Ultra-compact, high-Q silicon microdisk reflectors

doi:10.1364/OE.20.021840

Ultra-compact, high-Q silicon microdisk reflectors

Wei Shi, Han Yun, Wen Zhang, Charlie Lin, Ting Kai Chang, Yun Wang, Nicolas A. F. Jaeger, and Lukas Chrostowski »View Author Affiliations

Optics Express, Vol. 20, Issue 20, pp. 21840-21846 (2012)
http://dx.doi.org/10.1364/OE.20.021840

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– Abstract
1. Introduction
2. Design and simulation
3. Experiment and results
4. Multichannel reflective sensing system
5. Conclusions
– References and links

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Abstract

We demonstrate wavelength-selective reflectors based on silicon microdisk resonators integrated with compact Y-branch splitters, using a CMOS-photonics technology. A high quality factor (Q) of ∼ 88,000 was measured in the reflection spectrum for a 2.5-μm-radius device with a small footprint of 6 × 17 μm² and a wide free-spectral range (FSR) of over 41 nm. As the radius is reduced to 1.5 μm, corresponding to a device footprint of 4 × 15 μm², the spectrum shows an ultra-wide FSR of over 71 nm with the compromise of having a reduced Q of ∼ 4000. The coupling between a microdisk and a waveguide is numerically investigated. We further propose a multichannel sensing system using cascaded microdisk reflectors.

1. Introduction

Traveling-wave resonators (TWRs) have been used for implementing a variety of wavelength-selective reflectors, including reflective band-pass filters [1

Y. Chung, D.-G. Kim, and N. Dagli, “Reflection properties of coupled-ring reflectors,” J. Lightwave Technol. 24, 1865–1874 (2006). [CrossRef]

–5

I. Chremmos and N. Uzunoglu, “Reflective properties of double-ring resonator system coupled to a waveguide,” IEEE Photon. Technol. Lett. 17, 2110–2112 (2005). [CrossRef]

] and reflective notch filters [6

H. Sun, A. Chen, and L. R. Dalton, “A reflective microring notch filter and sensor,” Opt. Express 17, 10731–10737 (2009). [CrossRef] [PubMed]

, 7

W. Shi, R. Vafaei, M. Á. G. Torres, N. A. F. Jaeger, and L. Chrostowski, “Design and characterization of microring reflectors with a waveguide crossing,” Opt. Lett. 35, 2901–2903 (2010). [CrossRef] [PubMed]

]. These TWR reflectors are promising for applications such as tunable lasers [8

T. Chu, N. Fujioka, and M. Ishizaka, “Compact, lower-power-consumption wavelength tunable laser fabricated with silicon photonic-wire waveguide micro-ring resonators,” Opt. Express 17, 14063–14068 (2009). [CrossRef] [PubMed]

, 9

J. Scheuer, G. T. Paloczi, and A. Yariv, “All optically tunable wavelength-selective reflector consisting of coupled polymeric microring resonators,” Appl. Phys. Lett. 87, 251102–251102–3 (2005). [CrossRef]

], thermal and biological sensors [6

H. Sun, A. Chen, and L. R. Dalton, “A reflective microring notch filter and sensor,” Opt. Express 17, 10731–10737 (2009). [CrossRef] [PubMed]

, 7

], wavelength-devision multiplexing (WDM) drop filters [10

V. Van, “Dual-mode microring reflection filters,” J. Lightwave Technol. 25, 3142–3150 (2007). [CrossRef]

], and reflective optical modulators. A main advantage of TWRs over Bragg gratings lies in the device miniaturization, for which there has been much effort for the silicon platform due to its great potential for large-scale electronic-photonic integration [11

W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert, B. Luyssaert, J. V. Campenhout, P. Bienstman, and D. V. Thourhout, “Nanophotonic waveguides in silicon-on-insulator fabricated with CMOS technology,” J. Lightwave Technol. 23, 401–412 (2005). [CrossRef]

, 12

L. Chrostowski, S. Grist, J. Flueckiger, W. Shi, X. Wang, E. Ouellet, H. Yun, M. Webb, B. Nie, Z. Liang, K. C. Cheung, A. S. S, D. M. Ratner, and N. A. F. Jaeger, “Silicon photonic resonator sensors and devices,” Proceedings of SPIE 8236, 823620 (2012). [CrossRef]

