High-speed optical interconnects drive the need for compact microring resonators (MRRs) with wide free spectral ranges (FSRs). A silicon-on-insulator MRR based filter with bent contra-directional couplers that exhibits an FSR-free response, at both the drop and through ports, while achieving a compact footprint is both theoretically and experimentally demonstrated. Also, using bent contra-directional couplers in the couping regions of MRRs allowed us to achieve larger side-mode suppressions than MRRs with straight CDCs. The fabricated filter has a minimum suppression ratio of more than 15 dB, a 3dB-bandwidth of ~23 GHz, an extinction ratio of ~18 dB, and a drop-port insertion loss of ~1 dB. High-speed data transmission through our filter is also demonstrated at data rates of 12.5 Gbps, 20 Gbps, and 28 Gbps.
© 2016 Optical Society of America
The increasing demand for high data rates in data center applications and computing systems drives the need for low cost, high-speed optical links [1, 2]. To achieve large data rates in optical interconnects, wavelength-division multiplexing (WDM) systems are used [3,4]. Such WDM based links are required to have large channel capacities and large bandwidths per channel; this leads to large aggregate bandwidths. Ideally, chips in which such WDM systems are implemented should have small areas. The desired small areas are achieved by densely integrating the optical components. Hence, the compact footprints of silicon-on-insulator (SOI) devices, in general, make silicon-photonic chips attractive candidates for low cost, high-speed optical links. Accordingly, SOI add-drop filters, used in WDM based links, are required to have compact footprints, large bandwidths, and wide free spectral ranges (FSRs); where wide FSRs allow large numbers of channels to be multipexed/de-multiplexed.
SOI microring resonators (MRRs) are good candidates for such add-drop filters because they are capable of achieving the high bandwidth requirements while having compact footprints. Furthermore, to achieve extended FSRs in MRRs, multiple series-coupled microrings that use the Vernier effect  or two-point coupling  have been demonstrated. Although, such MRR designs have large FSRs, they require more on-chip real-estate than first-order (i.e., single-ring) MRRs. Nevertheless, single-ring MRR designs with contra-directional couplers (CDCs) offer FSR-free responses .
Previously proposed MRRs with CDCs were comprised of straight CDCs integrated into the coupling regions of racetrack resonators [7–9]. In these designs, the CDCs increased the footprints of the filters as compared to standard microring and racetrack resonators. However, by partially wrapping the CDCs around the microring, we demonstrate that MRRs with CDCs can be smaller than those previously demonstrated. Additionally, MRRs with bent CDCs allow for filter designs that can have larger side-mode suppressions as compared to using MRRs with straight CDCs. Hence, by utilizing bent CDCs in an MRR design, a filter is realized that has a more compact footprint and a large bandwidth while having FSR-free responses at both the drop and through ports. Here, by FSR-free we mean that our filter significantly suppresses the MRR side modes; achieving an amplitude response that appears as though it has no FSR. In this letter, we present the design of an SOI MRR based filter with bent CDCs as well as experimental results. The fabricated filter has an FSR-free response, a minimum side-mode suppression ratio (SMSR) of more than 15 dB, a 3dB-bandwidth (3dB-BW) of ~23 GHz, and an extinction ratio (ER) of ~18 dB.
2. Device structure
Figure 1 shows a schematic of our proposed MRR filter with two, identical, bent CDCs. The parameters to be designed for the CDCs include the widths of the bus waveguide, WB, and the ring waveguide, WR, the corrugation depths of the bus waveguide, ΔWB, and the ring waveguide, ΔWR, the couplers’ gap widths, g, and the perturbation period, Λ, as illustrated in the inset in Fig. 1, as well as the number of periods, N. In order to suppress the CDCs’ Bragg reflections, anti-reflection gratings are used at the external side-walls of the waveguides, in which the gratings are out-of-phase with the gratings used at the inner side-walls . The widths, WR and WB, are asymmetric so that the wavelengths of the reflections due to the CDCs are far from the drop-port peak wavelength, λD, [7, 11]. λD is the center wavelength of the main lobe of the CDC’s drop-port spectrum, and is chosen to coincide with one of the MRR’s longitudinal modes in the C-band. The bent CDCs are designed using previously proposed bent coupler designs [12–14].
