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Abstract
We propose and experimentally demonstrate a novel compact folded Michelson interferometer (FMI) modulator with high modulation efficiency. By folding the 0.5 mm-long phase shift arms, the length of the modulation area of the FMI modulator is only 0.25 mm. Meanwhile, the traveling wave electrode (TWE) is also shorter, which decreases the propagation loss of the RF signal and contributes to a small footprint. The Vπ-L of the present device is as low as 0.87 V·cm at −8 V bias voltage. The minimum optical insertion loss is 3.7 dB, and the static extinction ratio (ER) is over 25 dB. The measured 3-dB electro-optical (EO) bandwidth is 17.3 GHz at a −6 V bias. The OOK eye diagram up to 40 Gb/s is demonstrated under 2 V driver voltage.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
In recent years, Silicon photonics (SiPh) has been proven to be the primary technology to meet the rapidly growing demand for transmission capacity in optical communications and interconnects [1–3]. Among various photonic platforms, the silicon photonics platform is considered one of the most potentially valuable platforms due to the compatibility with the complementary metal-oxide-semiconductor (CMOS) fabrication processes [4]. Achieving a larger 3-dB electro-optical (EO) bandwidth and better modulation efficiency for the silicon photonics modulator has always been one of the critical challenges in SiPh. The Mach-Zehnder interferometers (MZI) and Microring-Resonators (MRR) are the primary optical structures of the carrier-depletion-based silicon modulators. The MRR devices have excellent modulation efficiency and a compact footprint. But they can only operate in a narrow optical bandwidth and are sensitive to environmental and manufacturing errors [5]. Unlike the MRR, the MZI devices have a broad wavelength operating range and good fabrication stability. However, these modulators have the apparent shortcomings of giant footprints. Many valuable efforts have been made to achieve lower Vπ-L for the MZI modulators, mainly optimizing doping conditions of the PN junction, such as designing interleaved-shaped [6], L-shaped [7], and U-shaped PN junctions [8,9]. The different optical structures are also proved beneficial to improve the modulation efficiency, such as slow-light [10,11], loop [12], and Michelson interferometer (MI) optical structures. Because the light passes through the phase shifter twice, the MI modulators were first demonstrated with a low Vπ-L of 0.72 ∼ 0.91 V·cm by Li et al [13]. By applying lumped electrodes, the eye diagrams of the MI modulators with 0.72 V·cm Vπ-L were up to 40 Gb/s [14]. Then the single-drive push-pull MI modulator was reported with 0.95 ∼ 1.26 V·cm Vπ-L [15]. Only depending on this structural characteristic, the insertion loss of these modulators is far lower than the modulators with the mentioned novel-shaped PN junctions. Nevertheless, the light passes through the modulation waveguides twice in opposite directions, resulting in an increased mismatch between microwave and light velocity, which limits the 3-dB bandwidths of the reported MI modulators. Folding the devices is an other way to shorten the length of modulators. It has been reported that the length of a folded MZI modulator can be reduced to one-half or one-fourth of the length before folding [16–18]. However, the width of these reported folded modulators increases with decreasing the length because of folding both the waveguides and electrodes. Shortening the length at the expense of width is not conducive to small device footprint. The above folding method have little impact on the device performance, as long as the electrical signal is always loaded on the modulated waveguides.
In this paper, a novel folded Michelson interferometer (FMI) modulator is first proposed to improve the EO bandwidth performance of silicon MI modulators and reduce the footprint of the devices. The entire length of the modulation region is reduced to half the length of the phase shift arms without increasing the width of the device. The length of the traveling wave electrode (TWE) is also reduced by half, improving the 3-dB EO bandwidth of MI modulators. Taking the time delay, microwave loss, and speed mismatch into consideration, we propose the model of the FMI modulators to simulate their bandwidth performance by theoretical analysis. The calculated result is in general agreement with the measurement data. The FMI modulator with a 500 µm total length of the phase shifter can reach 17.3 GHz EO bandwidth at −6 V reverse bias voltage. In the meantime, the Vπ-L is 0.87 V·cm at −8 V bias voltage. The eye diagram can reach 40 Gb/s with an extinction ratio (ER) of 2.26 dB by measurement. For all the FMI devices, the width of devices, mainly influenced by the TWE width, increases little when the length of modulation areas is half that of phase shift arms. So, these devices have a more compact footprint, which helps improve the integration degree of the SiPh chip compared to the traditional MI modulators.