]. Most of the TWR reflectors demonstrated so far are based on microring resonators [1

Y. Chung, D.-G. Kim, and N. Dagli, “Reflection properties of coupled-ring reflectors,” J. Lightwave Technol. 24, 1865–1874 (2006). [CrossRef]

–10

V. Van, “Dual-mode microring reflection filters,” J. Lightwave Technol. 25, 3142–3150 (2007). [CrossRef]

]. Compared with microrings, microdisks can have smaller footprints, wider free-spectral ranges (FSRs), and higher quality factors (Q’s) [13

M. Soltani, Q. Li, S. Yegnanarayanan, and A. Adibi, “Toward ultimate miniaturization of high Q silicon traveling-wave microresonators,” Opt. Express 18, 19541–19557 (2010). [CrossRef] [PubMed]

]. These advantages are desirable for WDM and sensing applications; wider FSRs allow more channels and larger detection ranges; for TWR-based tunable WDM filters and lasers [14

G. Yoffe, T. Nguyen, J. Heanue, and B. Pezeshki, “Efficient compact tunable laser for access networks using silicon ring resonators,” OFC/NFOEC, Los Angeles, CA, USA OW1G.4 (2012).

], the power needed to shift the spectrum of a TWR by one FSR is independent of the roundtrip length [15

J. E. Cunningham, I. Shubin, X. Zheng, T. Pinguet, A. Mekis, Y. Luo, H. Thacker, G. Li, J. Yao, K. Raj, and A. V. Krishnamoorthy, “Highly-efficient thermally-tuned resonant optical filters,” Opt. Express 18, 19055–19063 (2010). [CrossRef] [PubMed]

], therefore, smaller radii indicate higher tuning efficiency (in nm/W).

In this paper, we present narrow-bandwidth reflectors using silicon microdisk resonators, fabricated using a CMOS-photonic technology. We have adopted the scheme of integrating a TWR and two Y-branch splitters to obtain wavelength-selective reflection, which was first demonstrated by Paloczi et al. using a polymer microring with a large radius of ∼ 100 μm and a small FSR of ∼ 2 nm [2

G. T. Paloczi, J. Scheuer, and A. Yariv, “Compact microring-based wavelength-selective inline optical reflector,” IEEE Photon. Technol. Lett. 17, 390–392 (2005). [CrossRef]

]. The use of microdisks in our design gives rise to numerous advantages, as mentioned above, including μm-scale miniaturization and ultra-wide FSRs covering the entire span of the C-band in optical communications. The implementation of our devices on the silicon platform indicates great potential for integration with other electronic and photonic devices. We also present numerical modeling of the coupling between a waveguide and a microdisk using the 3D finite-difference time-domain (FDTD) method. Finally, we propose a multichannel reflective sensing system.

2. Design and simulation

2.1. Device structure

Figure 1 shows the proposed reflector that consists of a silicon microdisk resonator and two Y-branch splitters. As shown in Fig. 1, the input light is split by the first Y-branch splitter into two beams that travel through the microdisk in the clockwise and counter-clockwise directions, respectively. The resonant wavelengths are dropped by the opposite-side waveguides and then recombined by the first Y-branch splitter as the reflected signals. The other wavelengths are recombined by the second Y-branch splitter at the transmission port. Assuming ideally symmetric splitters, the reflector’s transmission and reflection should be the same as the through and drop responses, respectively, of a microdisk add-drop filter. For example, Fig. 1(b) shows the simulated spectra of a microdisk reflector using the transfer functions of TWR add-drop filters [16

D. G. Rabus, Integrated Ring Resonators (Springer, 2007).

] and the coupling coefficients calculated using the method discussed below.

Fig. 1 (a) Perspective view of a microdisk reflector. (b) Simulated spectra (1st-order TE-like transverse mode) of a microdisk reflector with R = 2.5 μm and G = 200 nm, assuming ideal 3-dB Y-branch splitters and a propagation loss of α = 1 dB/cm.

