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Abstract
Due to the difficulty of controlling the waveguide loss in the doping region, high-speed silicon micro-ring modulators usually have limited extinction ratio. In this work, we present a mode-division-multiplexing (MDM) resonance-enhanced silicon micro-ring modulator with an ultrahigh extinction ratio. We used a two-mode micro-ring resonator and a mode conversion circular structure to trap the light twice within a single micro-ring resonator. Proof-of-concept high extinction ratio up to 55 dB was obtained. 30 Gb/s PAM-8 and 50 Gb/s PAM-4 signaling with a bit error rate below the hard-decision forward error correction (HD-FEC) threshold were demonstrated with the fabricated modulator, indicating great potential for high-order pulse amplitude modulation (PAM).
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1. Introduction
Silicon modulator with high power efficiency and speed is a key building block of silicon photonics, a promising technology to overcome the bottleneck of current electrical interconnect systems. Currently, Mach-Zehnder modulator (MZM) and micro-ring modulator (MRM) are two main kinds of widely used modulators. Compared with MZM, MRM has some unique advantages such as small footprint, intrinsic wavelength-division-multiplexing (WDM) compatibility, a simpler driver architecture, and low power consumption [1]. During the past few years, silicon MRM has been extensively studied with data rates up to 128 Gb/s using on-off keying (OOK) modulation [2–5]. Higher data rates up to 200 Gb/s were demonstrated by using four-level pulse-amplitude-modulation (PAM-4) [6–10]. As the industry moves towards 400 Gb/s and even higher data rate, there are increasing demands on the high-performance modulator that can support 100G per-lane and further 200G per-lane transmission speed. As for MRMs, there are two main solutions to increase their supporting data rates. The first one is to increase the electro-optic (EO) bandwidth of the modulator, and the second option is to use high-order modulation formats such as PAM-4 and PAM-8. High-order modulation formats can significantly increase the data rate given the efficiency-bandwidth trade-off of a resonator modulator, which is 2 and 3 bits per symbol for PAM-4 and PAM-8, respectively [11]. In order to implement high-order PAM modulation, the micro-ring modulator requires a sufficient extinction ratio (ER) [12,13]. As for high ER will bring enhanced modulation depth between each modulation level, thus guarantees the modulation quality (eye opening) of the transmitted signal.
The ER of a micro-ring resonator depends on the relative magnitude of the micro-ring loss coefficient and transmission coefficient [14]. The difference between the two coefficients is given by $\Delta = |t-a|$, where $a$ is the loss coefficient, and $t$ is the transmission coefficient. A smaller value of $\Delta$ will result in a larger ER of a micro-ring resonator. From the simulation results using transfer matrix method shown in Fig. 1, we can see that even a small $\Delta$ perturbation will greatly influence the ER of the transmission spectrum of the micro-ring resonator. Figure 1(a) shows the transmission spectrum with different values of $\Delta$, and Fig. 1(b) shows the extracted ER as a function of $\Delta$. The loss coefficient of the micro-ring mainly relies on the absorption loss of the free carrier and is hard to control, thus makes it very difficult to obtain high ER for MRMs. Currently, most researchers adjust the coupling coefficient by fabricating a series of micro-ring arrays with different gaps between the micro-ring and the straight waveguide to obtain one micro-ring resonator with high ER. However, due to the limited fabrication accuracy provided by the microelectronics foundry, the gap step of the fabricated micro-ring modulator is usually set at about 20 nm. We simulated the transmission coefficient with different gaps by using Lumerical-FDTD Solution, and the result is shown in Fig. 1(c). It is clearly shown that a 20-nm variation of the coupler gap will result in a 0.1 change in the transmission coefficient $t$. The 0.1 change in transmission coefficient $t$ will thus greatly influence the variable $\Delta$ leading to great change in ER. Therefore, it is difficult to accurately control the micro-ring’s ER by adjusting the coupler gap. This is also the reason why the ER for silicon MRM is generally limited at about 20 dB level, which highly limits the potential of higher-order pulse amplitude modulation formats. Up to now, very limited experimental results have been reported for high-speed MRMs with high-order modulation formats such as PAM-6 and PAM-8. In [12], 45 Gb/s PAM-8 transmission was demonstrated using a silicon MRM with a static ER of 30 dB.
