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Abstract
Calibrating ring-based optical switches automatically is strongly demanded in large-scale ring-based optical switch fabrics. Supported by a machine-learning algorithm, we build an artificial neural network (ANN) model to retrieve the parameters of a 2×2 dual-ring assisted Mach-Zehnder interferometer (DR-MZI) switch from the measured spectra for the first time. The calibration algorithm is verified on several devices. The operating wavelength of the optical switch can be tuned to any wavelength in a free spectral range with an accuracy better than 90 pm. The extinction ratio exceeds 20 dB at the cross- and bar-states with no more than 7 calibration cycles. The voltage difference between the automatic calibration and manual tuning is less than 30 mV, showing the high accuracy of the calibration algorithm. Our scheme provides a new way to calibrate ring-based devices that work as optical switch fabrics and tunable optical filters.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Large-scale optical switches, with the key merits of low latency and low power consumption, are vital for accommodating ever-growing data exchange between servers in both intra- and inter-datacenters. Recently, integrated silicon photonics shows great potential for building large-scale optical switch fabrics for applications in next-generation all-optical networks due to the benefits of small footprint, fast response speed, and complementary metal-oxide-semiconductor (CMOS) compatible processes, compared with other technologies such as 3D micro-electro-mechanical-systems (MEMS) [1,2] and silica-based planar light-wave circuits (PLCs) [3,4].
Micro-ring resonators (MRRs) [5–7] and Mach-Zehnder interferometers (MZIs) [8–10] are widely used as 1 × 2 and 2 × 2 switch elements (SEs) to build large-scale silicon optical switch fabrics. MZI-based optical switches have the features of wavelength transparency and temperature insensitivity, but they also have a relatively high power consumption. In contrast, MRR-based optical switches show the advantages of lower power consumption, but they have a limited operation bandwidth and a high temperature sensitivity. In our previous work, we proposed a 2 × 2 SE, namely, dual-ring assisted Mach-Zehnder interferometer (DR-MZI) [11]. Such a structure combines the merits of resonance enhancement in MRRs and coherent inference in MZIs, which shows the low power consumption and broad bandwidth. Recently, 4×4 and 16×16 silicon optical switch fabrics based on DR-MZI SEs have been successfully demonstrated [12,13]. The 16 × 16 optical switch fabric can also function as a reconfigurable optical filter with various filtering orders [14].
For MRR-based optical switches, the operating wavelength is only around the resonance wavelength. However, due to random fabrication errors, the resonance wavelengths of the MRRs usually deviate from the design and thus the initial states of the fabricated DR-MZIs are unpredictable. Therefore, the resonant wavelengths of all the MRRs should be firstly aligned to the same operating wavelength. As the number of MRRs increases with the scale of switch fabrics, wavelength and state calibration become a time-consuming and heavy-duty task. Hence, fast automatic switching calibration of silicon optical switch fabrics is highly demanded, especially for MRR-based optical switches.
Recently, various automatic calibration schemes aimed at optical SEs and fabrics have been reported. The most widely used methods are based on real-time optical power monitoring and feedback control. Various iterative algorithms have been proposed to reduce the calibration time, like feedback loop algorithms [15–17], maximum searching algorithms [18–19], improved saddle point searching (SPS) algorithms [20], bacterial foraging optimization [21] and so on. The intra-resonator or on-chip contactless monitors can overcome additional insertion loss and area-cost caused by traditional on-chip photodiodes [16,17,22–25]. However, these calibration schemes require complicated off-chip digital circuits to amplify and extract the weak photocurrent. Another solution to get the switch parameters is to fit the measured spectrum with a heuristic model based on optical transfer matrices [26]. As nonlinear fitting depends strongly on the initial guess, multiple trials are needed to get the exact values. Therefore, fitting complexities grow exponentially with the scale of switch fabrics. Extensive research on natural language processing [27] and automatic face recognition [28] prove that machine learning is a powerful tool to overcome the “curse of dimensionality” existing in traditional optimization methods. Nowadays, machine learning is also applied in integrated photonic devices, which shows potential in the inverse design of photonics structures [29–31] and automatic wavelength control of MRR optical switches [32]. In this paper, we present an automatic calibration algorithm for 2 × 2 DR-MZI optical switches powered by machine learning. An artificial neural network (ANN) is trained to recognize the initial state of the DR-MZI. After calibration, the DR-MZI is tuned close to the perfect cross- or bar-state. The operating wavelength of DR-MZI can also be continually shifted in one free spectral range (FSR). It provides a powerful approach to automatically calibrate DR-MZI-based optical switches and lays the root for calibrating DR-MZI optical switch fabrics in the follow-up work. The same ANN can also successfully recognize the state of the DR-MZIs with different geometric parameters, indicating its universality.