2. Device design and simulation
Figure 1(a) shows the structural schematic of the designed FMI modulator. The optical structure of the FMI modulator mainly consists of one 3 dB 2 × 2 multimode interferometer (MMI) coupler and two doped phase-shift arms terminated with a loop reflector. The input light is split into two identical power beams with a 90-degree relative phase difference by the MMI. Subsequently, they are input into the corresponding doped silicon waveguides, where the light is modulated by the RF signal. At the end of these waveguides, beams reach the reflection structure and return to the MMI through the original path while modulated again, finally output from the other port of the MMI. Unlike the traditional MI modulators, the doped waveguides of the FMI modulators are folded by the bent waveguides, shortening the overall length of the device. The strip waveguides can constrain the optical field better than rib waveguides. So the bent radius can be smaller using the strip waveguides, which is beneficial to the compact footprint. Based on the above optical structure, the FMI modulators are designed with the Ground-Signal-Ground electrode driving style, which is widely used in silicon modulators. It works by applying driving signal voltages to the high-speed phase shifters.
Fig. 1. (a) The schematics of the designed FMI modulator and (b) the cross-section structure of the phase shift arms.
Figure 1(b) illustrates the cross-section structure of the FMI modulator arms. The two PN junctions on the same side are symmetrical, with the signal electrode as the central axis. For TWE modulators, electrode capacitances and PN junction capacitances are of great importance for their bandwidth performance. These PN junctions in the FMI modulators are in parallel, which causes the total junction capacitance to increase and then affects the bandwidth of these modulators. However, when the lengths of optical arms are the same, the length of electrodes shortens to half the typical MI modulators. This can decrease the loss of RF signal and improve the bandwidth performance.
The 2 × 2 MMI is of great importance for our devices. As shown in Fig. 2(a) and (b), the light is input into the MMI from port 1 and output from ports 2 and 3, then passes through the modulation area. The width (Wc) and length (Lc) of the core are designed as 5 µm and 29.58 µm, respectively, to balance size and loss. And the widths of the taper at both ends are 0.5 µm (Wi) and 1.21 µm (Wo), respectively. The length (Lt) and gap (Wg) of the tapers are 10 µm and 0.46 µm. The simulated electric field is illustrated in Fig. 2(c) when two modulated beams with different Δphase (the phase of the light from port 2 minus that from port 3) return into the MMI from ports 2 and 3. And the returned light will be output from port 4 when Δphase is −90°. When the light with a wavelength of 1550 nm is input from port 1, the losses of ports 2 and 3 are 3.16 dB and 3.35 dB, respectively, according to the simulation result shown in Fig. 2(d). At the same wavelength, when the phase difference of the input lights from ports 2 and 3 changes, the intensity of the two output lights (ports 1 and 4) alternates. According to Fig. 2(e), when the Δphase is −90°, the light is output from port 4 with a maximum transmission of about 0.93.
Fig. 2. (a) The schematics of the designed MMI; (b) the simulated electric field input from port 1, and (c) the simulated electric field input from ports 2 and 3 with different Δphase. (d) the simulated loss of ports 2 and 3 when the beam is input from port 1, and (e) the simulated transmission of ports 1 and 4 when the beam is input from ports 2 and 3 with different Δphase.
For all the FMI devices, the heights of the slab (Hslab) and waveguide (Hrib) are 90 nm and 220 nm, respectively. The waveguide width (Wrib) is 500 nm. The doping concentrations of the P and N areas are 3.29 × 1017/cm3 and 5.78 × 1017/cm3, respectively. Furthermore, the heavily doping concentrations of the P++ and N++ regions are 1.7 × 1020/cm3 and 3 × 1020/cm3. The offset of the PN junction is 100 nm to the N doped area because the change in the hole concentration results in a more significant change in the refractive index compared to the change in the electron concentration. The simulated electron concentration distribution of the designed junction at 0 V and −6 V bias is shown in Fig. 3(a). And Fig. 3(b) illustrates the variation of the effective refractive index with reverse bias voltages in phase shifter arms using the above junction design. The widths of the ground electrode (WG) and signal electrode (WS) are 20 µm and 8 µm, respectively. The gap of electrodes (WGAP) for the modulators is 3 µm. The height of all electrodes (HTWE) is 2 µm, and the gap between the bottom of the electrodes and the top of the slab silicon is 2.47 µm.
