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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 7 — Mar. 31, 2008
  • pp: 4621–4630
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Resonance-splitting and enhanced notch depth in SOI ring resonators with mutual mode coupling

Ziyang Zhang, Matteo Dainese, Lech Wosinski, and Min Qiu  »View Author Affiliations


Optics Express, Vol. 16, Issue 7, pp. 4621-4630 (2008)
http://dx.doi.org/10.1364/OE.16.004621


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Abstract

Resonance-splitting and enhanced notch depth are experimentally demonstrated in micro-ring resonators on SOI platform as a result of the mutual mode coupling. This coupling can be generated either by the nanometer-scaled gratings along the ring sidewalls or by evanescent directional coupling between two concentric rings. The transmission spectra are fitted using the time-domain coupled mode analysis. Split-wavelength separation of 0.68 nm for the 5-µm-radius ring, notch depth of 40 dB for the 10-µm-radius ring, and intrinsic Q factor of 2.6×105 for the 20-µm-radius ring are demonstrated. Notch depth improvement larger than 25dB has been reached in the 40-39-µm-radius double-ring structure. The enhanced notch depth and increased modal area for the concentric rings might be promising advantages for bio-sensing applications.

© 2008 Optical Society of America

1. Introduction

Micro-ring resonators have found wide applications in optical filtering/add-drop multiplexing [1–4

1. B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, “Ultra-compact Si/SiO2 microring resonator optical channel dropping filters,” IEEE Photon. Technol. Lett. 10, 549–551 (1998). [CrossRef]

], signal processing [5–9

5. Q. Xu, V. R. Almeida, and M. Lipson, “Micrometer-scale all-optical wavelength converter on silicon,” Opt. Lett. 20, 2733 (2005). [CrossRef]

], bio-sensing [10–12

10. A. Ksendzov and Y. Lin, “Integrated optics ring-resonator sensors for protein detection,” Opt. Lett. 30, 3344–3346 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=ol-30-24-3344. [CrossRef]

], and so on. In most cases, high quality factor (Q) and deep transmission notches are desired. There have been many reports of high Q rings in silicon-on-insulator (SOI) structure [13–16

13. T. J. Kippenberg, S. M. Spillane, D. K. Armani, and K. J. Vahala, “High-Q ring resonators in thin siliconon-insulator,” Appl. Phys. Lett. 83, 797 (2003). [CrossRef]

]. However, there are still two main issues that are not fully addressed. Firstly, it is challenging to achieve deep notches (>30dB) in the transmission spectra for a single-waveguide-single-ring structure. To reach the “conventional critical” coupling, the ring resonator intrinsic quality factor (Qi) and coupling quality factor (Qe) with the waveguide must be equal and the resonant channel is then completely dropped. The ring/waveguide distance and their individual widths have to be carefully tuned for that purpose. Secondly, for small-radius rings, the free-spectral range is usually large, which limits the number of channels that can be adopted for operation. In this paper, we show that by introducing mutual mode coupling the above mentioned two issues can be improved. Depending on the strength of this mutual coupling, the transmission spectra can greatly enhance the notch depths and further split the resonance. The split resonances allow more wavelengths for signal processing and thus increase the system capacity [9

9. Z. Zhang, Q. Li, F. Liu, T. Ye, Y. Su, and M. Qiu, “Wavelength Conversion in a Silicon Mode-split Microring Resonator with 1G Data Rate,” accepted for oral presentation at the Conference on Lasers and Electro-Optics (CLEO, CTuT2) 2008.

].

We present two ways of generating the mutual mode coupling. In Section 2, we show the effects of nanometer-scaled gratings on the ring sidewalls. In Section 3, the directional mutual coupling takes place between two concentric rings. Both sections start with the time-domain coupled mode analysis [17–18

17. B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” IEEE J. Lightwave Technol. 15, 998 (1997). [CrossRef]

], followed by experimental demonstration.

