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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 23 — Nov. 8, 2010
  • pp: 23784–23789
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GHz-bandwidth optical filters based on high-order silicon ring resonators

Po Dong, Ning-Ning Feng, Dazeng Feng, Wei Qian, Hong Liang, Daniel C. Lee, B. J. Luff, T. Banwell, A. Agarwal, P. Toliver, R. Menendez, T. K. Woodward, and Mehdi Asghari  »View Author Affiliations


Optics Express, Vol. 18, Issue 23, pp. 23784-23789 (2010)
http://dx.doi.org/10.1364/OE.18.023784


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Abstract

Previously demonstrated high-order silicon ring filters typically have bandwidths larger than 100 GHz. Here we demonstrate 1-2 GHz-bandwidth filters with very high extinction ratios (~50 dB). The silicon waveguides employed to construct these filters have propagation losses of ~0.5 dB/cm. Each ring of a filter is thermally controlled by metal heaters situated on the top of the ring. With a power dissipation of ~72 mW, the ring resonance can be tuned by one free spectral range, resulting in wavelength-tunable optical filters. Both second-order and fifth-order ring resonators are presented, which can find ready application in microwave/radio frequency signal processing.

© 2010 OSA

1. Introduction

Overcoming the limitations of traditional methods of microwave and radio frequency (RF) signal processing has stimulated much activity in the application of photonics to this area [1

1. RF photonic Technology in Optical Fiber Links, ed. W.S.C. Chang, (Cambridge University Press, 2002).

, 2

2. J. Capmany, B. Ortega, and D. Pastor, “A tutorial on microwave photonic filters,” J. Lightwave Technol. 24(1), 201–229 (2006). [CrossRef]

]. In particular, the use of fully integrated photonic devices and circuits to meet flexible wideband spectral processing requirements for both civilian and military applications is of great interest. Silicon photonics technology [3

3. G. T. Reed, Silicon photonics, the state of the art (John Wiley and Sons, 2008).

] has received much attention in recent years for application in long- and short-distance optical communications, including the demonstration of high speed optical modulators and detectors integrated with silicon waveguides, and it is becoming increasingly evident that this platform can also find ready application to previously intractable RF signal processing tasks [4

4. T. K. Woodward, T. C. Banwell, A. Agarwal, P. Toliver, and R. Menendez, “Signal processing in analog optical links,” Avionics, Fiber Optics, and Photonics Conference (AVFOP2009IEEE), pp. 17–18.

]. The compatibility of silicon-based optics with mature CMOS fabrication techniques enables manufacture of high-performance optical components at low cost and offers the possibility of monolithic electronic-photonic integration. Here, we demonstrate high-order ring resonator based silicon photonics GHz-bandwidth filters with large free spectral ranges (FSRs) and high extinction ratios. These are, to the best of our knowledge, the first high-order silicon-based filters with few-GHz bandwidths. This filter can work as a channelizing filter and be cascaded monolithically with other silicon photonic MHz-bandwidth RF filters, such as those demonstrated in Refs [5

5. M. S. Rasras, K.-Y. Tu, D. M. Gill, Y.-K. Chen, A. E. White, S. S. Patel, A. Pomerene, D. Carothers, J. Beattie, M. Beals, J. Michel, and L. C. Kimerling, “Demonstration of a tunable microwave-photonic notch filter using low-loss silicon ring resonators,” J. Lightwave Technol. 27(12), 2105–2110 (2009). [CrossRef]

, 6

6. P. Toliver, R. C. Menendez, T. C. Banwell, A. Agarwal, T. K. Woodward, N. N. Feng, P. Dong, D. Feng, W. Qian, H. Liang, D. C. Lee, B. J. Luff, and M. Asghari, A programmable optical filter unit cell element for high resolution RF signal processing in silicon photonics (OFC 2010 IEEE), paper OWJ4.

