Silicon optical filters reconfigured from a 16 × 16 Benes switch matrix

Reconfigurable optical filters with tailorable performances are highly demanded in multi-purpose adaptive signal processing applications. We demonstrate infinite impulse response (IIR) silicon optical filters with a variable filter order by switching the optical path in a 16 × 16 Benes switch chip. The basic unit of the optical filter is a dual-ring assisted MachZehnder interferometer. TiN microheaters are integrated in both ring resonators for resonance control, allowing for continuous tuning of the filter center wavelength and the bandwidth. Multiple high-order optical filters from the 2 order up to the 14 order are obtained. The filter bandwidth tuning range is from 0.19 nm (23.75 GHz) to 1.06 nm (132.5 GHz) with a 1-dB inband ripple. The out-of-band rejection ratio exceeds 30 dB for the 8 and 10-order filters, limited by the inter-path optical crosstalk in the Benes architecture. The results point to new ways of reutilizing an existing switch matrix to flexibly construct wavelength-filtering devices. © 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement


Introduction
Owing to the exponential growth of internet traffic, optical networks are rapidly evolving to allow for improved spectral efficiency and increased transmission capacity. Flexible optical networks in which resources and services are allocated in a flexible manner have been regarded as a promising solution [1,2]. Reconfigurable optical filters are the basic and indispensable devices for photonic signal processing in both digital and analog optical systems. Especially, in wavelength division multiplexing (WDM) optical networks, tunable filters are ubiquitous components applied to extract the required data from a bunch of WDM channels [3,4]. Furthermore, tunable filters can be used to dynamically route either a single data channel or a contiguous set of data channels to a specific destination in on-chip network routing and signal processing functionalities [4,5]. Therefore, the bandwidth and center wavelength tunability feature of an optical filter is becoming increasingly attractive. In the past decades, several optical tunable bandpass filters have been demonstrated by using cascaded or coupled microring resonators (MRRs) [6][7][8], cascaded asymmetric Mach-Zehnder interferometers (MZIs) [9], and structures consisting of both MRRs and MZIs [10][11][12][13]. Filter structures with MRR coupled MZI have improved device performances since the pole and zero locations can be specified independently [14]. Compared to finite impulse response (FIR) filters, the infinite impulse response (IIR) filters are much more compact since the resonant feedback loop provides the multiple taps required to form the desired filter shape [15].
In our previous work, we have reported a 2 × 2 dual-ring assisted MZI (DR-MZI) as a basic switch element (SE) [16] and implemented a 16 × 16 silicon Benes optical switch chip with such SEs [17]. The Benes architecture is a well-known rearrangeable non-blocking topology that requires the minimum number of SEs to build an N × N switch fabric. In addition, the Benes switch chip can also multicast an optical signal from one source to multiple destinations that can be used in beam steering [18]. In this paper, the DR-MZI based 16 × 16 Benes switch is reconfigured to implement a variable-order optical filter. A single DR-MZI SE works as a 2 nd -order optical add-drop filter upon slight wavelength detuning of the resonances in the two MZI arms. A higher-order optical filter is made up of cascaded DR-MZIs by properly setting up a light path in the 16 × 16 switch matrix. Both the filter center wavelength and bandwidth can be continuously tuned by changing the resonance wavelengths of the ring resonators. It opens a way towards the realization of software-defined photonic functionality in a general photonic integrated circuit. Although the switch matrix was originally designed for optical signal routing purpose, we demonstrate that it could also be reused for optical filtering by properly setting the states of the elementary switches. Therefore, this chip can be reconfigured to different functions, extending its versatile applications. This greatly shortens the chip development cycle and reduces fabrication cost compared to application-specific photonic chips.