This paper is organized as follows. Section 2 describes the device structure, the working principle, and the transfer matrix model of the DR-MZI as an optical switch. Then, an ANN is built and trained for inverse modeling of the DR-MZI in Section 3. Section 4 explains the calibration algorithm. Section 5 presents the experimental results when the algorithm is applied to several different DR-MZIs. Section 6 discusses the applicability of our algorithm to switch fabrics based on double-laryer network (DLN) topology. Section 7 summarizes the work.
2. Device structure and working principle
2.1 Structure of DR-MZI switch element
Figure 1(a) shows the schematic structure of a 2 × 2 DR-MZI consisting of a symmetric MZI coupled with a racetrack MRR in each arm. We define the cross-route and the bar-route as the optical path from I1 (I2) to O2 (O1) and I1 (I2) to O1 (O2), respectively. Two 2×2 multimode interferometer (MMI) couplers are employed as the 3-dB splitter and combiner for their advantages of wide optical bandwidth and high fabrication tolerance. The racetrack MRRs are designed with a radius of 10 µm, a coupling length LC of 4.2 µm, and a coupling gap size of 200 nm. Titanium nitride (TiN) micro-heaters and p-i-n diodes are integrated on the two MRRs for thermo-optic (TO) and electro-optic (EO) phase tuning, respectively, as shown in the inset of Fig. 1(a). Although TO phase tuning has a lower speed and higher power consumption than the EO phase tuning, it possesses a wide tuning range with a negligible loss [13]. Therefore, we adopt TO tuning in calibrating the switch. Isolation trenches around the MRRs and between the arms of MZI are used to improve TO tuning efficiency and suppress thermal crosstalk. Figure 1(b) illustrates the microscope image of the fabricated device.
Fig. 1. (a) Schematic drawing of the 2×2 DR-MZI. The inset shows the cross-section of the active waveguide in the MRR. (b) Microscope image of the fabricated device.
2.2 Working principle and device modeling
Figure 2 illustrates the working principle of the DR-MZI. As the two MRRs are designed with the same parameters and initially resonate at the same wavelength λp, the two arms of MZI have an identical phase response. After interference by the MZI, light from I1 is transmitted to O2. Therefore, the switch is at the cross-state. For lossless MRRs, the amplitude response is just the same as MZI-based optical switches with a broad optical bandwidth, as shown in Figs. 2(a) and 2(c). It should be noted that the MRRs are working at the over-coupling regime, generating a sharp phase change from 0 to 2π around the resonance wavelength λp. Therefore, a slight phase detuning of these two MRRs could produce a π phase difference between two arms at the wavelength λp. Input light at λp is thus switched from O2 to O1 and the switching state is changed to the bar-state.
Fig. 2. Working principle illustration of the DR-MZI. (a, b) Phase responses of the MZI arms coupled with MRRs at (a) the cross-state and (b) the bar-state. (c, d) Transmission spectra of the DR-MZI at (c) the cross-state and (d) the bar-state.
