1. Introduction

The R&D field of silicon photonics has gained significant advancement over the past decade and is quickly moving from upstream research into high-impact technological applications for optical interconnects in datacenters. Recently, researchers have developed single-chip microprocessors integrating over 70 million transistors and 850 silicon photonic components that work together to provide logic, memory, and interconnect functions and communicate directly using light [1]. The single-chip microprocessor uses silicon microring resonators as an electro-optic (EO) modulator with an integrated feedback circuit to stabilize the microring resonator resonance wavelength at the carrier wavelength.

Silicon microring resonators are widely regarded as one of the building blocks in silicon photonic integrated circuits, featuring the key merits of potentially low power consumptions and compact footprints. However, one major hurdle to overcome before practical applications of silicon microrings is that the resonance wavelengths of microrings are highly sensitive to dynamic variations of the working conditions, including the chip temperature and the laser carrier wavelength. The variations result in a misalignment between the microring resonance wavelength and the carrier wavelength, which potentially leads to a significant compromise of the microring performance. Although the chip temperature can be generally maintained through advanced packaging techniques, local temperature modulations at a microring due to local heat sources are hard to be suppressed. Thus, active stabilization of silicon microring resonance wavelengths is critical for practical uses, particularly for large-scale-integrated photonic circuits.

To date, researchers in the silicon photonics community have proposed and demonstrated two classes of methods to monitor the resonance wavelength for actively stabilizing silicon microrings, namely (i) photocurrent detection using an integrated photodetector [1–11], and (ii) conductivity detection using a contactless integrated photonic probe method [12, 13].

Class (i) utilizes photodetectors based on hybrid Ge-on-Si [4, 7], defect-state-absorption (DSA) [5, 6, 8], and surface-state-absorption (SSA) [10, 11]. Most demonstrated stabilization schemes employed off-resonator photodetectors that are integrated at the microring drop-port waveguide as a monitor [1–7] and feedback-controlled with a base-line method [3], a threshold-detection method [4], a dithering-signal detection method [5, 6], and a balanced-homodyne detection method [7].

However, the shortcoming with using an off-resonator photodetector as a monitor is that the monitoring cannot be readily localized to an individual microring in a large-scale-integrated photonic network or an N × N switch fabric of multiple microrings. Besides, the demonstrated schemes in the literature [1–7] only employed a thermo-optic (TO) tuner integrated with the microring for spectral realignment. The TO-tuner-only realignment schemes require power consumption to pre-heat the chip at an elevated chip operational temperature [1–7]. The heating imposed potentially causes thermal crosstalks among neighborhood devices, and thus complicates the chip thermal management.

Class (ii) utilizes the electric conductivity variations of the silicon waveguide surfaces caused by SSA for monitoring the on-chip optical power at the carrier wavelength [12, 13]. The method does not require integrated PIN diodes to extract the photocarriers. However, the detection of a minute conductivity change requires a high-precision conductance measurement with a resolution down to ~nS, upon a modulated electrical drive of ~10 V [13].

Our research group has previously invented and demonstrated a proof-of-concept of actively stabilized silicon microrings integrated with a DSA-based PIN photodetector as a monitor following class (i), and feedback-controlled using a threshold-detection method [8, 9]. We integrated in the microring an EO carrier-injection-based PIN diode tuner to blueshift the red-detuned resonance wavelength upon a temperature rise, or to blueshift the resonance wavelength upon a blue-drifted laser carrier wavelength. We also integrated in the microring a TO tuner in order to redshift the blue-detuned resonance wavelength upon a temperature drop, or to redshift the resonance wavelength upon a red-drifted laser carrier wavelength.

The threshold-detection method is simple, as it only compares the monitored photocurrent value with a pre-set threshold value [2, 8, 9]. However, it sends a false signal when the waveguide optical power drops below that is necessary for the threshold photocurrent value, while the resonance wavelength remains fixed. Thus, in order to improve the stabilization scheme to adapt to a variable waveguide power, we have recently extended the scheme to a slope-detection method [10, 11], which keeps track of the photocurrent drop between two processing loops and compares the drop with a pre-set slope threshold.

In this paper, we detail the latest version of our slope-detection method, with a further extension to comparing the monitored photocurrent change with a step-wise reduction in the slope threshold over processing loops. We experimentally demonstrate our enhanced active stabilization method using a foundry-fabricated silicon microring linear array, upon both an on-stage temperature modulation and an on-chip localized temperature modulation.