Fig. 3. (a) Simulated electron concentration distribution of the designed PN junction at different bias and (b) the simulated variation of the effective refractive index with reverse bias voltages.
For our FMI modulators, reducing the TWE length is beneficial to increase the EO bandwidth, although the bent waveguides will add the time delay. The theoretical equation to calculate the bandwidth of the MI modulators has been given in Ref. [19], but the microwave loss isn’t taken into account. To get reliable simulation results, we derive the theoretical bandwidth equation of FMI modulators by modifying the theoretical equations of the MI modulators and MZI modulators, taking the microwave loss into account [20]. Assuming the impedances of the signal source (Zs) and the terminator (Zt) are both 50 Ω, when the light passes through the modulation area for the first time, the average voltage Va1 applied to one doped rib waveguide at the signal frequency ωm is given by [20]
The equivalent circuit model of the FMI modulator and the relation between the circuit and the physical device is shown in Fig. 4. The Rtwe and Ltwe are the line resistance and the line inductance, respectively. The Cair is the capacitance of the air space above the electrode and beneath the Si substrate. The Cbox is the capacitance of the buried SiO2 (BOX) layer. Cvia and Cmetal are the capacitance between two vias and sidewalls of the signal and the two ground electrodes, respectively. The Cdep and Zsi are the capacitance of a single PN junction and the impedance of the doped silicon between the carrier depletion region and the contacts, respectively. Rsi is a resistance that respesents the loss of the longitudinal current inside the substrate and the Si waveguide layer. Csub and Gsub represent displacement currents and the transverse conductive in the Si substrate, respectively. Cssub is the capacitance between the signal metal and the Si substrate. To make the model valid at the high-frequency limit, the virtual capacitor Csub1 is necessary and does not represent any substantial part. All the parameters can be caculated referring to the Ref. [20]. Different from the model in Ref. [20], there are two PN junctions in parallel which causes the total capacitance of PN junctions twice that of a single PN junction and the total resistance of junctions to be half that of one junction. The electrical model of the right waveguide is same as the left and the capacitance of the premetal dielectric layer (PMD) is replaced by the capacitance of the via Cvia.
Fig. 4. (a) Transmission line equivalent circuit model of the traveling wave electrode shown in Fig. 1(b). (b) Relation between the circuit and the physical device.
The optical and microwave signals co-propagate at this moment. When the optical signal travels through the rib waveguide backward, it counter-propagates with the loaded microwave signal. So the average voltage Va2 is given by
For our designed FMI modulators, the R is 6 µm and the Mr is 337 µm. As shown in Fig. 5(a), the calculated 3-dB bandwidths of FMI modulators with 250 and 500 µm electrode lengths are 19.7 GHz and 12.3 GHz, respectively. And there is the comparison of calculated bandwidths of the FMI modulator and the MI modulator with the same bias voltage and modulation waveguides length in Fig. 5(b). The calculated bandwidth of the MI modulator is 16.4 GHz. Because of folding the modulation waveguides, the electrode length of FMI modulators is half of that of MI modulators, which improves the modulator bandwidth performance. The bandwidth performance of the FMI modulators is limited by the time delay that the light accumulates before traveling through the modulation area again. The longer length of the modulation area, bent waveguides, and reflect-loops will cause more delay. So the FMI modulators with a shorter phase shifter will have better bandwidth performance.
Fig. 5. The calculated EO frequency response of (a) FMI modulators at −6 V bias with 250 and 500 µm electrode lengths; (b) the FMI modulator and the MI modulator at −6 V bias with 500 µm modulation waveguides length.
