Silicon-Organic Hybrid (SOH) Mach-Zehnder Modulators for 100 Gbit/s on-off Keying

Electro-optic modulators for high-speed on-off keying (OOK) are key components of short- and medium-reach interconnects in data-center networks. Small footprint, cost-efficient large-scale production, small drive voltages and ultra-low power consumption are of paramount importance for such devices. Here we demonstrate that the concept of silicon-organic hybrid (SOH) integration perfectly meets these challenges. The approach combines the unique processing advantages of large-scale silicon photonics with unrivalled electro-optic (EO) coefficients obtained by molecular engineering of organic materials. Our proof-of-concept experiments demonstrate generation and transmission of OOK signals at line rates of up to 100 Gbit/s using a 1.1 mm-long SOH Mach-Zehnder modulator (MZM) featuring a π-voltage of only 0.9 V. The experiment represents the first demonstration of 100 Gbit/s OOK on the silicon photonic platform, featuring the lowest drive voltage and energy consumption ever demonstrated for a semiconductor-based device at this data rate. We support our results by a theoretical analysis showing that the nonlinear transfer characteristic of the MZM can help to overcome bandwidth limitations of the modulator and the electric driver circuitry. We expect that high-speed, power-efficient SOH modulators may have transformative impact on short-reach networks, enabling compact transceivers with unprecedented efficiency, thus building the base of future interfaces with Tbit/s data rates.


Chirp analysis of SOH modulators
For transmission of intensity-modulated signals, an unwanted phase modulation, also referred to as chirp, leads to increased sensitivity with respect to fiber dispersion and hence leads to a signal quality penalty 1 . Ideally, SOH MZM should not exhibit any chirpthe field-induced refractive index change of the polymer cladding according to the Pockels effect 2 allows to completely suppress chirp in an ideal, perfectly balanced push-pull Mach-Zehnder modulator (MZM) 3 . For real-world devices with finite extinction ratio (ER), however, chirp is introduced by an unbalance of the optical amplitudes in the two MZM arms. For quantifying the chirp of a data signal generated by such a device, we use the chirp parameter  that is essentially defined by the ratio of the phase modulation to the amplitude modulation 4,5 , and that can be estimated from a direct measurement of the static extinction ratio  (stat) , see Equations (7) and (8) of the main manuscript. To proof that finite static extinction ratio (ER) of the MZM is the dominant source of chirp in our devices, we compare the chirp parameter obtained from the ER to a direct measurement of . To this end, we use another SOH modulator with a device layout similar to that of the device used for the data transmission experiments, but with better static extinction ratio of  (stat) = 31 dB. For a direct measurement of the chirp parameter, we rely on the fiber response peak method 6 . Using a network analyzer, we measure the frequency response of the modulator with a 75 km fiber span. Erbium-doped fiber amplifiers (EDFA) are used to compensate the insertion loss of the modulator and the fiber span. The measured frequency response normalized to the back-to-back transmission is shown in Figure 1 a). For data evaluation, the product of the square of the resonance frequency f µ and the fiber length L is plotted in dependence of the resonance order µ, see Figure 1 b). The chirp parameter  and the fiber dispersion coefficient D can then be extracted from the slope and from the vertical offset of a straight line fitted to the data points 6 . Measurement analysis leads to a dispersion coefficient D of 16.8 ps/(nm km) for the 75 km fiber span and a chirp factor  of 0.09. The value compares well to the value || = 0.06 which we estimate directly from the measured (static) extinction ratio. This confirms that the chirp of SOH MZM is dominated by the influence of a finite ERthe slight differences are attributed to the finite measurement accuracies of the fiber response peak method.
Using the equations described above, we estimate a chirp factor | ≈ 0.42 for a static extinction ratio of 14 dB as obtained for the MZM used for the 100 Gbit/s data experiment in the manuscript, see discussion in the main manuscript.

Wavelength operating range of SOH modulators
SOH modulators can operate over a wide range of wavelengths. In essence, the operating range is only limited by the ability of the silicon photonic slot waveguide to efficiently guide the light and by the absorption of the organic EO material. The modulator structure as well as the organic material are well suited to operate over the entire range of infrared telecommunication wavelengths, comprising all relevant transmission bands between 1260 nm and 1675 nm. Absorption of the EO material is negligible above 1200 nm 7,8 and hence the material is transparent in wavelength regions beyond 1260 nm which are relevant for telecommunications. The performance of the slot waveguides can be quantified by considering the field interaction factor according to Eq. (2) of the main manuscript. For the device used in the transmission experiments of the main manuscript, the field interaction factor decreases from  ≈ 0.16 at  = 1550 nm to  ≈ 0.14 at  = 1310 nm, see Figure 2 for the associated mode field profiles. At the same time, the material-related figure-of-merit for EO activity, n EO 3 r 33 , increases 9 by about 40 %, which leads to an overall improvement of the modulation efficiency by about 16 %. In total, the device performance does hence not change significantly with wavelength.

Implementation of pulse shape for system simulation
The hardware used in our experiment features nonzero rise and fall times, see eye diagram in Figure 3 (a) for the measured electrical output signal. For an emulation of these signals in the simulation, we use cosine-shaped pulses in the time-domain (not to be confused with raised-cosine pulse shaping with a raised-cosine shaped spectrum). A mathematical description of the pulse shape p(t) is given as where T denotes the symbol duration. With the discrete symbols a k = {-1;1} which correspond to a logical "1" and a logical "0", respectively, with the Dirac function (t) representing the time-discrete nature of digital data, and with the peak-to-peak output voltage U pp , the (electrical) mean-free time-domain drive signal can be written as ( ) = ∑ ( − ) * ( ) (2) where * denotes a convolution operation. The eye diagram of the digitally generated waveform (with additive white Gaussian noise) is depicted in Figure 3 (b).

Figure 2:
Simulated mode fields for a center wavelength of 1310 nm (left) and 1550 nm (right). The color coding indicates the modulus of the transverse electrical field and is identical for both plots. For the shorter wavelength, the field is stronger in the silicon rails, and hence the field interaction factor is smaller by 17 %. This is overcompensated by an increase of the material-related figure-of-merit for EO activity, n EO 3 r 33 .