Here, we show that MRRs with bent CDCs can achieve larger side-mode suppressions than similar MRRs with straight CDCs. Typically, in an MRR with straight CDCs, two identical straight CDCs are used as the couplers of a racetrack resonator with the CDCs having coupling lengths, Lc, and with the bend radii of the racetrack being Rst, see Fig. 2. In our MRR with bent CDCs, two identical bent CDCs are used as the couplers to a microring with the CDCs having coupling lengths, Lc, and with the radius of the microring being, R, see Fig. 1.
In order for an MRR with CDCs to attain maximum side-mode suppressions, the MRR’s side modes should coincide with the nulls of the CDCs, as shown in Fig. 3, and therefore, the spacings between the first CDCs’ nulls, Δλnull, should be equal to twice the MRR’s FSR. The spacing Δλnull of a CDC and the FSR of an MRR are given by
In addition, for an MRR with bent CDCs to achieve Δλnull = 2FSR, Lc of each of the CDCs should satisfy the relation,
Using Eq. 3, the Rst required to satisfy Δλnull = 2FSR is calculated at various values of Lc. Also, using Eq. 4, the Lc required to satisfy Δλnull = 2FSR, is calculated at various values of R. Using the Rst and Lc values obtained from Eq. 3 and Eq. 4, we then calculate γ = (2Lc/Lrt) ∗ 100, where γ is the percentage of coverage of the roundtrip length of the MRR by the CDCs. γ is plotted versus various Lrt values in Fig. 4(a) for MRRs with straight CDCs and for MRRs with bent CDCs each for κo = 2000 m−1 and κo = 8000 m−1. Here, in these plots, we chose WR of the bent CDCs and the straight CDCs to be the same and to be 550 nm, as well as we chose WB of the bent CDCs and the straight CDCs to be the same and to be 450 nm. Clearly, in the MRRs with bent CDCs, we can fit both of the CDCs on the microrings’ circumference (γ < 100%) for all of our plotted Lrt values. Accordingly, an MRR with bent CDCs can be designed so that the MRR’s longitudinal modes are aligned with the CDCs’ nulls, and hence maximum side-mode suppressions can be achieved. On the other hand, in the MRR with straight CDCs, γ > 100% for all of our plotted Lrt values. In other words, there is no physical MRR design that exists that can satisfy Δλnull = 2FSR and achieves maximum suppression. This is because the group indicies of the waveguides of a straight CDC are typically smaller than the group indicies of the waveguides of a bent CDC with the same waveguide widths; this causes Δλnull of a straight CDC to be larger than Δλnull of a bent CDC. As a result, the Lc value required for an MRR with bent CDCs to achieve Δλnull = 2FSR will be less than that of an MRR with straight CDCs with the same κo and Lrt values.
Furthermore, an MRR with bent CDCs and with a large γ value will typically have larger side-mode suppressions than an MRR with straight CDCs with the same γ value. This is because, in an MRR with straight CDCs, as the coupling lengths of the CDCs are increased, to decrease Δλnull, the roundtrip length of the racetrack resonator decreases and the FSR of the MRR increases. Hence, this can cause the FSR to increase at a greater rate than the decrease in Δλnull, which leads to decreased suppression. However, in an MRR with bent CDCs increasing the coupling lengths of the CDCs will not effect the roundtrip length of the microring. As a result, Δλnull can be decreased without changing the FSR of the MRR which leads to an increase in suppression. For illustration purposes, a measure of side-mode suppression, Kc, is plotted at various Lrt values (ranging from 18 µm to 207 µm) for MRRs with both straight and bent CDCs each for κo = 2000 m−1 and κo = 8000 m−1. Plots of Kc versus Lrt at γ = 87% are shown in Fig. 4(b); γ = 87% is used to allow for bends in the bus waveguides needed to connect to external components, and to have enough space to place heaters on top of the sections of the microring that are not covered by CDCs for thermal tuning (see section 4 for further discussion on the device design). For our analysis, Kc is used as a metric that is directly proportional to the SMSR at the MRR resonances immediately adjacent to the resonant wavelength of the filter, SMSRadj. Specifically, Kc is the normalized contra-directional power coupling factor of a CDC evaluated at λD±1FSR assuming that λD coincides with one of the longitudinal modes of the MRR, see Fig. 4(c). In other words, Kc = |κc (λD ± 1FSR)|2/|κc (λD)|2 where κc (λD) is the field coupling factor of a CDC. From the plots in Fig. 4(b), the MRRs with bent CDCs achieve larger Kc values (i.e., larger suppressions) than the MRR with straight CDCs for all plotted Lrt and κo values.