We model the device using the optical transfer matrix method. The output electric fields ECross at port O2 and EBar at port O1 are related to the input electric field Ein at port I1 by the following equation [11]
Figure 3 shows the measured transmission spectra of six identical 2 × 2 DR-MZIs in different dies without active tuning. Due to fabrication errors, the resonance wavelengths of the MRRs vary from die to die. It is necessary to identify the initial wavelength position of the resonances so that we can tune the switches to the desired state at a certain operating wavelength.
Fig. 3. Transmission spectra of six as-fabricated DR-MZI switches, showing the large deviation in resonance wavelengths. Solid lines: bar-route. Dashed lines: cross-route.
Figures 4(a)–4(d) show the calculated transmission spectra of the DR-MZI using the above transfer matrix model with the common phase p = (p2+p1)/2 and the differential phase dp = p2−p1 as the two variables, while φMZI is fixed to 0.01π. We can see that adjusting p does not change the spectral shape but only shifts the spectra. In contrast, adjusting dp changes the spectral shape considerably. The dip in the cross-route (I1 – O2) spectrum gradually deepens and then splits into two as dp increases from 0 to 0.12π. Meanwhile, the peak in the bar-route spectrum firstly rises and then splits. The DR-MZI is close to the perfect cross- and bar-states when dp equals to 0 and 0.073π, respectively. Note that the power consumption for switching the DR-MZI SE is less than one-tenth of the MZI SE. However, it also means that the switching states of the DR-MZIs are very sensitive to dp. The parameter p can be easily extracted from the wavelength position of the peak or valley in the spectrum. The parameter |dp| can be calculated from the wavelength separation of the peaks or valleys when it is large, as in the case of Fig. 4(d). However, when |dp| is small, as in the case of Figs. 4(a)–4(c), only one peak/valley is present in the spectrum, and thus it is difficult to retrieve dp without spectrum fitting.
Fig. 4. Calculated transmission spectra of the DR-MZI switch when (a) dp = 0, φMZI = 0.01π, (b) dp = 0.073π, φMZI = 0.01π, (c) dp = 0.025π, φMZI = 0.01π, and (d) dp = 0.12π, φMZI = 0.01π. The other parameters are a = 0.99, t = 0.888, r = 0.046 and r2 = 1.
If φMZI equals to 0, two MRRs are indistinguishable because of the symmetry in structure. In this case, we are not able to determine the sign of dp from the spectrum. If φMZI is not 0, as in most cases due to fabrication errors, the structural symmetry is broken. Then, according to the spectral shape, once the sign of φMZI is known, we can deduce the sign of dp and vice versa. As shown in Figs. 5(a) and 5(b), when dp and φMZI have an opposite sign, the phase response curves of DR-MZI arms intersect at two wavelength λO1 and λO2, which means that the phase difference of DR-MZI arms is 0 at these two wavelengths. Therefore, two deep notches are observed at λO1 and λO2 in the bar-route spectrum, as seen from Fig. 5(c). Figures 5(d) and 5(e) show the phase spectra when dp and φMZI have the same sign. There is no intersection point between two phase response curves and notch is absent in the bar-route spectrum, as seen from Fig. 5(f). This observation is later employed to determine the sign of dp·φMZI.
Fig. 5. (a, b) Phase responses of the DR-MZI arms when (a) dp < 0, φMZI >0 and (b) dp > 0, φMZI <0. (c) Transmission spectra when dp·φMZI < 0. (d, e) Phase responses of the DR-MZI arms when (d) dp < 0, φMZI <0 and (e) dp > 0, φMZI >0. (f) Transmission spectra when dp·φMZI > 0.
3. Machine learning model for DR-MZI
We use machine learning to identify the parameter dp from the measured spectra when there are no or slightly split peaks/valleys observed in the bar/cross-route of the DR-MZI. In order to build an ANN with significant generalization capabilities, the design and generation of datasets become extraordinarily important. We use numerical simulations to generate the labeled data to train the network. Given the parameters a, t, dp, p, φMZI, r, r2 in a certain variation range, the spectrum of the DR-MZI switch can be calculated by the transfer function of Eq. (1).
