Abstract

We report the fabrication of a reconfigurable wide-band twenty-channel second-order dual filterbank, defined on a silicon-on-insulator (SOI) platform, with tunable channel spacing and 20 GHz single-channel bandwidth. We demonstrate the precise tuning of eleven (out of the twenty) channels, with a channel spacing of 124 GHz (~1 nm) and crosstalk between channels of about −45 dB. The effective thermo-optic tuning efficiency is about 27 μW/GHz/ring. A single channel of a twenty-channel counter-propagating filterbank is also demonstrated, showing that both propagating modes exhibit identical filter responses. Considerations about thermal crosstalk are also presented. These filterbanks are suitable for on-chip wavelength-division-multiplexing applications, and have the largest-to-date reported number of channels built on an SOI platform.

©2010 Optical Society of America

1. Introduction

Multi-channel high-order microring resonators are essential components for low-cost highly integrated wavelength-division-multiplexing (WDM) systems and photonic integrated circuits [1,2]. At wavelengths near 1.5 μm, silicon-on-insulator (SOI) platforms allow low-loss single-mode propagation in submicron structures and micron-sized bending radii [3]. The resonant frequency of a silicon microring resonator is extremely sensitive to fabrication errors. Therefore, in addition to high dimensional control and low sidewall roughness, post-fabrication trimming and tuning is normally required to achieve desired device parameters. The latter can effectively be achieved by thermal tuning, due to the large thermo-optic coefficient of silicon [4,5].

In silicon, multi-channel single-ring filters have been demonstrated [68], as well as second-order racetrack micro-resonators [9] and single-channel higher-order filters [10,11]. However, for maximum performance, i.e. high number of channels with minimal crosstalk within a single free spectral range (FSR), it is necessary to use filterbanks consisting of second- or higher-order microring filters. Previously, we reported progress in fabricating twenty-channel second-order dual filterbanks, both in silicon [12] and in silicon-rich silicon nitride [12,13]. In this work, we study such a twenty-channel second-order dual filterbank (in silicon) with reconfigurable channel spacing, and demonstrate precise tuning of eleven consecutive channels [14]. This filterbank has two sets of 20 channels. Each channel has a bandwidth of 20 GHz, and a tunable channel spacing which is set to 124 GHz, resulting in about −45 dB crosstalk between channels. The fabricated filterbank is intended as a multiplexer for a wavelength-demultiplexed photonic analog-to-digital converter [15,16]. In this application, it is desirable to use both outputs of the Mach-Zehnder modulator in order to linearize its transfer function [17]. Therefore, both halves of the dual filterbank need to have the same filter response, which presents additional fabrication challenges. If the filter responses of the twin channels are not identical, they need to be thermally tuned in order to match each other. An elegant alternative to bypass this additional tuning and to achieve the twin response is to use a counter-propagating architecture [12], which is also demonstrated in this work. A careful study of thermal crosstalk between the two rings forming a single channel is also presented in this paper.

2. Design and fabrication

The basic operation of a general second-order filterbank is illustrated in Fig. 1 , where three adjacent channels are represented. Each channel is tuned to a specific wavelength, and routs the corresponding signal into the respective drop port.

 

Fig. 1 Illustration of the operation of a general second-order filterbank, showing three adjacent channels tuned to different frequencies, routing the signal into the respective drop ports.

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In the case of the counter-propagating filterbank, light coupled into each of the two input ports (A and B) is dropped at different drop ports but sees the same pair of rings, and should therefore have the same filter response. Figure 2 illustrates the layout of one channel of the counter-propagating filterbank. This architecture reduces the total number of rings and heaters by half, and eliminates the need for the additional matching of the two paired channels.

 

Fig. 2 Layout of one channel of the second-order counter-propagating filterbank.

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In designing the filterbanks, several specifications need to be considered, namely the single-channel bandwidth, the channel frequency spacing, the free spectral range (FSR), and the extinction of each channel at the adjacent channels. These parameters are illustrated in Fig. 3 . The filterbanks were designed to have a 20 GHz channel-bandwidth and >30 dB extinction at ± 80 GHz from the channel center, with a 2 THz (16 nm) free spectral range, which corresponds to about half of the C-band telecom window. In this particular demonstration, the channel spacing was set to 124 GHz (to accommodate some channels with inoperative heaters), resulting in about −45 dB crosstalk between channels.

 

Fig. 3 Relevant parameters for designing filterbanks: single-channel bandwidth, channel spacing, free spectral range, and extinction of a channel at the location of adjacent channels.

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The filters were designed to operate for TE-polarized light, and the silicon waveguide dimensions were optimized to reduce sensitivity to sidewall roughness and dimensional variations in width [18], with cross-sections of 600 × 105 nm (ring waveguides) and 495 × 105 nm (bus waveguides). The filterbank was fabricated on an SOI wafer with a 3 μm-thick oxide undercladding, and a 105 nm silicon layer (thinned from 220 nm), similar to our previous work [10, 19]. The main bus, ring and gap dimensions are shown in Fig. 4(a) , corresponding to power coupling coefficients {κ1, κ2, κ3} = {3.8, 0.044, 3.8}%.

 

Fig. 4 Design details: (a) dimensions of the second-order silicon microring filter, fabricated on an SOI platform, and (b) material stack cross-section in the bus-ring coupling region. The bus waveguides are 495 × 105 nm, the ring waveguides are 600 × 105 nm, and the ring radius is 6.735 µm. In the filterbank, the resonant frequencies for each channel are adjusted by slightly changing the ring radius and the waveguide width of each microring resonator, with respect to the previous channel.

