The power consumption of silicon photonics electro-optic modulators is a key performance metric for their suitability to Datacom transceivers. Resonant enhancement in carrier depletion ring resonator modulators (RRMs) allows a drastic reduction of the required RF signal power [1]. However, this also comes at the cost of a narrow optical bandwidth and the requirement of an active RRM resonance wavelength stabilization system if the high thermo-optic coefficient of silicon is not counterbalanced by a nonstandard cladding material [2]. In state-of-the-art RRMs with ${\mathrm{SiO}}_2$ cladding [2,3], the power consumption for active stabilization in a 50 K range exceeds 14 mW [3], which is significantly higher than the power required by the modulator driver (0.8 mW at 10 Gbps [3]). The goal of this work is to obtain a substantial resonant enhancement while maintaining a large optical bandwidth, or equivalently, a large temperature range of operation without the necessity of active resonance wavelength stabilization. In the resonantly enhanced Mach–Zehnder modulator (RE-MZM) demonstrated in this work [Fig. 1(a)], the straight phase shifters of conventional MZMs are replaced by arrays of identical and collectively driven RRMs [4], optically coupled to the interferometer arms. In this configuration, each RRM is used as a phase modulator, which can exhibit a low-resonance quality ($Q$-) factor and thus a wide optical bandwidth since it only needs to generate a fraction of the total required phase shift. The straightforward solution to widen the optical bandwidth consists of highly overcoupling the resonators by increasing the coupling strength (${\kappa }^2$) between the bus waveguide and the cavity [Figs. 1(b) and 1(c)]. As a drawback, this approach also reduces the enhancement of the phase modulation caused by the resonant effect ($\mathrm{\Gamma }$), which can be calculated as the derivative of the phase applied to the light in the interferometer arm after the RRM with respect to the phase accumulated by the light after a single round trip inside the RRM [4]. When comparing the resonant phase shifter of the RE-MZM to a straight configuration (sized to achieve the same phase shift at a given drive voltage), the peak enhancement at the central resonance wavelength [${\mathrm{\Gamma }}_{\text{peak}}$ at ${\lambda }_{\text{res}}$, Fig. 1(d)] is a crucial figure of merit since it corresponds to the reduction of the cumulative PIN junction length, of its capacitance, and thus of the maximum achievable reduction in power consumption. Indeed, ${\mathrm{\Gamma }}_{\text{peak}}$ scales with the finesse of the resonator [the ratio of the free spectral range and the full width at half-maximum (FWHM)], which drops as the resonance $Q$-factor is reduced. It is still possible to recover a high finesse by reducing the resonator size as much as possible (thus increasing the FSR to compensate for the enlarged FWHM). It is then critical not to induce significant excess optical losses associated with the curvature of the waveguide or abrupt mode mismatch in the coupling section, as the resonator not only demultiplies the phase shift but also the optical round-trip losses. Since round-trip losses and phase shift are enhanced by the same amount, the commonly used figure of merit $V\pi ·L·\alpha$, consisting in the product of the drive voltage required to achieve a $\pi$ phase shift ($V\pi$), the length of the phase shifter ($L$), and linear optical losses (here the total loss in each arm divided by $L$), remains the same after embedding the phase shifters in the resonators in the absence of such excess optical losses. As a result, a successful RE-MZM device requires very small and highly overcoupled resonators with minimal excess losses.

 

Fig. 1. (a) Schematic representation of the proposed RE-MZM. (b) Resonance enhancement factor ($\mathrm{\Gamma }$) for a resonator with a radius of 5 μm and coupling strengths of 0.25 (red line) and 0.45 (green line). (c) FWHM of the resonance, as a measure of the optical bandwidth. (d) Peak enhancement factor (${\mathrm{\Gamma }}_{\text{peak}}$) at the central resonance wavelength (${\lambda }_{\text{res}}$) as a function of the coupling strength (${\kappa }^2$).