2. Grating-assisted single-ring counter-directional mutual mode coupling

2.1 Coupled mode analysis

dadt=(jωa1τa)ajκaS+1jub
(1)

Similarly,

dbdt=(jωb1τb)bjκbS+2jua
(2)

S2=ejβL(S+1jκa*a)
(3)

and

S1=ejβL(S+2jκb*b)
(4)

Fig. 1. Schematic of a ring resonator side coupled to a waveguide. Wave propagating from left to right (S +1) in the waveguide only generates the counter-clockwise travelling mode a(t) in the ring. Clockwise travelling mode b(t) are coupled with a(t) by coefficient u due to the grating along the ring. The grating is indicated as the red dashed circle.

We study the steady-state solution and assume ejωt time dependence for the resonator and waveguide modes. With only input from port 1 and S +2=0, the power of the outgoing wave can be derived from Eq. (1)–(4).

S22=S+121κa2BAB+u22
(5)

where A=j(ωωa)+1τa and B=j(ωωb)+1τb .

The transfer function can be written as

T(ω)=S22S+12=DC2
(6)

where C=AB+u 2 and D=C-|κ 2 a|B.

From Eq. (6), the transfer function in general is not of Lorentzian shape. The Q value of the system cannot be estimated by the division of resonance frequency by 3dB bandwidth. The transmission spectrum has to be fitted to obtain the Q factors numerically.

Let’s consider the conventional case, when mutual coupling coefficient u=0.

T=1κa2A2=4(ωωa)2+(1Qae1Qai)24(ωωa)2+(1Qae+1Qai)2
(7)

When the intrinsic Q and coupling Q of mode a(t) become the same, i.e., when Qae=Qai, T becomes zero at resonant frequency and the channel is completely dropped. This is the conventional critical coupling.

Further on, let’s analyse the case when u≠0. To simplify the analysis, we assume the two travelling modes a(t) and b(t) are degenerate in the sense that their resonant frequencies and decay rates are the same, thus A=B. For complete channel drop, both the real part and imaginary part of D must equal zero.

Im{D}=0ω=ωa=ωb.
Re{D}=0u2=um2=ωaωb4Qb(1Qae1Qai).
(8)

Since u is a real number, Eq. (8) can only be satisfied when Qai>Qae. In Eq. (8), um is defined as the optimal mutual coupling coefficient.

Fig. 2. Illustration of the dependence of transmission spectra on the mutual coupling coefficient u. With the presence of mutual coupling, the notch becomes deeper. At optimal coupling um, complete channel drop can be reached. When u further increases, mode splitting occurs.

It is convenient to define a mutual coupling Q factor Qu, and a mutual coupling life time τu=1/|u|. Assume ωa=ωb=ω 0, Qu=ω0τu2=ω02u. .

When u=um, 1Qum2=1Qb(1Qae1Qai) .

For Qa=Qb, 1Qum2=1Qae21Qai2 .

Figure 5–3 illustrates the transmission properties when Qu→∞ (u=0), Qu>Qm (u2<um 2), Qu≈Qm (u2≈um 2) and Qu<Qm (u2>um 2) for the case when Qai>Qae and A=B.

2.2 Device fabrication

We use a commercial single-crystalline SOI wafer (SOI Tech) with top silicon layer thickness 250nm and silica buffer thickness 3µm. The waveguide and ring pattern is first defined in the electron beam lithography (Raith 150, 25kV) with the negative resist ma-N 2405. Pseudocircular scan mode is chosen for the exposure of the rings. In this scan mode, the ring area is broken down into concentric polygons. The corner of these polygons will give rise to the “nodes” along the ring after resist developing. These “nodes” naturally form a grating on the sidewalls. By setting up the number of the vertices (corners) of the polygons, the E-beam scan step size, and the exposure dose, the period and amplitude of the grating can be tuned. For the optimal case, the grating only helps mutual mode coupling and does not significantly deteriorate the intrinsic Q of the ring. The scanning electron microscopy (SEM) photo of the grating on the ring sidewall is shown in Fig. 3(a). The width of the grating ridge is ~20nm. The period extends from ~50 nm to ~100 nm. The grating provides a weak perturbation along the ring. This perturbation creates a small reflection, which accumulates and generates the counter-travelling modes.