4. Device design and theoretical results
In order to design an MRR with bent CDCs that achieves maximum side-mode suppression, Lc of each of the CDCs should be chosen so that it satisfies Eq. 4. Clearly, this chosen Lc value should be less than half the microring’s circumference (i.e., Lc< πR) to accommodate both of the CDCs on a microring. Accordingly, R should be less than or equal to ~34 µm for κo values up to 8000 m−1 [see Fig. 5; here we assumed WB = 450 nm and WR = 550 nm]. Also, it is shown in Fig. 5 that the least possible coverage, Lc/πR, to satisfy Eq. 4 is approximately 0.964. Such coverage is insufficient to allow for the filter to be connected to other components (for example, the bus waveguides need bends in them of radius, Rwg, and to be separated from each other by Gwg, as illustrated in Fig. 1). Hence, it is difficult to realize a design for which the MRR’s side modes coincide exactly with the CDCs’ nulls. Here, in order to minimize radiation losses in the bends we use Rwg = 5 µm and to minimize cross-coupling between the buses we use Gwg = 2.5 µm. Accordingly, Lc is chosen to accommodate our chosen Rwg and Gwg for various R values. In Fig. 6, we have plotted the theoretical Kc, in dB, for κo values up to 8000 m−1. As can be seen from Fig. 6, the minimum Kc for κo ≤ 8000 m−1 and R = 34 µm is ~18 dB. Nevertheless, the minimum Kc for an MRR with R = 25 µm is also ~18 dB at κo = 8000 m−1. Given that the actual fabricated κo will typically be less than the simulated value, the Kc in the actual device should be greater than 18 dB for any κo < 8000 m−1 and for R values between 25 µm and 34 µm. However, since the footprint of our device almost doubles as R changes from 25 µm to 34 µm, we have picked the smaller radius for our device.
The CDCs are designed so that the widths of the waveguides, WB and WR, are 450 nm and 550 nm, respectively; also, a ΔWB of 30 nm and a ΔWR of 40 nm is used . Also, g = 280 nm and R = 25 µm. Λ, measured at the center of the gap, is designed for a target λD value that will satisfy the phase-match condition for bent CDCs,Fig. 7(a). Also, the power coupling factor, |κc|2, is fitted and κo is found to be ~6800 m−1 using the method in . The co-directional power coupling factor of a simulated bent CDC is ~0.015 at 1537.2 nm (λD). From the CDC transmission in Fig. 7(a), two notches are observed: a notch at 1537.2 nm (λD), due to the contra-directional coupling between the bus and ring waveguides, and a notch at ~1522 nm, from intra-waveguide Bragg reflections at the input port . For the contra-directional coupling, the electric field transfer function of the MRR filter with bent CDCs at the drop port, , and at the through port, , are derived using Mason’s rule, similar to the approach presented in . The resulting equations are
Using Eq. 6 and Eq. 7, and assuming a propagation loss of 3 dB/cm (α ≃ 69 m−1), the power transmission to the drop port, Tdrop, and to the through port, Tthru, can be calculated. In order to characterize the side-mode suppression of our filter using the drop-port response, we determine two side-mode suppression ratios: SMSRmin and SMSRadj, both of these measures are illustrated in Fig. 7(b). SMSRmin is the minimum side-mode suppression ratio within the wavelength span for which the response is measured. We use SMSRmin to typically mean the overall SMSR of the filter. SMSRadj is the suppression ratio of the side modes occurring at λD±1FSR; if the suppression ratio of the side mode at λD+1FSR is not equal to the suppression ratio of the side mode at λD−1FSR, the smaller ratio is chosen to be SMSRadj. From Tdrop, in Fig. 7(b), SMSR1 is 17.5 dB, which is expected given our choice of R = 25 µm to achieve Kc > 18 dB (as discussed above). Additionally, SMSRmin is ~15 dB, the 3dB-BW is ~35 GHz, and the insertion loss is 1.6 dB. From Tthru, in Fig. 7(b), the ER is 16.5 dB. Furthermore, the drop-port chromatic dispersion, within a 25 GHz window around 1537.2 nm, is ±42 ps/nm as shown in Fig. 7(c).