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The device was coated with a 1 μm-thick hydrogen silsesquioxane (HSQ) layer [20], and titanium microheaters were fabricated (with contact photolithography and lift-off) on top of the HSQ for thermal tuning of the resonant frequency of each individual ring. A small horizontal and rotation misalignment during this step resulted in a ~3.6 µm alignment error between the microheaters and rings on the tested samples. Typical heater-resistance values were measured between 1 and 2 kΩ. Figure 4(b) shows the cross-section of the material stack in the bus-ring coupling region. Optical micrographs of the fabricated filterbanks are shown in Fig. 5 : twenty-channel (a) dual filterbank and (b) counter-propagating filterbank, before the fabrication of the microheaters, and (c) a detailed view of two adjacent channels after the fabrication of the titanium microheaters.

 

Fig. 5 Optical micrographs of the fabricated filterbanks: (a) dual twenty-channel, (b) twenty-channel counter-propagating, and (c) detailed view of two adjacent channels, after the fabrication of the titanium microheaters.

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During fabrication, the control of the resonant frequency of each ring (and channel) is achieved by changing both the ring radius and waveguide width of each microring resonator, and requires a dimensional precision in the order of tens of picometer [12]. The resonant frequency depends on the optical path length of the microring, which depends on the physical length (i.e., radius) and the effective index of refraction neff. The effective refractive index can be controlled by changing the height and/or the width of the waveguide. Since the height of the waveguide is fixed, the two parameters used to control the resonant frequency are the radius and the width of the ring waveguides. Using a mode solver [21], we determined the frequency sensitivity to changes in the radius and the width to be about 16.2 GHz/nm and 40 GHz/nm, respectively [12].

3. Experimental results

The filterbanks were characterized using the setup schematically illustrated in Fig. 6 . Light from a tunable infrared laser is coupled into the filterbanks through a high-numerical-aperture lensed fiber, and the light exiting the through and drop ports is collected with a similar lensed fiber and coupled into an optical spectrum analyzer (OSA). The laser and the OSA are synchronously tuned and scanned. The input TE polarization is controlled with a polarization controller (PC), and an optional output PC can be used if extra polarization control is needed (e.g. for a subsequent device). Precise in- and out- coupling is achieved with 3-axis micro-positioning stages S1 and S3 controlled by piezoelectric (PZT) controllers. The sample is mounted on a copper block with good thermal contact, and then on a 4-axis stage S2 for precise control over its position and tilt angle. Top visual inspection and rough alignment is done with a charge-coupled device (CCD) camera and with an infrared camera (IRC). All microheaters are gold wire-bonded from the SOI chip to custom-made interface boards (which results in some additional unwanted resistance at the contact points) and then activated by a computer-controlled multi-channel digital-to-analog converter (DAC) board.

 

Fig. 6 Illustration of the experimental setup used to characterize the filterbanks. EPIC: Electronic Photonic Integrated Circuit under test.

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The individual rings have intrinsic quality factors of ~250k and ~130k, without and with the titanium microheaters, which corresponds to propagation losses of about 2-2.5 dB/cm and 4.5 dB/cm, respectively.

3.1 Dual filterbank

Inspection of the drop ports of the dual filterbank before thermal tuning shows frequency mismatches between the two rings forming each channel, in addition to non-uniform channel spacing. The drop-port response of one of the channels is represented in Fig. 7 , showing a frequency mismatch between the two coupled rings of about 39 GHz. In order to demonstrate the tuning capabilities, a target channel center wavelength is chosen, defining a single channel with channel bandwidth of 20 GHz (represented in the figure by the grey box). Both rings of the channel are first individually tuned in order to compensate for the inter-ring frequency mismatch, and then the entire channel is tuned to its targeted channel frequency. The tuned drop-port response is shown in the same figure, along with the respective through-port curve. The channel is now precisely aligned at the pre-set center frequency, with channel extinction over 35 dB at ± 80 GHz, which is well within the filter design requirement. The measured bandwidth of 20 GHz also agrees with the filter design. At ± 124 GHz ( ± 1 nm), which is the channel spacing used in this work, the extinction is about 45 dB (below the noise floor in our measurement, but extrapolated from fitting the experimental data with a coupled-mode theory model).

 

Fig. 7 Filter response of one channel of the dual filterbank, before (left curve) and after (right curves) thermal tuning. The channel is tuned to a pre-set center wavelength (grey box), and the aligned channel has a bandwidth of 20 GHz, with over 35 dB extinction at ± 80 GHz, and about 45 dB extinction at ± 124 GHz ( ± 1 nm).

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In our experiment, the electrical power delivered to each microheater is not measured directly, due to a varying and significant additional power drop caused by the contact resistance at each wire-bonding site. This unwanted resistance can be reduced with appropriate electrical packaging. In order to calculate the electrical power delivered to each microheater, we keep track of the resonant frequency shift that each microring resonator experiences when tuned from its initial frequency to its final frequency. For the second-order channel represented in Fig. 7, the total frequency shift (for both rings) is about 274 GHz. Using a thermo-optic tuning efficiency of about 27 μW/GHz, the total tuning power needed for this channel is about 7.4 mW. The value used for the tuning efficiency does not take into account the power dissipated at the wire-bonding sites, and is therefore used to calculate the actual power delivered to the microheaters. This tuning efficiency value is justified in Subsection 3.3.

This tuning procedure can now by extended to all remaining channels of the dual twenty-channel filterbank. All channels of the fabricated filterbank worked optically, but only the lower filterbank in Fig. 5(a) had microheaters for fine resonant frequency tuning. Some of the fabricated microheaters were damaged, and some of the wire-bond connections between the SOI chip and the DAC board did not have good electrical contact. Due to these limitations, only eleven channels (out of the twenty) of the lower filterbank were characterized. The drop-port responses of these eleven channels before any thermal tuning are shown in Fig. 8(a) , overlaid with a frequency grid showing 20 GHz-bandwidth channels spaced by 124 GHz. The detailed frequencies (and wavelengths) of the desired grid points are summarized in Table 1 .