Fig. 3. The SEM photo of (a) the grating on the side-walls of a 20-µm-radius ring resonator and (b) gold grating couplers at the tapered waveguide end to assist vertical light injection/detection with a single mode fiber.

Reactive ion plasma etching (ICP DRIE, STS) is then performed to transfer the pattern to the silicon layer. To couple light efficient from single mode fibre to silicon waveguide, gold gratings are added to both ends of the waveguides [19

19. S. Scheerlinck, J. Schrauwen, F. Van Laere, D. Taillaert, D. Van Thourhout, and R. Baets, “Efficient, broadband and compact metal grating couplers for silicon-on-insulator waveguides,” Opt. Express 15, 9625 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-15-9625. [CrossRef] [PubMed]

] during the single-resist-layer lift-off process. For period 590nm, filling factor 34% and thickness 25nm, the grating couples only TE light with an optimal fibre-to-fibre loss below 20 dB. The SEM photo of the gold grating coupler is shown in Fig. 3(b). The waveguide width starts with 10µm and gradually tapers down to 480nm. The ring cross-section is 480nm (wide) by 250nm (thick). The width of the air gap between the ring and waveguide is 100±10nm to ensure good coupling with the waveguide and thus Qae<Qai.

2.3 Experimental results

Figure 4 shows the SEM photo and measurement results of a 5-µm-radius ring, where obvious mode splitting occurs. The notches around 1550 nm are fitted using Eq. (6). The intrinsic Q value obtained is 6.0×104 and the coupling Q is 2.0×104. The mutual coupling Q of 2.27×103 is much smaller than Qum of 2.12×104, indicating a strong mutual coupling and thus mode splitting occurs. The split notches are still deeper than the case without mutual coupling (12dB compared to 6dB).

Fig. 4. (a) SEM photo of a 5-µm-radius ring. (b) broad spectrum transmission. (c) Curve fitting using Eq. (6) for one of the notch groups. The intrinsic Q value obtained is 6×104 and the coupling Q is 2×104. The split notches are deeper than the case without mutual coupling (12dB compared to 6dB).

Figure 5 shows the SEM photo and measurement results of a 10-µm-radius ring. The intrinsic Q value obtained is 1.5×105 and the coupling Q is 1.2×104. The Qu value obtained from curve fitting is 1.218×104, close to Qum 1.204×104, resulting in a notch depth of ~ 40 dB. Also note that the precision of the short-spectrum scan, as shown in Fig. 5(c), is much enhanced compared to the fast broad spectrum scan from 1530nm to 1580nm, where the notch bottom is missed due to insufficient scan points.

Fig. 5. (a) SEM photo of a 10-µm-radius ring. (b) broad spectrum transmission. (c) Curve fitting using Eq. (6) for one of the notch groups. The notch depth is much improved, 40dB compared to the case without mutual coupling, where the notch is barely visible.
Fig. 6. (a) SEM photo of a 20-µm-radius ring. (b) broad spectrum transmission. (c) Curve fitting using Eq. (6) for one of the notch groups. The intrinsic Q value obtained is 2.6×105 and the coupling Q is 1.9×104.

Figure 6 shows the SEM photo and measurement results of a 20-µm-radius ring. The intrinsic Q value goes up to 2.6×105. The obtained Qu value 2.15×104 is larger than Qum 1.91×104, and the notch depth is ~20dB.

3. Directional mutual mode coupling between two concentric rings

3.1 Coupled mode analysis

Since the deeper notch and mode splitting are the result of the secondary coupling between the ring resonator modes, it is possible to find another solution without generating the grating along the ring. The schematic is shown in Fig. 7. A second ring is placed, concentrically, inside the outer-ring. The waveguide/ring, ring/ring separation is set so that the waveguide mode only couples to one of the traveling mode in the outer-ring. The outer-ring mode then couples, along the same direction, with the inner-ring mode.