5. Device fabrication and measured results
The MRR filter with bent CDCs was fabricated using electron beam lithography at the University of Washington . The fabricated device has strip waveguides with 220 nm heights and a top oxide cladding. Metal heaters are used on top of the MRR waveguides for thermal tuning. A total of three sections of micro-heaters are used: two sections on top of the CDCs and another section on top of portions of the microring that don’t contain gratings, and each of the heater sections is tuned separately. A microscopic image of our fabricated MRR filter is shown in Fig. 8. The spectral responses (including the responses of the input and output grating couplers) at both the drop and through ports are shown in Fig. 9(a) for wavelengths between 1520 nm and 1580 nm. The drop-port spectral response shows a single resonant peak at ~1540.3 nm in a 60 nm wavelength span, which contains the C-band. In addition, the SMSRadj is 20.7 dB and the SMSRmin is more than 15 dB. Additionally, from the normalized responses (i.e., where the grating couplers’ responses have been de-embedded) in Fig. 9(b), the ER is 18 dB, the 3dB-BW is ~23 GHz, and the drop-port insertion loss (ILdrop) is ~1 dB. Furthermore, the suppressed notch at the through port, at 1533.1 nm, has a magnitude of 2.9 dB. The drop-port response is measured at various total tuning powers for both heater sections, and the responses are shown in Fig. 10(a). In these measurements, power is applied to the CDC heaters to shift the drop-port peak wavelength, while power is applied to the microring heater to align the microring’s response with the CDCs’ responses. The chromatic dispersion at the filter’s drop-port is measured using a Luna Optical Vector Analyzer™. From Fig. 10(b), the chromatic dispersion within a 25 GHz window centered on 1540.3 nm is ±90 ps/nm.
Table 1 gives a comparison between the as-designed results (obtained in section 4) and the measured results of our filter. Clearly, the measured dispersion is larger than the as-designed value because the κo of the fabricated device is less than that of the simulated device. This would be consistent with the reduction in the 3dB-BW and the increase in SMSRadj from the design value. The measured drop-port response is thus fitted to obtain κo and α of our fabricated filter. Our objective is to verify the model that we use to obtain the theoretical responses for MRRs with bent CDCs and to verify that κo of the fabricated device is less than our design value of 6800 m−1. Here, we fit the measured drop-port response to the magnitude-squared of Eq. 6, and κc and tc are obtained using the CDC’s coupled-mode equations in . From our fit, κo is found to be 5530 m−1 and α is found to be ~161 m−1 (i.e., a power propagation loss of 7 dB/cm). Clearly, κo of the fabricated device is smaller than the design value and α of the fabricated device is larger than the design value. and are then recalculated using Eq. 6 and Eq. 7 and using the fitted κo and α values. The magnitude-squared response of the calculated (fitted response), and the measured and theoretical (designed) drop-port responses are shown in Fig. 11; the fitted response shows a closer agreement to the measured response as compared to the designed response. The following are the extracted results from the calculated and responses: SMSRadj = 19.2 dB, ILdrop = 0.7 dB, 3dB-BW = 24 GHz (0.19 nm), and ER = 22.8 dB. These results closely agree with the measured results, see Table 1. Also, the chromatic dispersion within a 25 GHz window centered on 1540.3 nm is ±90 ps/nm; this dispersion matches the measured dispersion, see Table 1. We can thus safely conclude that our model closely approximates the fabricated device and that the assumptions we made during our design procedure (such as co-directional coupling is negligible) are valid.
