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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 6 — Mar. 25, 2013
  • pp: 6749–6755
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Silicon-on-insulator narrow-passband filter based on cascaded MZIs incorporating enhanced FSR for downconverting analog photonic links

Hongchen Yu, Minghua Chen, Pengxiao Li, Sigang Yang, Hongwei Chen, and Shizhong Xie  »View Author Affiliations


Optics Express, Vol. 21, Issue 6, pp. 6749-6755 (2013)
http://dx.doi.org/10.1364/OE.21.006749


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Abstract

A silicon-on-insulator (SOI) narrow-passband filter based on cascaded Mach-Zehnder interferometers (MZIs) is theoretically simulated and experimentally demonstrated, indicating that the free spectral range (FSR) of the proposed filter can be significantly enlarged by increasing the number of the MZI stages. A filter using three-stage cascaded MZIs structure is successfully realized in the experiment and a 3-dB bandwidth of about 1.536 GHz and FSR about 13.5 GHz have been achieved. The performance of a downconverting analog photonic link (APL) employing the designed filter for microwave signal processing is also measured and a spurious free dynamic range (SFDR) as high as 104.1dB-Hz2/3 is observed.

© 2013 OSA

1. Introduction

Silicon-on-insulator (SOI) integration based devices have been a hot topic in the area of integrated microwave photonics for signal processing as the state of art is mature, compatible with CMOS technology and immunity to electromagnetic interference, and the devices are small for it has high index contrast between Si and SiO2 etc [1

1. D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, “Integrated microwave photonics,” arXiv:1211.4114 (2012).

4

4. B. Jalali and S. Fathpour, “Silicon Photonics,” IEEE J. Lightw. Technol. 24(12), 4600–4615 (2006). [CrossRef]

]. Microwave photonic (MWP) signal processors based on reconfigurable filters with narrow bandwidth, wide FSR and linear phase response have attracted a lot of research interest [5

5. J. Capmany, J. Mora, I. Gasulla, J. Sancho, J. Lloret, and S. Sales, “Microwave photonic signal processing,” IEEE J. Lightw. Technol. 31(4), 571–586 (2013). [CrossRef]

,6

6. P. Toliver, R. Menendez, T. 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. Ashghari, “A programmable optical filter unit cell element for high resolution RF signal processing in silicon photonics,” Optical Fiber Communication Conference 2010, paper OWJ4 (2010).

]. Recently, several integrated microwave photonics filters have been reported [6

6. P. Toliver, R. Menendez, T. 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. Ashghari, “A programmable optical filter unit cell element for high resolution RF signal processing in silicon photonics,” Optical Fiber Communication Conference 2010, paper OWJ4 (2010).

12

12. P. Dong, N.-N. Feng, D. Feng, W. Qian, H. Liang, D. C. Lee, B. J. Luff, T. Banwell, A. Agarwal, P. Toliver, R. Menendez, T. K. Woodward, and M. Asghari, “GHz-bandwidth optical filters based on high-order silicon ring resonators,” Opt. Express 18(23), 23784–23789 (2010). [CrossRef] [PubMed]

]. Generally, there are three kinds of integrated filters: 1) infinite impulse response (IIR) filters, which usually have the feedback loop, a phase jump in the filter band and is sensitive to fabrication tolerances, 2) finite impulse response (FIR) filters, which are usually formed by the MZIs and the phase response are linear, 3) coupled hybrid unit cell filter having both zero and pole. Accordingly, FIR filters have attracted a lot of attention, for their stability, simplicity and linear phase response. An optical filter unit cell with the bandwidth of only 1-2 GHz and reconfigurable for both FIR and IIR filter was proposed by the Telcordia research group in [6

6. P. Toliver, R. Menendez, T. 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. Ashghari, “A programmable optical filter unit cell element for high resolution RF signal processing in silicon photonics,” Optical Fiber Communication Conference 2010, paper OWJ4 (2010).