 

Fig. 8 Drop-port responses of eleven adjacent channels of the fabricated second-order twenty-channel dual filterbank: (a) before and (b) after thermo-optic tuning of the resonant frequencies of the individual microring resonators. After tuning, the single-channel bandwidth is measured to be 20 GHz and the channel crosstalk is about −45 dB (extrapolated from data fit), for the pre-set channel-spacing of 124 GHz.

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Tables Icon

Table 1. Frequency (and wavelength) values for the 124 GHz-spaced grid used to align all eleven channels.

Before any thermal tuning, most of the channels are misaligned, with frequency mismatch between the two rings of a channel of up to 133 GHz, and a channel location mismatch of up to 476 GHz. For only two channels (2 and 11) are the two rings relatively well aligned. In terms of frequency shifts, some of the rings are blueshifted (to lower wavelengths) and some are redshifted (to larger wavelengths) with respect to the targeted fabrication center frequencies. Ideally, the tuning scheme for the resonant frequencies would return them to the original designed value. However, the thermo-optic control (done by heating the microrings) can only shift the resonances towards longer wavelengths. The thermal heat sink temperature (which was not turned on for our particular frequency grid) defined the starting resonant

wavelengths. For different frequency grids, the heat sink can be adjusted to make sure that every channel is located at a shorter wavelength than its desired grid point, which may require additional electrical power.

The approximate frequency mismatches of the various channels are summarized in Table 2 . This table indicates the frequency difference between each one of the individual rings (labeled Ring A and Ring B within a channel) and the defined frequency grid from Table 1, as well as the relative frequency mismatch between the two rings of each channel and the total tuning required to align both rings to the pre-set grid.

Tables Icon

Table 2. Approximate frequency mismatch (in GHz) of each ring with respect to the pre-set frequency grid.

As described before, both rings within each channel are fine tuned, and then the whole channel is shifted to its pre-set center frequency. The eleven drop-port responses after tuning are shown in Fig. 8(b). All channels are now sharply defined with 20 GHz single-channel bandwidths, channel-spacing of 124 GHz, and about 45 dB extinction at adjacent channels (extrapolated from data fit). The relative magnitudes (between the through and drop ports) of all channels indicate a small drop loss of about 1.5-2.5 dB. To achieve the result in Fig. 8(b), all 22 microrings (for the eleven channels) were precisely tuned using the multi-channel DAC which controlled the power of each ring-heater individually. Up to five channels were tuned simultaneously, limited only by the number of control ports available in the DAC.

The total electrical power needed to tune all eleven channels to the 124 GHz grid is about 180 mW, which corresponds to an average power of 16 mW per channel, with a tuning efficiency of about 27 μW/Ghz/ring. This electrical power dissipated on the chip can be significantly reduced with improved optimization in the fabrication, in order to reduce frequency mismatches between rings and more accurately define the channel center frequencies. Furthermore, a smaller frequency grid interval will also reduce the total power consumption. Further reduction in the tuning power is possible by implementing undercuts beneath the waveguides [22,23].

3.2 Counter-propagating filterbank

As mentioned in Section 1, some applications require having two identical filter responses, which can be achieved by using the counter-propagating filterbank represented in Fig. 5(b). In this configuration, light coupled into port A is dropped into the drop ports A of the different channels, and light coupled into port B is dropped by the same filters, but into drop ports B. The drop-port responses (A and B) of one of the counter-propagating channels are shown in Fig. 9 , before and after applying thermal tuning. As seen, both directions of propagation have identical filter responses. After tuning, the drop ports show a 20 GHz bandwidth.

 

Fig. 9 Drop-port responses of one channel of the counter-propagating filterbank, before (left curves) and after tuning (right curves). The tuned filter responses are similar and show a bandwidth of 20 GHz, with extinction of about 35 dB at frequencies ± 80 GHz apart form the center frequency, and about 45 dB at ± 124 GHz ( ± 1 nm).

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In this experiment, only the bottom microheater (on top of the microring with resonant wavelength around 1541.5 nm) was actuated. However, the power applied to this heater shifted both rings, which is a clear indication of non-negligible thermal crosstalk between the rings. Therefore, a more careful study of this thermal crosstalk is necessary, and is presented in Subsection 3.3. Based on the frequency shift of each microring and on the tuning efficiency of 27 μW/Ghz/ring, the power required to tune this channel is about 8 mW.

The optical crosstalk between the input port A and the drop port B (or input port B and drop port A) was measured to be around −11 dB, which is a high value for many applications. This optical crosstalk is caused by high end-facet reflections at the air-Si interface, and can be reduced by eliminating these interfaces by adding couplers to the input and drop waveguides and packaging the chip.

3.3 Thermal crosstalk between rings

During the thermo-optic tuning process, there was no significant thermal crosstalk between channels, due to their large (100 μm) separation. Any small inter-channel crosstalk was easily compensated for during the fine tuning of the channels. However, the thermal crosstalk between rings within the same channel was high, and is therefore considered in this subsection.

Each channel has two individual microheaters, one for each ring. Due to proximity, the power delivered to one of the microheaters will also change the temperature of the adjacent ring of the same channel. Furthermore, the asymmetric heater overlap with the microrings (due to misalignment of the mask during the contact photolithography fabrication step), as seen is Fig. 5(c), translates into different tuning efficiencies of the two microheaters and induces different crosstalk coefficients. The general relation between the frequency shift of each microring and the electrical power delivered to the respective microheater can be represented by the response matrix

[ΔνAΔνB]=[κAκABκBAκB][PAPB],

where the off-diagonal elements represent the thermal crosstalk. Ideally, the diagonal terms would be equal, and the off-diagonal terms zero. The matrix elements can be found by using a typical second-order channel with some frequency mismatch between the two rings. Figure 10 shows the drop-port responses of such a channel, where the black curves correspond to the resonant peaks of rings A and B before any thermal tuning. When microheater A is actuated (with about 1.5 mW), the peaks shift about 45 GHz and 8 GHz, for rings A and B, respectively (red curves). When microheater B is actuated (with about 2.1 mW), the peaks shift about 25 GHz and 58 GHz, for rings A and B, respectively. From these values, microheater B induces a larger crosstalk into ring A than microheater A into ring B, which is consistent with the slight overlap of heater B with ring A, as seen in Fig. 5(c). The measured frequency shifts return the following tuning response matrix:

[κAκABκBAκB]=[30.011.95.327.6]  (GHz/mW) ,
which leads to direct thermo-optic efficiencies of 33 and 36 μW/Ghz/ring (from the diagonal terms in the matrix). These values are slightly higher than the value obtained from the tuning of a single ring (28 μW/Ghz), from our previous work [4]. The reason for this difference is the simplified design of the microheaters used for these devices (when compared to Ref. 4), which has a higher fabrication yield but is a little less efficient.