2. Methodology

2.1 Working principle

Figure 1 illustrates the working principle of the slope-detection method applied to a silicon microring. For an in-microresonator photomonitor, the detected photocurrent is enhanced by the microring resonance and exhibits a resonance lineshape that follows the drop-transmission resonance lineshape [8–10]. Therefore, we can monitor the photocurrent value, I_s, to detect the alignment of a microring resonance with a carrier wavelength, λ_o (Figs. 1(a) and 1(b)). When a microring operates in the normal condition, the microring resonance wavelength aligns with λ_o (black-line). The photomonitor then detects a maximum photocurrent at λ_o at the beginning of the processing loop, I_s(0).

 

Fig. 1 (a)-(c) Schematics of the working principle of our actively stabilized silicon microrings with (a) drop-transmission and (b) photocurrent resonance spectra variations upon an increased temperature, and (c) the photocurrent value variation over time at the carrier wavelength λ₀. (d) Schematic of the waveguide-crossing-coupled actively stabilized silicon microring integrated with an in-resonator photomonitor, an EO tuner and a TO tuner. The microring is feedback-controlled by an off-chip microprocessor-based circuit. L.B.: leakage block. (e)-(f) Cross-sectional-view schematics of (e) the in-microresonator SSA-based photocurrent monitor, (f) the EO diode tuner and the TO tuner. Inset of (e): energy band-diagram of SSA in silicon in 1.55μm wavelengths.

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When the on-chip temperature rises over a sampling time, T_s, the microring resonance wavelength redshifts (red-line). This results in a transmission drop at λ_o and a corresponding photocurrent drop, ΔI_s, over time (Fig. 1(c)). If the photocurrent drop rate ΔI_s/T_s (red-arrow) exceeds a pre-set slope threshold (dashed-line), Κ_t, the microprocessor outputs a voltage, V_EO, to the EO tuner in order to blue-detune the microring resonance wavelength by injecting carriers and realign the resonance towards λ_o (green dashed-line). The photocurrent rises to I_s^’(0) (green-arrow), which is a new reference for comparison in the next processing loop. Ideally, we wish to have I_s^’(0) = I_s(0) when the resonance is realigned to λ_o. However, carriers injection is always accompanied by free-carrier absorption (FCA) losses, which reduce the resonance-enhanced cavity field and result in I_s^’(0) < I_s(0).

Similarly, when the on-chip temperature drops over a sampling time T_s, the microring resonance wavelength blueshifts. Likewise, this results in a transmission drop at λ_o and a corresponding photocurrent drop ΔI_s over time. If the photocurrent drop rate ΔI_s/T_s > Κ_t, the microprocessor outputs a voltage, V_TO, to the TO tuner in order to realign the microring resonance wavelength by a TO-induced redshift. It is possible to have the realigned I_s^’(0) = I_s(0) as the TO effect does not induce losses.

Figure 1(d) schematically shows a silicon microring wired with a feedback-control circuit for active stabilization. The microring is integrated with a SSA-based PIN photomonitor, an EO PIN diode tuner and a TO tuner. We separately integrate two PIN diodes, with each of them integrated along one arc of the microring, and isolated by a leakage block that is a p⁺-doped silicon wire [8]. The TO tuner comprises a TiN resistor integrated above the silicon microring and separated by a 2μm-thick silica cladding, along the same arc length of the EO tuner.

Figures 1(e) and 1(f) schematically show the cross-sectional view of the microring resonator across the photomonitor (Fig. 1(e)), the EO and TO tuners (Fig. 1(f)). We open an air-trench on top of the photomonitor in order to form air-silicon unpassivated surfaces along the microring arc waveguide for enhancing SSA. Inset of Fig. 1(e) schematically shows the energy band-diagram of SSA in silicon in 1.55 μm. We design the photomonitor in the form of a P⁺PINN⁺ diode in order to enable a short photodiode response time, with a narrow depletion width equals to the waveguide width.

For a proof-of-concept demonstration of the control system, we use an off-the-shelf microprocessor (MBED 1768) as the logic-control unit same as our previous work [8, 10, 11], with an analog input to detect the photocurrent value, I_s, an analog output to output a voltage V_EO to the EO tuner, and an 8-bit digital output to output a voltage V_TO to the TO tuner through an external digital-to-analog (D/A) converter.

