birefringence caused by geometrical core deformation and external stresses. It is known to be a dynamic problem that changes with time, owing to different environmental factors such as temperature and stress [1]. PMD is a complex phenomenon, but fortunately its impairments become significant only in high-bit-rate signals at 10 Gb/s and beyond and in relatively long-haul transport. Its complexity is further compounded by frequency-dependent higher-order contributions. However, the dominant effects still come from the contributions of first-order effects, i.e., DGD. During the past 5 years, PMD has been investigated extensively by several researchers [2–5,11–12]. Various innovative solutions have been proposed and demonstrated, each having its merits and limitations.

A typical approach for the first-order PMD on a single channel involves a constant optical delay that can be added to the fast mode relative to the other component of polarization (slow mode) at the receiver side that mitigates or counterbalances the effects of the PMD of the fiber. It appears simple, but in reality it is very challenging because of its frequency dependence, time-, and path-varying nature. Introducing either a polarization-maintaining fiber (PMF) or a short-length high-birefringent crystal in front of the receiver could add the desired optical delay. However, this delay compensates for the first-order PMD only at the time at which the PMD is equal or close to the added delay in the compensator. When the PMD magnitude differs from the fixed delay added by the compensator, especially when the PMD is very low, the compensator then adds undesired distortion to the signal. We discovered that by controlling the polarization angle with a rotator in front of the PMF or the crystal-based birefringent delay line that rotates SOP of the incoming light, the different PMD values are compensated.

The adverse effects of PMD on system performance were identified in the early 1990s [7–9] but the true extent of the impact were understood only in late 1990s when OC-192 testbeds were deployed as mentioned above. Several techniques and methods have been developed, but none provides a complete solution. For example, in Ref. [2] PMD compensation by “phase diversity detection” was achieved for first-order PMD only with a lot of component real estate, because each wavelength channel requires an independent module. Another approach utilizes multiple “optical equalizers” for 10, 20, and 40 Gb/s [3]. The reference also provides an excellent model with quite a complexity of parameters. Its complexity can be appreciated when we consider that the PM fiber is twisted by 64 stepper motors to provide compensation for a single channel. A fairly recent article describes effective PMD compensation of four WDM channels without demultiplexing. It employs statistical probability distribution of four channels and opts for correction of the worst channel by estimating the power penalty [5]. Similar new or other modified and enhanced techniques have been reported in the recent literature [11]. For a particular compensator design for certain span in the network, PMD can be measured with the optical-frequency-domain reflectometry technique [6].

The proposed technique has an advantage over various methods reported in the literature [2–11] because of its simplicity and cost-effectiveness. The technique mitigates first-order PMD effectively, and it also implicitly reduces the higher-order effects by optimization of monitoring signals and feedback to the SOP and delay controller. That is, real-time monitoring of PMD level by power spectral density (PSD) at select frequencies as discussed in later sections and subsequent feedback for optimal PSD signal correlates with the overall signal recovery. The following diagram shows the main concept of the device that can be used to mitigate the PMD effects in real time and as a dynamic method. The response time of such a technique is expected to be in the range of milliseconds, because it would involve an angular rotation (mechanical motion) of highly birefringent crystals (e.g., VO₄, ytterbium-vanadate). However, it will be appropriate for SONET-based wavelength-routed networks and point-to-point links because PMD variations due to environment are slow as well. It may not correct the individual optical packets but will suffice for SONET frames that require a 50-ms recovery time. With an electro-optic control of birefringent crystal, however, a fast response time in the range of microseconds to nanoseconds is possible.

 

Fig. 1. Block diagram of the transmission link including the PMD compensator.

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The rest of the paper is organized as following. After this brief introduction, Sections 2 and 3 describe the PMD emulator and monitoring, respectively. Section 4 provides an overview of the system simulations, Section 5 gives a summary of results with various graphical illustrations and a table, and Section 6 includes concluding remarks. A simulation movie is also included as Fig. 8.

2. PMD emulator

Different techniques can be used to emulate the effects of the PMD (see, for example, Refs. [12] and [13]). However, in the first-order PMD the DGD as well as the fiber PSPs are independent of the optical frequency [1]. The incoming light into the emulator will be horizontally or vertically polarized, that is, azimuth angle θ=0° or 90°, and then the ellipticity ε=0. However, when the SOP is along neither of the PSPs (components are along both directions), then PMD would introduce a delay on one of the polarization components, and this delay is known as DGD. In general the DGD is not constant; rather, it takes a random value that has a Maxwellian distribution. To simulate all these effects, first of all a polarization controller with ε=0 and θ=45° is introduced in order to rotate the polarization of the incoming light by 45°, and then the polarization beam splitter divides the two polarization components equally. Now a delay will be introduced in one of the components leaving the other component without any delay. This means that the delayed component is always slower by a certain delay time than the other polarization component. However, as stated above, this delay or DGD is a random variable and follows a Maxwellian distribution [1]. A diagram of such an emulator design is illustrated below in Fig. 2, and delay tool τ provides random delays. Each functional block contains the appropriate parameters to simulate the functions of each component.