], which could meet the requirement of high resolution radio frequency (RF) signal processing. In [8

8. H. W. Chen, A. W. Fang, J. Bovington, J. Peters, and J. Bowers, “Hybrid silicon tunable filter based on a Mach-Zehnder interferometer and ring resonantor,” in Proc. Microwave Photonics, Valencia, Spain, 2009, pp. 1–4.

], a ring assisted MZI tunable filter based on hybrid silicon platform was proposed. In [9

9. S. S. Djordjevic, L. W. Luo, S. Ibrahim, N. K. Fontaine, C. B. Poitras, B. Guan, L. Zhou, K. Okamoto, Z. Ding, M. Lipson, and S. J. B. Yoo, “Fully reconfigurable silicon photonic lattice filters with four cascaded unit cells,” IEEE Photon. Technol. Lett. 23(1), 42–44 (2011). [CrossRef]

], a four stage lattice based filter with fully configurable was demonstrated. However, all these proposed filters mainly rely on the traditional MZI scheme, whose FSRs are inversely proportional to their differential path length and proportional to their bandwidth [13

13. N. Takato, T. Kominato, A. Sugita, K. Jinguji, H. Toba, and M. Kawachi, “Silica-based integrated optic Mach-Zehnder multi/demultiplexer family with channel spacing of 0.01-250 nm,” IEEE J. Sel. Areas Comm. 8(6), 1120–1127 (1990). [CrossRef]

], limiting their application for fine processing for broadband signal processing, where an additional optical RF channelizer is always required to enlarge the FSR [12

12. P. Dong, N.-N. Feng, D. Feng, W. Qian, H. Liang, D. C. Lee, B. J. Luff, T. Banwell, A. Agarwal, P. Toliver, R. Menendez, T. K. Woodward, and M. Asghari, “GHz-bandwidth optical filters based on high-order silicon ring resonators,” Opt. Express 18(23), 23784–23789 (2010). [CrossRef] [PubMed]

], introducing extra loss and complexity to the whole system.

In this paper, an SOI multi-stage cascaded MZIs based narrow-bandwidth FIR filter with enhanced processing range is proposed and experimentally demonstrated, where the FSR of the filter can be enlarged by increasing the number of MZI stages. A three-stage cascaded MZIs based filter with a bandwidth of 1.536GHz and FSR nearly 13.5GHz has been successfully achieved, which can meet the requirement of RF signal processing bandwidth of from X- to Ka-band. Moreover, an intermediate frequency (IF) downconversion APL in K-band utilizing the proposed filter is presented as well and an SFDR of 104.1dB-Hz2/3 is observed.

2. Device design and simulation

Schematic diagram of the proposed filter based on multi-stage MZIs with enhanced processing range and negligible change in the 3-dB bandwidth is shown in Fig. 1
Fig. 1 Schematic of the N-stage cascaded MZIs tunable filter, in which each stage of the filter can be changed independently.
, where the input- and output-ports on the upper paths (port1 to port2N) are combined for each stage MZI. In our design, the differential path length of each stage MZI satisfies the condition by ∆L1 = L, ∆L2 = 2−1L,…, ∆LN = 2-(N-1)L, and the phase shifters are realized by the micro heaters covered on the upper arms of the MZIs. The transfer function of the filter can be written as
H11=i=1N(1κ2i11κ2iejϕiκ2i1κ2iγiejβ(2(i1)L)),
(1)
where κi (i<N)is the coupling coefficient of the ith waveguide coupler determined by the coupling length and the distance between the waveguide coupler, γi=eα(2(i1)L)/2 is the inherent loss induced by the silicon waveguide delay line (ΔLi=2(i1)L) where α is the waveguide power attenuation coefficient, βis the propagation constant along the waveguide, ϕi is the phase difference between the two arms.

Totally 2N couplers are needed for N stages filter. In order to minimize transfer-loss in passband, the coupling ratio of the coupler is set to be κ2i1=κ2i=(1+γi)1, so that all the zeros are on the unit circle [17

17. C. Madsen and J. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach (Wiley-Interscience, 1999), Chap. 4.

]. A simply π phase shift is introduced for each stage in our design to align their resonance, i.e. ϕ1=ϕ2...=ϕN=π.Therefore, the Eq. (1) can be simplified as
H11(1)N(1+z2(N1))(1+z2(N2))(1+z2(N3))...(1+z1),
(2)
where z=ejΩand Ω=β(2(N1))L.

