Silicon photonic modulators with a 2 × 1 Fabry–Perot cavity

2.1 Mode (de)multiplexer

Figure 1(b) shows the schematic of the mode (de)multiplexer, which incorporates an adiabatic dual-core tapered coupler for large fabrication tolerance and wavelength-insensitive operation. The operational principle of the mode (de)multiplexer relies on the adiabatic evolution of supermodes, as discussed in Ref. [43]. The details for designing the mode (de) multiplexer can be referred to in Supplementary Material 1. In our design, the widths of the two waveguides are configured to (w _a1, w _b1) = (0.42, 0.28) μm and (w _a2, w _b2) = (0.6, 0.12) μm. The gap widths w _g1, w _g2, and w _g3 have been selected as 1.5, 0.18, and 1.8 μm, respectively, with the taper lengths L ₀₁, L ₀₂, and L ₀₃ determined as 20, 35, and 15 μm, respectively.

2.2 AMWG and FP cavity

Figure 1(c) shows the schematic configuration of the proposed AMWG. Unlike the traditional Bragg gratings, an asymmetric wide waveguide featuring a half-period offset between two sidewall gratings facilitates the conversion of the input TE₀ (TE₁) mode into the reflective output TE₁ (TE₀) mode when the wavelength falls within the Bragg reflection bandwidth. The designed Bragg wavelength λ _B is determined as n _eff0 + n _eff1 = λ _B/Λ, where n _eff0 and n _eff1 represent the effective refractive indices of the TE₀ and TE₁ modes, respectively, and Λ is the grating period. The rib waveguide with a 90-nm-thick slab was selected to accommodate the necessary electrical connections and carrier transitions in the FP cavity modulator. To mitigate unwanted reflection losses at the front and back ends of the grating section caused by abrupt changes in the effective refractive index, adiabatic grating tapers are employed. Here, the corrugation depth δ of the gratings varies linearly from zero to the maximum to connect the straight waveguide and the Bragg grating waveguide. The period number N _tp of the tapered Bragg grating is optimized to be 20 for low reflection loss. The corrugation depth is optimized to be large enough to ensure a broad reflection bandwidth. The total length of the AMWG is determined to be L _AMWG = (2N _tp + N)Λ, where N is the period number of the Bragg grating in the middle. In our design, the corrugation depth is 180 nm with a corresponding grating period Λ of 306 nm to achieve a broad Bragg bandwidth around the centered wavelength of 1,550 nm. Figure 2(a) shows the calculated transmission (T) and reflection (R) of the designed AMWG for the launched TE₀ mode when the period number N = 40, where a simulated large reflective 3 dB bandwidth of approximately 35 nm is achieved. A prominent sidelobe is observed due to the absence of longitudinal apodization in our AMWG design. To explore the resonance characteristic of the proposed FP cavity modulator, the length L _wg of the straight section between the two AMWGs (i.e., the phase shifter region) is varied as 0, 10, 20, and 30 μm. Figure 2(b) shows the simulated resonant spectrum at the drop port for the cases with different L _wg and the same period number of 40. The free spectral range (FSR) decreases as the cavity length increases, and the maximum FSR of 16.6 nm is observed when L _wg = 0 and is mainly constrained by the introduction of the tapered grating. On the other hand, when increasing the length L _wg of the straight section whose width is broadened to be beyond the single-mode regime, the random variation of the resonance wavelength of the FP cavity can be reduced. As a trade-off, we choose the length L _wg to be 30 μm, and the corresponding FSR is around 6.7 nm.

Figure 2:

The simulated results for the FP-cavity modulators. (a) The calculated transmission (T) and reflection (R) of the AMWG for the launched TE0 mode when the period number N = 40; (b) the simulated resonant spectrum of the FP cavity silicon modulator under different L _wg; the simulated (c) Q factor and the corresponding Q-factor-limited bandwidth under different period numbers when L _wg = 0, 10, 20, and 30 μm, respectively.