This paper is organized as follows. Section 2 describes the device structure and the working principle of the DR-MZI as a basic unit for optical filters. The method to construct a variableorder optical filter from the 16 × 16 silicon optical switch matrix is presented. Then we discuss the factors that affect the out-of-band rejection ratio (OBRR) of the optical filters. Section 3 presents the fabrication and package methods of the 16 × 16 switch chip. Next, in Section 4, we report the experimental setup and measurement results of the optical filters with multiple configurations. The filter center wavelength and bandwidth can both be tuned by shifting the resonance wavelengths of MRRs. Section 5 discusses the method of reconfiguring the switch chip for parallel filtering processing. Section 6 gives the conclusions. Figure 1(a) presents the schematic structure of the DR-MZI as a basic filter unit. It is composed of a symmetric MZI coupled with a racetrack MRR in each arm. The device was designed for the transverse electric (TE) polarization. The four input and output ports are denoted as "I 1 ", "I 2 ", "O 1 ", and "O 2 ". A pair of 2 × 2 multimode interferometer (MMI) couplers are used as 3-dB splitters and combiners for their high fabrication tolerance and broad optical bandwidth. The two MRRs are integrated with titanium nitride (TiN) microheaters for low-loss thermooptic (TO) phase tuning. Although TO tuning has a moderate speed compared with electrooptic tuning, the TO tuner can offer a wide wavelength tuning range with negligible loss [19]. The isolation trenches around the MRRs are designed to improve power efficiency and reduce thermal crosstalk.

Basic DR-MZI optical filter unit
The transmission spectra of the DR-MZI can be calculated by using the transfer matrix method. As the 2 × 2 MMI couplers cannot have an exact 3-dB splitting ratio in practical devices, the coupling and transmission coefficients of the MMI couplers are set to 0.505 and 0.495, respectively. Due to the power imbalance and phase errors in the two arms, the light transmitted to the bar-port (I 1 -O 1 ) cannot be completely canceled upon destructive interference, limiting the OBRR of the filter. A phase difference of π/9 rad is added to the arms of the MZI in the modeling to account for the phase errors in real devices. For the DR-MZI, when the two MRRs resonate at the same wavelength, light from the input port I 1 is transmitted to the crossport O 2 with the maximum transmission. As shown in Fig. 1(b), the simulated transmission spectra of the cross-port (I 1 -O 2 ) and the bar-port (I 1 -O 1 ) exhibit nearly flat spectral responses. The DR-MZI is at the "cross-state". Figures 1(c) and 1(d) show the spectra when we oppositely shift the resonances of the two MRRs in the DR-MZI by increasing their phase separation Δφ in a push-pull manner [17]. The spectra exhibit deep notches at the cross-port and peaks at the bar-port around the resonance wavelengths. The DR-MZI changes into the "bar-state" when the phase difference of the two MZI arms at the resonance wavelength reaches π as illustrated by the black traces. In fact, the DR-MZI works as a 2 nd -order optical add-drop filter. The optical bandwidth can be expanded a little bit with an increased resonance detuning. However, the inband ripple (IBR) also becomes more significant when the two resonances are separated far apart, which degrades the filter performance. The IBR is defined as the ratio of the maximum transmission to the minimum transmission in the passband. To realize a near flat-top bandpass filter, the IBR is needed to be controlled within 1 dB.  Figure 2 shows the Benes architecture of the 16 × 16 silicon optical switch. It consists of 56 DR-MZI SEs, along with 88 waveguide crossings. The 16 × 16 switch chip was fabricated in a silicon-on-insulator (SOI) wafer. The 90°-crossed 1 × 1 MMIs with linear tapers are employed in the waveguide crossings to reduce loss and crosstalk [20]. The cross-sectional dimension of regular silicon ridge waveguides is 500 nm (width) × 220 nm (height) with a slab thickness of 60 nm. In order to reduce the propagation loss, the long straight connection waveguides are widened from 500 nm to 2 μm with 200-μm-long linear tapers. The radius of the racetrack MRR is 10 μm. The coupling length and the gap size between the MRR and the MZI arm are designed to be 4.2 μm and 0.2 μm, respectively. The free spectral range (FSR) of the MRRs is thus 8.3 nm. The transmission coefficient of the MRR couplers is 0.86. The coupling is relatively strong in order to ensure the MRRs work in the over-coupling regime for a broad filtering bandwidth. To characterize the initial states of all 56 SEs, waveguide taps based on directional couplers are added to all input and output ends in each SE, as shown in Fig. 1(a). The power splitting ratio of the taps is around 10%, resulting in ~5.6 dB total loss for an optical path in the switch chip. The loss can be eliminated by using on-chip optical power monitors based on the surface state absorption (SSA) or defect state absorption (DSA) [21].