], resulting in single-chip filter systems with high extinction ratios, narrow bandwidths, and large FSRs.

2. Device design and fabrication

Mutually coupled resonators have the ability to synthesize higher-order filter responses with a flat-top passband and high out-of-band signal rejection (extinction ratio), which are important in applications such as WDM and microwave filtering [7

7. C. K. Madsen, and J. H. Zhao, Optical filter design and analysis, a signal processing approach (Wiley 1999).

]. Flat-top bands minimize group delay variation in the passband and high extinction ratios minimize signal crosstalk between adjacent channels. High-performance high-order rings with a few GHz bandwidth have been demonstrated in silica-based materials [8

8. 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). [CrossRef]

11

11. J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho, “High order filter response in coupled microring resonators,” IEEE Photon. Technol. Lett. 12(3), 320–322 (2000). [CrossRef]

]. High-order silicon coupled rings have been also demonstrated, but usually with bandwidths larger than 100 GHz [12

12. S. Xiao, M. H. Khan, H. Shen, and M. Qi, “A highly compact third-order silicon microring add-drop filter with a very large free spectral range, a flat passband and a low delay dispersion,” Opt. Express 15(22), 14765–14771 (2007). [CrossRef] [PubMed]

14

14. F. Xia, L. Sekaric, M. O’Boyle, and Y. Vlasov, “Coupled resonator optical waveguides (CROWs) based on silicon-on-insulator photonic wires,” Appl. Phys. Lett. 89(4), 041122–041124 (2006). [CrossRef]

]. Here we use coupled ring resonators fabricated on a silicon-on-insulator platform to demonstrate few-GHz bandwidth filters. There are two major challenges to achieving narrow band silicon coupled-ring filters. First, although significant progress has been made in silicon photonics, silicon waveguide propagation losses are still too high for practical application to RF filters with large FSRs. While large-core silicon waveguides can have a propagation loss of ~0.1 dB/cm, they require large bending radii on the order of mm, which limits the FSR to less than 10 GHz. A large device area also results in more power consumption. Submicron silicon waveguides have been demonstrated with a bend radius of a few µm [12

12. S. Xiao, M. H. Khan, H. Shen, and M. Qi, “A highly compact third-order silicon microring add-drop filter with a very large free spectral range, a flat passband and a low delay dispersion,” Opt. Express 15(22), 14765–14771 (2007). [CrossRef] [PubMed]

14

14. F. Xia, L. Sekaric, M. O’Boyle, and Y. Vlasov, “Coupled resonator optical waveguides (CROWs) based on silicon-on-insulator photonic wires,” Appl. Phys. Lett. 89(4), 041122–041124 (2006). [CrossRef]

], but the waveguide propagation loss is usually larger than 1 dB/cm. Second, high-order coupled rings are very sensitive to fabrication tolerances. For instance, all mutually coupled rings in the filter are required to have precisely coincident resonant frequencies to achieve maximum efficiency. Unfortunately, the resonances of silicon rings built using submicron waveguides are very sensitive to fabrication imperfections [15

15. M. Popovic, Theory and design of high-index-contrast microphotonic circuits, PhD thesis, (MIT 2008).

].

The propagation loss of silicon waveguides arises mainly due to light scattering from the etched sidewalls. Minimizing the optical field overlap with etched interfaces can effectively reduce the waveguide propagation loss. Increasing waveguide width and decreasing etch depth can both realize this purpose. Here, we design a type of shallow-ridge waveguide [16

16. P. Dong, W. Qian, S. Liao, H. Liang, C.-C. Kung, N.-N. Feng, R. Shafiiha, J. Fong, D. Feng, A. V. Krishnamoorthy, and M. Asghari, “Low loss shallow-ridge silicon waveguides,” Opt. Express 18(14), 14474–14479 (2010). [CrossRef] [PubMed]

]. The waveguide width and height are 1 µm and 0.25 µm, respectively, and the etch depth to form the ridge waveguide is 0.06 µm. Simulation indicates that the effective index and group index of the fundamental quasi-TE mode are ~2.9 and ~3.8, respectively. Theoretical simulation shows that the radiation loss for a bending radius of 100 µm is on the order of 10−4 dB/cm. This bending radius can enable a ring resonator with an FSR of ~150 GHz.