Fig. 1. (a) Transmission spectrum of the micro-ring resonator with different values of $\Delta$. (b) Extracted extinction ratio with different values of $\Delta$. (c) Transmission coefficient of the micro-ring resonator with different gaps.
Improving the ER of the micro-ring resonator is not a new research topic. During the past decades, many researchers proposed different solutions to improve the ER of micro-ring resonators. The most common approach is to use a high-order coupled micro-ring structure [15–20]. For example, 34 dB ER was realized by using a 3$^{th}$ order coupled micro-ring resonator [19], 45 dB ER was realized by using a 10$^{th}$ order coupled micro-ring resonator [17], and 70 dB ER was realized by using a 7$^{th}$ order coupled micro-ring resonator [20]. However, due to the cascaded structure of the high-order coupled micro-ring resonator, these devices often feature a large footprint. At the same time, the large footprint also limits the switching rate of these devices to the level of several ns. Another approach is to use a micro-ring resonator with a 2${\times }$2 MZI coupler. In 2011, Sacher et al. demonstrated a silicon MRM with an integrated MZI coupler to tune the coupling coefficients of the micro-ring modulator and realized an dynamic ER in the range of 12-16 dB [21]. Very recently, a parallel-coupled dual-racetrack resonator structure was experimentally demonstrated with a dynamic ER of 9.4 dB at 50 Gb/s bit rates [22].
In this work, we presented a mode-division-multiplexing (MDM) resonance-enhanced silicon micro-ring modulator to achieve high ER MRM and realized higher-order PAM modulation. The proposed modulator is composed of a two-mode micro-ring resonator and a mode conversion-based circular structure to trap light twice within a single micro-ring resonator. L-shaped PN junction was utilized to provide efficient modulation for both TE$_0$ and TE$_1$ modes. Ultrahigh ER up to 55 dB was obtained, 30 Gb/s PAM-8 and 50 Gb/s PAM-4 signaling with a bit error rate below the 20% and 7% forward error correction threshold were experimentally demonstrated. Compared with the previous works, our design realizes high extinction ratio while features a small footprint. Only one micro-ring structure was used in our design. In addition, high speed data transmission indicates its great potential for high-order PAM modulation.
2. Principle and modulator design
Figure 2(a) shows the schematic structure of the proposed device. It is shown that the modulator is composed of a micro-ring resonator and two mode converters. The waveguide width of the MRM is 930 nm, supporting TE$_0$ and TE$_1$ mode. The MRM presented has a radius of 10 $\mu$m with a 20-$\mu$m long coupler length. The gap between the micro-ring and the bus waveguide is set to 0.2 $\mu$m. The mode converter was designed based on a directional coupler (DC) structure with a 5.5 $\mu$m coupling length. After passing through a tapered region, the input light first couples into the two-mode micro-ring resonator in TE$_0$ mode. The TE$_0$ mode resonates within the ring and outputs from the through port. Afterwards, the output TE$_0$ mode is converted to TE$_1$ mode by a DC mode converter and coupled again into the micro-ring in TE$_1$ mode. After resonating in the ring, the light converts to TE$_0$ mode by an identical mode converter and finally outputs. As a result, the final output spectrum of the device is the summation of the two waveguide modes. Two coupling processes enhanced the resonance of light in the micro-ring resonator and thus produced a transmission spectrum with high ER. Fig. 2(b) shows the cross-section structure of the phase shifter within the micro-ring modulator. The waveguide width is 930 nm, and the height is 220 nm with a 90-nm slab. An L-shaped PN junction is formed in the cross-section of the two-mode waveguide. Both the TE$_0$ and TE$_1$ mode are phase modulated with high-efficiency thanks to the large overlap between the depletion region of the L-shaped PN junction and the waveguide modes. The doping concentration is 1${\times }$10$^{18}$ cm$^{-3}$ for p-type region and 8${\times }$10$^{17}$ cm$^{-3}$ for the n-type region. The heavily doped n-type and p-type concentrations are 1${\times }$10$^{20}$ cm$^{-3}$. The heavily doped region is 500 nm away from the edge of the waveguide.