 

Fig. 10 Thermal crosstalk measurement: when microheaters A and B are actuated independently, different frequency shifts occur at each microring resonator. These shifts allow one to determine the elements of the tuning matrix.

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The inter-ring crosstalk can be seen as either detrimental or beneficial to the tuning scheme. On one hand, if the two rings within a channel are not matched in frequency, the crosstalk increases the power needed to align them, and pushes the location of the aligned channel towards longer wavelengths (as seen in Fig. 9). On the other hand, the power needed to shift the whole channel to a higher center wavelength is now reduced, since the crosstalk reuses the power sent to one ring in the other ring. The latter translates into an increase of the effective tuning efficiency of the channel. This effective tuning efficiency is calculated by computing the average frequency shift per unit of delivered power, taking into account the measured crosstalk: microheater A shifts a total of 53 GHz (45 GHz for ring A and 8 GHz for ring B) with 1.5 mW, and microheater B shifts 83 GHz (25 GHz for ring A and 58 GHz for ring B) with 2.1 mW. This results in 35.3 GHz/mW for microheater A and 39.5 GHz/mW for microheater B, which gives an average frequency shift of 37.4 GHz per mW for the whole channel. This corresponds to a thermo-optic efficiency of 27 μW/Ghz, which is the value used in Subsections 3.1 and 3.2. This value is in good agreement with the value of 28 μW/Ghz from Ref. 4. This similarity is expected, since the waveguide and ring dimensions are similar in both works, as well as the HSQ overcladding and the vertical separation between the waveguides and the heaters.

To reduce thermal crosstalk, additional thermal isolation techniques can be constructed, such as etched air trenches close to and under the microring waveguides [22,23]. This technique would permit a reduction in the spacing between channels while maintaining negligible channel crosstalk, and would increase the direct thermo-optic efficiency. Further enhancement in the tuning efficiency can be achieved by directly integrating the microheaters with the resonator, using adiabatic resonant microrings [24].

4. Conclusion

We fabricated a twenty-channel second-order dual filterbank in a silicon-on-insulator platform, and demonstrated the precise tuning and reconfigurability of eleven channels. The filterbank has a tunable channel spacing which was set to 124 GHz, single-channel bandwidths of about 20 GHz, and −45 dB crosstalk between channels. A counter-propagating filterbank was also studied, and the two drop-port responses of one of the channels were shown to have identical filter responses. The effective (average) tuning efficiency was calculated to be ~27 μW/GHz/ring, obtained through measurement of crosstalk between the two rings of a channel. The average power dissipated on the dual filterbank chip set to the channel spacing of 124 GHz is estimated to be around 16 mW per channel. This device has potential applications in on-chip WDM applications, or as a multiplexer in optically sampled analog-to-digital converters.

Acknowledgments

This work was supported in part by DARPA (HR0011-05-C-0155), AFOSR (FA9550-10-1-0063), and the NSF MRSEC at MIT.