2.2 Slope-detection algorithm

Here, we detail our slope-detection algorithm, as illustrated in Fig. 2. We adopt a multiple-slope-thresholds algorithm. Figure 2(a) illustrates the process flow of the algorithm. We pre-set a photocurrent tolerance, ΔI_s,min, and a detection interval, N × T_s, where N is an integer (N = 1, 2, 3…). We compare the monitored photocurrent values between a detection interval, and set multiple slope thresholds, K_t,N, as follows:

 

Fig. 2 (a) Schematic of the multiple-slope-detection control algorithm. (b), (c) Schematics of the active stabilization over multiple processing loops in time upon (b) a steep temperature rise, and (c) a gentle temperature rise above room temperature.

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Figures 2(b) and (c) schematically depict the multiple-slope-detection method upon a monotonic temperature rise above room temperature with a steep slope (Fig. 2(b)) and a gentle slope (Fig. 2(c)). For the initial control loop denoted as a_o, the microprocessor records a photocurrent value, I_{s_1}(0), at zero detuning at room temperature. When the temperature rises above room temperature (Fig. 2(b)), the microprocessor detects a ΔI_s drop from I_{s_1}(0) after a sampling period T_s. If the detected photocurrent slope of ΔI_s/T_s ≥ Κ_t,1, the microprocessor first turns on the EO tuner by applying a threshold voltage and adding an additional fixed voltage step, ΔV_EO, following the “EO-first” control algorithm [8]. Subsequently, both the detected I_s value and the drop-transmission rise in a discrete step after a tuner response time, T_r (~ns for the EO tuner). The microprocessor then records the raised I_s value at the sampling time T_s as the new initial photocurrent value, I_{s_2}(0), for the next control loop denoted as a₁. With the temperature rising following the same trend and after another sampling period T_s, another fixed ΔV_EO is added to the EO tuner and the raised I_s is recorded as I_{s_3}(0) for the next control loop a₂. Similarly, the microprocessor repeats the operations in every following sampling loop, given the same temperature rising slope.

If the temperature change follows a gentler slope, as illustrated in Fig. 2(c) as an example, after a sampling time of T_s from the initial control loop a₀, ΔI_s/T_s < Κ_t,1, the microprocessor takes no action at T_s. The microprocessor is programmed not to buffer the I_s value at T_s. At the next sampling time, 2T_s, the microprocessor detects the photocurrent again and compares the value with the buffered I_{s_1}(0) value 2T_s before. If the slope is still smaller than K_t,2 (ΔI_s/2T_s < K_t,2), the microprocessor again takes no action. At the third sampling time, 3T_s, the microprocessor detects the photocurrent and compares the value again with the buffered I_{s_1}(0) value 3T_s before. If the photocurrent slope is larger than K_t,3, the microprocessor then triggers the EO tuner.

In summary, our multiple-slope-detection scheme allows the microprocessor to keep monitoring the photocurrent every T_s time and comparing the value with the buffered initial value N × T_s time before, until the photocurrent slope exceeds the pre-set slope threshold, i.e., ΔI_s/(N × T_s) > Κ_t,N then triggers the microprocessor to realign the microring resonance. The process repeats over the following processing cycles.

In the case of a monotonic temperature fall below room temperature, the multiple-slope-detection scheme keeps the same as in the temperature rise case, except that the microprocessor turns on the TO tuner with a fixed step voltage increment of ΔV_TO, after first turning on the EO tuner following the “EO-first” algorithm [8].

Our algorithm can readily stabilize the microring upon a transition of temperature change. For example, at the transition when the temperature changes from a rising trend to a falling trend above room temperature, the microprocessor first increases V_EO by ΔV_EO following the previous operation. A following temperature falling slope then causes I_s to drop at the subsequent sampling time. This signals the microprocessor to reduce (V_EO + ΔV_EO) by 2ΔV_EO, outputting (V_EO - ΔV_EO), and re-measure a subsequently increased I_s value as the new initial photocurrent value for the next control loop. Thus, our active stabilization algorithm can work upon various temperature modulations.

In principle, we could set ΔI_s,min as small as possible, with a short T_s, in order to define a sufficiently small slope threshold to trigger the active realignment and stabilize the resonance wavelength against any small photocurrent and transmission perturbations in every processing loop. However, in practice, ΔI_s,min needs to be larger than the noise level of the feedback circuit. This minimum ΔI_s,min, along with the shortest T_s we can set limited by the algorithm processing time, limits the K_t,1 and thus limits the system’s stabilization tolerance, as a photocurrent slope < K_t,1 will take N processing loops until the slope becomes equal to or exceeding K_t,N in order to trigger the stabilization.