Fig. 2. (a) Schematic structure of the full modulator structure. (b) Cross-section structure of the micro-ring modulator.
We first used the transfer matrix method to analyze the device performance theoretically. In the simulation, the transmission coefficient $t$ of TE$_0$ and TE$_1$ mode were calculated based on the structure parameter of the fabricated MRM using Lumerical-FDTD Solution, which is 0.934 for TE0 and 0.591 for TE$_1$, respectively. We assumed the loss coefficient $a$ of TE$_1$ mode is lower than the TE$_0$ mode, corresponding to a higher waveguide loss of TE$_1$ mode. The higher loss for TE$_1$ mode is consistent with the real device, which mainly comes from the absorption from larger overlap with the highly-doped p$^{++}$ and n$^{++}$ region. The simulated transmission spectra of the modulator are shown in Fig. 3. Figure 3(a) shows the individual transmission spectrum of TE$_0$ and TE$_1$ modes, and Fig. 3(b) shows the output transmission spectrum of the MRM. It suggests that a high ER is always obtainable when the resonance peaks of the two waveguide modes coincide in the transmission spectrum.
Fig. 3. (a) The simulated transmission spectrum of TE$_0$ and TE$_1$ mode. (b) The simulated transmission spectrum of the MRM. (c) Required spectral length and total ER as a function of the mode effective index difference between TE$_0$ and TE$_1$ mode. (d) Transmission spectrum of typical single ring (yellow) and dual-mode ring (blue) modulator
As shown in Fig. 3(a), the two waveguide modes have different free spectral ranges (FSR), which leads to the fact that not every resonance peak in the MRM transmission spectrum has a high ER. Only when the two resonance peaks coincide (e.g., at 1599 nm in Fig. 3(b)), the resonance enhancement effect appear. While the FSR difference between the two waveguide modes also determines the required spectral length for the coincidence of the two resonance peaks and the total ER of the device. FSR is determined by the effective refractive index of the waveguide mode. Thus, we further investigated the relationship between the required spectral length for the coincidence of two mode’s resonance peaks and the mode effective refractive index difference of the two waveguide modes, as shown in Fig. 3(c). It can be seen that the larger the effective refractive index difference between the two modes, the shorter spectral length is required to coincidence the resonance peak. While at the same time, the cost is that the total ER improvement of the device is less obvious. The enhanced static ER will consequently benefit the modulation depth of the modulator at a fixed resonance shift. In Fig. 3(d), we simulated the transmission spectra of a single ring and a dual-mode ring, and compared their dynamic ER under the same resonance shift. The resonance shift of both structure is set to 240 pm, assuming a drive voltage of 4 V based on the simulated refractive index change. The ER of the single ring is 8 dB, while the ER of the dual-mode ring is 25 dB indicating great enhancement of the modulation depth.
The mode converter is also a key component of the proposed modulator. We used a rib waveguide directional coupler (DC) to achieve effective mode conversion between TE$_0$ and TE$_1$ modes. Figure 4(a) shows the top view of the designed DC, and Fig. 4(b) shows the cross-section of the DC. The upper waveguide width is 0.4 $\mu$m, and the bottom waveguide width is 0.93 $\mu$m. The coupling length is 5.5 $\mu$m, and the coupling gap is 0.2 $\mu$m. Simulation of the mode converter was carried out using Lumerical-FDTD Solution, and the simulated electrical field is shown in Fig. 4(c). The simulated spectral response of the DC is shown in Fig. 4(d). It is shown that the DC can achieve high coupling efficiency (CE) with insertion loss lower than 0.5 dB at 1550 nm wavelength. And the crosstalk (XT) of the TE$_0$ mode is under −30 dB from 1500 to 1600 nm.
Fig. 4. (a) Top view of the designed DC mode converter. (b) Cross-section of the DC mode converter. (c) Simulated electric field of the mode converter. (d) Calculated CE and XT of the mode converter.