In conventional resonant modulators, the modulation bandwidth is constrained by the RC time constant and the photon lifetime within the cavity. Regarding the compactness of the cavity, the Q factor often exerts a critical influence over the modulation bandwidth. For FP cavities, the Q factor is primarily constrained by the AMWGs’ reflectivity, which can be designed flexibly by adjusting the period number of the AMWG. In order to employ a moderate Q factor in the FP-cavity modulator for balancing the bandwidth and the modulation extinction ratio, it is imperative to choose the period number appropriately. Figure 2(c) shows the simulated Q-factor for the cases with different L _wg as the period number increases and the corresponding modulation bandwidth is given in Figure 2(d). As it can be seen, the Q factor increases with the cavity length as well as the period number. In the present case, the Q factor increases from 2,000 to 48,000 (when L _wg = 30 μm) as the period number increases from 10 to 60 and the corresponding modulation bandwidth constrained by the Q factor decreases from 100 GHz to 4 GHz. Finally, the FP modulator is designed with a Q factor of 9,400 and a finesse of 40.6.

2.3 Tolerance analysis

Although resonant modulators benefit from compact footprints, their sensitivity to fabrication variations necessitates substantial thermal tuning power to manage the resonance wavelength, thereby leading to increased power consumption. A viable approach is utilizing multimode photonics technology, particularly with optical waveguides broadened far beyond the single-mode regime [44]. For optical resonators, the resonance wavelength shift is dependent on the effective refractive index deviation δn _eff arising from the variation of the waveguide dimensions (ΔW and ΔH) and one has:

where ∂n _eff/∂H and ∂n _eff/∂W are the derivatives of the effective refractive index versus thickness and width, respectively. For 220-nm-thick SOI waveguides, ∂n _eff/∂H is a constant around 3.75 μm⁻¹ and the thickness’s random variation is negligible within a small area. Consequently, we concern more to minimize the coefficient ∂n _eff/∂W to greatly reduce the deviation δn _eff due to the variation ΔW. Figure 3(a) and (b) show the calculation results for n _eff and ∂n _eff/∂W for both TE₀ and TE₁ modes in the rib waveguide as the core width varies, clearly demonstrating that ∂n _eff/∂W decreases rapidly when the waveguide is broadened to be far beyond the single-mode regime (e.g., W > 900 nm). For example, one has ∂n _eff/∂W as low as 0.2 μm⁻¹ for the TE₀ mode when W = 1 μm. In contrast, for the 0.45-μm-wide optical waveguide, one has ∂n _eff/∂W = 1.3 μm⁻¹. For the TE₁ mode, the value of ∂n _eff/∂W drops from 1.2 μm⁻¹ to 0.7 μm⁻¹ when the core width increases from 0.7 μm to 1 μm. Even though one can reduce ∂n _eff/∂W further by increasing the core width W, one should make a trade-off to avoid the reduction of the electro-optic bandwidth due to the increased capacitance in the resonator with broadened waveguides.

Figure 3:

Calculated effective refractive index and its derivative versus waveguide width for (a) TE₀ and (b) TE₁ mode; (c) simulated resonant-wavelength variation under ±0.5 and ±1 nm waveguide width variation for MRM with a 450-nm-wide waveguide and FPM with 1-μm-wide waveguide.

Figure 3(c) shows the calculated wavelength variation of a conventional MRM equipped with a 450-nm-wide bent waveguide and an FP-cavity modulator featuring a 1-μm-wide straight waveguide. Here, the random variation of the core width ΔW is assumed as ±0.5 nm and ±1 nm. In particular, the length L _wg is chosen as 0 μm and 30 μm, respectively, to give a comparison, showing that longer L _wg enables smaller wavelength variation, which is consistent with that discussed above. The reduction in resonant-wavelength shift compared with the MRM confirms the feasibility of embedding a broadened straight waveguide section in the FP-cavity modulator for minimizing the random wavelength variation. In contrast, it is inconvenient to introduce broadened waveguides for MRMs due to the difficulty of achieving sufficient coupling and depressing the higher-order mode excitation in the cavity. As it can be seen from Figure 3(c), the random resonant-wavelength variation for the FP-cavity with a broadened waveguide is much lower than MRMs with a single-mode waveguide in theory as desired.