Variable-order optical filters
High-order optical filters made up of cascaded DR-MZIs have flexible tunability in passband shape. The Benes topology allows for non-blocking optical switching. When the state of an SE in an optical path is changed, the established optical path will be interrupted and a new path will be built. As presented in Section 2.1, the "bar-state" transmission for optical paths I 1 -O 1 and I 2 -O 2 in a DR-MZI with slightly wavelength-detuned resonances exhibit a 2 nd -order passband feature. Therefore, by setting the number of "bar-state" DR-MZIs along the optical path to be N (1  N  7), a (2N) th -order bandpass optical filter is realized. Since each optical path goes through seven SEs, a maximum 14 th -order optical filter can be constructed from the 16 × 16 switch matrix. It should be noted that reconfiguring the filter order for a given pair of I/O ports is actually limited, i.e., for the combination of I 1 -O 1 , only filters with the 2 nd , 6 th , 10 th and 14 th orders can be implemented. The other orders of filters can be obtained by changing the I/O port, for example, I 1 -O 2 for filters with the 4 th , 8 th , 12 th orders. We simulated the optical transmission spectra of the entire 16 × 16 switch using the transfer matrix method. The optical paths for all seven different orders of optical filters are highlighted in Fig. 2. The MRRs in all "bar-state" SEs have the same resonance detuning value. Firstly, we considered the ideal case where the MMIs have an exact 3-dB splitting ratio, the waveguide crossings have no crosstalk, the MRRs are lossless, and there are no phase errors in the two arms of MZI. Figure 3(a) presents the simulation results of the various orders of ideal optical filters. It can be seen that as the filter order increases, the OBRR of the filter increases. The OBRR is defined as the power difference between the passband and the stopband (background floor). It can be seen that the higher-order filter has a narrower passband and a faster roll-off as expected. Next, we took into consideration the imperfections of practical devices as in the simulation of the filter unit (section 2.1). The crosstalk from waveguide crossings is assumed to be 40 dB and the waveguide loss is neglected. Figure 3(b) presents the simulation results with degraded filter performances. The OBRR first increases with the order number when there is no significant inter-path crosstalk. The OBRR reaches the maximum for the 8 th -order filter. After that, the degradation of OBRR mainly comes from the accumulated noise light from the undesired optical paths due to the limited switching extinction ratio of the DR-MZIs and the waveguide crossings.
We further analyzed the influence of the phase differences between two MZI arms on the filter OBRR. The OBRR of a single DR-MZI filter (OBRR unit ) is given by the incomplete interference of the MZI. The phase detuning of the two MRRs was fixed to 0.24 rad to produce a passband in the bar-port. We changed the phase difference between the two arms of the MZI from π/180 rad to 2π/9 rad, thus changing OBRR of the entire filter. Figure 3(c) shows the simulated OBRR as a function of OBRR unit . We can see that OBRR improves as OBRR unit increases. The highest OBRR is near 40 dB, ultimately limited by the crosstalk from the waveguide crossings. The OBRR first increases and then decreases with the filter order, coincident with the experimental observation (section 4). It is interesting to see that the OBRR of the 2 nd -and 14 th -order filters, the 4 th -and 12 th -order filters, and the 6 th -and 10 th -order filters are almost the same. That is because the leaked light from the other noise paths accumulates with the increasing number of "bar-state" SEs and eventually shows up as the out-of-band noise, which as a result reduces the OBRR. For a 2 × (8-n) th -order filter, the noise level has a comparable magnitude with that of a 2n th -order filter (n = 1, 2, 3).
