1. Introduction

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 [5] or two-point coupling [6] 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 [7].

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, W_B, and the ring waveguide, W_R, the corrugation depths of the bus waveguide, ΔW_B, and the ring waveguide, ΔW_R, 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 [10]. The widths, W_R and W_B, are asymmetric so that the wavelengths of the reflections due to the CDCs are far from the drop-port peak wavelength, λ_D, [7, 11]. λ_D 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].

 

Fig. 1 Schematic of an MRR filter with bent CDCs, as well as an inset illustrating some of the CDCs’ design parameters. The dark blue traces are the corrugated waveguides (gratings) of the CDCs.

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3. Motivation

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, L_c, and with the bend radii of the racetrack being R_st, 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, L_c, and with the radius of the microring being, R, see Fig. 1.

 

Fig. 2 Schematic of an MRR with straight CDCs.

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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, Δλ_null, should be equal to twice the MRR’s FSR. The spacing Δλ_null of a CDC and the FSR of an MRR are given by

 

Fig. 3 A CDC’s spectral response (dashed trace) and an MRR’s response (solid trace) when Δλ_null = 2FSR.

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In addition, for an MRR with bent CDCs to achieve Δλ_null = 2FSR, L_c of each of the CDCs should satisfy the relation,

Using Eq. 3, the R_st required to satisfy Δλ_null = 2FSR is calculated at various values of L_c. Also, using Eq. 4, the L_c required to satisfy Δλ_null = 2FSR, is calculated at various values of R. Using the R_st and L_c values obtained from Eq. 3 and Eq. 4, we then calculate γ = (2L_c/L_rt) ∗ 100, where γ is the percentage of coverage of the roundtrip length of the MRR by the CDCs. γ is plotted versus various L_rt values in Fig. 4(a) for MRRs with straight CDCs and for MRRs with bent CDCs each for κ_o = 2000 m⁻¹ and κ_o = 8000 m⁻¹. Here, in these plots, we chose W_R of the bent CDCs and the straight CDCs to be the same and to be 550 nm, as well as we chose W_B 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 L_rt 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 L_rt values. In other words, there is no physical MRR design that exists that can satisfy Δλ_null = 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 Δλ_null of a straight CDC to be larger than Δλ_null of a bent CDC. As a result, the L_c value required for an MRR with bent CDCs to achieve Δλ_null = 2FSR will be less than that of an MRR with straight CDCs with the same κ_o and L_rt values.

 

Fig. 4 (a) Plots of γ required to achieve maximum suppression versus L_rt for MRRs with straight CDCs and MRRs with bent CDCs. (b) Plots of K_c, in dB, versus L_rt for MRRs with straight CDC and MRRs with bent CDCs at γ = 87%. (c) The CDC’s and the MRR’s spectral responses when Δλ_null > 2FSR.

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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 Δλ_null, 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 Δλ_null, 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, Δλ_null 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, K_c, is plotted at various L_rt values (ranging from 18 µm to 207 µm) for MRRs with both straight and bent CDCs each for κ_o = 2000 m⁻¹ and κ_o = 8000 m⁻¹. Plots of K_c versus L_rt 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, K_c 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, SMSR_adj. Specifically, K_c is the normalized contra-directional power coupling factor of a CDC evaluated at λ_D±1FSR assuming that λ_D coincides with one of the longitudinal modes of the MRR, see Fig. 4(c). In other words, K_c = |κ_c (λ_D ± 1FSR)|²/|κ_c (λ_D)|² where κ_c (λ_D) is the field coupling factor of a CDC. From the plots in Fig. 4(b), the MRRs with bent CDCs achieve larger K_c values (i.e., larger suppressions) than the MRR with straight CDCs for all plotted L_rt and κ_o values.

4. Device design and theoretical results

In order to design an MRR with bent CDCs that achieves maximum side-mode suppression, L_c of each of the CDCs should be chosen so that it satisfies Eq. 4. Clearly, this chosen L_c value should be less than half the microring’s circumference (i.e., L_c< πR) to accommodate both of the CDCs on a microring. Accordingly, R should be less than or equal to ~34 µm for κ_o values up to 8000 m⁻¹ [see Fig. 5; here we assumed W_B = 450 nm and W_R = 550 nm]. Also, it is shown in Fig. 5 that the least possible coverage, L_c/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, R_wg, and to be separated from each other by G_wg, 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 R_wg = 5 µm and to minimize cross-coupling between the buses we use G_wg = 2.5 µm. Accordingly, L_c is chosen to accommodate our chosen R_wg and G_wg for various R values. In Fig. 6, we have plotted the theoretical K_c, in dB, for κ_o values up to 8000 m⁻¹. As can be seen from Fig. 6, the minimum K_c for κ_o ≤ 8000 m⁻¹ and R = 34 µm is ~18 dB. Nevertheless, the minimum K_c for an MRR with R = 25 µm is also ~18 dB at κ_o = 8000 m⁻¹. Given that the actual fabricated κ_o will typically be less than the simulated value, the K_c in the actual device should be greater than 18 dB for any κ_o < 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.