The zeros diagram in z-plane of three-stage cascaded MZIs filter is shown in Fig. 2
Fig. 2 Zeros diagram of three-stage filter. Zeros for first stage (green), second stage (yellow) and the third stage (red). The angel covered by the blue line represents the amplitude of Ω, and the arrow stands for the positive direction. ΔΩ3dBis corresponding to the 3-dB bandwidth of filter.
, in which zeros distribute around the circle uniformly. One can see from the zeros diagram, the FSR of the filter is determined by the last stage of the filter shown in Fig. 1, which can also be derived from Eq. (2)
FSR=FSRN=(c/neff)/(2(N1)L),
(3)
where c is the velocity of the light in vacuum, neff is the effective index of the proposed structure, N is the stage number and FSRN is the FSR of the last stage. As the number of the stages increases, the FSR of the filter is enlarged by 2N-1. ΔΩ3dB is corresponding to the 3-dB bandwidth of filter, which is confined by the two-zeros separated by the real axis and generated by the first stage transfer function as shown in Fig. 2, i.e. the bandwidth of the filter is mainly determined by the first stage MZI, meanwhile, the bandwidth will become narrower a little as the number of the stages increases. In addition, the zeros will rotate around the unit circle when the phase difference of each stage MZI changes, which performs a tunable and reconfigurable filter.

The simulation results of the filter response when N = 1, 3, 5 are shown in Fig. 3
Fig. 3 Simulated amplitude and phase response of multi-stage cascaded MZIs filter. (a) N = 1, (b) N = 3, (c) N = 5.
. For N = 1, the FSR is nearly 2 times the Δλ3dB and the extinction ratio is about 6.5dB as shown in Fig. 3(a). For N = 3, the FSR of the filter is enlarged by 4 times to 16GHz, nonetheless the Δλ3dB decreased a little to 2.02GHz and the extinction ratio is about 17dB. When N = 5, the FSR is enlarged to 64GHz and the extinction ratio is about 30dB. The phase response is linear as for its FIR features as shown in Fig. 3. In this simulation, we assumed L is about 2.98cm,αis about 3dB/cm [18

18. S. Xiao, M. H. Khan, H. Shen, and M. Qi, “Compact silicon microring resonators with ultra-low propagation loss in the C band,” Opt. Express 15(22), 14467–14475 (2007). [CrossRef] [PubMed]

], and a fixed coupling ratio of 0.5 considering the narrow wavelength range, which is in correspondence with the practical devices. The results also indicate that as N increases, the FSR can be enlarged by 2N-1 times, while the Δλ3dB almost does not change and the extinction ratio of the filter can also be significantly improved.

3. Fabrication and device test

The proposed filter with three-stage cascaded MZIs is fabricated on SOI wafer, considering the current fabrication tolerance, phase matching requirement and the insertion loss as shown in Fig. 4(a)
Fig. 4 Proposed optical processor with enhanced FSR. (a) Micrograph of the cascaded MZI filter. (b) Measured amplitude and phase of the filter.
. The SOI platform applied is based on 220nm thick silicon layer laid on top of 2um buried-oxide layer by LETI foundry using 193nm DUV lithography. The width and height of the etched silicon waveguide used in this filter is about 450nm and 220nm, meanwhile the gap between the coupler waveguides is 200nm and coupling length is about 10um. The heaters and electrical contact pads, which consist of 110nm Ti/TiN are deposited on a buried channel waveguides by means of 600nm thick silica layer grown on the structure.

Due to the limitation of the current SOI technology, the characteristics, for instance, the feather size and propagation loss, of the waveguiding structure may be not identical as that of our designed ones, which would result in negative influence on the performance of the fabricated devices. There are two methods can be adopted to mitigate these limitations. Firstly, gradual changed exposure and oxidation process are adopted in the optimization procedure to compensate the exposure dose variation and smooth the waveguide surface, respectively. Secondly, considering the inevitable technological fabrication tolerances, micro-heaters covered on the isolation oxide layer are employed to tune the effective parameters of the device to modify the filtering response of the device.