According to the measurements of fabricated devices, the variation ranges for a, t, φMZI, r and r2 are set as [0.98, 0.999], [0.86, 0.92], [-0.13π, 0.13π], [0.4, 0.5] and [0.8, 1.2], respectively. The common phase p can be fixed to 0 as it does not influence the spectral shape. The variation range for the differential phase dp in the ANN model is set as [0, 0.12π]. Here, we set positive values for dp in order to avoid ambiguity in parameter extraction. As seen from Fig. 5, there are always two possible device configurations with an opposite sign of dp and φMZI for a certain spectrum. The sign of dp will be determined during the cross-state calibration.
We only focus on a 6-nm-range segment of the spectrum. It is smaller than the 8.4 nm FSR of the DR-MZI but is still large enough to contain the main features of the resonance spectrum. There are 601 data points in the cross or bar spectrum with a wavelength spacing of 10 pm. Therefore, 1202 data points are recorded in a vector X = [x1,x2,…,x1202], to be fed into the neural network. We generate 250,000 spectrum samples from the above parameter space with the Monte-Carlo sampling method. Figure 6(a) shows a typical spectrum sample generated using our theoretical model.
Fig. 6. (a) An example of the generated spectrum sample. (b) ANN structure incorporating one input layer, three hidden layers, and one output layer.
Figure 6(b) illustrates the structure of the ANN. The ANN is designed and trained on the Google Tensorflow platform carried on the workstation with NIVIDA GTX1080Ti graphics cards. It is composed of an input layer, three hidden layers, and an output layer. The number of neurons in the input and output layers is 1202 and 4, mapping to the input spectrum and the output parameters (a, t, dp, and φMZI), respectively. The number of hidden layer neurons determines the training result of ANN. It will give non-fitting (over-fitting) results if the hidden layer is over-simplified (over-complicated). In our model, we use three hidden layers with 500, 4000 and 500 neurons, generating 4,623,206 weights and biases in total. Before feeding the spectrum samples into the ANN, by convention, the datasets are divided into training set, validation set and testing set randomly, with the proportion being 75%, 15%, and 10%, respectively.
To improve the training efficiency, the Adam optimizer [33] and the mini-batch gradient descent (MBGD) [34], a strategy combining the advantages of batch gradient descent (BGD) and stochastic gradient descent (SGD), are selected to train the ANN. The batch size is fixed as 800 and the training is terminated after 50,000 iterations before overfitting. The loss function of the training set is the mean-square error (MSE) between the output parameters and the real values. The learning rate is 3 × 10−7. The MSE reaches about 10−4 after terminating the training process, as shown in Fig. 7.
Although it takes several hours to train the ANN, the weights and biases of the ANN are fixed and saved into a file once the training is finished. Therefore, the parameters could be retrieved easily and quickly from the measured spectrum with the established ANN. Based on the above analysis, the trained ANN can retrieve the differential phase dp from the spectrum. As for the common phase p, which decides the operating wavelength of the device, is obtained directly by using another algorithm, as will be discussed in the initialization of calibration algorithm introduced in chapter 4.
[AQ: The previos sentence references Chapter 4; please reword accordingly.]
4. Calibration algorithm for DR-MZI
An ANN has been trained to identify the differential phase dp from the measured spectra. To realize automatic switching state calibration, there are still some other issues to be solved. Firstly, as we fix p to 0 in the ANN model, the operating wavelength of DR-MZI cannot be identified from the ANN. Secondly, the sign of dp cannot be determined as discussed previously. Lastly, the thermal tuning efficiencies of MRRs and the resistances of TO phase shifters are uncertain and different from device to device due to the fabrication deviations, hence, even with a known dp, we cannot get the accurate driving voltages to tune the DR-MZI to the cross- or bar-state. Therefore, we propose a calibration algorithm to tune the DR-MZI switch to the cross- or bar-state at any desired operating wavelength. Figure 8 depicts the overall flow of the calibration algorithm. It includes three parts: initialization, cross-state calibration, and bar-state calibration.
