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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.

6.2.1 Experimental set-up

In our set-up, depicted in Fig. 6.3(a), the light from a tunable laser is passed into an inte-grated transmitter. The transmitter uses a serializer to produce four 28Gb/s electrical pseudo-random signals of length 215− 1, each shifted by 8192 bits, which feed a quad-driver and a polarization-multiplexed nested Mach-Zehnder modulator. It generates a data stream at 112Gb/s PDM-QPSK, including 12% protocol and forward error correction (FEC) overhead.

This stream is sent to an optical amplifier, connected to an input of the mode multiplexer, for mode conversion and coupling into the FMF. The LCOS surface hosts ten spots programmed with the phase mask corresponding to the desired mode, as depicted in Fig. 6.3(b). Each mode needs two spots for its horizontal (H) and vertical (V) polarization components. In our configuration the only used multiplexer input “In1” is set to convert the fundamental mode into the LP11b mode. The converted signals are then collimated into the FMF at the multi-plexer output. This 40-km long FMF supports up to 4 spatial modes (LP01, LP11, LP21, and LP02), with low attenuation (0.22 dB/km) and large effective areas (>120 µm2) for all guided modes. The differential mode group delay (DMGD) per unit length between LP01 and LP11 is quite large, at 4.35 ps/m (4872 symbols after 40km at 28GBaud) and their effective-index difference is > 10−3, which suggests negligible mode coupling as in [76].

At the receiver end, the FMF goes into the 1x3 mode-demultiplexer, which performs mode conversion using the remaining 6 spots on the LCOS phase modulator and collimates the light to the three SMF-fibers at the outputs. The first two outputs are used for the back-conversion of the LP11b and LP11a modes of the FMF and are detected by a noise-loaded coherent re-ceiver with joint mode/polarization diversity. The third output is not converted and it is sent to an SMF which captures mainly the LP01 mode of the FMF, which is measured with a power meter. Outputs 1 and 2 go through variable attenuators, optical preamplifiers and filters for setting the desired received OSNR before the coherent receivers. Each coherent receiver uses a free-space coherent mixer, a free-running local oscillator and four balanced photodiodes in a polarization diversity configuration. Sampling is performed with two real-time oscillo-scopes (16GHz analog bandwidth) synchronously triggered. They provide 4 complex signals containing the optical field. To discriminate between the degenerated modes LP11 along the two polarization axes, a 4x4 MIMO equalizer is needed, as opposed to the conventional 2x2 MIMO equalizer used for polarization demultiplexing over SMF [42].

One important characteristic of the LCOS device is its possibility to independently pro-gram its pixels on a gray scale with many discrete values. This scale corresponds through a given monotonic function to a phase shift ϕ in the range [0 : 2π]. The masks required for LP11 conversion are programmed using a simple phase shift ϕ = π on half of the surface.

Figure 6.3: System setup (a); LCOS surface with phase mask (b) and ϕ represented as a gray value (c).

The relationship between the gray value and the phase shift is dependent on the position of the mask on the LCOS surface, which we take into account using a mask-specific additive phase term ϕM. To compensate for ϕM we apply a gray correction parameter ε to the phase shift ϕ = π + επ + ϕM, which is represented as a different gray value in Fig 6.3(c). Ideally, a phase shift ϕ = π should be applied by the spatial light modulator, which means that an op-timum value of the gray correction parameter ε0= −ϕM/π should be found. A first method to quantify this optimum value is to minimize the residual LP01 power that propagates in the FMF whenever a “sub-optimal” phase mask of the multiplexer does not convert all the power of the LP01 into LP11. A second method for its optimization is to measure the phase shift impact on the Q-factor. Both these techniques will be applied for the optimization of the LP11 phase mask used at the input “In 1” of the multiplexer. The masks of the demultiplexer have already been optimized with similar procedure.

6.2.2 Experimental results

In a first test we transmitted a signal al λ = 1533.47nm through the “In 1” port of the mul-tiplexer (LP11b) and we varied the gray correction parameter of both horizontal (εH) and vertical (εV) polarization phase masks. This variation generates a residual LP01 mode at the transmitter side, which is coupled into the FMF together with the LP11b mode. The power of this residual LP01 mode is demultiplexed through the “Out 3” port and measured. In Fig.

6.4(a) the LP01 power at the “Out 3” port is reported as a function of εH and εV. For each curve, only the ε of one polarization’s mask is varied, while the ε of the other mask is set to

its optimum value. We found that these two phase masks have different optimum values for ε , i.e., εH0 = 0.03 and εV0 = 0.09 give the minimum LP01 power corresponding to the lowest cross-talk contribution of the “In 1” port mode converter. Because of these different optimum ε0values, we will consider only variations ∆ε = (εH0 − εH) = (εV0 − εV) with respect to the optimum couple of values, hence ∆ε = 0 corresponds to optimum ε = ε0for each polariza-tion (ϕ = π). Fig. 6.4(b) depicts the residual LP01 power as a funcpolariza-tion of ∆ε. We observe a rapid residual LP01 power increase for increasing |∆ε|, which becomes larger than 5 dB for

|∆ε| > 0.2. From our definition of phase shift this value corresponds to a phase mismatch of

±36°. In a second test we measured the Q-factor of LP11 by varying the ∆ε in the range of [-0.4:0.4], which corresponds to a phase mismatch of ±72°. In Fig. 6.5(a), LP11 Q-factors of both polarization tributaries are reported. Despite a constant offset in their performance, we measured a Q-factor penalty below 1dB in the range of ±27° for both polarizations. This corresponds to an interfering power increase of roughly 3 dB, as depicted in Fig. 6.4(b).

Figure 6.4: Residual LP01 power (“Out 3”), for different ε of the horizontal (H) and vertical (V) polarization phase mask (a), and for various ∆ε = (εH0 − εH) = (εV0 − εV) , where ∆ε = 0 corresponds to optimum ε0for each polarization (b). The corresponding phase shift and phase mismatch are reported as reference.

We then repeated the ε optimization using two other wavelengths, namely 1532.29nm and 1534.64nm. Interestingly, here, the optimum values differed from the values obtained at 1533.47nm, being εH0 = 0.09 and εV0 = −0.09 at 1532.29 and εH0 = 0.09 and εV0 = 0.09 at 1534.64nm respectively. Starting from these ε0 values, we measured the LP11 Q-factor penalty by varying phase mismatch as in the previous case. The results are depicted in Fig.

6.5(b) using empty and full symbols for the two polarization tributaries. We observe a similar phase mismatch impact for the three wavelengths although εH0 and εV0 are different for the three wavelengths. This shows that the gray correction parameter ε, as defined above, shows not only the spatial dependency but also the wavelength dependency of the LCOS. However,

the varying ε0values could cause severe Q-factor penalties in potential WDM transmissions, where all wavelengths of one mode could be converted by the same phase mask.

Figure 6.5: LP11 Q-factor (a) and LP11 Q-factor penalty for three wavelengths, versus ∆ε and phase mismatch (b).