2.4 PN junction

Owing to the introduction of the AMWGs to separate the input light and the output modulated light, both the TE₀ mode and TE₁ modes resonate in the FP cavity. Previously, a lateral PN junction is often employed in silicon modulators to facilitate overlap between the TE₀ mode and the depletion region. However, selecting a lateral PN structure results in a minor overlap between the TE₁ mode and the depletion region, consequently inducing a small phase shift for the TE₁ mode. A vertical PN junction is preferable for both TE₀ and TE₁ mode modulation. However, the standard foundry does not provide the vertical PN junction due to its complex ion implantation process. Here, we introduce an interleaved PN junction combined with the lateral PN junction [42], as shown in Figure 1(d). This interleaved doping structure, characterized by periodic P- and N-doping with a PN period (Λ_pn), differs from the conventional interleaved doping structure previously reported [45]. We introduce the parameter of W _e to achieve an additional lateral PN junction with an offset of W/2−W _e. The additional lateral PN junction, featuring a PN offset, is advantageous for enhancing the per-length effective refractive-index variation Δn _eff-TE1 of the TE₁ mode while preserving a high variation for the TE₀ mode (Δn _eff-TE0). On the other hand, one should notice that the present interleaved doping structure might have a large parasitic capacitance when compared with lateral PN junctions, leading to bandwidth degradation, particularly for the structure with broadened waveguide. As a result, even though using the broadened waveguide helps reduce the random resonance-wavelength variation, one should make a trade-off by choosing the waveguide width appropriately to achieve improved resonance-wavelength uniformity and high bandwidth. Here, we choose the core width as 1 μm. The medium doping concentration was introduced at two sides of the rib waveguide with a distance of W _d from the edge of the rib waveguide. This distance is optimized to be 350 nm to reduce the sheet resistance of the PN junction and eliminate the carrier absorption loss induced by medium-concentrated doping. Another critical parameter of the interleaved doping is the doping period Λ_pn, which is set to minimally 0.6 μm, aiming to enhance modulation efficiency for both modes, albeit at the expense of reduced bandwidth. It should be noticed that the bandwidth could be substantially compensated by the optical peaking enhancement effect [41]. The period for the interleaving doping is limited by the minimum 0.3 μm feature width for the P and N doping required by the foundry. Details about the simulation analysis of the modulation efficiency for the TE₀ and TE₁ modes with the varied parameters are given in Supplementary Material 4. Finally, the parameter W _e is set to 0.1 μm for a high modulation efficiency for TE₀ and TE₁ mode.

3.1 Static measurements

Figure 4(a) shows the microscopic image of the fabricated FP-cavity modulators. The input continuous light is launched from the input port and output from the drop port by a pair of grating couplers with a total of ∼10 dB coupling loss. The pads at the bottom of the devices function as the heating pad for tuning the centered Bragg wavelength of the AMWGs. The spectral responses were characterized utilizing an optical spectrum analyzer (OSA) and a broadband amplified spontaneous emission (ASE) light source. The transmission spectra of the devices were normalized by deducting the spectral responses obtained from a pair of grating couplers. Initially, the mode (de)multiplexer integrated within the FP-cavity modulator was characterized, as depicted in Figure 4(b). To assess the excess loss and crosstalk of the mode (de)multiplexer, two identically structured mode (de)multiplexers were interconnected, functioning as multiplexer and demultiplexer, respectively, as illustrated in the inset. The pair of mode (de)multiplexers exhibited a measured insertion loss of <1 dB and a crosstalk of <−25 dB. The spectral response at the FP-cavity modulator’s drop port (equivalent to the through port for MRM) was measured, as plotted in Figure 4(c). The FP-cavity modulator demonstrated an excess loss of less than 1 dB and a static extinction ratio of 15 dB. For the AMWG, increasing the period number from the designed value of 35 to the actual value of 280 becomes necessary for achieving sufficient reflectivity when fabricated with standard CMOS lithography. It is due to the optical proximity effects induced in the deep ultraviolet (DUV) lithography process, which tends to smooth the sharp corners of the designed Bragg grating structure and thereby reduce the equivalent corrugation depth. Consequently, the reflective bandwidth decreases from the designed value of 35 nm to the measured value of 7 nm and the FSR of the FP cavity decreases from 6.7 nm to 3.3 nm. Supplementary Material 5 discussed these discrepancies caused by the optical proximity effect when using the 193 nm DUV.