The working principle of an MRM is to shift the resonance wavelength by means of index modulation. Shifting the resonance wavelength away from the optical carrier results in an intensity modulation for the output optical signal. As for the proposed modulator, the resonance shift of TE$_0$ and TE$_1$ mode are required to be consistent so that the final output spectrum could remain in shape to keep high ER during the index modulation. We used an L-shaped PN junction to achieve high modulation efficiency for both TE$_0$ mode and TE$_1$ mode. Compared with lateral PN junction, the depletion region of the L-shaped PN junction could grow with the waveguide width, thus providing a large overlap with both TE$_0$ and TE$_1$ mode. The simulated refractive index variation for TE$_0$ and TE$_1$ modes as a function of reverse bias is shown in Fig. 5(a). The TE$_0$ and TE$_1$ mode overlap with the L-shaped PN junction are shown in Figs. 5(b) and (c), respectively.
Fig. 5. (a) Refractive index variations for TE$_0$ and TE$_1$ modes as a function of reverse bias voltage. (b) TE$_0$ and (c) TE$_1$ mode overlap with the L-shaped PN junction.
3. Device characterization
The designed MRM was fabricated via a standard silicon photonic processing project provided by Advanced Micro Foundry (AMF, Singapore). The top silicon layer is 220 nm, and the buried oxide thickness is 2 $\mu$m. The microscope image taken at 20-$\mu$m scale of the fabricated modulator is shown in Fig. 6(a). Figures 6(b), (c), and (d) show the zoom-in image of the grating coupler, mode converter, and micro-ring resonator of the device.
Fig. 6. Optical microscope image of (a) the fabricated MDM resonance-enhanced modulator, (b) the grating coupler, (c) the mode converter and (d) the micro-ring resonator.
The static transmission spectrum was first measured using a tunable CW laser (Santec TSL-710) and a photodetector. The result is shown in Fig. 7(a). The figure shows that the transmission spectrum is the summation of two resonance spectra with different FSR. One comes from TE$_0$ mode, and the other comes from TE$_1$ mode. The resonance spectrum of TE$_0$ mode has a smaller full width half maximum (FWHM) while the FWHM of TE$_1$ mode is larger because of its higher transmission loss in the resonator. The peak of the two resonance spectra finally meets each other at 1572.7 nm, leaving a sharp resonance peak with 40 dB static ER. The transmission spectrum under different reverse bias voltages is shown in Fig. 7(b). Record high ER reaches 55 dB at −2 V bias voltage. The resonance shift is 49 pm/V, corresponding to a modulation efficiency of 0.79 V$\cdot$cm. The high modulation efficiency mainly attributes to the large overlap between the L-shaped PN junction and the two waveguide modes. The phase modulation efficiency of TE$_0$ and TE$_1$ modes were also measured respectively when the modes are not overlapping, and the results are shown in Figs. 7(c) and (d). Two resonance peaks at 1553.1 nm and 1554 nm were selected for the modulation efficiency measurement of the two modes just as its marked in Fig. 7(a). From the result, we can see that the resonance shift is 52 pm/V for TE$_0$ mode and 44 pm/V for TE$_1$ mode. Since the modulation efficiency difference between TE$_0$ and TE$_1$ mode is very small (only 8 pm/V), the final output spectrum could always remain in shape with high ER during the index modulation.
Fig. 7. (a) Measured transmission spectrum of the modulator. (b) Transmission spectrum under various reverse bias voltages for TE$_0$+TE$_1$ mode. (c) Transmission spectrum under various reverse bias voltages for TE$_0$ mode. (d) Transmission spectrum under various reverse bias voltages for TE$_1$ mode.
We experimentally evaluate the performance of the mode converter using a four-port structure shown in the inset of Fig. 8. Figure 8(a) shows the spectra when the optical power is launched from Port 1. The insertion loss of the TE$_0$-TE$_1$ link (S41) is 0.92 dB at 1550 nm wavelength, and the cross talk (S31) is lower than −25 dB over the whole wavelength measurement range. Figure 8(b) shows the spectra when the optical power is launched from Port 2. In this case, most optical power should be captured from Port 4, indicating no mode conversion happens. The experiment results are consistent with that expectation. The insertion loss of TE$_0$ mode is 1.21 dB at 1550 nm (S42). The cross talk (S32) is lower than −25 dB. In addition, the mode converter also features a large 1-dB bandwidth of over 100 nm from 1500 nm to 1600 nm.