3. Device design

We demonstrate the proof-of-concept of the active stabilization scheme utilizing a 1-by-4 silicon microring array fabricated on an 8” silicon-on-insulator (SOI) wafer by a foundry multiple-project wafers (MPW) process (IME, A*STAR, Singapore). We design identically four square-shape microrings, with a bend radius of 10 μm and an interaction length of 5 μm. Each microring is laterally coupled to a multimode-interference (MMI)-based waveguide crossing [15]. The silicon waveguide has a designed width of 500 nm, a waveguide height of 160 nm and a silicon slab thickness of 60 nm on a 2μm-thick buried-oxide layer. The air-clad PIN photomonitor has a length of ~31 μm integrated along the lower arc of each microring away from the waveguide-coupling regions. The width of the air trench is 2 μm. Both the EO and TO tuners have the same length of ~31 μm integrated along the upper arc of each microring along the waveguide input-coupling region. Figure 3(a) shows the top-view scanning-electron micrograph (SEM) of the fabricated array. Figure 3(b) shows the top-view optical micrograph of one of the microrings in the fabricated array.

 

Fig. 3 (a) Top-view SEM of the fabricated 1-by-4 silicon microring array. (b) Top-view optical micrograph of a single microring in the array. G: ground, S: signal.

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4. Device characterization

4.1 Microrings and photomonitors characterization

Figure 4(a) shows the measured transverse-electric (TE)-polarized drop-transmission spectrum and the simultaneously measured photocurrent spectrum from microring 1 in 1550nm wavelengths. The transmission resonance exhibits a Lorentzian lineshape with a 3dB linewidth of ~0.58 nm, corresponding to a quality (Q) factor of ~2700. The photocurrent resonance lineshape follows the transmission resonance lineshape. We measure the resonant photocurrent at the resonance wavelength of 1548.5 nm as a function of the estimated waveguide input power of up to ~4 mW, upon bias voltages of −1 V and −2 V applied across the photomonitor, as shown in Fig. 4(b). Our linear fits suggest on-resonance responsivity values of ~0.76 mA/W upon −1 V and of ~0.90 mA/W upon −2 V. The dark current upon −2 V is ~2 nA. We estimate the waveguide input power based on a calibrated inverted tapered waveguide input/output facet loss of ~4 dB (with a designed 200nm tapered width) upon lensed fiber input coupling and a waveguide propagation loss of ~2 dB/cm.

 

Fig. 4 (a) Measured drop-transmission and photocurrent spectra of microring 1 in the 1-by-4 microring linear array upon −2 V applied across the photomonitor. (b) Measured on-resonance photocurrent values upon −1 V and −2 V as a function of the estimated waveguide power. (c)-(f) Measured drop-transmission (red-lines) and photocurrent (black-lines) spectra of microrings 1 – 4 in the 1-by-4 microring array. PD: photodetector

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Figures 4(c)-4(f) show the measured drop-transmission spectra (red-line) and photocurrent spectra (black-line) from the four photomonitors from microrings 1 - 4, respectively. We measure the photocurrent spectra under a reverse-bias voltage of 2 V applied across each photomonitor at a time. The photocurrent resonance lineshapes match well with the drop-transmission resonance lineshapes. We note that though the microrings were identically designed, the resonance wavelengths of the four microrings spread over ~1.8 nm (not shown) due to fabrication imperfections. In order to avoid interference from microring 1 located in the upstream when measuring spectra of microrings 2 - 4, we have applied a 4V voltage to the TO tuner of microring 1 to redshift the resonance of microring 1, while applying a voltage of 4, 4, and 2 V, respectively, to the TO tuners of microrings 2 – 4 for moving their resonance wavelengths to ~1548.5 nm. We note that the photocurrent (and the drop-transmission) resonance lineshapes of all the four microrings exhibit a similar Lorentzian lineshape, with the same Q factor values of ~2700 and resonant photocurrent values of ~2 μA.

4.2 EO and TO tuners characterization

Figure 5(a) shows the measured resonance wavelength blueshifts and redshifts of microring 1 induced by the EO and TO tuners, respectively. Upon a V_EO of 1.35 V, the resonance wavelength is blueshifted by ~0.65 nm (blue-line). We observe a 1.5dB drop in the on-resonance drop-transmission and a corresponding ~70% photocurrent drop due to the FCA loss. Upon a V_TO of 2.5 V, the resonance wavelength is redshifted by ~0.8 nm. Figures 5(b) and 5(c) reveal the resonance wavelength blueshifts and redshifts as functions of V_EO and V_TO, respectively, and the corresponding electrical power consumptions (according to the calibrated current-voltage (IV) curves).

