Design and realization of a two-stage microring ladder filter in silicon-on-insulator

We report the design and experimental realization of a new type of microring filters consisting of two parallel-cascaded microring doublets connected by a π-phase shift element. Interference between the two secondorder microring stages gave rise to a fourth-order filter response with flattop passband and a bandwidth of 100GHz. The result demonstrates the feasibility of realizing advanced integrated optics filters based on parallel cascades of high-order microring networks. ©2012 Optical Society of America OCIS codes: (130.3120) Integrated optics devices; (130.7408) Wavelength filtering devices; (230.4555) Coupled resonators. References and links 1. B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, “Very high order microring resonator filters for WDM applications,” IEEE Photon. Technol. Lett. 16(10), 2263–2265 (2004). 2. M. L. Cooper, G. Gupta, M. A. Schneider, W. M. Green, S. Assefa, F. Xia, Y. A. Vlasov, and S. Mookherjea, “Statistics of light transport in 235-ring silicon coupled-resonator optical waveguides,” Opt. Express 18(25), 26505–26516 (2010). 3. V. Van, “Synthesis of elliptic optical filters using mutually-coupled microring resonators,” J. Lightwave Technol. 25(2), 584–590 (2007). 4. M. A. Popovic, T. Barwicz, P. T. Rakich, M. S. Dahlem, C. W. Holzwarth, F. Gan, L. Socci, M. R. Watts, H. I. Smith, F. X. Kartner, and E. P. Ippen, “Experimental demonstration of loop-coupled microring resonators for optimally sharp optical filters,” IEEE Conf. on Lasers and Electro-Optics, paper CTuNN3 (2008). 5. C. K. Madsen, “General IIR optical filter design for WDM applications using all-pass filters,” J. Lightwave Technol. 18(6), 860–868 (2000). 6. H. L. Liew and V. Van, “Exact realization of optical transfer functions with symmetric transmission zeros using the double-microring ladder architecture,” J. Lightwave Technol. 26(14), 2323–2331 (2008). 7. B. E. Little, S. T. Chu, J. V. Hryniewicz, and P. P. Absil, “Filter synthesis for periodically coupled microring resonators,” Opt. Lett. 25(5), 344–346 (2000). 8. R. Grover, V. Van, T. A. Ibrahim, P. P. Absil, L. C. Calhoun, F. G. Johnson, J. V. Hryniewicz, and P.-T. Ho, “Parallel-cascaded semiconductor microring resonators for high-order and wide-FSR filters,” J. Lightwave Technol. 20(5), 900–905 (2002). 9. H. G. Martinez and T. W. Parks, “Design of recursive digital filters with optimum magnitude and attenuation poles on the unit circle,” IEEE Trans. Acoust., Speech, Signal Proc. 26(2), 150–156 (1978). 10. A. Canciamilla, S. Grillanda, F. Morichetti, C. Ferrari, J. Hu, J. D. Musgraves, K. Richardson, A. Agarwal, L. C. Kimerling, and A. Melloni, “Photo-induced trimming of coupled ring-resonator filters and delay lines in As2S3 chalcogenide glass,” Opt. Lett. 36(20), 4002–4004 (2011).


Introduction
Microring resonators are flexible integrated optics elements which have found widespread applications in photonic integrated circuits, especially for the realization of compact, highorder optical filters.For example, serially coupled microring filters of up to the eleventh order have been demonstrated in the glass material system [1], and coupled resonator optical waveguides (CROWs) consisting of more than 200 coupled microracetracks have been realized in Silicon-on-Insulator (SOI) [2].Most high-order microring devices to date are based on the serial coupling configuration because of its simplicity in terms of design and fabrication.However, the serial coupling topology has a limitation in that it can only realize filter transfer functions containing all poles and no transmission zeros.This is due to the fact that all signal paths through the microring array are in phase, so that it is not possible to achieve destructive interference of the signals to produce a transmission null at the drop port.As a result only simple filter responses with relatively slow skirt roll-offs, such as the Butterworth filters, can be realized with the serial coupling configuration.To overcome this constraint, more advanced microring architectures capable of realizing high-order transfer functions with transmission zeros have been proposed, including two-dimensional coupled microring networks [3,4], ring-loaded Mach-Zehnder Interferometer filters [5], and microring "ladder filters" composed of parallel cascaded microring networks [6].Among these types of filters, the ladder filter offers several advantages such as the simplicity of its architecture, the ability to design and optimize each stage separately, and as will be shown in this paper, the ease with which the device can be tuned to correct for resonance mismatch caused by fabrication imperfections.
Parallel cascades of single add-drop microring resonators connected by two bus waveguides, such as shown in Fig. 1(a), have been theoretically investigated [7] and experimentally demonstrated in the GaAs/AlGaAs material system [8].In this type of structures, the output signal in each microring stage is fed backward to the previous stage, causing additional resonances in the array which cannot be independently controlled from those of the microrings.In other words the structure has more poles than free device parameters, which makes the design and tuning of the device difficult.By contrast, the microring ladder filter investigated in this paper consists of a parallel cascade of feed-forward microring networks, such as the structure shown in Fig. 1(b), in which each stage consists of a microring doublet.Here the output signal of each stage propagates forward to the next stage, and since there is no feedback among the stages, the structure has exactly 2N poles (or resonances), where N is the number of stages.Another essential feature of the ladder filter is a differential π-phase shift element connecting two adjacent microring stages.In general the phase shift is necessary for achieving destructive interferences between different signal pathways in the array to produce filter response with transmission zeros at the drop port.Analysis of the cascaded array of microring doublets in Fig. 1(b) has shown that the structure can realize transfer functions consisting of up to 2N -2 transmission zeros [6].In this paper we report the first experimental realization of a two-stage microring ladder filter in the Silicon-on-Insulator (SOI) material.Silicon was chosen for its high index contrast, which allows for a compact filter design.To correct for resonance mismatch in the microrings caused by fabrication imperfections, microheaters were fabricated on the microrings to enable post-fabrication trimming of the device.Although there was still some residual resonance mismatch in the tuned device, the measured filter spectrum exhibited a characteristic fourth-order response which arose from the interference between the two second-order microring stages.