The devices demonstrated below are made of silicon with a height of 220 nm. The Y-branch splitter uses two 500-nm-wide, S-shape strip waveguides, with a bend radius of 5 μm, tangentially contacting each other. This S-bend design enables a compact size and an adjustable opening width of the Y-branch splitter. The branches are tapered to 400-nm-wide bus waveguides of the microdisk for more efficient coupling between the bus waveguides and the resonator.

2.2. Numerical simulation of the bus-microdisk coupling

Transverse and longitudinal modes of a microdisk can be found using a mode solver or the FDTD method [12

]. The bus-resonator coupling condition is critical to a TWR’s transmission properties, such as extinction ratio and Q [17

A. Yariv, “Critical coupling and its control in optical waveguide-ring resonator systems,” IEEE Photon. Technol. Lett. 14, 483–485 (2002). [CrossRef]

]. The coupling coefficients can be calculated using coupled-mode analysis [18

M. Soltani, S. Yegnanarayanan, Q. Li, and A. Adibi, “Systematic engineering of waveguide-resonator coupling for silicon microring/microdisk/racetrack resonators: theory and experiment,” IEEE J. Quantum Electron. 46, 1158–1169 (2010). [CrossRef]

], however, it does not consider the effect of phase perturbations of the bus waveguide and the resonator. Such perturbations can be important as they make the coupling more dispersive [18

]. The 3D-FDTD method does not have the approximation of no phase-perturbation; thus, its accuracy is only limited by numerical errors.

The microdisk, even with a very small radius, down to a couple of μm, still has multiple whispering gallery modes (WGMs). In order to distinguish a specific mode (fundamental mode in this case) from other WGMs, we use a wide bent waveguide to approximate the microdisk in the 3D-FDTD simulation of the bus-microdisk coupling, as illustrated in Fig. 2(a), with the selected mode imported from a mode solver as the input optical source. The 1st and 2nd TE-like modes of a microdisk (R = 2.5 μm), calculated using the mode solver, are shown in Fig. 2(b). We can see that the electric field of the fundamental mode approaches zero ∼ 1 μm away from the disk edge, which indicates that the mode profile is hardly affected if the microdisk is replaced by a bent waveguide wider than 1 μm. This method is verified numerically in Fig. 2(c) where we can see that the effective index of the fundamental mode becomes constant when the bent waveguide is wider than 1 μm. A width of 1.2 μm is chosen in the 3D-FDTD calculation of the coupling coefficient. The calculated quality factor due to the bus-microdisk coupling (Q_c) is shown in Fig. 2(d), with Q_c = −(πLn_g)/(λlog|t|) where L, n_g, λ, and t are the roundtrip length of the microdisk, the group index, the wavelength, and the straight-through coupling coefficient, respectively. It is worth pointing out that, even though the microdisk can be treated as a multimode waveguide in simulation, the disk geometry enables many applications; for example, the disk center can be used as a support in an undercut structure or be metalized for thermal or electrical tuning.

Fig. 2 Simulation of a microdisk resonator with R = 2.5 μm: (a) perspective view of the FDTD model (with the perfect-matched-layer boundary condition) used to obtain the coupling coefficient of the 1st TE-like mode (the arrow indicates the position of the imported mode source and the insets show the optical intensity profiles recorded by the monitors); (b) mode profiles of the first two TE-like modes with silica cladding; (c) calculated effective indices of the first two TE-like modes of a bent waveguide as functions of the waveguide width; (d) calculated Q_c as a function of λ for various coupler gaps and claddings.

3. Experiment and results

The devices were fabricated using a CMOS-compatible technology with 193-nm optical projection lithography by Imec, Belgium accessed via ePIXfab. The measurement schematic is shown in Fig. 3. Fiber grating couplers [11

], designed for TE polarization, were used for measurement.

Fig. 3 Measurement schematic. The insets show the SEM images of a Y-branch splitter, for the reflection measurement, and an S-bend Y-branch splitter, with a 5-μm-opening, used in the microdisk reflector.