3. Device characterization
The FMI devices were fabricated on silicon-on-insulator (SOI) via a standard silicon photonic processing platform provided by Advanced Micro Foundry (AMF). The doping concentrations and the structure of the device are as alleged above. We induct two kinds of modulators with different lengths of phase shifter arms (0.5 mm and 1 mm). And they are named FMI-0.25 and FMI-0.50 according to the length of the modulation areas (0.25 mm and 0.5 mm), half the length of the total phase shifters.
With a high-precision tunable laser scanning a broad wavelength span, the static transmission spectrums of the above FMI modulators were measured under various reverse bias voltages. The on-chip propagation loss for the FMI-0.25 modulator and FMI-0.50 are 3.7 dB and 4.3 dB (excluding the loss of grating couplers), as illustrated in Fig. 6(a) and (b). The static ER of all devices is above 25 dB under all reverse bias voltages. And the maximal ER of these devices is about 45 dB. We extract the phase changes of two different FMI modulators at around 1550 nm wavelength, as shown in Fig. 6(c). According to the curve, 8 V is very close to the voltage of π phase shift for FMI-0.50. Because the Vπ of the FMI-0.25 is larger than the breakdown voltage of PN junctions, the modulator efficiency of these devices is calculated by using the formula Vπ-L =(V×FSR×L) / (2×Δλ) where V is the bias voltage, FSR is the free spectral range, L is the total length of the phase shifter arm, and Δλ is the shift of the spectrum nick. The calculated Vπ-L at −8 V of the FMI-0.25 and FMI-0.50 modulators are 0.87 V·cm and 0.84 V·cm. For a conventional silicon modulator, the length of the phase shifter arm is equal to the length of the entire modulation zone. However, for the FMI modulator, the former is twice as long as the latter. If the length in the calculation equation is defined in the calculation equation as the length of the modulation area, the result will be half of the original one.
Fig. 6. The transmission spectra of (a) FMI-0.25 modulator and (b) FMI-0.50 modulator. (c) Extracted phase change under different bias voltages.
We got the 3-dB EO bandwidth of our devices by measuring the S21 parameter, as illustrated in Fig. 7. A 67 GHz performance network analyzer (PNA, Keysight, N5227B) was used during the measurement, assisted by a lightwave component analyzer (LCA, Keysight, N4373E). And a standard 50 Ω terminal resistance was connected to one of the probes. All the measured curves are normalized to 100 MHz. For the FMI modulators, the 3-dB EO bandwidths increase with the bias voltage. When applying a −6 V bias, the bandwidths are 17.3 GHz and 10.4 GHz, respectively, in general agreement with the above simulation results (19.7 GHz for the FMI-0.25 modulator and 12.3 GHz for the FMI-0.50). The deviation is about 2 GHz, which may mainly come from the signal loss before the RF signal travels along the TWE and the difference in the capacitance of the PN junction compared to the simulation. All the frequency responses of these modulators have a dip at around 33 GHz for the short devices and 25 GHz for the long devices. In our opinion, the dips in frequency responses are caused by the accumulated time delay because of the repeated interaction between optical signals and RF signals. Similarly, it also happened in the work of Liu et al [12]. As shown in Fig. 7, the longer the device is, the larger the delay is, and the smaller the 3-dB EO bandwidth is. The limited bandwidth can also be improved by shortening the length of loop reflectors and bent waveguides, which decreases the time delay. The different dip frequency between the simulation and the measurement may be mainly caused by the deviation of the estimated time that light through the reflector with the actual time. The model simplifies the complex group velocity variation during the reflection of light through the bending waveguides and the MMI, and the process errors also can result in a change in the group refractive index of the waveguide. So there is a deviation of the estimated time. The impact of the reflection time increases as device length decreases. So the FMI-0.5 has better consistency of dip frequency between simulation and the measurement than the FMI-0.25.