 

Fig. 5 Measured drop-transmission and photocurrent spectra under different tuner conditions. Black lines: no tuner voltage, blue lines: V_EO = 1.35 V, red lines: V_TO = 2.5 V. (b) Measured resonance wavelength blue-tuning as a function of V_EO (black squares) and the corresponding electrical power consumption (red circles). (c) Measured resonance wavelength red-tuning as a function of V_TO (black squares) and the corresponding electrical power consumption (red circles).

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Upon a resonance wavelength blue-tuning of ~0.65 nm, the EO tuner power consumption is ~3.4 mW. This indicates an EO tuning efficiency of ~5.2 mW/nm. Upon a resonance wavelength red-tuning of ~0.8 nm, the TO tuner power consumption is ~16.3 mW. This suggests a TO tuning efficiency of ~20.3 mW/nm. We expect that the TO tuning power consumption can be reduced by decreasing the ~2μm SiO₂ layer thickness to ~1 μm between the TO tuner and the waveguides.

5. Active stabilization characterization

For characterizing the active stabilization against temperature modulations, we mount the chip on a thermal-electric cooler (TEC) driven by a function generator. As a proof of concept, we characterize the active stabilization performance of microring 1 in the array. We subject microring 1 to various operational condition variations, including (i) an external temperature modulation above and below room temperature (25 °C) by modulating the TEC, (ii) an on-chip temperature modulation above and below room temperature by modulating the TO tuner of microring 2, and (iii) a waveguide input power drop at a fixed stage temperature. In each case, we initially align the carrier wavelength at the microring 1 resonance wavelength of ~1548.5 nm at room temperature, with an estimated waveguide power of 6~7 mW.

5.1 External temperature modulations

Figure 6 shows the simultaneously measured drop-transmitted intensity and photocurrent over 500 s, with a 20mHz sine-wave-modulated stage temperature between 25 °C and 31 °C. Without stabilization (black lines), the intensity drops over 7.5 dB and the photocurrent falls over 6 μA within a modulation cycle, with a maximum photocurrent falling slope of ~1 μA/s.

 

Fig. 6 Measured transmitted intensity and photocurrent variations upon a 20mHz sine-wave modulated temperature above room temperature with (red-line) and without (black-line) stabilization.

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We turn on the stabilization scheme with a T_s of 0.1 s, a ΔI_s,min ≈0.24 μA and a ΔV_EO of 0.05 V. This gives K_t,N ≈2.4/N μA/s. Here, we set T_s to be relatively long at 0.1 s as the external temperature modulation exhibits a relatively long response time in the order of seconds. In principle, we could set T_s to be < 1 ms limited by the feedback system response time. The choice of ΔI_s,min ≈0.24 μA is limited by the noise level in the feedback circuit.

With stabilization (red-lines), the transmitted intensity variation is improved to within ~2.2 dB and the photocurrent variation is improved to within ~2.2 μA. We attribute the ~2.2dB intensity modulation partly to the FCA loss of ~1.5 dB, as shown in Fig. 5(a).

We attribute the rest of the intensity drop to the accumulated drop of I_s(0) over multiple processing loops. This is because ΔV_EO is a fixed value, which corresponds to a non-uniform blue-detuning Δλ over each ΔV_EO step, following the non-linear resonance wavelength shift as a function of V_EO, as shown in Fig. 5(b). Hence, it is likely that the resonance wavelength is not exactly aligned with λ₀ at each processing loop. The misalignment may accumulate up to a certain alignment tolerance.

In order to attain an optimal alignment, our method therefore will benefit from a precise calibration between the two tuner voltages and the nonlinear power drop at the channel wavelength. Given that a switch fabric with identically designed microring switches may preserve resonance filter profiles with a similar lineshape, as shown in Figs. 4(c)–(f), we can in principle adopt a generic calibration for different microrings in the switch fabric.