Based on the proposed waveguide geometry, we designed second and fifth order Butterworth filters with a maximally flat passband response. The FSR and bandwidth are targeted at 50 GHz and 1 GHz, respectively. The coupling ratios between rings are obtained based on Butterworth type response [7

7. C. K. Madsen, and J. H. Zhao, Optical filter design and analysis, a signal processing approach (Wiley 1999).

]. The ring radius is chosen as 248 µm. Due to fabrication variations, active control of ring resonance has to be used to make all the rings have coincident resonant frequencies. Individual heaters on the top of each ring are designed to fine tune the resonant frequency.

We fabricated the devices using silicon-on-insulator wafers with a 0.25 µm thick silicon layer and a 3 µm thick buried oxide layer. An oxide layer was deposited on the wafers by plasma enhanced chemical vapor deposition to act as a hard mask for waveguide etching. Resist patterns were defined by an i-line stepper. The pattern was transferred to the oxide hard mask using a CHF3/O2 chemistry. We then removed the resist and etched the silicon layer using an HBr-based silicon dry etch recipe. Both the oxide and silicon etch recipes were optimized to reduce sidewall roughness. We found that the use of oxide hard mask helps reduce the silicon waveguide loss. A 1.2 µm thick oxide was then deposited on the wafers as a cladding layer. A thin Ti metal was deposited on top of the ring to act as a heating resistor. This heater is connected by Al metals to test pads (shown in Fig. 1
Fig. 1 Optical images of fully fabricated 2nd-order (a) and 5th-order ring filters.
).

3. Waveguide loss measurement

Characterizing waveguide loss is particularly important to assess ring performance. Test waveguides with different lengths together with ring filters were fabricated for this purpose. We tested the waveguide loss using an amplified spontaneous emission source with a wavelength centered at 1550 nm and an optical spectrum analyzer. Lensed fibers were used to couple light into and collect light from the waveguides. In Fig. 2(a)
Fig. 2 (a) Insertion loss spectra for waveguides with different lengths. (b) Waveguide propagation loss spectrum obtained from linear fitting between insertion losses and waveguide lengths. (c) Average waveguide loss in C-band for ten different chips.
, we show the insertion losses measured for different waveguide lengths as a function of wavelength. The insertion losses are normalized to the power measured from direct fiber to fiber coupling, and include both the fiber coupling loss to waveguides and the waveguide propagation loss. From the insertion loss at a particular wavelength for different waveguide lengths, we can extract the waveguide propagation loss using linear fitting. The results shown in Fig. 2(b) demonstrate a waveguide loss of ~0.48 dB/cm in the C-band. Figure 2(c) presents the average waveguide loss in the C-band for ten different chips across the whole wafer. The wafer-level average waveguide loss is 0.507 dB/cm with a standard derivation of 0.015 dB/cm, demonstrating uniform waveguide quality on the wafer level. Given this propagation loss, the round trip loss of the ring is about 0.1 dB. It is to be noted that the spectra in Fig. 2(a) are very smooth, indicating nearly single mode propagation through the waveguides. Although theoretical simulations predict two quasi-TE modes, the coupling from the input fiber mode to the first-order mode and the fundamental mode to the first-order mode is weak due to opposite symmetry. In addition, the large index difference between two waveguide modes prevents efficient coupling between them.