Design of a two-stage microring ladder filter
Figure 2(a) shows the layout of the microring ladder filter with two cascaded stages, each stage consisting of a microring doublet.The two stages are connected by two parallel bus waveguides with a π-phase shifter in the upper waveguide.All four microrings are assumed to be synchronous tuned.Within each stage k = {1, 2}, the bus-to-ring and ring-to-ring field coupling coefficients are denoted by κ k1 and κ k2 , respectively.The response of each stage can be described by a 2 × 2 transfer matrix S (k) , whose elements are given by the through-port (S 11 , S 22 ) and drop-port (S 12 , S 21 ) transfer functions of the microring doublet: ( ) In the above, with φ rt being the roundtrip phase of the microrings.The transfer matrix of the ladder filter is given by the product S = S (2) ΛS (1) , where Λ = diag[−1, 1] is the transfer matrix of the π-phase shift element.Explicitly, the through-port and drop-port transfer functions of the filter are given by Since R k and Q k are second-degree polynomials, Eq. ( 4) shows that the two-stage ladder filter has a fourth-order response (4 poles) with two transmission zeros at the drop port (and a dummy zero at z −1 = 0).In the filter design, we chose to realize a fourth-order filter response with a flat-top passband and two transmission zeros placed on either side of the passband to give a steep rolloff.The filter bandwidth was designed to be 100GHz and the target free spectral range (FSR) was 10nm.Using the filter approximation method in [9], we obtained a fourth-order transfer function which satisfies the above specifications, with the poles and zeros shown in the table in Fig. 2(b).The target spectral responses at the drop port and through port are shown by the solid lines in the plot in Fig. 2(b).From the given transfer function we computed the required coupling coefficients in the two microring stages of the ladder filter using the method in [6].Essentially, the coupling coefficients can be determined by recognizing from (4) that each microring doublet is responsible for generating a pair of conjugate poles in the transfer function of the ladder filter.From the transfer function of each stage in (2), we find that each doublet has a pair of poles given by { , } ( )/ .
Thus given a pole p k , we can determine the coupling coefficients of stage k from The coupling values obtained for the target filter are summarized in the table in Fig. 2(a).
For the implementation of the filter, we used a SOI chip with a 340nm-thick Si layer and a 1μm-thick SiO 2 buffer layer.The device was designed for the TM polarization.The waveguide width was chosen to be 300nm and the microring radius was fixed at 8μm to give an FSR of about 10nm.The required coupling gaps between the microrings as well as between the rings and the bus waveguides were computed using the Coupled Mode Theory and shown in the table in Fig. 2(a).In the device layout the two doublet stages were separated by a distance of 25μm.The π-phase shift element in the upper waveguide was implemented by widening a section of length L p of the waveguide to a width W p = 600nm.Tapers of length L t = 5μm were used to ensure adiabatic transitions between the nominal bus width and the wide phase shift section.In order to achieve a differential π-phase shift in the upper bus with respect to the lower bus, we determined by numerical simulation the required length of the phase shift section to be L p = 1.65μm.The entire physical layout of the device is shown in Fig. 2(a).We also performed 2D FDTD simulation of the structure to verify the device layout.The simulated responses obtained at the drop port and through port are shown by the dashed lines in Fig. 2(b), which are in good agreement with the theoretical filter responses.