Table 1 also gives a comparison between the measured results of our filter and previously reported values for a single-ring MRR with straight CDCs . Our MRR filter achieves larger SMSRadj and SMSRmin than those of the previously demonstrated MRR filter with straight CDCs even though κo of our filter is larger. In addition, our MRR filter with bent CDCs has a footprint of ~1963 µm2, which is significantly more compact, less than one-third the area, as compared to the previously demonstrated MRR with straight CDCs. In section 3, we have shown that an MRR with bent CDCs will achieve larger side-mode suppressions than an equivalent MRR with straight CDCs, see Fig. 4(b). As a result, we designed our proof-of-concept MRR with bent CDCs so as to achieve higher side-mode suppressions and to be more compact than other demonstrated MRRs with straight CDCs. Our proof-of-concept filter achieved our predicted design results and demonstrated a more attractive alternative to MRRs with straight CDCs that has higher suppressions and is more space-efficient while still having the advantages of integrating CDCs in the coupling regions.
7. High-speed testing
In order to characterize the demonstrated filter for high-speed data transmission, an experimental setup is used similar to the one proposed in . The setup is composed of a pulse pattern generator, a Mach-Zehnder modulator (MZM), an erbium-doped fiber amplifier (EDFA), a variable optical attenuator, an optical tunable filter, a photo-detector (PD), and a digital communication analyzer. The EDFA and the attenuator together provide variable gain at the output of our filter. The total gain of this stage is set so that the peak power of the data at the PD is 0 dBm. NRZ signals with 231 − 1 pseudorandom binary sequence (PRBS) patterns and data rates of 12.5 Gbps, 20 Gbps, and 28 Gbps are used in our characterizations.
Eye diagrams of the modulated NRZ data are measured at the input and at the drop port of our filter at 1540.3 nm for data rates of 12.5 Gbps, 20 Gbps, and 28 Gbps, see Figs. 12(a)–12(f). A wavelength of 1540.3 nm corresponds to the center wavelength of our filter. Here, the signal at the input to our filter is the signal from the MZM. As can be seen from Figs. 12(a)–12(f), the eyes exhibit small reductions in the signal quality at the drop port of our filter. Also, eye diagrams are measured at the input and at the through port of our filter at 1533.1 nm, which corresponds to the major suppressed notch. The major suppressed notch was chosen because it is the point at which the largest deterioration of the signal is expected . The eye diagrams are shown in Figs. 12(g)–12(i) at the input to our filter and in Figs. 12(j)–12(l) at the through port of our filter. The patterns maintain open eyes at the through port’s notch at 1533.1 nm for data rates up to 28 Gbps with minimal reduction in the signal quality.
In conclusion, we present the design of an SOI MRR based filter with bent CDCs in which the CDCs are partially wrapped around the MRR. With the aid of bending the CDCs, a relatively compact filter design with an FSR-free response, a relatively high SMSR, and a large 3dB-BW is achieved. Our design facilitates the use of MRR based multiplexers/de-multiplexers for densely integrated optical interconnects in WDM systems, where large channel capacities and small chip footprints are desired. The fabricated MRR filter with bent CDCs is experimentally demonstrated showing an FSR-free response at both the drop port and the through port. Moreover, the measurements show an SMSRmin of more than 15 dB; such an SMSR will be difficult to obtain using MRRs with straight CDCs. Also, our filter has a 3dB-BW of 23 GHz and has an ER of ~18 dB. The eye diagrams of NRZ 231 − 1 PRBS patterns, for data~rates up to 28 Gbps, exhibit small reductions in the signal quality at the drop port and the through port of our filter.
Natural Sciences and Engineering Research Council of Canada (NSERC) DISCOVERY GRANT (2014-05271); NSERC CREATE SiEPIC program (414122-12).
We gratefully acknowledge CMC Microsystems for the provision of services that facilitated this research as well as Lumerical Solutions, Inc., and Mentor Graphics, Corp., for the design tools. Part of this work was conducted at the University of Washington Nanofabrication Facility, a member of the NSF National Nanotechnology Infrastructure Network.
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