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References

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  1. B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, E. 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).
    [Crossref]
  2. G. T. Reed, Silicon Photonics: The State of the Art (Wiley, 2008).
  3. Y. A. Vlasov and S. J. McNab, “Losses in single-mode silicon-on-insulator strip waveguides and bends,” Opt. Express 12(8), 1622–1631 (2004).
    [Crossref] [PubMed]
  4. F. Gan, T. Barwicz, M. A. Popović, M. S. Dahlem, C. W. Holzwarth, P. T. Rakich, H. I. Smith, E. P. Ippen, and F. X. Kärtner, “Maximizing the thermo-optic tuning range of silicon photonic structures,” in Proceedings of IEEE Conference on Photonics in Switching (San Francisco, CA, 2007), pp. 67–68.
  5. M. A. Popović, T. Barwicz, M. S. Dahlem, F. W. Gan, C. W. Holzwarth, P. T. Rakich, M. R. Watts, H. I. Smith, F. X. Kärtner, and E. P. Ippen, “Hitless-reconfigurable and bandwidth-scalable silicon photonic circuits for telecom and interconnect applications,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OTuF4.
  6. M. H. Khan, H. Shen, Y. Xuan, S. J. Mao, and M. H. Qi, “Eight-Channel Microring Resonator Array with Accurately Controlled Channel Spacing,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper CTuNN6.
  7. M. M. Geng, L. X. Jia, L. Zhang, L. Yang, P. Chen, T. Wang, and Y. L. Liu, “Four-channel reconfigurable optical add-drop multiplexer based on photonic wire waveguide,” Opt. Express 17(7), 5502–5516 (2009).
    [Crossref] [PubMed]
  8. H. Shen, M. H. Khan, L. Fan, L. Zhao, Y. Xuan, J. Ouyang, L. T. Varghese, and M. H. Qi, “Eight-channel reconfigurable microring filters with tunable frequency, extinction ratio and bandwidth,” Opt. Express 18(17), 18067–18076 (2010).
    [Crossref] [PubMed]
  9. S. Xiao, M. H. Khan, H. Shen, and M. Qi, “Multiple-channel silicon micro-resonator based filters for WDM applications,” Opt. Express 15(12), 7489–7498 (2007).
    [Crossref] [PubMed]
  10. M. A. Popović, T. Barwicz, M. S. Dahlem, F. Gan, C. W. Holzwarth, P. T. Rakich, H. I. Smith, E. P. Ippen, and F. X. Kärtner, “Tunable, Fourth-Order Silicon Microring-Resonator Add-Drop Filters,” presented at the European Conference on Optical Communication, Berlin, Germany, Sept. 2007, paper 1.2.3.
  11. F. N. Xia, M. Rooks, L. Sekaric, and Y. Vlasov, “Ultra-compact high order ring resonator filters using submicron silicon photonic wires for on-chip optical interconnects,” Opt. Express 15(19), 11934–11941 (2007).
    [Crossref] [PubMed]
  12. C. W. Holzwarth, A. Khilo, M. Dahlem, M. A. Popovic, F. X. Kärtner, E. P. Ippen, and H. I. Smith, “Device architecture and precision nanofabrication of microring-resonator filter banks for integrated photonic systems,” J. Nanosci. Nanotechnol. 10(3), 2044–2052 (2010).
    [Crossref] [PubMed]
  13. C. W. Holzwarth, R. Amatya, M. Dahlem, A. Khilo, F. X. Kärtner, E. P. Ippen, R. J. Ram, and H. I. Smith, “Fabrication strategies for filter banks based on microring resonators,” J. Vac. Sci. Technol. B 26(6), 2164–2167 (2008).
    [Crossref]
  14. M. S. Dahlem, C. W. Holzwarth, A. Khilo, F. X. Kärtner, H. I. Smith, and E. P. Ippen, “Eleven-Channel Second-Order Silicon Microring-Resonator Filterbank with Tunable Channel Spacing,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper CMS5.
  15. M. Y. Frankel, J. U. Kang, and R. D. Esman, “High-performance photonic analogue-digital converter,” Electron. Lett. 33(25), 2096–2097 (1997).
    [Crossref]
  16. F. X. Kärtner, R. Amatya, M. Araghchini, J. Birge, H. Byun, J. Chen, M. Dahlem, N. A. DiLello, F. Gan, C. W. Holzwarth, J. L. Hoyt, E. P. Ippen, A. Khilo, J. Kim, M. Kim, A. Motamedi, J. S. Orcutt, M. Park, M. Perrott, M. A. Popovic, R. J. Ram, H. I. Smith, G. R. Zhou, S. J. Spector, T. M. Lyszczarz, M. W. Geis, D. M. Lennon, J. U. Yoon, M. E. Grein, and R. T. Schulein, “Photonic analog-to-digital conversion with electronic-photonic integrated circuits,” in Silicon Photonics III, J. A. Kubby and G. T. Reed, eds., Proc. SPIE 6898, 689806 (2008).
  17. J. C. Twichell and R. Helkey, “Phase-encoded optical sampling for analog-to-digital converters,” IEEE Photon. Technol. Lett. 12(9), 1237–1239 (2000).
    [Crossref]
  18. M. A. Popović, T. Barwicz, E. P. Ippen, and F. X. Kärtner, “Global design rules for silicon microphotonic waveguides: sensitivity, polarization and resonance tunability,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference, OSA Technical Digest (CD) (Optical Society of America, 2006), paper CTuCC1.
  19. M. S. Dahlem, C. W. Holzwarth, H. I. Smith, E. P. Ippen, and M. A. Popović, “Dynamical Slow Light Cell based on Controlled Far-Field Interference of Microring Resonators,” in Integrated Photonics Research, Silicon and Nanophotonics, OSA Technical Digest (CD) (Optical Society of America, 2010), paper IMC4.
  20. C. W. Holzwarth, T. Barwicz, and H. I. Smith, “Optimization of hydrogen silsesquioxane for photonic applications,” J. Vac. Sci. Technol. B 25(6), 2658–2661 (2007).
    [Crossref]
  21. M. A. Popović, “Complex-frequency leaky mode computations using PML boundary layers for dielectric resonant structures,” in Integrated Photonics Research, A. Sawchuk, ed., Vol. 91 of OSA Trends in Optics and Photonics (Optical Society of America, 2003), paper ITuD4.
  22. P. Dong, W. Qian, H. Liang, R. Shafiiha, N. N. Feng, D. Z. Feng, X. Z. Zheng, A. V. Krishnamoorthy, and M. Asghari, “Low power and compact reconfigurable multiplexing devices based on silicon microring resonators,” Opt. Express 18(10), 9852–9858 (2010).
    [Crossref] [PubMed]
  23. P. Dong, W. Qian, H. Liang, R. Shafiiha, X. Wang, D. Z. Feng, G. Li, J. E. Cunningham, A. V. Krishnamoorthy, and M. Asghari, “1x4 reconfigurable demultiplexing filter based on free-standing silicon racetrack resonators,” Opt. Express 18(24), 24504–24509 (2010).
    [Crossref] [PubMed]
  24. M. R. Watts, W. A. Zortman, D. C. Trotter, G. N. Nielson, D. L. Luck, and R. W. Young, “Adiabatic resonant microrings (ARMs) with directly integrated thermal microphotonics,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper CPDB10.

2010 (4)

2009 (1)

2008 (1)

C. W. Holzwarth, R. Amatya, M. Dahlem, A. Khilo, F. X. Kärtner, E. P. Ippen, R. J. Ram, and H. I. Smith, “Fabrication strategies for filter banks based on microring resonators,” J. Vac. Sci. Technol. B 26(6), 2164–2167 (2008).
[Crossref]

2007 (3)

2004 (2)

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, E. 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).
[Crossref]

Y. A. Vlasov and S. J. McNab, “Losses in single-mode silicon-on-insulator strip waveguides and bends,” Opt. Express 12(8), 1622–1631 (2004).
[Crossref] [PubMed]

2000 (1)

J. C. Twichell and R. Helkey, “Phase-encoded optical sampling for analog-to-digital converters,” IEEE Photon. Technol. Lett. 12(9), 1237–1239 (2000).
[Crossref]

1997 (1)

M. Y. Frankel, J. U. Kang, and R. D. Esman, “High-performance photonic analogue-digital converter,” Electron. Lett. 33(25), 2096–2097 (1997).
[Crossref]

Absil, P. P.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, E. 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).
[Crossref]

Amatya, R.

