In this section we provided an intuitive explanation of the reasons behind the effectiveness of the XPM suppressor against XPolM. To this aim we analyzed the XPolM-induced SOP rota-tion and channel depolarizarota-tion along propagarota-tion, getting a picture of the SOP and Degree Of Polarization (DOP) of a reference signal at specific coordinates along the optical line. We simulated a WDM system based on a central Constant Wave (CW) signal of power -10 dBm surrounded by 18 NRZ-PDM-QPSK signals with power of 5 dBm each. The CW channel was oriented along the bS1axis, while the PDM-QPSK channel were randomly oriented. The CW channel allows us to easily measure the DOP and to better visualize its SOP rotation during the propagation.
The transmission link was based on 20 × 100 km spans of SMF. Three different setups were considered: 1) a DM link with zero RDPS (labeled DM0), 2) the same DM link in which a XPM suppressor is applied at the end of each span (labeled DM0+XPM supp) and 3) a NDM link. In all these links, pre-compensation was not applied and the overall cumulated dispersion was set to zero.
We start showing in Fig. 5.10 the CW DOP at different points along the link, discretized with steps of 1 km. The measurement was repeated for five different random seeds, which correspond to random interfering channel pattern realizations and random SOP orientations.
Concerning the DM0 link, in Fig. 5.10(left) we note a monotonically decreasing DOP for in-creasing distance, with a regular repeating pattern. Within the effective length of each trans-mission SMF fiber the DOP experiences an abrupt change, and then slows down in the fol-lowing low-power km. Such a pattern induces an almost parabolic decrease of the DOP from span to span, with different curvatures depending on the random seed. The parabolic behavior ceases towards the end of the link because of the decrease of the power levels.
0 5 10 15 20
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Figure 5.10: CW DOP decreasing along the link, when it propagates with 18 NRZ-PDM-QPSK channels in three links: DM link with zero RDSP (DM0), DM0 link in which XPM suppressor at the end of each span (DM0 + XPM supp) and NDM link.
For the NDM link (center figure) and the DM0 link with XPM suppressor (right figure), we observe that the DOP evolution along the link is much more irregular. Furthermore the final DOP (after 20 spans) is by far larger than for the DM0 link, indicating a smaller XPolM-induced depolarization (please note the different scales). The larger depolarization XPolM-induced by XPolM in the DM0 link without XPM suppressor is an indicator that the performance is more sensitive to the interfering channel SOPs. On the contrary in the NDM and the DM0 link with XPM suppressor we expect a chaotic behavior along propagation, which does not allow specific bad orientations of interfering SOPs to add constructively (i.e., resonantly) along propagation [2].
Now we move to analyze the CW SOPs rotation induced by XPolM in the three trans-mission links. We fixed the time at the beginning and at the end of the first 35.7 ps (symbol duration at 28 Gbaud) of the CW channel, reporting in Fig. 5.11 their SOP trajectory during propagation, with steps of 1 km.
During the propagation along the DM0 link (Fig. 5.11 left), we note that the two CW samples evolved on the Poincarè sphere with an almost periodic pattern similar to a “spring”.
Figure 5.11: CW SOP evolution along the link due to the XPolM-induced rotation coming form the propagation with 18 NRZ-PDM-QPSK interfering channels in a DM0 with and without XPM suppressor and in a NDM link. Two different samples are considered: beginning and end of 35.7 ps time slot. Random seed 1.
These trajectories have a periodic component (a “drifts”) and an uncorrelated component that leads to a random-like motion. The difference between the two final SOPs provides a direct estimation of the depolarization within a symbol period.
In Fig. 5.12 we zoomed over such a SOP trajectory, visualizing the SOP evolution of a single sample along five spans. In the figure we indicated the starting/ending coordinates of the optical fibers encountered along propagation. For each transmission fiber we also indi-cated the coordinate of the corresponding effective length.
We note that the CW follows similar trajectories during the propagation along each span.
The reason is strictly related to the chosen zero RDPS that perfectly re-aligns in time all channels at the beginning of each span, thus creating a periodic interference with period equal to the span length. This means that, under a first approximation, the nonlinear rotation induced by the interfering patterns is the same in each span except for a different starting point, whatever the initial SOP of the interfering channels. Hence, this perfect re-alignment creates a constructive addition of the SOP trajectories that forces the CW SOP to follow a
Figure 5.12: DM0 link: SOP evolution along the first five span of a single CW sample.
long trajectory on the Poincarè sphere.
We also note that the DCF fibers (purely linear in our simulations) induce a SOP change through their GVD1. The DCF-induced trajectory is of opposite direction w.r.t the one in-duced by the transmission fiber. Hence, XPolM may be partially resonant in dispersion com-pensated links, since its contribution slowly changes direction along propagation. Without the DCF each ring of the apparent “spring” motion is not recovered, thus the SOP trajectory changes quickly and chaotic along propagation, as shown in Fig. 5.11 (center and left).