By independently tuning the micro heaters covered on the MZI arms, we can achieve the phase matching between different stages, and the amplitude and phase response of the device measured by an optical vector analyzer (OVA) are shown in Fig. 4(b). The bandwidth of the filter is about 1.536GHz and the FSR is enhanced to 13.5GHz, which meets the processing bandwidth of from X- to Ka-band, while the phase response is linear which agrees well with the theoretical results. The extinction ratio of the measured results is a little decrease mainly due to the fabrication error and mismatching between different MZI stages. Vertical coupling based on grating coupler is used for coupling light from single mode fiber to the silicon waveguide where the fiber to waveguide loss is about 10dB and insertion loss of the filter itself is about 9dB. Since the silicon waveguide and the coupling rate of the grating couplers are both polarization sensitive, a polarization controller (PC) has to be used to control the light polarization before the light coupling into the chip.

4. Application in downconverting APL

In our experiment, a downconverting APL utilizing our proposed multi-stage MZIs filter as a key component for microwave signal processing is demonstrated as shown in Fig. 5
Fig. 5 Experiment setup of the downconversion APL employing the proposed silicon based signal processor.
. A continuous wave (CW) is sent to a null-biased Mach-Zehnder modulator (MZM), which is modulated by a strong local oscillator (LO) RF signal. Two coherent optical sideband generated from MZM is then separated by an interleaver. The upper sideband is used as an optical LO for downconversion and lower sideband is served as the optical carrier and phase-modulated by the input broadband RF signal [19

19. P. Li, R. Shi, M. Chen, H. Chen, S. Yang, and S. Xie, “Downconversion and linearization of X- and K-band analog photonic links using digital post-compensation,” Optical Fiber Communication Conference 2013, paper JW2A.59 (2013).

]. The optical signal is then processed using our proposed narrow-passband silicon filter. Thanks to the narrow-passband and large FSR of the filter, the processor can precisely filter out the interesting signal over a wide RF frequency band of from X-band to Ka-band. To maintain phase correlation of the upper and lower paths, their path lengths and polarization states are carefully matched using optical delay line and the PCs. The filtered signal and the optical LO are then combined in an optical coupler and detected by balanced photodetector (BPD).

5. Conclusion

Acknowledgment

This work was partially supported by National Program on Key Basic Research Project (973) under Contract 2012CB315703, NSFC under Contract 61120106001, 61271134, 61090391 and the Program for New Century Excellent Talents in University (NCET-10-0520), and the Open Fund of Key Laboratory of Optical Communication and Lightwave Technologies (BUPT), China

References and links

1.

D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, “Integrated microwave photonics,” arXiv:1211.4114 (2012).

2.

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007). [CrossRef]

3.

J. Yao, “Microwave Photonics,” J. Lightwave Technol. 27(3), 314–335 (2009). [CrossRef]

4.

B. Jalali and S. Fathpour, “Silicon Photonics,” IEEE J. Lightw. Technol. 24(12), 4600–4615 (2006). [CrossRef]

5.

J. Capmany, J. Mora, I. Gasulla, J. Sancho, J. Lloret, and S. Sales, “Microwave photonic signal processing,” IEEE J. Lightw. Technol. 31(4), 571–586 (2013). [CrossRef]

6.

P. Toliver, R. Menendez, T. 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. Ashghari, “A programmable optical filter unit cell element for high resolution RF signal processing in silicon photonics,” Optical Fiber Communication Conference 2010, paper OWJ4 (2010).

7.

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]

8.

H. W. Chen, A. W. Fang, J. Bovington, J. Peters, and J. Bowers, “Hybrid silicon tunable filter based on a Mach-Zehnder interferometer and ring resonantor,” in Proc. Microwave Photonics, Valencia, Spain, 2009, pp. 1–4.

9.