 

Fig. 2. PMD emulator used in the system simulation.

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3. PMD monitoring

As a part of the feedback system, the PMD monitoring circuit is used to measure the PMD level and provide feedback to the control circuit of the compensator accordingly. For PMD monitoring, a widely used technique measures the power spectral densities (PSDs) at certain frequencies and uses those measurements as an indicator of the PMD level [14,15]. For our design, the frequency component at the half-bit-rate frequency is extracted from the base-band signal spectrum by a narrow-bandpass filter. The relation between the intensity of this signal (PSD) and the PMD coefficients is explored to optimize the PSD as function of PMD coefficients. For this purpose the following schematic was designed with modules from a software package [16], and each block represents the labeled device or subsystems whose characteristics and parameter can be modified to simulate the model, in a manner quite close to that of the real device and the respective response functions.

 

Fig. 3. PMD measurement circuit schematic.

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The PMD coefficient in the fiber were changed from 1×10^-15s/√m=0.03 ps/√km to 60×10^-15s/√m=1.9ps/√km. For a 40 Gb/s transmission rate, the following graph (Fig. 4) was obtained, which plots the intensity of the 20 GHz (half-bit-rate) signal with the PMD coefficients. The use of half-bit-rate frequency also allows the use of relatively lower-speed devices, i.e., PIN photodiode and electronic bandpass filters. The PMD fiber model includes DGD and the higher orders of the PMD as well. Since the signal is attenuated after propagating through the long-haul fiber, an amplifier (optional) in the diagram is incorporated to boost the optical signal before the signal goes to the monitoring circuit.

As shown in Fig. 4, for a 40 Gb/s transmission system, the intensity of a 20 GHz signal is decreasing for increasing PMD coefficients. Therefore, our goal is to design a feedback system to maximize the intensity of PSD in this signal in order to minimize the effects of the convoluted PMD. This inverse proportionality between the half-bit-rate frequency intensity and the PMD coefficient is more monotonic in the 10 and 20 Gb/s systems than in the 40 Gb/s. We can note in the graph that the monotonic relation between PSD and PMD coefficients deviates for higher the values of coefficients in 40 Gb/s. This is just more evidence of how the effect of nonlinear high-order terms of PMD become more severe along with high bit rates and high PMD coefficients for small bit periods.

 

Fig. 4. Intensity of the half-bit (20 GHz) component and the PMD coefficient relationship for a 40 Gb/s signal. The deviation from monotonic decreasing behavior is peculiar for OC-768 and was not present for 10 and 20 Gb/s. The origin of this deviation around 38 ps (cumulative PMD) is not clear but we suspect it arises from second- or higher-order effects, which become more severe for high-bit-rate signals as the bit period becomes short.

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4. System simulation

Unlike quartz or other birefringent retardation waveplates, Fresnel rhombs can be angle tuned to a new wavelengths (i.e., they are achromatic) since the phase shift is a function of the glass index and optical path, which varies only slightly over the design wavelength range. Therefore, with a birefringent Fresnel rhomb it is possible to rotate the input SOP over a broadband wavelength range. The same rhomb can be angle tuned to provide phase-delay for different groups of λ-channels.

In the PMD-compensator design, the delay line uses a high-quality birefringent crystal that can be as short as 20 mm. By rotating the SOP of the lightwave one controls which component of the light is to be delayed. As discussed above, a feedback technique using half-bit-rate extracted frequency amplitude is used as the PMD gauging indicator that provides a feedback to the compensator. Using such broadband polarization components in the compensator allows the mitigation of the first-order PMD and reduces convolved higher-order effects without isolating them. This is based simply on signal recovery by monitoring PSD and providing feedback to the delay module involving cumulative effects.

Figure 5 shows the schematic of an optical system that performs simulation with the VPI software package [16]. In this simulation, a Mach-Zehnder modulator was used to modulate a NRZ 40 Gb/s (OC-768) signal on a cw laser. The schematic uses the PMD emulator shown in Fig. 1 that emulates the PMD effects in fiber. The PMF or the birefringent crystal [17] is exactly like the PMD emulator but with a constant delay added to one of the components rather than a variable delay as in the emulator case. A typical delay Δτ in the crystal [17] is assigned to be ~15 ps. The polarization controller rotates the SOP of the incoming light by different angles, and the effect of this rotation on the eye diagram of the received signal is observed on the oscilloscope. The simulation was run for different DGDs in the emulator, and for each DGD value, the rotation-angle of polarization rotator was swept from -90° to 90° to cover the complete range of SOP.