Fig. 8. Flow of the calibration algorithm: (a) initialization, (b) cross-state calibration, and (c) bar-state calibration.
The goal of the initialization is to shift the resonant wavelengths of two MRRs nearby the target operating wavelength. The resonant wavelengths can be obtained by reading the valley/peak point from the measured cross/bar-route spectrum. In a typical device with its spectra shown in Fig. 9(a), there is only one valley/peak at 1545.894 nm in the spectrum. It suggests that the resonant wavelengths of two MRRs λ1,2 are very close. The target operating wavelength λt is arbitrarily set to 1550 nm. The required wavelength shift of MRRi is defined as dλi (i = 1, 2).
Fig. 9. Evolution of the measured transmission spectra during the calibration procedure (a) before initialization, (b) with applied trial voltages, (c) after initialization, (d) during the cross-state calibration, (e) with the differential phase of dp1 and dp2, and (f) during the bar-state calibration.
As mentioned before, the trained ANN can only identify |dp| from the spectra. The sign of dp can be determined by a trial test. We intentionally introduce a slight wavelength detuning δλ of ± 0.06 nm with respect to the target wavelength λt to the two MRRs, respectively. The required wavelength shift dλi then is |λt-λi+(-1)i+1|δλ||, where λi is the initial resonant wavelength. Thus, dp is guaranteed to be positive after the initialization.
Tuning resonance to the target wavelength by an appropriate voltage is a kind of “trial-and-error” process. The required wavelength shift dλ1 and dλ2 are 4.166 nm and 4.046 nm, respectively. Due to the unknown thermal tuning efficiencies and resistances of the TO phase shifters, we set the tuning efficiency ηi of MRRi to an initial value of 0.36 nm/V2 according to separate test devices. The tuning voltage is given by Ui=(dλi/ηi)1/2. Figure 9(b) shows the spectra when either MRR1 or MRR2 is tuned. For comparison, we also plot the initial spectrum before tuning. Note that shifting away the resonances from their overlap increases the resonance notch depth because the MRRs are over-coupled [11]. The actual resonant wavelength shift after tuning MRR1 and MRR2 is dλ'1 = 4.590 nm and dλ'2 = 3.956 nm. We can see that the applied voltage U1 is larger than the required while U2 is slightly lower. The tuning efficiency η'i is then revised as η'i = dλ'i/dλi×ηi and accordingly, the tuning voltage U'i becomes U′i=(dλi/η′i)1/2. The initialization is finished when the resonances shift close to the target wavelengths. Figure 9(c) shows the spectra after initialization.
The goal of cross-state calibration is to make resonant wavelengths of two MRRs completely overlap, that is, the differential phase dp is 0 after cross-state calibration. In the previous initialization step, dp is forced to be a positive value. Therefore, the sign of φMZI can be decided according to the bar-route spectral shape. The operating wavelength λ0 after initialization is usually slightly deviated from the target wavelength λt. To make the operating wavelength exactly at λt, we blue-shift MRR2 when λ0>λt and red-shift MRR1 when λ0<λt. Considering the example shown in Fig. 9(c), the operating wavelength of DR-MZI after initialization is 1550.04 nm. Hence, we only blue-shift MRR2 during the cross-state calibration.