S. S. Djordjevic, L. W. Luo, S. Ibrahim, N. K. Fontaine, C. B. Poitras, B. Guan, L. Zhou, K. Okamoto, Z. Ding, M. Lipson, and S. J. B. Yoo, “Fully reconfigurable silicon photonic lattice filters with four cascaded unit cells,” IEEE Photon. Technol. Lett. 23(1), 42–44 (2011). [CrossRef]

10.

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

11.

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]

12.

P. Dong, N.-N. Feng, D. Feng, W. Qian, H. Liang, D. C. Lee, B. J. Luff, T. Banwell, A. Agarwal, P. Toliver, R. Menendez, T. K. Woodward, and M. Asghari, “GHz-bandwidth optical filters based on high-order silicon ring resonators,” Opt. Express 18(23), 23784–23789 (2010). [CrossRef] [PubMed]

13.

N. Takato, T. Kominato, A. Sugita, K. Jinguji, H. Toba, and M. Kawachi, “Silica-based integrated optic Mach-Zehnder multi/demultiplexer family with channel spacing of 0.01-250 nm,” IEEE J. Sel. Areas Comm. 8(6), 1120–1127 (1990). [CrossRef]

14.

V. J. Urick, F. Bucholtz, J. D. McKinney, P. S. Devgan, A. L. Campillo, J. L. Dexter, and K. J. Williams, “Long-haul analog photonics,” J. Lightwave Technol. 29(8), 1182–1205 (2011). [CrossRef]

15.

I. Gasulla and J. Capmany, “Analytical model and figures of merit for filtered microwave photonic links,” Opt. Express 19(20), 19758–19774 (2011). [CrossRef] [PubMed]

16.

A. Agarwal, T. Banwell, and T. K. Woodward, “Optically filtered microwave photonic links for RF signal processing applications,” IEEE J. Lightw. Technol. 29(16), 2394–2401 (2011). [CrossRef]

17.

C. Madsen and J. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach (Wiley-Interscience, 1999), Chap. 4.

18.

S. Xiao, M. H. Khan, H. Shen, and M. Qi, “Compact silicon microring resonators with ultra-low propagation loss in the C band,” Opt. Express 15(22), 14467–14475 (2007). [CrossRef] [PubMed]

19.

P. Li, R. Shi, M. Chen, H. Chen, S. Yang, and S. Xie, “Downconversion and linearization of X- and K-band analog photonic links using digital post-compensation,” Optical Fiber Communication Conference 2013, paper JW2A.59 (2013).

20.

D. Vermeulen, S. Selvaraja, P. Verheyen, G. Lepage, W. Bogaerts, P. Absil, D. Van Thourhout, and G. Roelkens, “High-efficiency fiber-to-chip grating couplers realized using an advanced CMOS-compatible silicon-on-insulator platform,” Opt. Express 18(17), 18278–18283 (2010). [CrossRef] [PubMed]

21.

A. Biberman, M. J. Shaw, E. Timurdogan, J. B. Wright, and M. R. Watts, “Ultralow-loss silicon ring resonators,” Opt. Lett. 37(20), 4236–4238 (2012). [CrossRef] [PubMed]

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

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: January 28, 2013
Revised Manuscript: March 4, 2013
Manuscript Accepted: March 5, 2013
Published: March 11, 2013

Citation
Hongchen Yu, Minghua Chen, Pengxiao Li, Sigang Yang, Hongwei Chen, and Shizhong Xie, "Silicon-on-insulator narrow-passband filter based on cascaded MZIs incorporating enhanced FSR for downconverting analog photonic links," Opt. Express 21, 6749-6755 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-6-6749


