The DPMZM has two linearization parameters: an r-f and an optical split. These parameters must achieve a tolerance given in Table 3-3, which is prohibitively challenging with the normal implementations of the splits: an unbalanced Y-junction for the optical split and a microwave directional coupler for the r-f split. Even if adequate accuracy were attained in the microwave split at one frequency, it is also challenging to maintain that accuracy over the microwave signal bandwidth. Figure 5 - 4 and Figure 5 - 5 show properties that can be exploited to achieve a practical implementation of the DPMZM modulation scheme.
Figure 5 - 4: The optimal optical split as a function of the RF split.
The original publication of the DPMZM in Ref. [3.3] and subsequent summary publications such as Ref. [3.4] refer to either one optimal r-f and optical split, or a set of distinct optimal points. However, only one degree of freedom is required to achieve the linearization. The basic MZMs in the linearization scheme are biased at their point of anti-symmetry, generating no even-order harmonic distortion. The two precise signal levels are only used in nulling the third-order intermodulation distortion term. There is a redundancy in the degrees of freedom of the modulator. Figure 5 - 4 demonstrates this by plotting that optimal optical split as a function of the r-f split. This forms a curve of points that correspond to a local optimum in dynamic range. Holding either r-f or the optical split constant, and optimizing the other split leads to a point on this curve. Figure 5 - 5 shows the value of the optimum versus the r-f split.
There is a global optimum, however, the curve is nearly flat over a wide range. If the r-f split is
imprecise but at least uneven, the linearization mechanism still works given precise control of the optical split. And this is the idea behind a sensitivity split.
Figure 5 - 5: The optimal dynamic range as a function of the RF split of the DPMZ; at every value of the r-f split the optical split has been re-optimized
In the implementation of a DPMZM, the r-f path consists of one transmission line and the r-f power is never split. Figure 5 - 6 shows such a modulator schematically. 1) shows a top-down view of the optical waveguides of the modulator, 2) shows the waveguides again, but with a push-pull electrode structure on top of them, 3) and 4) show end views of the waveguides and electrodes for the two different Mach-Zehnders labeled B and C. Circles represent the waveguides and rectangles show the electrodes above them. The key difference between 3) and 4) is that in 3) the waveguides of MZM B are centered in the region of the crystal that has the strongest electric fields, while in 4) the waveguides of MZM C are off-center just enough to build in a distinct sensitivity split between the two Mach-Zehnder modulators. That is, even
though there is one uniform electrode, the effect of that electrode on the modulation in the two Mach-Zehnders is different.
1)
2) r-f bias
bias
3)
MZM
4)
MZM
Figure 5 - 6: A DPMZ with a precise optical split and an imprecise “sensitivity” split implemented by the structure of the waveguides, so the RF is never physically split.
Block A is a passive directional coupler with DC electrodes only. The optical split between the path to the MZMs B and C is set approximately by the choice of coupler length and the applied voltage is used only for fine tuning. The coupler controls the optical output to the precision of the bias voltage, which may be set after fabrication and even dynamically during operation. The directional coupler introduces a phase shift between the output and the photodetector. If two distinct fibers, two distinct laser wavelengths, or two distinct polarization states are used, then this phase shift is irrelevant because the currents of the two signals are summed in the photodetector incoherently. However, one proposal in the literature, Ref. [2.3], uses one laser, one polarization, and one fiber, and combines the two
MZM outputs in a passive directional coupler. This configuration requires an additional phase shifter, used to keep the two signals in phase quadrature so that they don’t interfere. If the single output fiber approach is used with the sensitivity split shown here, then the phase change introduced by the coupler section A will need to be counteracted in addition to the precision phase shift to guarantee that the two signals are in quadrature. This is could be located at block D. Or alternatively, the directional coupler at block A could consist of two bias electrodes, which with different voltages is enough to give a precise power split and phase split, thus eliminating a need for a separate phase shift region at block D.
MZMs B and C appear in series spatially, but they are parallel, each modulator is fed from a different optical path. The r-f flows through one continuous transmission line element that passes over both B and C. This creates a time delay between the two modulation signals, but the path length from the input to the output of this chip is the same for both the optical signal that traverses modulator B and the one that traverses C. While it is beneficial to avoid physically splitting the r-f, the total roll-off, governed by the entire length of the traveling wave electrode structure, is now twice as long as the individual MZMs. For frequency regimes in which microwave loss is significant, other approaches (such as the antenna segmented approach discussed in Chapter 2) may need to be combined with this approach.
Figure 5 - 5 shows that the r-f power split must be uneven. The schematic diagrams B) and C) from Figure 5 - 6 show how this unevenness is obtained. The waveguides in MZM C are intentionally placed non-optimally so that the sensitivity of the MZM is reduced because the modulation field within the optical waveguide is no longer optimally aligned with the direction for maximum modulation of the polarized optical wave in the x-cut crystal. If the waveguides are not directly centered in the waveguide gap, the sensitivity will be reduced, and then the two modulators will have different sensitivities, creating an effective r-f split, even though the r-f power has never been split. Obviously this positioning cannot be manufactured to yield a precise split. However any split between 1:20 and 1:4 yields near optimal dynamic range provided the optical split is precise and configurable after fabrication. The end result is a realizable modulator for which the dynamic range performance is robust to frequency.