Figure 4:

The measured results for the FP-cavity modulators. (a) Microscopic image of the fabricated FP-cavity modulators; (b) measured transmissions for mode (de)multiplexer. Inset: the test structure for mode (de)multiplexer; (c) measured spectral response at the drop port of the FP-cavity modulator; (d) measured spectral response near the resonance wavelength; (e) the extracted Q factor and Q-factor limited bandwidth for the different FP-cavity modulators with varied period numbers from 120 to 280; (f) measured normalized optical transmissions under different reverse bias voltages; (g) extracted wavelength shifts and the tuning efficiencies under different reverse bias voltages.

We also measured the spectral responses of the FP-cavity modulators with varied period numbers from 120 to 280. Figure 4(d) and (e) shows the measured transmissions near the resonance wavelength and the corresponding Q factors, respectively. It can be seen that the Q factor increases with the period number. When choosing the period number as 120, 160, 200, 240, and 280, the Q factor is about 1,800, 3,150, 4,900, 8,100, and 12,000, respectively, while the corresponding Q-factor limited bandwidths are 120 GHz, 62 GHz, 40 GHz, 24 GHz, and 16 GHz.

The measured finesse of the FP cavity is 25.6. The reduction in finesse compared with the simulated value results from the FSR of the fabricated device is as small as 3.3 nm and is beneficial for improving modulation efficiency. Additionally, the extinction ratio decreases as the period number increases. For example, as the period number increases from 120 to 280, the initially high extinction ratio of 28 dB declines to 15 dB, indicating that the FP cavity moves away from the critical coupling as the period number increases. In the present case, less period number is required for achieving the critical coupling regarding the absorption loss in the PN-doped section and the scattering losses due to the corrugation.

Here, the electric tuning efficiency for the FP-cavity modulator was also evaluated. Figure 4(f) shows the normalized optical transmission as the reverse bias voltage varies. The measured modulation efficiency is about 8 pm/V at 1 V, as shown in Figure 5(g). Therefore, the V _π L is determined to be 0.62 V cm under 1 V. The V _π L of the modulator increases with voltage, as the PN junction is gradually fully depleted under high voltage. For the present case, the effective cavity, which includes the segments of two AMWGs, extends beyond the central straight waveguide, suggesting that only a fraction of the cavity undergoes doping and is amenable to electrical tuning. Enhancement of the modulation efficiency is feasible by expanding the PN doping to include the AMWGs. Finally, considering the FP modulator may work with wavelength detuning from the resonance wavelength, we also extracted the measured dynamic extinction ratio versus the wavelength, shown in Figure 4(h). The extinction ratio reaches a maximum of 8 dB at the resonance wavelength and decreases with wavelength detuning.

Figure 5:

The bandwidth measurement results for the FP-cavity modulators. (a) The E-O bandwidth under different bias voltages at a fixed wavelength (40 pm wavelength detuning) for the FP-cavity modulator with period number of 280; (b) the E-O bandwidth under different wavelength detuning at a fixed 3 V bias voltage for FP-cavity modulator with period number of 280; (c) the E-O bandwidth under different bias voltages at a fixed wavelength (20 pm wavelength detuning) for FP-cavity modulator with period number of 240; (d) the E-O bandwidth under different wavelength detuning at a fixed 3 V bias voltage for FP-cavity modulator with period number of 240.