C. W. Holzwarth, R. Amatya, M. Dahlem, A. Khilo, F. X. Kärtner, E. P. Ippen, R. J. Ram, and H. I. Smith, “Fabrication strategies for filter banks based on microring resonators,” J. Vac. Sci. Technol. B 26(6), 2164–2167 (2008).
[Crossref]

Asghari, M.

Barwicz, T.

C. W. Holzwarth, T. Barwicz, and H. I. Smith, “Optimization of hydrogen silsesquioxane for photonic applications,” J. Vac. Sci. Technol. B 25(6), 2658–2661 (2007).
[Crossref]

Chen, P.

Chu, S. T.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, E. 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).
[Crossref]

Cunningham, J. E.

Dahlem, M.

C. W. Holzwarth, A. Khilo, M. Dahlem, M. A. Popovic, F. X. Kärtner, E. P. Ippen, and H. I. Smith, “Device architecture and precision nanofabrication of microring-resonator filter banks for integrated photonic systems,” J. Nanosci. Nanotechnol. 10(3), 2044–2052 (2010).
[Crossref] [PubMed]

C. W. Holzwarth, R. Amatya, M. Dahlem, A. Khilo, F. X. Kärtner, E. P. Ippen, R. J. Ram, and H. I. Smith, “Fabrication strategies for filter banks based on microring resonators,” J. Vac. Sci. Technol. B 26(6), 2164–2167 (2008).
[Crossref]

Dong, P.

Esman, R. D.

M. Y. Frankel, J. U. Kang, and R. D. Esman, “High-performance photonic analogue-digital converter,” Electron. Lett. 33(25), 2096–2097 (1997).
[Crossref]

Fan, L.

Feng, D. Z.

Feng, N. N.

Frankel, M. Y.

M. Y. Frankel, J. U. Kang, and R. D. Esman, “High-performance photonic analogue-digital converter,” Electron. Lett. 33(25), 2096–2097 (1997).
[Crossref]

Geng, M. M.

Gill, D.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, E. 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).
[Crossref]

Helkey, R.

J. C. Twichell and R. Helkey, “Phase-encoded optical sampling for analog-to-digital converters,” IEEE Photon. Technol. Lett. 12(9), 1237–1239 (2000).
[Crossref]

Holzwarth, C. W.

C. W. Holzwarth, A. Khilo, M. Dahlem, M. A. Popovic, F. X. Kärtner, E. P. Ippen, and H. I. Smith, “Device architecture and precision nanofabrication of microring-resonator filter banks for integrated photonic systems,” J. Nanosci. Nanotechnol. 10(3), 2044–2052 (2010).
[Crossref] [PubMed]

C. W. Holzwarth, R. Amatya, M. Dahlem, A. Khilo, F. X. Kärtner, E. P. Ippen, R. J. Ram, and H. I. Smith, “Fabrication strategies for filter banks based on microring resonators,” J. Vac. Sci. Technol. B 26(6), 2164–2167 (2008).
[Crossref]

C. W. Holzwarth, T. Barwicz, and H. I. Smith, “Optimization of hydrogen silsesquioxane for photonic applications,” J. Vac. Sci. Technol. B 25(6), 2658–2661 (2007).
[Crossref]

Hryniewicz, J. V.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, E. 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).
[Crossref]

Ippen, E. P.

C. W. Holzwarth, A. Khilo, M. Dahlem, M. A. Popovic, F. X. Kärtner, E. P. Ippen, and H. I. Smith, “Device architecture and precision nanofabrication of microring-resonator filter banks for integrated photonic systems,” J. Nanosci. Nanotechnol. 10(3), 2044–2052 (2010).
[Crossref] [PubMed]

C. W. Holzwarth, R. Amatya, M. Dahlem, A. Khilo, F. X. Kärtner, E. P. Ippen, R. J. Ram, and H. I. Smith, “Fabrication strategies for filter banks based on microring resonators,” J. Vac. Sci. Technol. B 26(6), 2164–2167 (2008).
[Crossref]

Jia, L. X.

Johnson, F. G.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, E. 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).
[Crossref]

Kang, J. U.

M. Y. Frankel, J. U. Kang, and R. D. Esman, “High-performance photonic analogue-digital converter,” Electron. Lett. 33(25), 2096–2097 (1997).
[Crossref]

Kärtner, F. X.

C. W. Holzwarth, A. Khilo, M. Dahlem, M. A. Popovic, F. X. Kärtner, E. P. Ippen, and H. I. Smith, “Device architecture and precision nanofabrication of microring-resonator filter banks for integrated photonic systems,” J. Nanosci. Nanotechnol. 10(3), 2044–2052 (2010).
[Crossref] [PubMed]

C. W. Holzwarth, R. Amatya, M. Dahlem, A. Khilo, F. X. Kärtner, E. P. Ippen, R. J. Ram, and H. I. Smith, “Fabrication strategies for filter banks based on microring resonators,” J. Vac. Sci. Technol. B 26(6), 2164–2167 (2008).
[Crossref]

Khan, M. H.

Khilo, A.

C. W. Holzwarth, A. Khilo, M. Dahlem, M. A. Popovic, F. X. Kärtner, E. P. Ippen, and H. I. Smith, “Device architecture and precision nanofabrication of microring-resonator filter banks for integrated photonic systems,” J. Nanosci. Nanotechnol. 10(3), 2044–2052 (2010).
[Crossref] [PubMed]

C. W. Holzwarth, R. Amatya, M. Dahlem, A. Khilo, F. X. Kärtner, E. P. Ippen, R. J. Ram, and H. I. Smith, “Fabrication strategies for filter banks based on microring resonators,” J. Vac. Sci. Technol. B 26(6), 2164–2167 (2008).
[Crossref]

King, O.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, E. 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).
[Crossref]

Krishnamoorthy, A. V.