We redefine u as the mutual inter-ring coupling coefficient. From the same time-domain coupled mode analysis, Eqs. (1)–(4) can be re-written as

dadt=(jωa1τa)ajκaS+1jub
(9)
dbdt=(jωb1τb)bjua
(10)
S2=ejβL(S+1jκa*a)
(11)
S1=ejβLS+2
(12)
Fig. 7. Schematic of two concentric ring resonators side coupled to a waveguide. Wave propagating from left to right (S +1) in the waveguide only generates the counter-clockwise travelling mode a(t) in the outer ring. Counter-clockwise travelling mode b(t) in the inner ring can then be generated by evanescent directional coupling from a(t).

T(ω)=S22S+12=DC2
(6)

where A=j(ωωa)+1τa , B=j(ωωb)+1τb .

and C=AB+u 2, D=C-|κ 2 a|B.

Fig. 8. (a) SEM photo of a single 40-µm-radius ring. (b) SEM photo of a dual 40-39-µm-radius ring structure. (c) broad spectrum transmission for both cases. The double ring structure exhibits much enhanced notch depth. (d)-(e) Curve fitting for two of the deep notches using Eq. (6).

3.2 Experimental results

The magnitude of the mutual inter-ring coupling coefficient mainly depends on the perimeters of the rings and the separation width between them. Here we experimentally demonstrate the enhancement of notch depth by use of a second ring. The results and SEM photos are shown in Fig. 8. The outer ring has a radius of 40 µm. The inner ring radius is 39 µm. The waveguide/ring gap width is 150 nm and the ring/ring gap width is 480 nm. In Fig. 8 (d)–(e) the curves were fitted using Eq. (6) assuming A=B.

The scan-mode in electron beam lithography has been switched to real circular scan and the periodic nodes have disappeared. The coupling between the propagating and counter-propagating modes in the individual ring is thus eliminated. Therefore, the notches appear very shallow, around 1-3dB, in the transmission spectrum for the single ring structure, seen as the black solid curve in Fig. 8(c). However, by adopting a second ring and allowing inter-ring mutual coupling, the notch depths are much improved to 25-30dB, seen as the red dashed curve in Fig. 8(c) and Fig. 8(d)–(e). For the notch around 1549.6nm, the intrinsic Q and coupling Q are estimated to be 1.6×105 and 1.3×104, respectively.

4. Conclusion

Acknowledgments

This work is supported by the Swedish Foundation for Strategic Research (SSF) through the INGVAR program, the SSF Strategic Research Center in Photonics, and the Swedish Research Council (VR).

References and links

1.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, “Ultra-compact Si/SiO2 microring resonator optical channel dropping filters,” IEEE Photon. Technol. Lett. 10, 549–551 (1998). [CrossRef]

2.

F. 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, 11934–11941 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-19-11934. [CrossRef] [PubMed]

3.

M. S. Nawrocka, T. Liu, X. Wang, and R. R. Panepucci, “Tunable silicon microring resonator with wide free spectral range,” Appl. Phys. Lett. 89, 071110 (2006). [CrossRef]

4.

B. Timotijevic, F. Gardes, W. Headley, G. Reed, M. Paniccia, O. Cohen, D. Hak, and G. Masanovic, “Multi-stage racetrack resonator filters in silicon-on-insulator,” J. Opt. A: Pure Appl. Opt. 8S473–S476 (2006). [CrossRef]

5.

Q. Xu, V. R. Almeida, and M. Lipson, “Micrometer-scale all-optical wavelength converter on silicon,” Opt. Lett. 20, 2733 (2005). [CrossRef]

6.

F. Xia, L. Sekaric, and Yu. A. Vlasov, “Ultra-compact optical buffers on a silicon chip,” Nature Photon. 1, 65–71 (2007). [CrossRef]

7.

B. Lee, B. Small, K. Bergman, Q. Xu, and M. Lipson, “Transmission of high-data-rate optical signals through a micrometer-scale silicon ring resonator,” Opt. Lett. 31, 2701 (2006). [CrossRef] [PubMed]

8.