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References

  1. D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, “Integrated microwave photonics,” arXiv:1211.4114 (2012).
  2. J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics1(6), 319–330 (2007). [CrossRef]
  3. J. Yao, “Microwave Photonics,” J. Lightwave Technol.27(3), 314–335 (2009). [CrossRef]
  4. B. Jalali and S. Fathpour, “Silicon Photonics,” IEEE J. Lightw. Technol.24(12), 4600–4615 (2006). [CrossRef]
  5. J. Capmany, J. Mora, I. Gasulla, J. Sancho, J. Lloret, and S. Sales, “Microwave photonic signal processing,” IEEE J. Lightw. Technol.31(4), 571–586 (2013). [CrossRef]
  6. P. Toliver, R. Menendez, T. 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. Ashghari, “A programmable optical filter unit cell element for high resolution RF signal processing in silicon photonics,” Optical Fiber Communication Conference 2010, paper OWJ4 (2010).
  7. 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]
  8. H. W. Chen, A. W. Fang, J. Bovington, J. Peters, and J. Bowers, “Hybrid silicon tunable filter based on a Mach-Zehnder interferometer and ring resonantor,” in Proc. Microwave Photonics, Valencia, Spain, 2009, pp. 1–4.
  9. S. S. Djordjevic, L. W. Luo, S. Ibrahim, N. K. Fontaine, C. B. Poitras, B. Guan, L. Zhou, K. Okamoto, Z. Ding, M. Lipson, and S. J. B. Yoo, “Fully reconfigurable silicon photonic lattice filters with four cascaded unit cells,” IEEE Photon. Technol. Lett.23(1), 42–44 (2011). [CrossRef]
  10. S. J. Xiao, M. H. Khan, H. Shen, and M. H. Qi, “Multiple-channel silicon micro-resonator based filters for WDM applications,” Opt. Express15(12), 7489–7498 (2007). [CrossRef] [PubMed]
  11. 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. Express15(22), 14765–14771 (2007). [CrossRef] [PubMed]
  12. P. Dong, N.-N. Feng, D. Feng, W. Qian, H. Liang, D. C. Lee, B. J. Luff, T. Banwell, A. Agarwal, P. Toliver, R. Menendez, T. K. Woodward, and M. Asghari, “GHz-bandwidth optical filters based on high-order silicon ring resonators,” Opt. Express18(23), 23784–23789 (2010). [CrossRef] [PubMed]
  13. N. Takato, T. Kominato, A. Sugita, K. Jinguji, H. Toba, and M. Kawachi, “Silica-based integrated optic Mach-Zehnder multi/demultiplexer family with channel spacing of 0.01-250 nm,” IEEE J. Sel. Areas Comm.8(6), 1120–1127 (1990). [CrossRef]
  14. V. J. Urick, F. Bucholtz, J. D. McKinney, P. S. Devgan, A. L. Campillo, J. L. Dexter, and K. J. Williams, “Long-haul analog photonics,” J. Lightwave Technol.29(8), 1182–1205 (2011). [CrossRef]
  15. I. Gasulla and J. Capmany, “Analytical model and figures of merit for filtered microwave photonic links,” Opt. Express19(20), 19758–19774 (2011). [CrossRef] [PubMed]
  16. A. Agarwal, T. Banwell, and T. K. Woodward, “Optically filtered microwave photonic links for RF signal processing applications,” IEEE J. Lightw. Technol.29(16), 2394–2401 (2011). [CrossRef]
  17. C. Madsen and J. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach (Wiley-Interscience, 1999), Chap. 4.
  18. S. Xiao, M. H. Khan, H. Shen, and M. Qi, “Compact silicon microring resonators with ultra-low propagation loss in the C band,” Opt. Express15(22), 14467–14475 (2007). [CrossRef] [PubMed]
  19. P. Li, R. Shi, M. Chen, H. Chen, S. Yang, and S. Xie, “Downconversion and linearization of X- and K-band analog photonic links using digital post-compensation,” Optical Fiber Communication Conference 2013, paper JW2A.59 (2013).
  20. D. Vermeulen, S. Selvaraja, P. Verheyen, G. Lepage, W. Bogaerts, P. Absil, D. Van Thourhout, and G. Roelkens, “High-efficiency fiber-to-chip grating couplers realized using an advanced CMOS-compatible silicon-on-insulator platform,” Opt. Express18(17), 18278–18283 (2010). [CrossRef] [PubMed]
  21. A. Biberman, M. J. Shaw, E. Timurdogan, J. B. Wright, and M. R. Watts, “Ultralow-loss silicon ring resonators,” Opt. Lett.37(20), 4236–4238 (2012). [CrossRef] [PubMed]

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