Li, G.

Liang, H.

Little, B. E.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, E. 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).
[Crossref]

Liu, Y. L.

McNab, S. J.

Ouyang, J.

Popovic, M. A.

C. W. Holzwarth, A. Khilo, M. Dahlem, M. A. Popovic, F. X. Kärtner, E. P. Ippen, and H. I. Smith, “Device architecture and precision nanofabrication of microring-resonator filter banks for integrated photonic systems,” J. Nanosci. Nanotechnol. 10(3), 2044–2052 (2010).
[Crossref] [PubMed]

Qi, M.

Qi, M. H.

Qian, W.

Ram, R. J.

C. W. Holzwarth, R. Amatya, M. Dahlem, A. Khilo, F. X. Kärtner, E. P. Ippen, R. J. Ram, and H. I. Smith, “Fabrication strategies for filter banks based on microring resonators,” J. Vac. Sci. Technol. B 26(6), 2164–2167 (2008).
[Crossref]

Rooks, M.

Seiferth, E.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, E. 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).
[Crossref]

Sekaric, L.

Shafiiha, R.

Shen, H.

Smith, H. I.

C. W. Holzwarth, A. Khilo, M. Dahlem, M. A. Popovic, F. X. Kärtner, E. P. Ippen, and H. I. Smith, “Device architecture and precision nanofabrication of microring-resonator filter banks for integrated photonic systems,” J. Nanosci. Nanotechnol. 10(3), 2044–2052 (2010).
[Crossref] [PubMed]

C. W. Holzwarth, R. Amatya, M. Dahlem, A. Khilo, F. X. Kärtner, E. P. Ippen, R. J. Ram, and H. I. Smith, “Fabrication strategies for filter banks based on microring resonators,” J. Vac. Sci. Technol. B 26(6), 2164–2167 (2008).
[Crossref]

C. W. Holzwarth, T. Barwicz, and H. I. Smith, “Optimization of hydrogen silsesquioxane for photonic applications,” J. Vac. Sci. Technol. B 25(6), 2658–2661 (2007).
[Crossref]

Trakalo, M.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, E. 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).
[Crossref]

Twichell, J. C.

J. C. Twichell and R. Helkey, “Phase-encoded optical sampling for analog-to-digital converters,” IEEE Photon. Technol. Lett. 12(9), 1237–1239 (2000).
[Crossref]

Van, V.

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, E. 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).
[Crossref]

Varghese, L. T.

Vlasov, Y.

Vlasov, Y. A.

Wang, T.

Wang, X.

Xia, F. N.

Xiao, S.

Xuan, Y.

Yang, L.

Zhang, L.

Zhao, L.

Zheng, X. Z.

Electron. Lett. (1)

M. Y. Frankel, J. U. Kang, and R. D. Esman, “High-performance photonic analogue-digital converter,” Electron. Lett. 33(25), 2096–2097 (1997).
[Crossref]

IEEE Photon. Technol. Lett. (2)

J. C. Twichell and R. Helkey, “Phase-encoded optical sampling for analog-to-digital converters,” IEEE Photon. Technol. Lett. 12(9), 1237–1239 (2000).
[Crossref]

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, E. 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).
[Crossref]

J. Nanosci. Nanotechnol. (1)

C. W. Holzwarth, A. Khilo, M. Dahlem, M. A. Popovic, F. X. Kärtner, E. P. Ippen, and H. I. Smith, “Device architecture and precision nanofabrication of microring-resonator filter banks for integrated photonic systems,” J. Nanosci. Nanotechnol. 10(3), 2044–2052 (2010).
[Crossref] [PubMed]

J. Vac. Sci. Technol. B (2)

C. W. Holzwarth, R. Amatya, M. Dahlem, A. Khilo, F. X. Kärtner, E. P. Ippen, R. J. Ram, and H. I. Smith, “Fabrication strategies for filter banks based on microring resonators,” J. Vac. Sci. Technol. B 26(6), 2164–2167 (2008).
[Crossref]

C. W. Holzwarth, T. Barwicz, and H. I. Smith, “Optimization of hydrogen silsesquioxane for photonic applications,” J. Vac. Sci. Technol. B 25(6), 2658–2661 (2007).
[Crossref]

Opt. Express (7)

P. Dong, W. Qian, H. Liang, R. Shafiiha, N. N. Feng, D. Z. Feng, X. Z. Zheng, A. V. Krishnamoorthy, and M. Asghari, “Low power and compact reconfigurable multiplexing devices based on silicon microring resonators,” Opt. Express 18(10), 9852–9858 (2010).
[Crossref] [PubMed]

P. Dong, W. Qian, H. Liang, R. Shafiiha, X. Wang, D. Z. Feng, G. Li, J. E. Cunningham, A. V. Krishnamoorthy, and M. Asghari, “1x4 reconfigurable demultiplexing filter based on free-standing silicon racetrack resonators,” Opt. Express 18(24), 24504–24509 (2010).
[Crossref] [PubMed]

F. N. Xia, M. Rooks, L. Sekaric, and Y. Vlasov, “Ultra-compact high order ring resonator filters using submicron silicon photonic wires for on-chip optical interconnects,” Opt. Express 15(19), 11934–11941 (2007).
[Crossref] [PubMed]

Y. A. Vlasov and S. J. McNab, “Losses in single-mode silicon-on-insulator strip waveguides and bends,” Opt. Express 12(8), 1622–1631 (2004).
[Crossref] [PubMed]