3.2 High-speed measurements

Electro-optical (E-O) bandwidth and eye diagrams were measured to elucidate the high performance of the fabricated FP-cavity modulators. The E-O bandwidth under different bias voltages at a fixed wavelength and the E-O bandwidth under different wavelengths at a fixed bias voltage were measured for the FP modulator with a period number of 240 and 280. For the FP-cavity modulator with a period number of 280 (correspondingly, one has a moderate Q factor of 12,300 and a Q-limited bandwidth of 16 GHz), the bandwidth versus the voltage at a fixed wavelength with 40 pm detuning to the resonance wavelength was quantified and illustrated in Figure 5(a). The bandwidth increases from 22 GHz to 28 GHz as the voltage increases from 1 V to 3 V. The reduction in parasitic capacitance under a high reverse voltage, coupled with the increased wavelength detuning via electrical tuning, contributed to the improvement in bandwidth. When operated with increased voltages, the elevated S21 curves peaking at higher frequencies substantiate the optical peaking enhancement effect. Given the relatively low modulation efficiency of the FP-cavity modulator, the electrical tuning induced by the optical peaking enhancement effect in different voltages is poor. At higher voltages, the decrease in the parasitic capacitance markedly influences the enhancement of bandwidth.

Figure 5(b) shows the bandwidth versus different wavelength detuning when the reverse voltage is fixed at 3 V. In this experiment, the wavelength detuning ranged from 20 pm to 70 pm. The distinct optical peaking enhancement effect was corroborated in the proposed FP-cavity modulator, which was previously observed in MRMs [29], [41]. The Q-factor limited bandwidth is expected to be 16 GHz, as is shown in Figure 4(d), and the RC-limited bandwidth is calculated to be 17.5 GHz. The bandwidth without detuning is estimated to be 12.4 GHz under 3 V reverse bias, which is 3.4 GHz smaller than the bandwidth under 20 pm detuning. A more prominent optical peaking enhancement effect and larger bandwidth for the FP-cavity modulator are realized with larger wavelength detuning. With a wavelength detuning extended to 70 pm, the FP-cavity modulator achieves a bandwidth of 37 GHz accordingly. For the FP-cavity modulator with a period number of 240 (Q = 8,100, i.e., Q-limited bandwidth = 24 GHz), the bandwidth variations at different voltages and different wavelength detuning exhibit a pattern akin to that observed in the FP-cavity modulator with a period number of 280. E-O response to varied voltages was quantified when introducing a 20 pm wavelength detuning, as depicted in Figure 5(c). The bandwidth increases from 31 GHz to 36 GHz as the voltage increases from 1 V to 3 V. Figure 5(d) depicts the bandwidth measured at a fixed voltage of 3 V with a wavelength detuning varying from 20 pm to 120 pm. Upon selecting larger wavelength detuning, this FP-cavity modulator achieves a bandwidth exceeding 40 GHz, surpassing the capabilities of the Vector Network Analyzer (VNA) in the lab.

In summary, significant enhancement of bandwidth through the wavelength detuning underscores the potential for high-speed modulation, despite the FP-cavity modulator’s high Q factor and limited RC bandwidth. It is important to note that the bandwidth expansion achieved through wavelength detuning comes at the cost of a reduced extinction ratio, as shown in Figure 4(h). Greater wavelength detuning invariably leads to a diminished extinction ratio of the transmitter’s eye diagram. Consequently, a moderate wavelength detuning is often chosen for making a trade-off between the bandwidth and the modulation efficiency to realize open eye diagrams with a high extinction ratio.