4. Heater characterization

We characterized the heater efficiency and thermal crosstalk by measuring the drop-port transmission spectra with different heating powers for the second-order filter as shown in Fig. 1(a). The heaters on two neighboring rings are located on opposite sides of the rings, however, thermal crosstalk may still occur since silicon has very low thermal impedance. Although designed to have the same resonances, transmission spectra at the drop port usually show two resonant peaks corresponding to different resonances of the two rings, as shown in Fig. 3(a)
Fig. 3 (a) Transmission spectra at the drop port with heater off and on. (b) Resonance shifts for both rings as a function of heating power.
. This is due to resonance mismatch from fabrication imperfections. Applying heating power on one ring and monitoring the resonance shifts for both peaks give us information on both tuning efficiency and thermal crosstalk. Here the thermal crosstalk is defined as the ratio between the wavelength/frequency shift of the second to the first ring while heating the first ring. The wavelength shifts as a function of tuning power are shown in Fig. 3(b), from which we determine that the tuning power per unit frequency is 1.44 mW/GHz and the thermal crosstalk is 7.3%. Since the free spectral range (FSR) is 0.4 nm or 50 GHz, ~72 mW is needed to tune one whole FSR of a single ring. The thermal crosstalk can be reduced if air trenches are fabricated around the rings and metal heaters [17

17. P. Dong, W. Qian, H. Liang, R. Shafiiha, N.-N. Feng, D. Feng, X. 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]

].

5. GHz-bandwidth 2nd- and 5th-order ring filters

With the current waveguide geometry, the theoretical ring frequency sensitivity to waveguide width is approximately 4 GHz/nm, i.e., a 1 nm variation in waveguide width results in a resonant frequency shift of 4 GHz. The ring frequency is even more sensitive to etch depth and silicon thickness, with a theoretical sensitivity of about 26 GHz/nm and 150 GHz/nm, respectively. As the bandwidth of the ring is only ~1 GHz, it would not be practical to expect that the rings’ resonant frequencies can be identical without any active tuning. Here we use the thermo-optic effect to control the ring resonance. Silicon has a large thermal coefficient of 1.86×10−4 /°C, with which value the ring resonant frequency shift is estimated as 9.6 GHz per degree. Therefore, the temperature of the ring has to be controlled with an accuracy of better than 0.02 °C in order to align the ring resonant frequencies together. The use of partial heating of the ring relaxes this accuracy requirement to about 0.1 °C for local temperature. We use a multi-channel current source to control the heaters, and each heater can be controlled independently. After optimizing the heater currents, we obtain spectra for through and drop with a maximally flat response, shown in Fig. 4
Fig. 4 Transmission spectra for the 2nd-orer ring filter (a) and 5th-order ring filter (b) after optimizing the heating power. The transmission is normalized to the maximum power of through ports. Insets: enlarged drop-port spectra at the resonance peaks.
for both 2nd- and 5th-order ring filters. The filter demonstrates a 3 dB bandwidth f3dB = 1.0 GHz and 1.9 GHz for the 2nd- and 5th-order rings, respectively. The insertion losses (not including fiber coupling loss) are 2 dB and 3.5 dB. The out-of-band rejection of both filters is more than 50 dB. In Fig. 5
Fig. 5 Normalized drop-port transmission spectra for the 2nd-orer and 5th-order ring filters. The frequency is normalized to the filter’s own 3dB bandwidth and the transmission is normalized to the maximum power of the drop port itself.
, we plot the filter response in drop ports for both rings by normalizing the frequency to their own 3dB bandwidths and normalizing the transmission to their own peak values. At a frequency of 2f3dB, the transmission at the drop port drops to ~46 dB and ~25 dB for the 5th-order and 2nd-order filters, respectively, demonstrating an excellent box-like transmission. The measured bandwidth for the 5th-order ring is larger than the target value (1 GHz), possibly due to uncertainty of coupling coefficients from fabrication tolerance variations. Since the five rings in the 5th-order filters are all tunable in wavelength with a thermal tuning efficiency of 72 mW per free spectral range, the resonant wavelength can have a large tunability range with a total power of about 0.36 W. This tuning power can be significantly reduced, using thermal isolation trenches [17

17. P. Dong, W. Qian, H. Liang, R. Shafiiha, N.-N. Feng, D. Feng, X. 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]

] or undercuts beneath the rings [18

18. P. Dong, W. Qian, H. Liang, R. Shafiiha, D. Feng, G. Li, J. E. Cunningham, A. V. Krishnamoorthy, and M. Asghari, “Thermally tunable silicon racetrack resonators with ultralow tuning power,” Opt. Express 18(19), 20298–20304 (2010). [CrossRef] [PubMed]

].