To investigate the scalability of the variable-order optical filters based on the Benes topology, we further simulated a 32 × 32 switch matrix with OBRR unit being 15.5 dB, 21.8 dB, and 39.8 dB as shown by the black lines in Figs. 3(d)-3(f). These three OBRR unit values are corresponding to phase differences of π/9, π/18, and π/180 rad between the MZI arms, representing different levels of phase errors. The red lines represent the filters with no crosstalk from waveguide crossings, and the blue lines represent the filters based on series-connected DR-MZIs in a one-dimensional lattice structure (no inter-path crosstalk). For the filters based on the 32 × 32 switch matrix, the highest filter order reaches 18. It can be seen that both the waveguide crossing-induced crosstalk and the Benes connection-induced inter-path crosstalk significantly affect the final OBRR. When the filter order exceeds 10, the OBRR drops rapidly with the increasing filter order due to the accumulated leaked light from additional noise paths. Typically, the crosstalk from a waveguide crossing is lower than that from a DR-MZI. Therefore, we can conclude that for a 2 N × 2 N Benes switch, the (2N) th -order filter has the highest OBRR, decided by the Benes architecture. The lower limit of OBRR is dominated by the single DR-MZI unit, which can be further improved by integrating phase shifters in MZI arms to compensate for the initial phase errors.  The chip area is mostly occupied by the routing waveguides to connect the 56 DR-MZI SEs in a Benes architecture. It also leaves enough space for fiber array coupling and electrical wire bonding. The top silicon layer thickness is 220 nm and the buried silicon dioxide (BOX) layer thickness is 2 μm. The ridge waveguides were patterned using 248nm deep ultra-violet (DUV) photolithography and plasma dry etch. A 120-nm-thick TiN layer was deposited and patterned to form the microheaters.

Chip fabrication and package
As highlighted by the red dashed box in Fig. 4(a), an array of 36 grating couplers with a uniform pitch of 630 nm and an etched depth of 70 nm were positioned in the chip center for vertical coupling with a fiber array (FA). Two auxiliary U-shaped waveguides are placed at the left and right ends along with the 32 I/O ports for fiber coupling alignment. The fabricated chip was firstly wire-bonded to a printed circuit board (PCB) so that electrical signals can be applied to the TiN resistive microheaters, as shown in Fig. 4(b). Then, a 34-channel 127-μm-pitch FA was precisely aligned to the grating couplers by coupling the outmost two channels of the FA to the U-shaped waveguide. Ultra-violet (UV) light curable adhesive, whose refractive index is close to silicon dioxide, was used to attach the fiber array to the switch chip. The coupling loss is around 5.2 dB/coupler at the 1550 nm wavelength after package. The coupling loss can be reduced to below 1 dB by using a more complicated grating design [22][23][24]. In order to control the chip temperature, a thermoelectric cooler (TEC) and a thermistor were mounted at the back side of the chip. A temperature controller (Thorlabs, TED 4015) with the proportionintegration-differentiation (PID) control is used to monitor and stabilize the chip temperature. Figure 4(c) shows the photo of the home-packaged switch chip. The on-chip optical power monitoring [25,26] and software-defined automatic tuning systems [9,27] could be adopted for realizing automatic resonance control and wavelength stabilization.

Experiment and results
We used a software controlled multi-channel power supply as the voltage source. A tunable laser and a four-channel optical power-meter were used to measure the spectral response of the chip. Output light from the laser was set to transverse electric (TE) polarization by using a polarization controller and then coupled in and out of the chip via on-chip grating couplers. The light paths that we measured in the experiment were highlighted by the colorful lines in Fig. 2. The DR-MZIs in the as-fabricated chip were initially not exactly at the "cross-state" due to fabrication errors. We first aligned the resonances of all 112 MRRs in the switch chip to roughly the same wavelength around 1547 nm. Hence, all 56 SEs in the switch chip were at the "crossstate". The average power consumption to align the resonances to the target one is around 27 mW per SE. It can be reduced by using advanced fabrication tools with higher precision and uniformity. Light from input port I 9 is routed to the output port O 1 . The output transmission spectrum exhibits a dip of about 8 dB deep at the resonance wavelength due to the intrinsic loss of the MRRs [17].