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The modulator has been designed for fabrication in the standard 248 nm DUV silicon photonics technology line at IME A*STAR with a 220 nm core thickness, a deep etch of 130 nm (resulting in a 90 nm slab height), and a full etch for the definition of the interconnection waveguides [5]. In order to simultaneously fulfill all the aforementioned requirements, we designed a novel resonator geometry with a 5 μm radius in which the waveguide is defined by the deep etch and adiabatically transitions from a wide cross section to a narrow width in the coupling region [Fig. 2(a)] with marginal excitation of high-order modes. The narrow width expands the evanescent field of the cavity mode and thus increases the coupling strength. On the other hand, the wider waveguide section reduces the round-trip bending loss from $\sim 0.5\mathrm{dB}$ to below 0.03 dB. The slab on the opposite side of the bus waveguide has been fully etched in order to provide a high-index contrast and suppress the radiative losses that would otherwise occur in the narrow waveguide region. The optimization of the angle $\theta$ (determining the length of the coupling section) provides a weak tapering of the gap with a smooth conversion of the optical field from the bus waveguide into the resonator [6]. Furthermore, a minimum gap of 200 nm allows a reliable fabrication with optical lithography. With waveguide widths of 370 nm in the bus and 425 nm in the resonator, we adjusted the coupling strength to a value of ${\kappa }^2=0.4$ for a resonator FWHM of $\sim 2\mathrm{nm}$, resulting in a peak enhancement factor (${\mathrm{\Gamma }}_{\text{peak}}$) of 8. Waveguide transitions from fully etched into asymmetrically etched waveguides (90 nm slab on one side and full etch on the other side) were included at the input and output of the resonator array. For the implementation of the phase shifters, we embedded a reverse-biased lateral PIN junction within the rib waveguide extending over an unfolded length of 22 μm per resonator ($L_{\mathrm{PS}}$). The cathode is contacted via the center of the cavity and a highly p-doped region for anode connection surrounds ¾ of the resonator [excluding the coupling region to avoid optical loss in the bus waveguide, Fig. 2(c)]. The doping concentrations (detailed in [5]) were specifically optimized for high-speed single RRMs aimed at amplitude modulation, leading to a relatively high phase shifter efficiency in reverse bias ($V\pi ·L$ of $1.3\mathrm{V}·\mathrm{cm}$) but also high propagation loss due to carrier absorption ($\sim 5.5\mathrm{dB}/\mathrm{mm}$). Following the simulation procedure described in [7], we placed the depletion region near the outer edge of the resonator so as to maximize the optical field overlap. When compared to a straight phase shifter with optimized width (reference case with 400 nm width) the wider cross section of the resonator introduces a 15% total penalty due to the enlarged mode profile and thus reduces the effective phase shift enhancement from 8 down to 6.8.

 

Fig. 2. (a) Schematic layout of the proposed resonator. (b) Cross section and (c) top view of the lateral PIN junction phase shifter embedded inside the resonator. (d) Microscope image of the fabricated device.

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The MZI was implemented in a symmetric configuration with $1\times 2$ MMI and $2\times 2$ MMI as splitter and combiner elements, respectively. Assuming ideal MMIs with $50:50$ splitting ratios, the power levels at the outputs of the MZI combiner vary according to

For selecting the number of resonators per array ($N$), we maximized the optical modulation amplitude (OMA) of the MZM, obtained by inserting Eq. (3) into Eqs. (1) and (2) and by calculating the difference between the maximum output power $P_1$ (high level) and the minimum output power $P_0$ (low level), both normalized to the input power ($P_{\text{in}}$), according to the definition of the OMA:

 

Fig. 3. (a) Calculated OMA of the RE-MZM with $2V_{pp}$ in push–pull driving as a function of wavelength for $N=3$ (blue), 5 (green), and 7 (red) resonators loaded on each arm. (b) OMA spectra for a RE-MZM with $N=5$ and operating temperatures shifted by $\mathrm{\Delta }T=-25°\mathrm{C}$ (blue), 0 (black), and $+25°\mathrm{C}$ (red).

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A scanning electron microscope (SEM) image of the fabricated resonator array and a microscope image of the proposed modulator are, respectively, shown in Figs. 4(a) and 4(b). Detailed characterization of the RE-MZM’s optical transfer function at both outputs revealed a slight mismatch between the resonators on the upper and lower arms corresponding to the resonances being collectively shifted by 0.1 nm. At the resonant wavelength, this resulted in a 41° phase error relative to the MZM quadrature condition that was compensated, together with the 10° phase error resulting from mismatch between the two bus waveguides, by the thermal phase tuners.

 

Fig. 4. (a) SEM image of a fabricated resonator array. (b) Micrograph of the fabricated RE-MZM with electrical contacts for push–pull operation. (c) Electro-optical transmission of the fabricated modulator measured in a 50 Ω environment.