Fig. 8. Measured spectra of the mode converter when (a) the optical power is launched in Port 1, and (b) the optical power is launched in Port 2.
Then, we carried out the frequency response measurement of the proposed modulator in terms of the EO S parameter. A 43-GHz vector network analyzer (VNA, Anritsu, MS46322B) was utilized, and the measured S$_{21}$ curve was normalized to 100 MHz. The EO S$_{21}$ curve at a bias voltage of −2 V is shown in Fig. 9. A 3-dB EO bandwidth of about 5 GHz is obtained at −2 V bias voltage. It should be noticed that the measured EO bandwidth is for the whole system, comprising the modulator, the GS probe, the high-speed electrical cable, and also the photodetector. Therefore, the EO bandwidth of the modulator should be higher than the presented result.
To verify the high-speed performance of the proposed modulator, we further set up the high-speed measurement. The experiment setup for the high-speed measurement is shown in Fig. 10. The CW laser source is tuned near 1572.7 nm with 10 dBm output power. A 2$^7$-1 pseudo-random binary sequence (PRBS) signal was generated from a 64-GSa/s arbitrary wave generator (AWG, Keysight, M8192A) and amplified by an RF amplifier (SHF807C). The RF signal is combined with −2 V DC bias by a bias-tee and loaded onto the modulator by an RF probe (GGB, Model 40A). The DC voltage is applied to adjust the appropriate operating point of the modulator. The modulated optical signal is amplified via an Erbium-doped fiber amplifier (EDFA) and received by a high-speed photodetector (PD) after passing through an optical bandpass filter (BPF). The photocurrent signal was finally sent to a digital communication analyzer (DCA) for eye diagram sampling or to a real-time oscilloscope (Keysight, DSOZ592A) for data collection and offline digital signal processing (DSP).
We perform the on-off keying (OOK) modulation first. The CW laser source is tuned to 1572.8 nm (225 pm away from the resonance peak at 0 V reverse bias voltage) with 10 dBm output power. The high-speed signal generated from the AWG has a Vpp of 600 mW. After amplified by the RF amplifier (SHF807C), the Vpp of drive swing on the ring modulator is 3.97 V. The measured eye diagram is shown in Fig. 11. By driving the proposed MDM resonance-enhanced modulator with OOK signals at 10 Gb/s, the incident received power is 3 dBm. The measured eye diagram is wide open, with an ER of 7.55 dB.
The high ER brought by MDM resonance will provide wider eye opening for high-order PAM signal. In order to verify the high-speed performance for supporting high-order PAM signal, we further carried out high-speed data transmission by using PAM-4 and PAM-8 modulation format. The modulated optical signal was received by a photodetector and then sent into a real-time oscilloscope with a sample rate of 160 GSa/s for offline digital signal processing (DSP). High-speed PAM-4 and PAM-8 signals were transmitted on the chip by means of the root raised cosine filter with a roll-off factor of 0.01 to compress the signal bandwidth. The matched filter and the time-domain feed-forward-equalization (FFE) were applied at the receiver side to obtain lower BER. The BER curves of the 40 Gb/s PAM-4, 50 Gb/s PAM-4 and 30 Gb/s PAM-8 signals are plotted in Fig. 12(a). The corresponding eye diagrams after post FFE with the lowest BERs in each curve are shown in Figs. 12(b), (c), and (d) respectively.
Fig. 12. (a) BER curves of 40 Gb/s, 50 Gb/s PAM-4 and 30 Gb/s PAM-8 signals. (b) Off-line post-FFE eye diagrams of 40 Gb/s PAM-4 (c) 50 Gb/s PAM-4 and (d) 30 Gb/s PAM-8 with the lowest BERs.