Figure 8 illustrates the experimental setup for high-speed OOK modulations using the FMI −0.25 modulator. The light from the tunable laser passed through the polarization controller (PC) and then was coupled into the FMI modulator. In the meantime, a non-return-to-zero (NRZ) pseudorandom binary sequence (PBRS) signal of length 27-1 produced by the signal generator (Keysight M8045A) was output by the pattern generator remote head (PGRH, Keysight M8057B). Subsequently, the RF signal was amplified by a system amplifier (SA, Keysight N4985A) and loaded onto the device with a DC bias voltage (−4 V) by the GSG probe. Another end of the TWE was also connected with an external 50 Ω resistor. The light was modulated by the loaded signal in the FMI modulator and then amplified through an erbium-doped optical amplifier (EDFA) to ensure enough optical power. A filter was used to pass the optical signal only at 1549 nm. Then the optical signal was divided into two equal parts in the clock data recovery (CDR, Keysight N1078A). One part was input directly into the digital communication analyzer (DCA, Keysight N1000A), and the other was converted to an RF signal as the trigger of the DCA. The measured results of the OOK eye diagram are shown in Fig. 9(a)–(c). At 20 Gb/s and 30 Gb/s data rates, the dynamic ERs are 4.59 dB and 3.43 dB, respectively. At 40 Gb/s, the highest achievable data rate, the eye diagram is limited and becomes relatively unclearer than at a lower data rate because the EO bandwidth is only around 13 GHz at −4 V bias voltage. And the ER is reduced to 2.26 dB. All the cases are applied with a peak-to-peak voltage (Vpp) of 2 V and a DC bias of −4 V. The measured bit error rate (BER) curves as a function of Vpp and received power are illustrated in Fig. 9(d) and (e). When the Vpp and received power increase, the BERs improve. Under 20 Gb/s and 30 Gb/s, the BERs are close to each other and far lower than under 40 Gb/s. A higher bias voltage can also improve the BER at 40 Gb/s by increasing the 3-dB EO bandwidth.
Fig. 9. Measured OOK eye diagrams at (a) 20 Gb/s, (b) 30 Gb/s, and (c) 40 Gb/s. Measured BER curves under different (d) Vpp and (e) received power.
4. Discussion
Table 1 shows the comparison between the performances of our FMI modulator and other TWE MI modulators on SOI and Lithium niobate on insulator (LNOI) platforms. Compared with the traditional MI modulators on the SOI platform, the FMI modulator can achieve a large bandwidth while having a low Vπ-L. And the shortened length of the modulation areas means a compact footprint, which is beneficial for chip integration. Because of the material properties, the MI modulators on LNOI hybrid platforms, such as the SOI-LNOI platform [21] and silicon-rich nitride (SRN)-LNOI platform [22], have better bandwidth performance but less compatibility with CMOS fabrication processes. The bandwidth performance is still limited due to the time delay and counter-propagation of the RF and optical signals. Besides changing the gap and width of the TWE to match electric and optical signals better, shortening the bent waveguides and loop mirror structures can also increase 3-dB bandwidth by reducing the time delay. As illustrated in Fig. 10, reducing the Mr and Zt can improve the bandwidth of the FMI modulators. As the Mr and Zt decrease, the device bandwidth performance increases gradually. Considering the short length of the electrodes, applying lumped electrodes is also helpful for achieving a large 3-dB bandwidth, which has been proved in MI modulators [14]. And the photonic and electronic co-designed is a great method to further increase the device bandwidth [18].
Table 1. Performance comparison of TWE MI modulators
5. Conclusion
In summary, we propose and experimentally demonstrate a compact silicon FMI modulator with a short length of TWE. By folding the 500 µm-long phase shifter arm, the length of our device modulation area is cut in half, which benefits the compact footprint. The low Vπ-L is 0.87 V·cm at the −8 V bias voltage. And with only 2 V drive voltage, the data rate of OOK modulation can reach 40 Gb/s. Because of the short TWEs caused by the fold effect, the EO bandwidth of our FMI modulator is obtained as 17.3 GHz, the largest recorded bandwidth of the silicon TWE modulator based on the MI structure. This FMI modulator has a significant advantage in compact device footprint and improves the integration degree of silicon photonic chips. And it is a great choice under the demand of short-reach interconnects.
Funding
National Key Research and Development Program of China (2019YFB2203502); Strategic Pioneer Research Projects of Defense Science and Technology (501100013351) (XDB43020500); Key project of National Natural Science Foundation of China (61935003); National Outstanding Youth Foundation of China (501100010225) (61904185); Shanghai Sailing Program (20YF1456900).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this work are not publicly available at this moment but may be obtained from the authors upon reasonable request.
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