6. Conclusions

We have presented the experimental realization of tunable high-order ring-resonator based filters on a silicon photonics platform. The filters have a bandwidth of 1-2 GHz, FSRs of 50 GHz, and out-of-band extinction ratios of 50 dB at the drop port. To the best of our knowledge, these filters have the narrowest optical bandwidth for so far demonstrated high-order silicon ring filters. Such filters, when combined with appropriate unit-cell filters [5

5. M. S. Rasras, K.-Y. Tu, D. M. Gill, Y.-K. Chen, A. E. White, S. S. Patel, A. Pomerene, D. Carothers, J. Beattie, M. Beals, J. Michel, and L. C. Kimerling, “Demonstration of a tunable microwave-photonic notch filter using low-loss silicon ring resonators,” J. Lightwave Technol. 27(12), 2105–2110 (2009). [CrossRef]

, 6

6. P. Toliver, R. C. Menendez, T. C. Banwell, A. Agarwal, T. K. Woodward, N. N. Feng, P. Dong, D. Feng, W. Qian, H. Liang, D. C. Lee, B. J. Luff, and M. Asghari, A programmable optical filter unit cell element for high resolution RF signal processing in silicon photonics (OFC 2010 IEEE), paper OWJ4.

], are key building blocks suitable for diverse optical signal processing applications [4

4. T. K. Woodward, T. C. Banwell, A. Agarwal, P. Toliver, and R. Menendez, “Signal processing in analog optical links,” Avionics, Fiber Optics, and Photonics Conference (AVFOP2009IEEE), pp. 17–18.

].

Acknowledgements

This material is based upon work supported by the Defense Advanced Research Projects Agency PhASER program under Contract No. HR0011-08-C-0026. The views, opinions, and/or findings contained in this article are those of the authors and should not be interpreted as representing the official views or policies, either expressed or implied, of the Defense Advanced Research Projects Agency or the Department of Defense. Approved for Public Release, Distribution Unlimited.

References and links

1.

RF photonic Technology in Optical Fiber Links, ed. W.S.C. Chang, (Cambridge University Press, 2002).

2.

J. Capmany, B. Ortega, and D. Pastor, “A tutorial on microwave photonic filters,” J. Lightwave Technol. 24(1), 201–229 (2006). [CrossRef]

3.

G. T. Reed, Silicon photonics, the state of the art (John Wiley and Sons, 2008).

4.

T. K. Woodward, T. C. Banwell, A. Agarwal, P. Toliver, and R. Menendez, “Signal processing in analog optical links,” Avionics, Fiber Optics, and Photonics Conference (AVFOP2009IEEE), pp. 17–18.

5.

M. S. Rasras, K.-Y. Tu, D. M. Gill, Y.-K. Chen, A. E. White, S. S. Patel, A. Pomerene, D. Carothers, J. Beattie, M. Beals, J. Michel, and L. C. Kimerling, “Demonstration of a tunable microwave-photonic notch filter using low-loss silicon ring resonators,” J. Lightwave Technol. 27(12), 2105–2110 (2009). [CrossRef]

6.

P. Toliver, R. C. Menendez, T. C. Banwell, A. Agarwal, T. K. Woodward, N. N. Feng, P. Dong, D. Feng, W. Qian, H. Liang, D. C. Lee, B. J. Luff, and M. Asghari, A programmable optical filter unit cell element for high resolution RF signal processing in silicon photonics (OFC 2010 IEEE), paper OWJ4.