 

Fig. 5 Optical system simulation to show the effect of the polarization rotation on the 40 Gb/s received signal.

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It must be noted that the representations of the emulator and the compensator look alike, but their parameters are different in files. Their axes are not aligned in general, and the polarization rotator does rotate the SOP to achieve a desired delay in the compensator made from highly birefringent material (e.g., Nd:YVO₄) rhomb that by rotation can provide variable delays to any selected λ channels in the 1200-1700 nm band.

5. Results

The DGD value in the emulator was varied from 0 to 25 ps with a step width of 5 ps as a parameter. These DGD values are practically equivalent to a ~150 km span of an old fiber span with a PMD coefficient of 2 ps/√km or more than 10,000 km spans of the new fiber types with coefficients near 0.1 ps/√km. For each DGD value the angle of the polarization rotator was varied in the range -90° to 90° with a step width of 1° resolution, looking for the value that gives the best eye diagram of the received signal. Table 1 shows sample DGD values and the corresponding rotation angle values. At these angles the polarization controller can be driven with a feedback system that rotates the SOP of the incoming light with the specific value of the angle according to the DGD value, which could be monitored by use of the suggested monitoring technique in Section 3.

 

Fig. 6. Eye-diagram of the input signal.

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Table 1. DGD values of the emulator and the corresponding values of the polarization rotation angles, at which optimum compensation was achieved.

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From the example data table it is observed that for high values of PMD in the range 15 to 25 ps, a clear eye diagram was achieved without any polarization rotation. On the other hand, for low values of PMD the need for polarization rotation is essential in order to achieve a wide eye diagram as well as a low BER in the received signal. In Fig. 6 the eye diagram illustrates the input signal for reference and comparison with subsequent long-haul signal transport in ~150 km high PMD or 10,000 km ultralow PMD fiber. The attenuation parameters in the fiber were set to be negligible. Likewise, the polarization-dependant loss and power penalty were also not considered because these parameters have very small values for the proposed components or material (i.e., Nd:YVO₄ has low attenuation and short length of ~20 to 30 mm).

Figure 7 shows a sequence of eye-diagram traces for the signal of Fig. 6 through the same fiber at the other end with and without PMD compensation. Each part of Fig. 7 shows the quality of the eye diagram as related to severity of PMD (various delays in emulator) and then subsequently compensation by angular adjustment of the polarization vector of the input signal.

 

Fig. 7. Eye-diagram of a 40 Gb/s signal transported through a birefringent fiber with an assumed ultralow attenuation coefficient. First column, accumulated PMD; second column, eye pattern of the transported signal; third column, eye pattern with PMD compensation using control of input SOP and the high-bi-fi crystal.

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We can note that an attempt to correct low PMD (~5 ps) passing through a compensator distorts the eye diagram; this perhaps results from overcompensation. This also illustrates the importance of dynamic compensators, because these would respond only to those signals with low PSD parameters. The following diagram (Fig. 8) shows a movie for PMD compensation.

 

Fig. 8. Movie demonstration (1452 KB) of dynamic first-order PMD mitigation in OC-192 (40 Gb/s) with rotation of birefringent crystal creating a variable delay and resulting correction of in the eye diagram.

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6. Conclusion and remarks

A simple technique and design for a dynamic compensation of the PMD effects was investigated by use of real-time monitoring and achromatic SOP control. A variable delay can be introduced for fast mode by angle-tuning of a Fresnel rhomb made from highly birefringent crystals such as Nd:YVO₄ [17]. The role of dynamic compensation by SOP rotation (polarization-mode delay) in the recovery of PMD convoluted signal was established by simulation with the VPI software package [16]. A half-bit-rate signal PSD was optimized by means of feedback to control circuit. The signal recovery was verified by the quality of an eye diagram. In this technique the SOP of the signal is rotated (by the angle-tuning of the Fresnel rhomb), which provides variable delays to one of the polarization modes of selected λ channels, leaving the other without any delay. For a WDM system, the proposed compensator, like many others in the literature, would require MUX/DEMUX and a rhomb for each λ channel. But the rhombs would be identical and affect a given channel through the angle of orientation. This achromatic behavior would bring much simplicity and compactness in the functional modules. The method is the subject of further research and optimization, and a hardware implementation of the final design is also underway.