Indeed, Fig. 5.11 (center) shows for the NDM the predicted chaotic behavior (random walk) that averages itself without letting the SOP travel long distances over the sphere. Also the distance between the final SOP of the two samples and consequently the depolarization are smaller than after the propagation along the DM0 link. The application of the XPM sup-pressor to the DM0 link seems to delete the periodicity of the SOP pattern, leading to an overall SOP evolution like a random walk, as in the NDM link.
Based on these observations, we can conclude that in a DM map the XPolM-induced rotations at each span add constructively, inducing a larger signal depolarization and conse-quently a stronger Q-penalty. The application of the XPM suppressor at the end of each span breaks such a resonance reducing both the depolarization and the Q-factor penalties, as in the NDM link.
1GVD does not depolarize in the frequency domain, but here we are in the time domain.
Chapter 6
Mode Division Multiplexing using an LCOS-based Spatial
Modulator
As discussed in Chapter 2 mode division multiplexing (MDM) over few-mode fibers (FMF) has recently appeared as a promising alternative to keep up with transmission capacity growth [41, 42, 43, 44]. In this chapter we summarize the experimental work made at Alcatel-Lucent Bell-Labs France on this topic, focusing mainly on the modal cross-talk induced by a mode converter based on a liquid-crystal on silicon (LCOS) spatial modulator. For our transmission experiments, we employed a LCOS-based mode converter spatial modulator and a prototype FMF [45]. This LCOS-based approach to mode conversion is attractive because of the pos-sibility to reconfigure the phase plates to any desired mode conversion. The FMF has the advantage of exhibiting very large effective-index differences and very large group delays between different modes and thus low linear crosstalk between modes, with only 0.22dB/km loss.
In Sec. 6.1 we describe the mode converter and the scheme of mode multiplexer and de-multiplexer. In Sec. 6.2 we evaluate the impact of the modal cross-talk induced by imperfect mode multiplexing/demultiplexing in LCOS device on a 100 Gb/s PDM-QPSK performance.
In Sec. 6.3, we demonstrate the transmission of two 100Gb/s PDM-QPSK signals on two modes of the FMF, which we shall call LP11a and LP11b, using an additional coherent detec-tor and a more sophisticated DSP with respect to the standard single mode transmission. More
details on the receiver algorithms and other transmission experiments obtained using the com-bination of LCOS-based mode converter and FMF are discussed in [42, 72, 73, 74, 75].
6.1 Mode Conversion and (De-)Multiplexing
We realized in a single device two distinct functions: mode conversion and mode multiplex-ing/demultiplexing. For what concerns mode conversion, an LCOS-based spatial modulator is used to change the phase of the transverse distribution of the optical field in a so-called 4f-correlator configuration, where the spatial light modulator is placed in the center, as depicted in Fig. 6.1. Input fiber and output fiber are collimated by a lens, whose distance from the fiber output corresponds to its focal length ‘f’. As a result, the two-dimensional Fourier transform of the spatial light distribution in the fiber is obtained in the central plane, spaced by another
‘f’ between the lenses. This Fourier transform is modulated in phase using a multiplicative mask, which is programmed on the LCOS. The resulting field distribution in the output fiber can be easily calculated by applying the inverse Fourier transform to the product of mask and incoming Fourier transform. In Fig. 6.1 the signal coming from a single-mode fiber (SMF) is converted into one of the modes supported by the output FMF: LP11a.
Figure 6.1: Scheme of mode conversion using spatial light modulator (SLM) phase mask on the Fourier plane of a 4f configuration.
By mode multiplexing, we mean the combination of more than one converted mode into the output FMF. In a simple but inefficient way this can be achieved by using free-space half-mirrors after mode conversion in a scheme like the one of Fig. 6.2. Each half mirror adds a 3dB loss. In our case we have built two devices that can be used as both multiplexers or demultiplexers. One of them has two SMF inputs/outputs and the other has four SMF inputs/outputs. We choose to use as a multiplexer the one with two SMF inputs and as a demultiplexer the one with four SMF outputs, where only 3 ports can be used for mode conversion and the fourth is directly coupled into SMF from FMF.
These two devices share a single LCOS of 1920x1080 pixels, operated in reflective mode.
Figure 6.2: Scheme of mode multiplexer (2x1) and demultiplexer (1x4). The mode converters are realized with a polarization diversity scheme depicted in the inset and each beam uses a spot of the LCOS surface that can be programmed with on of the three possible masks.
The 2x1 converter uses the lower size of the LCOS screen. At each one of its two inputs, the light beam from the collimated SMF pigtail is split along two optical paths, one for each po-larization, by a polarization splitter, and hits the LCOS onto two of four possible spots. Note that we use only phase modulation, whereas ideal mode conversion would require phase and amplitude masks, at the expense of an excessively complex design. Each spot on the LCOS device counts approximately 80x80 pixels and is programmed with the phase mask corre-sponding to the desired mode, i.e., according to the profiles in Fig. 6.2. Light from all four paths is sent back to two polarization beam combiners, then into a 2x1 free-space combiner and collimated into the FMF. At the receiver end, the 1x4 demultiplexer is designed similarly, but with four SMF-fiber pigtails as output ports (hence 6 spots on the LCOS phase modulator for polarization diversity plus a directly connected output port without mode conversion), the input being the FMF. It uses the upper part of the LCOS device.