4. Discussion
One practical hurdle with ring modulators is their sensitivity to temperature. To investigate the temperature sensitivity of our device, a numerical simulation was carried out using Lumerical-FEEM Solution. In the simulation model, an aluminum heater was placed 2 $\mu$m above the rib waveguide and act as the heat source. The input power was swept from 20 to 30 mW. The cross section temperature map for 20 mW heating input power is shown in Fig. 13(a). The mode effective index n$_{eff}$ of TE$_0$ and TE$_1$ under different heating power were simulated and the results are shown in Fig. 13(b). At a fixed heating power, a mode effective index difference of 2${\times }$10$^{-4}$ between TE$_0$ and TE$_1$ modes could be clearly seen, indicating different thermal tuning efficiency for TE$_0$ and TE$_1$ mode. We further substitute the n$_{eff}$ of TE$_0$ and TE$_1$ mode into the transfer matrix of the dual-mode ring and calculated the transmission spectrum under 20 mW heating power. The result is shown in Fig. 13(c). When the temperature changes, the resonance wavelength of the two modes no longer overlap with each other, which indicates that the proposed modulator is sensitive to the temperature variation and it is hard to tune it back even with a heater.
Fig. 13. (a) Temperature map of the waveguide cross section at 20 mW heating input power. (b) Refractive index variations for TE$_0$ and TE$_1$ modes as a function of heating input power. (c) Transmission spectrum of the dual-mode ring under different heating input power.
The extinction ratio of the dual-mode ring modulator was greatly enhanced by the transmission spectrum overlapping of the two waveguide modes. However, the enhanced extinction ratio also brings extra insertion loss of the device and may degrade the optical modulation amplitude (OMA). We further investigate the relationship between the ER and OMA with the detuning of bias point. The results are shown in Figs. 14(a) and (b). From the result, we can see that the OMA and ER of a dual-mode ring modulator can be separately optimized at different wavelength detuning. An enhanced ER of 25 dB can be obtained with detuning set as 30 pm with a sacrificed OMA. With detuning larger than 420 pm, both the ER and OMA of the dual-mode ring are slightly higher than that in a single ring structure, corresponding to a limited benefit under these working condition.
Fig. 14. (a) ER versus wavelength detuning for a dual-mode ring and a single ring modulator. (b) OMA versus wavelength detuning for a dual-mode ring and a single ring modulator.
To investigate the reason why the EO bandwidth of the modulator is limited, the electrical S$_{11}$ response of the modulator was also measured at a bias voltage of −2 V using a VNA. The results were fitted to a small-signal circuit model of ring modulators built on SOI substrate as shown in Fig. 15(a) [23]. Figures 15(b) and (c) show the real and imaginary part of the electrical S$_{11}$ response, respectively. According to the extracted parameters in the small-signal circuit model, the resulting RC limited bandwidth of the modulator is 11 GHz. The loaded quality factor Q of the modulator was also calculated from the measured transmission spectrum shown in Fig. 7(a). The dual-mode ring modulator has a loaded quality factor of about 2600 which corresponds to a photon-lifetime-limited bandwidth of approximately 73 GHz. Therefore, the EO bandwidth of the modulator is mainly subject to the RC-limit. It is expected that further improvement of electrical design of the MDM micro-ring modulator would be beneficial for enhancement in the speed of modulation.
Fig. 15. (a) Small-signal circuit model for reverse-biased ring modulators built on SOI substrate. (b) Curve-fitting of the real part of measured S$_{11}$. (c) Curve-fitting of the imaginary part of the measured S$_{11}$.
5. Conclusion
We proposed and experimentally demonstrated an MDM resonance-enhanced silicon micro-ring modulator. The ultrahigh extinction ratio of 55 dB was realized by resonating the light twice within the micro-ring resonator with different waveguide modes. 50-Gb/s PAM-4 modulation with BER under 7% FEC and 30-Gb/s PAM-8 with BER under 20% FEC were experimentally demonstrated. The high extinction ratio benefits the performance of the high-order PAM signals. High-order modulation formats like PAM-4 and PAM-8 provide enhanced spectral efficiency, and will drastically reduce the required operating frequency and power consumption of driving and logic circuits for a CMOS-photonic integrated system. We totally believe that this work will pave the way towards the realization of higher-order modulation formats by using micro-ring modulator. In addition to the application to optical communications, the high static extinction ratio brought by the resonance of two waveguide modes may also benefit applications like optical filters and microwave photonic filters, where there are higher requirements to the filtering extinction ratio and lower requirements to the tuning rate.
Funding
National Natural Science Foundation of China (61875049, 61935011, 62122047).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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