Upon detuning of the two MRRs in S 84 to approach "bar-state", the optical path is changed from I 9 -O 1 to I 9 -O 9 . The new optical path exhibits a 2 nd -order bandpass spectrum. When we further detune the two MRRs in S 84 by increasing the heating power on one MRR and reducing the power on the other MRR, the passband in the spectrum then evolves into two peaks with an increased bandwidth and a larger IBR. On the contrary, when the detuning decreases, the peak becomes smaller with a reduced bandwidth. In a push-pull detuning manner, the filter center wavelength is fixed. The 3-dB bandwidth of the passband is tunable from 0.37 nm to 0.9 nm while the IBR is kept below 1dB, as shown in Fig. 5(a). When we also change S 85 to the "barstate", the optical path becomes I 9 -O 15 and then it exhibits a 4 th -order bandpass spectrum. Figure  5(b) illustrates the bandwidth tunability of the 4 th -order filter. By varying the heating power on the four MRRs, the resonance shift can be well controlled, resulting in a variable bandwidth with a low IBR. The same tuning was performed to the other SEs to implement higher-order optical filters. When an optical path incorporates seven stages of "bar-state" DR-MZIs, a highest 14 th -order optical filter is constructed. Figures 5(c)-5(g) show the measured output spectra for the 6 th -, 8 th -, 10 th -, 12 th -, and 14 th -order bandpass filters, respectively. The tuning of the filter bandwidth is performed by detuning the microring resonances in each unit. The passband insertion loss gradually deteriorates when the separation of the resonances increases. We replotted the spectra with the largest OBRR and the smallest IBR in each filter in Fig. 5(h) in order to make a comparison with the simulation results in Fig. 3(b). It can be seen that the spectral evolution trend of the various orders of filters in the experiment overall follows that of the simulation results. The degradation of OBRR after the 8 th order filter is mainly caused by the accumulated noise light from the undesired optical paths due to the finite switching extinction ratio of DR-MZIs and the scattering from waveguide crossings. Fig. 5. Measured normalized passband spectra for (a) the 2 nd -order, (b) the 4 th -order, (c) the 6 thorder, (d) the 8 th -order, (e) the 10 th -order, (f) the 12 th -order, and (g) the 14 th -order filters. In each filter configuration, the passband width is tuned with the IBR kept below 1 dB. P 1 and P 2 represent the total TO power consumptions on the top and bottom MRRs, respectively. (h) Measured normalized passband spectra of seven different orders of optical filters. Table 1 lists the extracted 3-dB bandwidth (BW), roll-off rate, OBRR, shaping factor (SF) and insertion loss (IL) for all seven optical filters. Practical applications may require a small IBR below 1 dB, which limits the bandwidth tuning range of the filters. The 3-dB bandwidth of the optical filters overall can be tuned from 0.19 nm (23.75 GHz) to 1.06 nm (132.5 GHz). The 8 th -order filter has the largest OBRR. It can be seen that when the filter order increases from 2 to 12, the filter passband roll-off rate rises from 40.2 dB/nm to 231.9 dB/nm. The filter SF is defined as the ratio between 1 dB and 10 dB bandwidths. An ideal bandpass filter should have a box-like passband with SF 1. As shown in Table 1, the SF of different orders of filters is in the range of 0.31 and 0.63. The higher-order filters do not have significantly improved SF, probably due to the influence of inter-path crosstalk. The on-chip insertion loss varies from 8.7 dB to 21.1 dB, coming from the seven SEs, the waveguide crossings, and the routing waveguides. The loss variation is affected by several factors: the loss difference between the "cross-state" and the "bar-state" of DR-MZI, the reduced transmission for a larger resonance detuning in a DR-MZI, the different number of crossings and waveguide length in optical paths.  Figure 6 shows the wavelength dependence of the 6 th -order filter in a wavelength range from 1520 nm to 1580 nm. The FSR is 8.3 nm, determined by the MRR size. The passband shape of the filter is almost unchanged across multiple FSRs. Next, we demonstrate the filter center wavelength tunability by simultaneously shifting both MRRs in each DR-MZI. Figure 7 shows the measured transmission spectra of the seven different orders of filters. The thermal power applied to each MRR is linearly increased with the same rate so that the passband shape remains almost unchanged upon wavelength tuning. The center wavelength of each filter is red-shifted by more than half of the free spectral range (FSR) of the MRR, limited by the supply voltage. The average thermo-optic power tuning efficiency of the SE is 0.14 nm/mW. It can be improved by etching off the silicon substrate beneath the MRRs [28].