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The electro-optical characterization of the modulator in a 50 Ω environment revealed a cutoff frequency of 23.5 GHz mainly limited by the RC time constant as penalized by the driver output impedance. We determined an optical insertion loss below 6 dB at the resonant wavelength ${\lambda }_{\text{res}}=1542.9\mathrm{nm}$ [Fig. 5(a)]. Moreover, after biasing the interferometer to its quadrature point at ${\lambda }_{\text{res}}$ by means of the thermal phase tuners, we applied DC reverse-biased drive voltages of $2V_{pp}$ and $4V_{pp}$ in push–pull configuration and measured peak extinction ratios of 3 dB and 6 dB, respectively. These correspond to penalizations of the OMA by, respectively, $-4.8\mathrm{dB}$ and $-2.2\mathrm{dB}$ due to the finite drive voltages. For comparison purposes, we included in the same chip a conventional (nonresonant) MZM with straight phase shifters relying on the same PIN junction design (with 400 nm wide waveguides) and sized to result in the same $V\pi$. As expected, this linear modulator features a measured modulation efficiency $V\pi ·L$ of $1.3\mathrm{V}·\mathrm{cm}$. Considering the cumulative RE-MZM PIN junction length and its DC response, we extract a modulation efficiency $V\pi ·L$ of $0.19\mathrm{V}·\mathrm{cm}$ at ${\lambda }_{\text{res}}$, which represents a reduction by a factor of 6.8 relative to the reference case. The 5.7 dB insertion loss of the RE-MZM at ${\lambda }_{\text{res}}$ is slightly above that of the reference modulator (4.5 dB) due to 0.24 dB excess loss per resonator associated with waveguide junction losses and bending losses not present in the reference case. This corresponds to 8.5× the losses associated with the unfolded 110 μm junction length, i.e., here the multiplicative factor is slightly above ${\mathrm{\Gamma }}_{\text{peak}}$ due to the excess losses (so that the net effect results in a 25% increase of $V\pi ·L·\alpha$). We estimate the reduction in power consumption compared to a reference MZM driven as a series of lumped elements with a distributed driver. In this case, the power consumption simply scales as $C_T·V^2$, the product of the capacitance with the voltage squared [8]. If the linear modulator is sized to achieve the same extinction ratio at a given drive voltage, the RE-MZM power consumption is reduced by a factor of 6.8 due to the smaller capacitance. However, since the RE-MZM exhibits 1.2 dB additional insertion losses, it needs to be operated with a 32% larger drive voltage in order to obtain the same OMA as the reference modulator, which reduces the effective power enhancement to a factor of 4. Importantly, the reduction in modulator length removes the necessity of a distributed driver or a traveling wave (TW) configuration. Compared to the TW case or factoring in the power overhead dissipated inside a distributed driver, the power enhancement factor would be significantly higher (~20× when compared to a TW MZM, in which the power consumption would be ~5× higher than in a well-designed lumped element configuration [7]).

 

Fig. 5. (a) DC optical transmission measurements for reverse-biased drive voltages of $2V_{pp}$ and $4V_{pp}$ (with the RE-MZM biased at its quadrature point, the blue curve shows the total output power). (b) RE-MZM efficiency as a function of wavelength. The efficiency of a conventional phase shifter with equivalent PIN configuration is indicated by a dashed red line.

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Finally, we evaluated the modulator’s wavelength and temperature ranges of operation by recording eye diagrams at 30 Gbps and extracting the corresponding signal $Q$-factors at different wavelengths/temperatures (Fig. 6) according to the methodology presented in [5]. At a wavelength of 1544.5 nm (with a signal $Q$-factor that exceeds the value at ${\lambda }_{\text{res}}$ due to reduced insertion losses), the signal $Q$-factor remained within a factor of 2 of its peak value within a 55°C temperature range (from 20°C to 75°C). At a fixed temperature of 25°C, the signal $Q$-factor also remained within a factor of 2 of its peak value within a 3.8 nm wavelength range (from 1541.1 to 1544.9 nm).

 

Fig. 6. Eye diagrams and extracted signal $Q$-factor (a) as a function of wavelength at a fixed temperature of 25°C and (b) as a function of temperature at a fixed wavelength of 1544.5 nm.

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In conclusion, we have demonstrated a novel RE-MZM for silicon photonics that aggressively reduces the size and power consumption of conventional MZMs based on straight waveguide phase shifters. At the resonant wavelength, a device with five resonators on each arm exhibits a $V\pi ·L$ of $0.19\mathrm{V}·\mathrm{cm}$ and less than 6 dB excess optical loss. At a carrier wavelength offset by 1.5 nm from the resonance, we have demonstrated an operating temperature range of 55°C, drastically reducing the requirements on thermal control.

Table 1. Modulator Metrics for Different Numbers of Resonators Loaded on Each Arm

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