F. Liu, Q. Li, Z. Zhang, M. Qiu, and Y. Su, “Optically Tunable Delay Line in Silicon Microring Resonator Based on Thermal Nonlinear Effect,” to be published in IEEE J. Sel. Top. Quantum Electron. (2008).

9.

Z. Zhang, Q. Li, F. Liu, T. Ye, Y. Su, and M. Qiu, “Wavelength Conversion in a Silicon Mode-split Microring Resonator with 1G Data Rate,” accepted for oral presentation at the Conference on Lasers and Electro-Optics (CLEO, CTuT2) 2008.

10.

A. Ksendzov and Y. Lin, “Integrated optics ring-resonator sensors for protein detection,” Opt. Lett. 30, 3344–3346 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=ol-30-24-3344. [CrossRef]

11.

K. De Vos, I. Bartolozzi, E. Schacht, P. Bienstman, and R. Baets, “Silicon-on-Insulator microring resonator for sensitive and label-free biosensing,” Opt. Express 15, 7610–7615 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-12-7610. [CrossRef] [PubMed]

12.

I. White, H. Oveys, X. Fan, T. Smith, and J. Zhang, “Integrated multiplexed biosensors based on liquid core optical ring resonators and antiresonant reflecting optical waveguides,” Appl. Phys. Lett. 89, 191106 (2006). [CrossRef]

13.

T. J. Kippenberg, S. M. Spillane, D. K. Armani, and K. J. Vahala, “High-Q ring resonators in thin siliconon-insulator,” Appl. Phys. Lett. 83, 797 (2003). [CrossRef]

14.

J. Niehusmann, A. Vörckel, P. H. Bolivar, T. Wahlbrink, W. Henschel, and H. Kurz, “Ultrahigh-quality-factor silicon-on-insulator microring resonator,” Opt. Lett. 29, 2861 (2004). [CrossRef]

15.

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, 14467 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-22-14467. [CrossRef] [PubMed]

16.

P. Dumon, W. Bogaerts, V. Wiaux, J. Wouters, S. Beckx, J. V. Campenhout, D. Taillaert, B. Luyssaert, P. Bienstman, D. V. Thourhout, and R. Baets, “Low-Loss SOI Photonic Wires and Ring Resonators Fabricated With Deep UV Lithography,” IEEE Photon. Technol. Lett. 16, 1328 (2004). [CrossRef]

17.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” IEEE J. Lightwave Technol. 15, 998 (1997). [CrossRef]

18.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of Modes Analysis of Resonant Channel Add-Drop Filters,” IEEE J. Quantum Electron. 35, 1322 (1999). [CrossRef]

19.

S. Scheerlinck, J. Schrauwen, F. Van Laere, D. Taillaert, D. Van Thourhout, and R. Baets, “Efficient, broadband and compact metal grating couplers for silicon-on-insulator waveguides,” Opt. Express 15, 9625 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-15-9625. [CrossRef] [PubMed]

OCIS Codes
(230.3990) Optical devices : Micro-optical devices
(230.5750) Optical devices : Resonators
(250.5300) Optoelectronics : Photonic integrated circuits

ToC Category:
Optical Devices

History
Original Manuscript: February 12, 2008
Revised Manuscript: March 11, 2008
Manuscript Accepted: March 14, 2008
Published: March 19, 2008

Virtual Issues
Vol. 3, Iss. 4 Virtual Journal for Biomedical Optics

Citation
Ziyang Zhang, Matteo Dainese, Lech Wosinski, and Min Qiu, "Resonance-splitting and enhanced notch depth in SOI ring resonators with mutual mode coupling," Opt. Express 16, 4621-4630 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-7-4621