M. M. Geng, L. X. Jia, L. Zhang, L. Yang, P. Chen, T. Wang, and Y. L. Liu, “Four-channel reconfigurable optical add-drop multiplexer based on photonic wire waveguide,” Opt. Express 17(7), 5502–5516 (2009).
[Crossref] [PubMed]

H. Shen, M. H. Khan, L. Fan, L. Zhao, Y. Xuan, J. Ouyang, L. T. Varghese, and M. H. Qi, “Eight-channel reconfigurable microring filters with tunable frequency, extinction ratio and bandwidth,” Opt. Express 18(17), 18067–18076 (2010).
[Crossref] [PubMed]

S. Xiao, M. H. Khan, H. Shen, and M. Qi, “Multiple-channel silicon micro-resonator based filters for WDM applications,” Opt. Express 15(12), 7489–7498 (2007).
[Crossref] [PubMed]

Other (11)

M. A. Popović, T. Barwicz, M. S. Dahlem, F. Gan, C. W. Holzwarth, P. T. Rakich, H. I. Smith, E. P. Ippen, and F. X. Kärtner, “Tunable, Fourth-Order Silicon Microring-Resonator Add-Drop Filters,” presented at the European Conference on Optical Communication, Berlin, Germany, Sept. 2007, paper 1.2.3.

F. Gan, T. Barwicz, M. A. Popović, M. S. Dahlem, C. W. Holzwarth, P. T. Rakich, H. I. Smith, E. P. Ippen, and F. X. Kärtner, “Maximizing the thermo-optic tuning range of silicon photonic structures,” in Proceedings of IEEE Conference on Photonics in Switching (San Francisco, CA, 2007), pp. 67–68.

M. A. Popović, T. Barwicz, M. S. Dahlem, F. W. Gan, C. W. Holzwarth, P. T. Rakich, M. R. Watts, H. I. Smith, F. X. Kärtner, and E. P. Ippen, “Hitless-reconfigurable and bandwidth-scalable silicon photonic circuits for telecom and interconnect applications,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OTuF4.

M. H. Khan, H. Shen, Y. Xuan, S. J. Mao, and M. H. Qi, “Eight-Channel Microring Resonator Array with Accurately Controlled Channel Spacing,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper CTuNN6.

M. S. Dahlem, C. W. Holzwarth, A. Khilo, F. X. Kärtner, H. I. Smith, and E. P. Ippen, “Eleven-Channel Second-Order Silicon Microring-Resonator Filterbank with Tunable Channel Spacing,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper CMS5.

G. T. Reed, Silicon Photonics: The State of the Art (Wiley, 2008).

M. A. Popović, T. Barwicz, E. P. Ippen, and F. X. Kärtner, “Global design rules for silicon microphotonic waveguides: sensitivity, polarization and resonance tunability,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference, OSA Technical Digest (CD) (Optical Society of America, 2006), paper CTuCC1.

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Figures (10)

Fig. 1
Fig. 1 Illustration of the operation of a general second-order filterbank, showing three adjacent channels tuned to different frequencies, routing the signal into the respective drop ports.
Fig. 2
Fig. 2 Layout of one channel of the second-order counter-propagating filterbank.
Fig. 3
Fig. 3 Relevant parameters for designing filterbanks: single-channel bandwidth, channel spacing, free spectral range, and extinction of a channel at the location of adjacent channels.
Fig. 4
Fig. 4 Design details: (a) dimensions of the second-order silicon microring filter, fabricated on an SOI platform, and (b) material stack cross-section in the bus-ring coupling region. The bus waveguides are 495 × 105 nm, the ring waveguides are 600 × 105 nm, and the ring radius is 6.735 µm. In the filterbank, the resonant frequencies for each channel are adjusted by slightly changing the ring radius and the waveguide width of each microring resonator, with respect to the previous channel.
Fig. 5
Fig. 5 Optical micrographs of the fabricated filterbanks: (a) dual twenty-channel, (b) twenty-channel counter-propagating, and (c) detailed view of two adjacent channels, after the fabrication of the titanium microheaters.
Fig. 6
Fig. 6 Illustration of the experimental setup used to characterize the filterbanks. EPIC: Electronic Photonic Integrated Circuit under test.
Fig. 7
Fig. 7 Filter response of one channel of the dual filterbank, before (left curve) and after (right curves) thermal tuning. The channel is tuned to a pre-set center wavelength (grey box), and the aligned channel has a bandwidth of 20 GHz, with over 35 dB extinction at ± 80 GHz, and about 45 dB extinction at ± 124 GHz ( ± 1 nm).
Fig. 8
Fig. 8 Drop-port responses of eleven adjacent channels of the fabricated second-order twenty-channel dual filterbank: (a) before and (b) after thermo-optic tuning of the resonant frequencies of the individual microring resonators. After tuning, the single-channel bandwidth is measured to be 20 GHz and the channel crosstalk is about −45 dB (extrapolated from data fit), for the pre-set channel-spacing of 124 GHz.
Fig. 9
Fig. 9 Drop-port responses of one channel of the counter-propagating filterbank, before (left curves) and after tuning (right curves). The tuned filter responses are similar and show a bandwidth of 20 GHz, with extinction of about 35 dB at frequencies ± 80 GHz apart form the center frequency, and about 45 dB at ± 124 GHz ( ± 1 nm).
Fig. 10
Fig. 10 Thermal crosstalk measurement: when microheaters A and B are actuated independently, different frequency shifts occur at each microring resonator. These shifts allow one to determine the elements of the tuning matrix.

Tables (2)

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Table 1 Frequency (and wavelength) values for the 124 GHz-spaced grid used to align all eleven channels.

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Table 2 Approximate frequency mismatch (in GHz) of each ring with respect to the pre-set frequency grid.

Equations (2)

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[ Δ ν A Δ ν B ] = [ κ A κ AB κ BA κ B ] [ P A P B ] ,
[ κ A κ AB κ BA κ B ] = [ 30.0 11.9 5.3 27.6 ]   (GHz/mW) ,

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