Ultimately, high-speed eye diagrams of the fabricated FP-cavity modulator were obtained to corroborate its performance in high-speed data transmission. Eye diagrams were recorded at different bit rates varying from 20 Gbps to 50 Gbps, each under distinct wavelength detuning. Figure 6(a) and (b) shows the reference eye diagrams of the RF driver amplifier under 20 Gbps and 50 Gbps. Figure 6(c)–(f) shows the optical eye diagrams of the FP-cavity modulator at 20, 30, 40, and 50 Gbps, respectively. The eye diagrams were measured for the FP-cavity modulator with a period number of 280, which has a low bandwidth and requires wavelength detuning to support high-speed modulation. Wavelength detuning increased with higher bit rates to enhance the bandwidth, albeit at the expense of reduced extinction ratio. Improved eye diagrams could be anticipated by further extending the PN junction to encompass the two AMWG sections, thereby improving the modulation efficiency; concurrently, reducing the period number may allow higher bandwidth and preserve an acceptable modulation extinction ratio.

Figure 6:

Measured NRZ eye diagram of the RF driver under (a) 20 Gbps and (b) 50 Gbps; measured NRZ eye diagram of the FP-cavity modulator with period number of 280 under (c) 20 Gbps, (d) 30 Gbps, (e) 40 Gbps, and (f) 50 Gbps.

3.3 Wafer-level measurements

An 8-inch wafer-level measurement encompassing 25 chips was performed to record the resonance wavelengths of both MRMs and FPMs on the same chips. Each chip contained three identical MRMs and FPMs, spaced 200 μm between adjacent devices. The maximum resonance-wavelength variation Δλ _res of the fabricated FPMs and MRMs on the same chip was recorded, and the corresponding wafer maps are, respectively, shown in Figure 7(a) and (b). According to the foundry’s datasheet, the MRMs equipped with 0.45-μm-wide waveguides exhibit an average wavelength variation of 0.55 nm. In contrast, the resonance-wavelength variation can be reduced to Δλ _res = 0.34 nm by using the MRMs developed here with a waveguide whose core width is widened to 0.65 μm, as shown in Figure 7(b). As a comparison, the wafer-level average resonance-wavelength variation is further reduced by 43 % to Δλ _res = 0.19 nm when using the present FPMs. Figure 7(c) shows the box plot of the resonance-wavelength variation for FPMs and MRMs across 25 chips. Evidently, the FPMs achieve a significant reduction in random wavelength variation compared to the MRMs. We also count the chips exhibiting a resonance-wavelength variation greater than 0.2 nm and less than 0.2 nm for FPMs and MRMs, respectively, as depicted in Figure 7(d). For FPMs, there are 15 out of 25 chips demonstrated a minor variation of less than 0.2 nm. In contrast, for MRMs, there are only 4 out of 25 chips feature a variation of less than 0.2 nm. In other words, 60 % of the FPMs feature Δλ _res < 0.2 nm, whereas only 16 % of the MRMs feature Δλ _res < 0.2 nm. To conclude, the wafer-level measurement verified the advancement of the FPMs developed here in reducing resonant-wavelength variation. This 0.15 nm resonance wavelength variation reduction can reduce the power consumption of the heating tuning for wavelength alignment, as the heating for wavelength alignment accounts for most of the power consumption in the resonant modulator. Considering the 0.11 nm/mW heating tuning efficiency and 50 Gbps transmitting, the FPM shows an overall estimated 22 fJ/bit power consumption reduction compared with the MRM. The detailed power consumption discussion for the FPM and MRM can be referred to Supplementary Material 3.

Figure 7:

The wafer-level measurement of the resonance-wavelength variation (a) for FPMs (Δλ(FPM)) and (b) for MRMs (Δλ(MRM)) on each chip; (c) the box plot of the resonance-wavelength variation for FPMs and MRMs across 25 chips; (d) the number of chips on which the resonance-wavelength variation is larger than 0.2 nm and less than 0.2 nm for FPMs and MRMs, respectively.