In our current proof-of-concept system, with a fixed ΔV_EO = 0.05 V (see Fig. 5(b)), the resonance wavelength is blue shifted by ~0.02 nm (assuming V_EO is at the turn-on voltage of ~0.7 V) in the first processing loop. This results in an imperfect correction with a ~0.03nm misalignment from a minimum red detuning of ~0.05 nm at the slope threshold under a temperature rise. With a continuous temperature rise for subsequent loops, each additional fixed ΔV_EO will result in an accumulated imperfect alignment. With V_EO built up to 1.35 V, we estimate based on Fig. 5(b) that the accumulated misalignment can reach ~0.2 nm. Our experiments indicate a consistent misalignment of ~0.17 nm at ~1dB accumulated transmission power drop. Comparing the ~2.2dB intensity oscillation to the measured blue-tuned microring drop-transmission spectrum (blue-line) in Fig. 5(a), we obtain a stabilization tolerance of ~0.14 nm upon a 6°C temperature modulation above room temperature.

A potential solution to minimize the transmission variation is to introduce a variable or an adaptive ΔV_EO in order to obtain a uniform Δλ over each ΔV_EO step, and thus to minimize the alignment tolerance. Besides, smaller ΔI_s,min or larger photodetector responsivity (using ion-implanted defect-state absorption [16] or cladding engineering [17]) allows smaller wavelength shift to triggering active realignment, potentially reducing the misalignment.

Figure 7(a) shows the simultaneously measured drop-transmitted intensity and photocurrent over 400 s, with a 20mHz square-wave-modulated temperature between 25 °C and 17 °C. Without stabilization (black-lines), the intensity drops over 10 dB and the photocurrent falls over 7 μA within a modulation cycle, with a maximum photocurrent falling slope of ~1 μA/s. With stabilization (red-lines), upon slope thresholds of ~2.4/N μΑ/s and a ΔV_TO of 0.2 V, the transmitted intensity variation is improved to within ~1.3 dB and the photocurrent variation is improved to within ~2.2 μA. Comparing the ~1.3dB intensity oscillation amplitude to the measured red-tuned microring drop-transmission spectrum (red-line) in Fig. 5(a), we obtain a stabilization tolerance of ~0.16 nm upon an 8°C temperature modulation below room temperature.

 

Fig. 7 (a) Transmitted intensity and photocurrent variations upon a 20mHz square-wave modulated temperature below room temperature with (red-line) and without (black-line) stabilization. (b) Transmitted intensity and photocurrent variations upon a chirped sine-wave modulated temperature below troom temperature with and without stabilization.

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For temperature modulations below room temperature, we have varied the slope thresholds from 1.6/N μΑ/s to 10.0/N μΑ/s by keeping T_s = 0.1 s and varying ΔI_s,min from 0.16 μA to 1.0 μA, as listed in Table 1. When ΔI_s,min = 0.16 μA, which is within the noise level of the feedback circuit, the variations of the stabilized transmission and photocurrent are at the maximum, as the noise may lead to a false signal to the microprocessor. With ΔI_s,min varies within 0.24 μA ~0.56 μA, we obtain a minimum transmission variation of ~1.3 dB with a minimum photocurrent variation of ~2.2 μA. Further increasing ΔI_s,min leads to an increased oscillation as larger ΔI_s,min sets a larger tolerance for each processing loop.

Table 1. Stabilized transmitted intensity and photocurrent variations upon various slope thresholds for temperature modulations of 8 °C below room temperature.

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We also study the active stabilization performance upon a chirped external temperature modulation. For example, we vary the sine-wave-modulated driving signal frequency from 5 mHz to 40 mHz within a duration of 500 s, with a temperature oscillation between 25 °C and 17 °C on the TEC. This yields a chirped modulation to the microring resonance wavelength without stabilization, leading to a maximum intensity drop of ~8 dB and photocurrent drop of ~6 μA (Fig. 7(b)). At 620 s, we turn on the stabilization. The stabilized transmitted intensity oscillates within ~1 dB. The stabilized photocurrent oscillates within ~1.6 μΑ.

Figure 8 shows the simultaneously measured transmitted intensity and photocurrent variations upon a 5mHz sawtooth-function-modulated temperature between 17 °C and 31 °C. Before 380 s and without stabilization, the transmitted intensity drops over 10 dB and the photocurrent falls over 5.5 μA. After 380 s and with stabilization, the transmitted intensity variation is stabilized within ~2.5 dB and the photocurrent variation is controlled within ~2 μA. The observed active stabilization tolerance is ~ ± 0.16 nm upon the 14°C external temperature modulation, as shown in the inset of Fig. 8.