7.

C. K. Madsen, and J. H. Zhao, Optical filter design and analysis, a signal processing approach (Wiley 1999).

8.

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). [CrossRef]

9.

T. Barwicz, M. A. Popović, M. R. Watts, P. T. Rakich, E. P. Ippen, and H. I. Smith, “Fabrication of add-drop filters based on frequency-matched microring resonators,” J. Lightwave Technol. 24(5), 2207–2218 (2006). [CrossRef]

10.

J. K. S. Poon, L. Zhu, G. A. DeRose, and A. Yariv, “Transmission and group delay of microring coupled-resonator optical waveguides,” Opt. Lett. 31(4), 456–458 (2006). [CrossRef] [PubMed]

11.

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho, “High order filter response in coupled microring resonators,” IEEE Photon. Technol. Lett. 12(3), 320–322 (2000). [CrossRef]

12.

S. Xiao, M. H. Khan, H. Shen, and M. Qi, “A highly compact third-order silicon microring add-drop filter with a very large free spectral range, a flat passband and a low delay dispersion,” Opt. Express 15(22), 14765–14771 (2007). [CrossRef] [PubMed]

13.

S. H. Tao, J. Song, Q. Fang, M. B. Yu, G. Q. Lo, and D. L. Kwong, 50th order series-coupled micro-ring resonator (IPGC 2008 IEEE), pp. 1 – 3.

14.

F. Xia, L. Sekaric, M. O’Boyle, and Y. Vlasov, “Coupled resonator optical waveguides (CROWs) based on silicon-on-insulator photonic wires,” Appl. Phys. Lett. 89(4), 041122–041124 (2006). [CrossRef]

15.

M. Popovic, Theory and design of high-index-contrast microphotonic circuits, PhD thesis, (MIT 2008).

16.

P. Dong, W. Qian, S. Liao, H. Liang, C.-C. Kung, N.-N. Feng, R. Shafiiha, J. Fong, D. Feng, A. V. Krishnamoorthy, and M. Asghari, “Low loss shallow-ridge silicon waveguides,” Opt. Express 18(14), 14474–14479 (2010). [CrossRef] [PubMed]

17.

P. Dong, W. Qian, H. Liang, R. Shafiiha, N.-N. Feng, D. Feng, X. 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]

18.

P. Dong, W. Qian, H. Liang, R. Shafiiha, D. Feng, G. Li, J. E. Cunningham, A. V. Krishnamoorthy, and M. Asghari, “Thermally tunable silicon racetrack resonators with ultralow tuning power,” Opt. Express 18(19), 20298–20304 (2010). [CrossRef] [PubMed]

OCIS Codes
(070.1170) Fourier optics and signal processing : Analog optical signal processing
(230.3120) Optical devices : Integrated optics devices
(230.5750) Optical devices : Resonators
(060.5625) Fiber optics and optical communications : Radio frequency photonics

ToC Category:
Optical Devices

History
Original Manuscript: September 9, 2010
Revised Manuscript: October 15, 2010
Manuscript Accepted: October 19, 2010
Published: October 27, 2010

Citation
Po Dong, Ning-Ning Feng, Dazeng Feng, Wei Qian, Hong Liang, Daniel C. Lee, B. J. Luff, T. Banwell, A. Agarwal, P. Toliver, R. Menendez, T. K. Woodward, and Mehdi Asghari, "GHz-bandwidth optical filters based on high-order silicon ring resonators," Opt. Express 18, 23784-23789 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-23-23784