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References

  1. B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, "Ultra-compact Si/SiO2 microring resonator optical channel dropping filters," IEEE Photon. Technol. Lett. 10, 549-551 (1998). [CrossRef]
  2. F. 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, 11934-11941 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-19-11934. [CrossRef] [PubMed]
  3. M. S. Nawrocka, T. Liu, X. Wang, and R. R. Panepucci, "Tunable silicon microring resonator with wide free spectral range," Appl. Phys. Lett. 89, 071110 (2006). [CrossRef]
  4. B. Timotijevic, F. Gardes, W. Headley, G. Reed, M. Paniccia, O. Cohen, D. Hak, and G. Masanovic, "Multi-stage racetrack resonator filters in silicon-on-insulator," J. Opt. A: Pure Appl. Opt. 8S473-S476 (2006). [CrossRef]
  5. Q. Xu, V. R. Almeida, and M. Lipson, "Micrometer-scale all-optical wavelength converter on silicon," Opt. Lett. 20, 2733 (2005). [CrossRef]
  6. F. Xia, L. Sekaric, and Yu. A. Vlasov, "Ultra-compact optical buffers on a silicon chip," Nature Photon. 1, 65-71 (2007). [CrossRef]
  7. B. Lee, B. Small, K. Bergman, Q. Xu, and M. Lipson, "Transmission of high-data-rate optical signals through a micrometer-scale silicon ring resonator," Opt. Lett. 31, 2701 (2006). [CrossRef] [PubMed]
  8. F. Liu, Q. Li, Z. Zhang, M. Qiu, and Y. Su, "Optically Tunable Delay Line in Silicon Microring Resonator Based on Thermal Nonlinear Effect," to be published in IEEE J. Sel. Top. Quantum Electron. (2008).
  9. Z. Zhang, Q. Li, F. Liu, T. Ye, Y. Su, and M. Qiu, "Wavelength Conversion in a Silicon Mode-split Micro-ring Resonator with 1G Data Rate," accepted for oral presentation at the Conference on Lasers and Electro-Optics (CLEO, CTuT2) 2008.
  10. A. Ksendzov and Y. Lin, "Integrated optics ring-resonator sensors for protein detection," Opt. Lett. 30, 3344-3346 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=ol-30-24-3344. [CrossRef]
  11. K. De Vos, I. Bartolozzi, E. Schacht, P. Bienstman, and R. Baets, "Silicon-on-Insulator microring resonator for sensitive and label-free biosensing," Opt. Express 15, 7610-7615 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-12-7610. [CrossRef] [PubMed]
  12. I. White, H. Oveys, X. Fan, T. Smith, and J. Zhang, "Integrated multiplexed biosensors based on liquid core optical ring resonators and antiresonant reflecting optical waveguides," Appl. Phys. Lett. 89, 191106 (2006). [CrossRef]
  13. T. J. Kippenberg, S. M. Spillane, D. K. Armani, and K. J. Vahala, "High-Q ring resonators in thin silicon-on-insulator," Appl. Phys. Lett. 83, 797 (2003). [CrossRef]
  14. J. Niehusmann, A. Vörckel, P. H. Bolivar, T. Wahlbrink, W. Henschel, and H. Kurz, "Ultrahigh-quality-factor silicon-on-insulator microring resonator," Opt. Lett. 29, 2861 (2004). [CrossRef]
  15. 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, 14467 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-22-14467. [CrossRef] [PubMed]
  16. P. Dumon, W. Bogaerts, V. Wiaux, J. Wouters, S. Beckx, J. V. Campenhout, D. Taillaert, B. Luyssaert, P. Bienstman, D. V. Thourhout, and R. Baets, "Low-Loss SOI Photonic Wires and Ring Resonators Fabricated With Deep UV Lithography," IEEE Photon. Technol. Lett. 16, 1328 (2004). [CrossRef]
  17. B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, "Microring resonator channel dropping filters," IEEE J. Lightwave Technol. 15, 998 (1997). [CrossRef]
  18. C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, "Coupling of Modes Analysis of Resonant Channel Add-Drop Filters," IEEE J. Quantum Electron. 35, 1322 (1999). [CrossRef]
  19. S. Scheerlinck, J. Schrauwen, F. Van Laere, D. Taillaert, D. Van Thourhout, and R. Baets, "Efficient, broadband and compact metal grating couplers for silicon-on-insulator waveguides," Opt. Express 15, 9625 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-15-9625. [CrossRef] [PubMed]

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