 

Fig. 5 Plots of the MRR’s coverage with the CDCs (Lc/πR) versus R at various κ_o values.

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Fig. 6 A plot of K_c, in dB, versus R at κ_o = 8000 m⁻¹.

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The CDCs are designed so that the widths of the waveguides, W_B and W_R, are 450 nm and 550 nm, respectively; also, a ΔW_B of 30 nm and a ΔW_R of 40 nm is used [15]. Also, g = 280 nm and R = 25 µm. Λ, measured at the center of the gap, is designed for a target λ_D value that will satisfy the phase-match condition for bent CDCs,

 

Fig. 7 Theoretical spectral responses of (a) the power coupling for our bent CDC, |κ_c|², at the drop port and the power transmission, |t_c|², at the through port, and (b) MRR our filter with bent CDCs transmission at the drop port, T_drop, and at through port, T_thru. (c) A plot of the theoretical chromatic dispersion at the drop-port for a ±0.1 nm (~25 GHz) window around 1537.2 nm.

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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, T_drop, and to the through port, T_thru, 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: SMSR_min and SMSR_adj, both of these measures are illustrated in Fig. 7(b). SMSR_min is the minimum side-mode suppression ratio within the wavelength span for which the response is measured. We use SMSR_min to typically mean the overall SMSR of the filter. SMSR_adj is the suppression ratio of the side modes occurring at λ_D±1FSR; if the suppression ratio of the side mode at λ_D+1FSR is not equal to the suppression ratio of the side mode at λ_D−1FSR, the smaller ratio is chosen to be SMSR_adj. From T_drop, in Fig. 7(b), SMSR₁ is 17.5 dB, which is expected given our choice of R = 25 µm to achieve K_c > 18 dB (as discussed above). Additionally, SMSR_min is ~15 dB, the 3dB-BW is ~35 GHz, and the insertion loss is 1.6 dB. From T_thru, 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 [16]. 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 SMSR_adj is 20.7 dB and the SMSR_min 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 (IL_drop) 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.

 

Fig. 8 Microscopic image of our MRR filter with metal heaters; the inset shows a scanning electron microscope (SEM) image of a portion of a bent CDC.

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Fig. 9 (a) Spectral responses of our MRR filter at the drop and through ports. (b) The responses relative to 1540.3 nm, after normalizing them with respect to the grating couplers’ responses.

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Fig. 10 (a) Drop-port responses at various total tuning powers. (b) Chromatic dispersion at the drop port in a ±0.1 nm (~25 GHz) relative to 1540.3 nm.

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6. Discussion

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 κ_o 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 SMSR_adj from the design value. The measured drop-port response is thus fitted to obtain κ_o 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 κ_o 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 κ_c and t_c are obtained using the CDC’s coupled-mode equations in [19]. From our fit, κ_o 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, κ_o of the fabricated device is smaller than the design value and α of the fabricated device is larger than the design value. ${\overline{E}}_{drop}$ and ${\overline{E}}_{thru}$ are then recalculated using Eq. 6 and Eq. 7 and using the fitted κ_o and α values. The magnitude-squared response of the calculated ${\overline{E}}_{drop}$ (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 ${\overline{E}}_{drop}$ and ${\overline{E}}_{thru}$ responses: SMSR_adj = 19.2 dB, IL_drop = 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. Summary of the as-designed, measured, and fitted results of our MRR filter with bent CDCs and its comparison with the results of an MRR with straight CDCs demonstrated in [7].

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Fig. 11 Drop-port spectral responses from the measured data and from ${\overline{E}}_{drop}$ calculated using fitted κ_o and α values relative to 1540.3 nm, as well as the theoretical drop-port response obtained in section 4 relative to 1537.2 nm.

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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 [7]. Our MRR filter achieves larger SMSR_adj and SMSR_min than those of the previously demonstrated MRR filter with straight CDCs even though κ_o 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 [17]. 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 [18]. 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.

 

Fig. 12 Eye diagrams of NRZ data at the input of our filter at 1540.3 nm for data rates of (a) 12.5 Gbps, (b) 20 Gbps, and (c) 28 Gbps as well as at the drop port (output) for data rates of (d) 12.5 Gbps, (e) 20 Gbps, and (f) 28 Gbps. Eye diagrams of NRZ data at 1533.1 nm at the input of our filter for data rates of (g) 12.5 Gbps, (h) 20 Gbps, and (i) 28 Gbps as well as at the through port (output) for data rates of (j) 12.5 Gbps, (k) 20 Gbps, and (l) 28 Gbps.

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8. Summary

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 SMSR_min 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.