It should be noted that the filter center wavelength and bandwidth can be independently controlled. The filter wavelength is shifted by simultaneously increasing or decreasing the thermal power on both MRRs. On the other hand, the bandwidth of the filter is varied by tuning the MRRs in a push-pull manner. The response time for thermal tuning is measured to be around 15-17 μs. Fig. 7. Demonstration of the filter center wavelength tuning for (a) the 2 nd -order, (b) the 4 thorder, (c) the 6 th -order, (d) the 8 th -order, (e) the 10 th -order, (f) the 12 th -order, and (g) the 14 thorder filters. The symbol P in the graphs represents the total power consumption required to tune the filter center wavelength.

Discussion
As the 16 × 16 Benes architecture contains 8 × 7 = 56 units, it is possible to configure multiple parallel optical filters from one single chip, which is highly demanded in parallel signal processing. Figure 8 illustrates the parallel light paths used to construct various orders of optical filters. There are many options for the optical paths, as long as the following two criteria are satisfied to avoid inter-path crosstalk. First, the parallel paths should not share the same "barstate" unit. Second, the out-of-band optical signals from the first "bar-state" unit should not cross any other optical paths. There are maximally 8 parallel 2 nd -order optical filters that can be reconfigured from the chip. In the exemplary configuration of Fig. 8(a), the 8 units in the last column are set to "bar-state", while the others are all set to "cross-state". Similarly, we can find four optical paths to build the 4 th -order to 10 th -order filters, as shown in Figs. 8(b)-8(e). The "bar-state" units in each optical path are in the last few stages to achieve the maximum number of parallel filters. For the 12 th -order and 14 th -order filters, we can only find two optical paths in each case under the above two criteria, as seen from Figs. 8(f) and 8(g). Fig. 8. Light path illustration for implementation of parallel optical filters with (a) the 2 nd -order, (b) the 4 th -order, (c) the 6 th -order, (d) the 8 th -order, (e) the 10 th -order, (f) the 12 th -order, and (g) the 14 th -order. The units with filled boxes represent "bar-state" DR-MZIs and the units with unfilled boxes represent "cross-state" DR-MZIs.

Conclusion
We have experimentally demonstrated a reconfigurable silicon optical filter using an existing 16 × 16 DR-MZI Benes switch chip. By thermally tuning the resonances of the MRRs and choosing a light path through seven DR-MZI elements, the chip is reconfigured to IIR optical filters with various orders. The bandwidth of the filter is tunable from 0.19 nm (23.75 GHz) to 1.06 nm (132.5 GHz) with IBR smaller than 1 dB. The filter roll-off rate and shaping factor can reach 231.9 dB/nm and 0.63 for the 12 th -and 10 th -order filter, respectively. The OBRR can be larger than 30 dB for the 8 th -and 10 th -order filters. The OBRR can be further improved by lowering the crosstalk of the waveguide crossings and improving the switch extinction ratio of DR-MZI SEs. The filter center wavelength is tuned over a half FSR with the passband shape almost unchanged. In our experiment, we only used a small number of SEs to construct the optical filters. In fact, there exist multiple optical paths in the switch matrix, allowing for parallel processing. Meanwhile, it also increases the chip tolerance to device failure as the malfunctional device can be easily bypassed by switching to another optical path. The OBRR is affected by the inter-path optical crosstalk in the Benes architecture. We note that the approach introduced in this paper can be generalized to schemes that use an N × N switch matrix for wavelength-selective devices, opening a way towards the realization of softwaredefined photonic functionality in a general photonic integrated circuit.