We notice that the resistance of the TO phase shifter slightly changes with the applied voltage, which as a result changes the tuning efficiency ηi and generates estimation errors in the required tuning voltage. Therefore, we still use the “trial-and-error” method to revise the tuning voltages. The calibration is stopped when the optical power extinction ratio (ERc) between the cross- and bar-routes at the operating wavelength reaches 20 dB. Moreover, we observe that there are ripples in the bar-route spectrum as it has a low optical transmission. This makes the identification inaccurate when dp is very close to 0. Therefore, in order to reduce the identification error during the subsequent retrieval of dp by the trained ANN, we set the tuning efficiency ηi with a smaller initial value (ηi=0.12 nm/V2) and the tuning voltage U''i is given by
The spectra of DR-MZI can be recorded after U''i is applied to MRRi. Because the tuning efficiency is set to a smaller value purposely, dp is changed to a negative value and notch is absent in the bar-route spectrum, as shown by the blue traces in Fig. 9(d). We fed the spectra into the ANN to retrieve the exact value of dp. Then, the tuning efficiency η'i is revised as:
where dp0 is the differential phase retrieved from the spectra after initialization [red traces in Fig. 9(d)]. The driving voltage is then updated using the revised tuning efficiency according to Eq. (5). We repeat this process until ERc reaches 20 dB as described in Fig. 8(b). In our device, with two cycles of parameter retrieval and tuning voltage revision, the DR-MZI reaches the cross-state with ERc over 25 dB as seen in Fig. 9(d).Finally, the DR-MZI is calibrated to the bar-state by red-shifting MRR1 and blue-shifting MRR2 with a phase shift of |dpb/2| or the reverse. However, it is not easy to obtain the required dpb precisely. We use the dichotomy to adjust the switching state. We try to get a high optical power extinction ratio (ERb) between the bar-route and the cross-route at the operating wavelength. We choose |dp1|=0.05π and |dp2|=0.1π as the bottom and upper limit. When dp equals |dp1|, there is only one valley observed in the cross-route spectrum; When dp equals to |dp2|, two valleys are observed, as shown in Fig. 9(e). Next, we define |dp3| as the average of the two boundary values, i.e., |dp3| =(|dp1|+|dp2|)/2. The applied voltages are calculated by Eq. (5) with the final thermal tuning efficiencies in cross-state calibration. With the calculated voltages applied to the device, we measure ERb at the operating wavelength and count the number of valleys Nv on the measured cross-route spectrum. If ERb is lower than 20 dB, and Nv equals 2, the upper-limit |dp2| is assigned to |dp3|. The differential phase |dp3| and the applied voltages are revised accordingly. Otherwise, if Nv is 1, the bottom-limit |dp1| is assigned to |dp3|. We continually update |dp3| and the applied voltages until ERb exceeds 20 dB as described in Fig. 8(c). Figure 9(f) illustrates the evolution of the spectra during this process. The ERb reaches over 40 dB after three cycles of updating, indicating that the bar-state is calibrated successfully. The entire calibration process is thus completed.
5. Experimental results
We measured the transmission spectra of our devices by a tunable laser source and a power meter. The tuning voltages were applied by a programmable power supply (PPS). The software part mainly includes spectrum interception module, resonance wavelength reading module, ANN recognition module, tuning efficiency correction module, driving voltage calculation module, MATLAB/Python software interface, and system interruption. All software modules are driven by the NI-Labview carried on a personal computer (PC).
5.1 Calibration results of DR-MZI switches
We calibrated 5 identical DR-MZI switches in different dies. Figures 10(a)–10(d) show the evolution of the measured spectra during the calibration of one DR-MZI at 4 target operating wavelengths of 1548 nm, 1550 nm, 1552 nm, and 1554 nm. The resonant wavelengths of the DR-MZI for the as-fabricated device are around 1545.89 nm and 1554.37 nm with an FSR of 8.48 nm. There is only a pair of peak/valley in the bar-/cross-route spectrum and the operating wavelength is close to the target. The ER after the cross-state and bar-state calibration is larger than 25.5 dB and 30.6 dB, respectively. The variation of ER after the cross-state calibration at the 4 target wavelengths is due to the resistance change of TO phase shifters caused by temperature fluctuation, local thermal crosstalk, and identification errors, etc. The operating wavelength deviates within 70 pm from the target wavelength after calibration. In comparison, we also manually adjust the switching states of the DR-MZI by tuning the ERs to the maximum at the target wavelength. Figures 10(e) and 10(f) show the manually calibrated cross-state and bar-state spectra, which are very close to the automatic calibration results.
Fig. 10. (a-d) Measured transmission spectra in the automatic calibration of one DR-MZI device (a) before initialization, (b) after initialization, (c) after cross-state calibration, and (d) after bar-state calibration. (e, f) Transmission spectra with manual tuning to (e) the cross-state and (f) the bar-state.