 

Fig. 8 Measured transmitted intensity and photocurrent variations upon a 5mHz sawtooth-function-modulated temperature between 17 °C and 31 °C. Inset: zoom-in-view resonance spectra at the maximum misalignments upon EO and TO tuners under modulations.

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We remark that there are smooth transitions from below room temperature (the TO tuner is on) to above room temperature (the EO tuner is on). However, the transitions from above room temperature to below room temperature cause unexpected spikes in the transmitted intensity and the photocurrent. We are currently further investigating such phenomena and fine-tuning our algorithm to minimize the spikes during such transitions.

Figure 9 shows the measured eye-diagrams for data transmissions at 30 Gb/s at 1548.5 nm. We use an external 40Gb/s EO modulator to encode a non-return-to-zero (NRZ) pseudo-random binary sequence (PRBS) signal with a pattern length of 2³¹-1. Figure 9(a) shows the eye-diagram measured at room temperature with a signal-to-noise (S/N) ratio of ~6.5 dB.

 

Fig. 9 Measured 30Gb/s eye diagrams at the drop-transmission of microring 1 under (a) room temperature, (b)-(c) a 10mHz sine-wave temperature modulation between 25 °C and 31 °C without (b) and with (c) stabilization, (d)-(e) a 10mHz sine-wave temperature modulation between 25 °C and 17 °C without (d) and with (e) stabilization.

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Figure 9(b) shows the measured eye-diagram without stabilization during a period of the 10mHz-sine-wave temperature modulation between 25 °C and 31 °C, showing a reduced S/N ratio of < 1 dB. With stabilization, we obtain an open eye-diagram with an S/N ratio of ~6 dB, as shown in Fig. 9(c).

Similarly, Fig. 9(d) shows the measured eye-diagram without stabilization during a period of the sine-wave temperature modulation between 25 °C and 17 °C, showing a reduced S/N ratio of < 1 dB. With stabilization, we obtain an open eye-diagram with an S/N ratio of ~6.3 dB, as shown in Fig. 9(e).

5.2 On-chip thermal crosstalks

In practice, the drift of the resonance wavelength of a silicon microring is most likely affected by local heat sources on the chip, such as on-chip laser sources, integrated TO tuners and electronics in the neighborhood. In order to mimic the effects of such local heat sources to the monitored microrings, we utilize the TO tuners on the following microrings (e.g., microring 2) of the array as local heat sources, and stabilize microring 1 against thermal crosstalks. The center-to-center separation between microrings 1 and 2 is 700 μm.

Figure 10(a) reveals the measured resonance wavelength redshifts of microring 2 upon various bias voltage values applied across the TO tuner of microring 2. Upon a V_TO of 8 V, we obtain a resonance wavelength redshift of ~7.9 nm. Given a calibrated wavelength-shift-to-temperature ratio of ~0.08 nm/°C by using the TEC and an on-stage temperature sensor, the 7.9nm resonance wavelength redshift indicates a ~100°C local temperature rise at microring 2.

 

Fig. 10 (a)-(b) Measured drop-transmission spectra of (a) microring 2 and (b) microring 1 with the TO tuner on microring 2 biased at various voltage values. Inset: zoom-in view of resonance wavelength redshifts. (c) Measured microring 1 transmitted intensity and photocurrent variations with a modulated 8V-bias voltage applied across the TO tuner of microring 2.

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Figure 10(b) reveals the measured resonance wavelength redshifts of microring 1 upon V_TO of 0 V, 6 V and 8 V applied across microring 2. At 8 V, the resonance wavelength redshift is only ~0.26 nm, with a ~2.5dB transmitted intensity drop at the original resonance wavelength of 1548.5 nm. This corresponds to a local temperature rise of only ~3.2 °C at microring 1.

Figure 10(c) reveals the measured transmitted intensity and photocurrent variations upon microring 1 at the resonance wavelength, with an 8V-amplitude modulation applied to the TO tuner of microring 2. Before 355 s and without stabilization, the thermal crosstalk from microring 2 results in a transmitted intensity modulation of ~2 dB and a photocurrent modulation of ~2.6 μA at microring 1. After 355 s and with stabilization, the thermal-crosstalk-induced modulation of the transmitted intensity reduces to ~0.8 dB and of the photocurrent reduces to ~0.8 μA.