Device fabrication and measurement results
The device was fabricated by first defining the microring structure on a SOI chip using electron beam lithography (EBL) and PMMA as the resist.The device pattern was then transferred onto the Si layer using ICP RIE dry-etching.Figure 3(a) shows a scanning electron microscope (SEM) image of the device after etching and resist removal.For postfabrication tuning of the device, serpentine microheaters made of Ti/W alloy were fabricated on top of each microring.The heaters were fabricated by first depositing a 10μm-thick layer of SiO 2 on the chip by PECVD, then etching the oxide back to a thickness of about 1μm to obtain a planar surface.Next the heater patterns were laid down using EBL and PMMA resist.A 150nm-thick layer of Ti/W alloy was deposited onto the chip by RF sputtering, followed by metal lift-off.Figure 3(b) shows an optical micrograph of the device with the overlaid heaters.The heater wires were 0.7μm wide and the resistances of the heaters were measured to be in the range of 4-6kΩ.The chip was then cleaved and mounted onto a PCB board, as shown in Fig. 3(c), where it was wirebonded to external electrodes.The spectral response of the device was measured using a continuous-wave tunable laser with the polarization set to TM. Lensed tapered fibers were used to couple light on chip from the laser as well as off chip for detection.The fiber-to-waveguide butt-coupling loss was about 10dB per facet.Figure 4(a) shows the drop-port spectral response of the as-fabricated device prior to tuning.Three transmission peaks (per FSR) are observed, one corresponding to transmission through stage 1 (rings 1 and 2), and two closely-spaced peaks corresponding to rings 3 and 4 of stage 2. In general the resonance frequency mismatch between two microrings in the same stage is less pronounced than mismatch between microrings in different stages because of the closer proximity of the rings in the former case.As a result the as-fabricated spectrum of a microring ladder filter typically shows distinct transmission peaks corresponding to the different stages.This greatly facilitates the tuning of the device because it allows each stage to be tuned separately and then merged together at the final step.By contrast, in a serially coupled microring filter, resonance detunings among the microrings can completely suppress power transmission through the as-fabricated device [10], especially in higher-order structures, thereby rendering the tuning process more difficult.
To tune the microring ladder filter, we first aligned the resonances of microrings 3 and 4 by applying 2.1mA of current to heater 3 and 1.1mA to heater 4. The resulting spectrum is shown by the red line in Fig. 4(b).Note that the transmission peak of stage 1 was also slightly red-shifted by 0.2nm (25GHz) due to thermal crosstalk from heaters 3 and 4. Next we tuned the transmission peak of stage 1 to overlap that of stage 2 by applying 6.25mA to both heaters 1 and 2. The average tuning rate was about 0.8nm/mA.The final tuned spectrum of the device is shown in Fig. 4(c), where only one transmission peak appears (per FSR).A close-up scan of the filter response is shown in Fig. 4(d), which shows a relatively flat-top passband with a 3dB bandwidth of 100GHz.
To verify that the tuned filter spectrum is indeed a fourth-order response, we performed curve fitting of the measured spectrum with the transfer function of a doublet stage (2ndorder) and that of two cascaded stages (4th-order).In the models we also included microring loss as a parameter and allowed for resonance detunings among the microrings.The optimized curve fits are shown in Fig. 4(d) for comparison with the measurement.It is seen that the measured filter roll-off follows that of the 4th-order response down to at least −15dB, confirming that the ladder structure indeed exhibited a 4th-order spectral response resulting from the interference of the two microring doublet stages.The device parameters obtained from the curve fit are: κ 11 = 0.5, κ 12 = 0.1, κ 21 = 0.3, κ 22 = 0.25, phase shift = 0.82π, resonance frequency detunings Δf 1 = 10GHz, Δf 2 = −10GHz, Δf 3 = −20GHz, Δf 4 = 5GHz, and microring roundtrip amplitude attenuation coefficient of 0.95.The fitted values of the coupling coefficients are in good agreement with the designed values.However, there are still some residual resonance detunings in the microrings which are attributed to the limitation in our tuning resolution as well as thermal crosstalks among the four heaters.The resonance detunings caused the filter passband to be not as flat and the skirt roll-off not as sharp as the target filter shape in Fig. 2(b).The detunings also caused the insertion loss of the filter, estimated to be 6.5dB from the fitted response, to be somewhat higher than expected.Also, from the roundtrip attenuation coefficient of 0.95, the intrinsic Q factors of the microrings can be determined to be close to 10,000.The high intrinsic loss may be attributed to extra scattering loss from the coupling junctions since the microrings are fairly strongly coupled.With finer wavelength tuning capability, decreased thermal crosstalk by increasing the separation between the two stages, as well as thermooptic control of the phase shifter, we expect the device can be further optimized to achieve the target spectral response with welldefined transmission nulls in the stop band.

Conclusion
In summary we have presented the design and experimental demonstration of a new type of microring filters consisting of two cascaded microring doublet stages connected by a phase shift element.Measurement indicated that interference between the two doublet stages gave rise to a 4th-order response as expected.Future work will focus on achieving better control of the microring resonances and minimizing thermal crosstalk to obtain optimized filter response with well-defined transmission nulls.The present work serves to demonstrate the feasibility of realizing advanced integrated optics filters based on parallel cascades of high-order microring networks.

Fig. 1 .
Fig. 1.(a) Schematic of a parallel cascaded array of N single add-drop microring resonators; (b) schematic of a microring ladder filter consisting of a parallel cascaded array of N microring doublets.
the roundtrip phase delay variable,

Fig. 3 .
Fig. 3. (a) SEM image of the fabricated SOI microring ladder filter; (b) optical micrograph of the device with overlaid heaters; (c) device mounted on a PCB board.