Figure 11 shows the TO tuning power on MRRs during calibration. The cross-state and bar-state calibrations require 2 and 3 cycles of tuning power modification, respectively. The difference between the automatically calibrated voltages and the manually obtained voltages is less than 30 mV. It indicates that the calibration algorithm has worked successfully on the device.
Fig. 11. TO tuning power on two MRRs during the automatic calibration with the target wavelength set to (a) 1548 nm, (b) 1550 nm, (c) 1552 nm, and (d) 1554 nm. I: initialization; II: cross-state calibration; III: bar-state calibration.
Figure 12 shows the statistics of the ER, wavelength deviation and insertion loss for 5 DR-MZIs after automatic calibration. The ER varies in the range from 20.85 dB to 34.91 dB in the cross-state, while from 20.03 dB to 48.73 dB in the bar-state. The operating wavelength deviation is in the range from -90 pm to 70 pm, which is within 1.1% of FSR. One may notice that the operating wavelengths of the DR-MZIs after calibration are slightly smaller than the target wavelength in most scenarios. This is because we only blue-shifted the MRR with a longer resonant wavelength in the cross-state calibration. In the future, the cross-state calibration can be improved by shifting the resonant wavelengths of both MRRs simultaneously and then accurate tuning efficiencies for both MRRs can be derived. As a result, it can reduce the wavelength deviation at both the cross-state and the bar-state. The fiber-to-fiber insertion loss of DR-MZIs is in range of 11.74 ∼13.52 dB at the cross-state and 11.31∼12.43 dB at the bar-state. The coupling loss is about 11 dB, which can be improved by optimizing the grating couplers. The on-chip insertion loss is mainly caused by the MRRs and MMIs. The loss variation among the measured samples is due to the non-uniformity of the grating couplers and DR-MZIs.
Fig. 12. Statistics of 5 DR-MZIs. (a) ER at the cross-state, (b) ER at the bar-state, (c) wavelength deviation at the cross-state, (d) wavelength deviation at the bar-state
5.2 Calibration of DR-MZI switches with different design parameters
The ANN, which is regarded as the kernel of the algorithm, is trained by the spectrum samples of the DR-MZI with the radius, the coupling length, and the coupling gap being 10 µm, 4.2 µm, and 200 nm, respectively. The coupling length LC affects the FSR and the transmission coefficient t of the MRRs. In order to verify the universality of our algorithm, we applied it to DR-MZIs with a different LC of 3.8 µm and 4.6 µm. Figure 13 shows the evolution of the measured spectra. The small peak at the 1550 nm wavelength in the bar-route spectrum after the cross-state calibration may be caused by identification error. In principle, the effect of the coupling length can be taken into consideration in the DR-MZI transfer matrix model to generate a more sophisticated dataset to train the ANN. Yet, the calibration results based on the existing ANN trained using a fixed LC are acceptable in general, which verifies the universality of our algorithm and system. Table 1 lists the ER and wavelength deviation for three devices with a variable coupling length.
Fig. 13. Measured transmission spectra of DR-MZI devices (a,b) at the passive state, (c,d) after the cross-state calibration, and (e,f) after the bar-state calibration. The coupling length LC of the microring resonator is (a, c, e) 3.8 µm and (b, d, f) 4.6 µm.
Table 1. Calibration results for DR-MZIs with three coupling lengths.
6. Discussion
In the future, the proposed calibration algorithm can be modularized to calibrate DR-MZI element in switch fabrics, which is highly demanded in large-scale optical switches. Figure 14 shows a 4×4 DLN switch fabric based on 2 × 2 DR-MZIs, which serves as an example to show the wide applicability of our proposed algorithm to various switch fabrics. To be mentioned, the same ANN model for the 2 × 2 DR-MZI calibration is used for the 4 × 4 switch fabric.