5.3 Waveguide input power drop

Figure 11 shows the simultaneously measured transmitted intensity and photocurrent variations at λ_o during the power-decreasing period upon using (a) the slope-detection method and (b) our previous threshold-detection method [8, 9]. We linearly reduce the estimated waveguide input power from ~7 mW to ~3.6 mW (a ~3dB drop) within the 180s measurement period. This introduces a linearly decreased photocurrent with a slope of ~0.016 μA/s. For the slope-detection method (Fig. 11(a)) using a slope threshold of 3.5/N μA/s (given by an ΔI_s,min ~0.35 μA, T_s = 0.1 s), the transmitted intensity linearly drops from ~-1.1 dBm to ~-4.2 dBm without obvious oscillations, which is consistent with the input power drop. The lack of oscillations represents a stabilized resonance wavelength during the power-drop period.

 

Fig. 11 Measured transmitted intensity and photocurrent variations over time with decreasing waveguide input power. (a) Slope-detection method, (b) threshold-detection method.

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In contrast, using the threshold-detection method (Fig. 11(b)), we observe that the transmitted intensity drop, besides following the linear input power drop, also oscillates randomly after the photocurrent drops below the pre-set threshold value of I_th = 6 μA. The random oscillations indicate random resonance wavelength oscillations from the carrier wavelength. The random oscillations occur because once the photocurrent drops below the threshold value due to the input power drop, the threshold-detection method obtains a “false” signal for resonance misalignment, and thus keeps randomly varying the V_EO and V_TO. Although the slope-detection method also detects a photocurrent falling slope, it locks the original tuner voltage after a quick variation of the tuner voltage, as no photocurrent increase is subsequently detected.

6. Discussions and Conclusion

In summary, we have proposed and experimentally demonstrated actively stabilized silicon microrings in a 1-by-4 microring linear array using a slope-detection method with multiple slope thresholds. We utilized SSA-based PIN photodiodes integrated along the microring arc as the photocurrent monitor for the feedback-control system. Our proof-of-concept experiments revealed that the active stabilization could effectively reduce the microring transmitted intensity variations caused by various temperature modulation conditions. We have observed significant suppression in transmission intensity variations from ~10 dB (without stabilization) to ~2.5 dB (with stabilization) upon a 5mHz temperature modulation between 17 °C and 31 °C. The alignment tolerance over a 14°C temperature modulation is ~0.16 nm. We have observed open eye-diagrams at a data transmission rate of up to 30 Gb/s under the temperature modulations between 25 °C and 31 °C and between 17 °C and 25 °C.

Here, we benchmark our work with the state-of-the-art in Table 2. Comparing with our previously demonstrated threshold-detection method [8], we note that our proposed method earns the additional advantage of being insensitive to waveguide input power variations.

Table 2. Key methods and performance of active resonance wavelength stabilization schemes for silicon microresonators

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Comparing with other recently published state-of-the-art stabilization methods [1–7], we note that our slope-detection method features the key benefits of being insensitive to input power variations, without using stimulus in every detection loop and without using a pre-set TO tuner voltage. The latter two benefits will enable a power-efficient active stabilization scheme, especially when the number of microrings scales up in a switch fabric or a large-scale-integrated photonic circuit.

Our total control range is ~14 K under the use of both EO and TO tuning without an initially elevated temperature, which is on the low end among the state of art. Nevertheless, we believe that the EO-tuning range is difficult to compensate for a temperature rise exceeding ~10 K, given the ohmic heat generated during carrier injection can saturate the blue-tuning and the resultant FCA can reduce both the transmission and the Q factor of the microring. Whereas in principle, the TO tuning can be extended to compensate for a temperature drop of few tens of degree.

We remark that our demonstrated active stabilization scheme can be most useful in stabilizing silicon microrings against on-chip heat sources that cause local temperature modulations within 10 °C. A larger thermal fluctuation of the whole chip can be taken care of by means of advanced silicon photonic chip packaging with thermal management. Besides, the accumulated misalignment effect can be minimized by introducing variable EO and TO tuning steps, and minimizing the electrical circuit current noise for a small ΔI_s,min.

Our currently demonstrated actively stabilization is based on SSA-based photodetectors with an air-trench on top, which may introduce a reliability issue over time. In order to address this issue, the effects of different cladding (such as SiO₂ with hydrogen silsesquioxane residues [17]) should be carefully studied for SSA-based photodetectors in order to replace the air-trench. Alternatively, we could use DSA-based photodetectors [16] as photocurrent monitors. Such designs without an air-trench could potentially increase the reliability and boost the on-resonance responsivity to tens of mA/W [16, 17].