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References

  1. RF photonic Technology in Optical Fiber Links, ed. W.S.C. Chang, (Cambridge University Press, 2002).
  2. J. Capmany, B. Ortega, and D. Pastor, “A tutorial on microwave photonic filters,” J. Lightwave Technol. 24(1), 201–229 (2006). [CrossRef]
  3. G. T. Reed, Silicon photonics, the state of the art (John Wiley and Sons, 2008).
  4. T. K. Woodward, T. C. Banwell, A. Agarwal, P. Toliver, and R. Menendez, “Signal processing in analog optical links,” Avionics, Fiber Optics, and Photonics Conference (AVFOP2009IEEE), pp. 17–18.
  5. M. S. Rasras, K.-Y. Tu, D. M. Gill, Y.-K. Chen, A. E. White, S. S. Patel, A. Pomerene, D. Carothers, J. Beattie, M. Beals, J. Michel, and L. C. Kimerling, “Demonstration of a tunable microwave-photonic notch filter using low-loss silicon ring resonators,” J. Lightwave Technol. 27(12), 2105–2110 (2009). [CrossRef]
  6. P. Toliver, R. C. Menendez, T. C. Banwell, A. Agarwal, T. K. Woodward, N. N. Feng, P. Dong, D. Feng, W. Qian, H. Liang, D. C. Lee, B. J. Luff, and M. Asghari, A programmable optical filter unit cell element for high resolution RF signal processing in silicon photonics (OFC 2010 IEEE), paper OWJ4.
  7. C. K. Madsen, and J. H. Zhao, Optical filter design and analysis, a signal processing approach (Wiley 1999).
  8. 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). [CrossRef]
  9. T. Barwicz, M. A. Popović, M. R. Watts, P. T. Rakich, E. P. Ippen, and H. I. Smith, “Fabrication of add-drop filters based on frequency-matched microring resonators,” J. Lightwave Technol. 24(5), 2207–2218 (2006). [CrossRef]
  10. J. K. S. Poon, L. Zhu, G. A. DeRose, and A. Yariv, “Transmission and group delay of microring coupled-resonator optical waveguides,” Opt. Lett. 31(4), 456–458 (2006). [CrossRef] [PubMed]
  11. J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P.-T. Ho, “High order filter response in coupled microring resonators,” IEEE Photon. Technol. Lett. 12(3), 320–322 (2000). [CrossRef]
  12. S. Xiao, M. H. Khan, H. Shen, and M. Qi, “A highly compact third-order silicon microring add-drop filter with a very large free spectral range, a flat passband and a low delay dispersion,” Opt. Express 15(22), 14765–14771 (2007). [CrossRef] [PubMed]
  13. S. H. Tao, J. Song, Q. Fang, M. B. Yu, G. Q. Lo, and D. L. Kwong, 50th order series-coupled micro-ring resonator (IPGC 2008 IEEE), pp. 1 – 3.
  14. F. Xia, L. Sekaric, M. O’Boyle, and Y. Vlasov, “Coupled resonator optical waveguides (CROWs) based on silicon-on-insulator photonic wires,” Appl. Phys. Lett. 89(4), 041122–041124 (2006). [CrossRef]
  15. M. Popovic, Theory and design of high-index-contrast microphotonic circuits, PhD thesis, (MIT 2008).
  16. P. Dong, W. Qian, S. Liao, H. Liang, C.-C. Kung, N.-N. Feng, R. Shafiiha, J. Fong, D. Feng, A. V. Krishnamoorthy, and M. Asghari, “Low loss shallow-ridge silicon waveguides,” Opt. Express 18(14), 14474–14479 (2010). [CrossRef] [PubMed]
  17. P. Dong, W. Qian, H. Liang, R. Shafiiha, N.-N. Feng, D. Feng, X. 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]
  18. P. Dong, W. Qian, H. Liang, R. Shafiiha, D. Feng, G. Li, J. E. Cunningham, A. V. Krishnamoorthy, and M. Asghari, “Thermally tunable silicon racetrack resonators with ultralow tuning power,” Opt. Express 18(19), 20298–20304 (2010). [CrossRef] [PubMed]

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