There are three DR-MZI elements in each routing path. The key step in the calibration procedure is to shift the non-target DR-MZI elements in the routing path out of the wavelength range that is used by the ANN. For our DR-MZIs, the FSR is about 8.4 nm, while the wavelength range for ANN identification is 6 nm. Thus, we shift the resonant wavelengths of two non-target DR-MZIs to λt ± 4 nm in order to get the spectral response from only one target DR-MZI in the 6 nm wavelength range. This DR-MZI is then calibrated using our calibration algorithm. Consequently, it is set to the cross state and the rest of the DR-MZIs in the routing path is calibrated one by one with a similar procedure.
Here, we present the calibration procedure of E41, E22 and E13 in the optical path I4-O1 for details, as shown in Fig. 15. According to the initial measured transmission spectrum of I′4-O1, we can move the resonances of MRRs in E41 and E22 out of the calibration wavelength range (e.g., at λt ± 4 nm). Therefore, the paths I′4-O′1 and I′4-O1 are equivalent to the bar-route and cross-route of E13, respectively. The calibration of E13 can be done with our proposed algorithm using the measured spectra of I′4-O′1 and I′4-O1. The other DR-MZIs in Stage 3 (E23, E33, and E43) can be calibrated in the same way. To calibrate E22, E13 and E23 are adjusted to the cross state and E41 remains out of the calibration wavelength range. Thus, the paths I′4-O2 and I′4-O1 can be recognized as the bar-route and cross-route of E22, respectively. Thus, E22 can be identified and calibrated using the algorithm. Calibrating E41 is much easier when E22 and E13 are configured to the cross state. The paths O1-I4 and O1-I′4 are measured as the bar-route and cross-route of E41, respectively, and its calibration can be performed accordingly. The rest of the elements can be calibrated with the similar method by choosing different routing paths. The calibration method is also applicable to other well-known switching topologies, such as Benes, Crossbar, Switch-and-Select, etc., with a larger port-count.
Fig. 15. Transmission route chosen for calibration of (a) E13, (b) E22, and (c) E41. The orange, blue and green blocks represent nontarget element, target element and cross-state element, respectively.
The complexity for the calibration scheme is dependent on the number of DR-MZI elements in the switch fabric. For a 2N×2N DLN switch fabric, the elements needed to be calibrated in a transmission route is (2N-1) and we need to apply the calibration algorithm [(5/4)N2-2N] times to fully calibrate the entire switch matrix. It inevitably increases the calibration time. However, this is the common issue also encountered by other calibration schemes for larger-scale optical switch fabrics.
7. Summary
We have developed a calibration algorithm powered by machine learning to calibrate 2×2 DR-MZI switches. Near-perfect cross and bar switching states can be freely set at any target operating wavelength within an FSR. Based on the algorithm, an automatic calibration system has been built to experimentally verify its accuracy and effectiveness. Calibration of five identical DR-MZIs shows that the switching ER reaches more than 20 dB for both cross and bar states. The operating wavelength of the switches is tuned to four wavelengths in an FSR with a wavelength deviation of less than 90 pm. The automatic calibration system is also applied to DR-MZIs with different MRR coupling lengths, revealing that the ER is still larger than 20 dB and wavelength deviation less than 100 pm. These results demonstrate the usefulness and universality of our algorithm. Besides, our method shows a potential applicability for calibrating large-scale DR-MZI switch fabrics.
In our experiments, it takes about 40 seconds to finish each calibration cycle. The speed is mainly limited by slow laser wavelength scanning and data transfer among hardware systems. Nevertheless, our method requires no on-chip monitors and fewer iteration cycles compared with the conventional calibration methods. Our method provides a useful solution to calibrate ring-based devices working as optical switches or tunable filters in a general photonic integrated circuit.
Funding
National Key Research and Development Program of China (2019YFB2203203, 2018YFB2201702); National Natural Science Foundation of China (61535006, 61705129); Science and Technology Commission of Shanghai Municipality (2017SHZDZX03).
Acknowledgment
We acknowledge AMF Singapore for device fabrication.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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