3.1. Transmission and reflection spectra

Figure 4 shows the measured transmission and reflection spectra of an air-clad device with a radius, R, of 2.5 μm and a gap between the microdisk resonator and the bus waveguide, G, of 200 nm. Although the microdisk resonator intrinsically has multiple transverse modes, only the fundamental mode is effectively excited due to the very weak coupling between the bus waveguides and the higher-order modes in the microdisk resonator. The FSR between the resonant peaks at 1492.37 nm and 1533.1 nm is about 41.6 nm. As shown in Fig. 4(a), the 3-dB bandwidth of the reflection spectrum at 1492.37 nm is about 17 pm, corresponding to a high Q of ∼ 88,000. Using the calculated coupling coefficient or Q_c, the intrinsic quality factor, Q_i, is estimated to be over 10⁵. Figure 5 shows the measured spectra of another device with a smaller radius of 1.5-μm and an ultra-wide FSR of over 71 nm. The device has a very small effective area, including one microdisk resonator (∼ 4×3 μm²) and two Y-branch splitters (∼ 4×6 μm² each), of approximately 4 × 15 μm². The 3-dB bandwidth of the reflection spectrum, shown in Fig. 5(b), is about 0.37 nm, corresponding to a Q of ∼ 4,000, much lower than the 2.5-μm-radius device; this indicates higher losses due to the smaller radius.

Fig. 4 Measured spectra of a microdisk reflector with R ≃ 2.5 μm and G ≃ 200 nm: (a) transmission and reflection spectra (the inset shows an SEM image of the microdisk resonator); (b) spectra zoomed in near the resonant wavelength.

Fig. 5 Measured spectra of a silica-clad microdisk reflector with R ≃ 1.5 μm and G ≃ 160 nm: (a) transmission and reflection spectra (the insets show SEM images of an air-clad device with the same radius); (b) spectra zoomed in near the resonant wavelength.

3.2. Loss measurement of Y-branch splitters using ring resonators

The insertion losses of the reflectors mainly come from the Y-branch splitters. The conventional method for measuring losses of optical components, such as waveguide crossings and Y-branch splitters, is to cascade a series of these components and measure their total transmission [11

]. It usually requires multiple measurements to compensate the uncertainty in the fiber-waveguide coupling. In addition, it may have significant errors when the measured losses are comparable with or smaller than the fiber-waveguide coupling losses. Here we use a microring-based technique. Our method is to characterize spectral responses of mircroring resonators, with a number of Y-branches inserted inside the ring resonators, and to subtract the round-trip loss by fitting the measured transmission spectrum. This method relies only on the shape of the spectra, not the insertion floor, and, therefore, is not affected by the fiber-waveguide coupling losses. The measured and fit spectra of a reference ring resonator are shown in Fig. 6(a), for which the roundtrip loss is determined to be 0.4 dB. Figure 6(b) shows the measured and fit spectra of another ring resonator with two pairs of Y-branch splitters inserted in the optical cavity, for which the round-trip loss is determined to be 6 dB. The excess loss induced by the Y-branch splitters is then extracted and found to be 5.6 dB, which implies an insertion loss of 1.3 dB per Y-branch splitter. This causes a loss of over 2.6 dB in each reflector, as well as undesired reflections in the optical circuit, which can be significantly reduced by optimizing the Y-branch splitters.

Fig. 6 Measured and fit transmission spectra of: (a) a ring resonator; (b) a ring resonator with 2 pairs of Y-branch splitters.The insets show the device geometries.

4. Multichannel reflective sensing system

Reflective filters, combined with a single optical fiber delivering both input and output signals, are particularly useful for remote sensing applications [6

H. Sun, A. Chen, and L. R. Dalton, “A reflective microring notch filter and sensor,” Opt. Express 17, 10731–10737 (2009). [CrossRef] [PubMed]

, 7

]. Here we propose a multichannel reflective sensing system, shown in Fig. 7, using cascaded microdisk resonators with slightly different radii. Due to their ultra-wide FSRs, the demonstrated microdisk reflectors will enable more channels than microring resonators do in a cascaded sensing system [12

]. Furthermore, since all the microdisk resonators share one Y-branch splitter, the average footprint of each channel will be mainly determined by the microdisk resonators.

Fig. 7 Sensing system using cascaded microdisk reflectors and an optical circulator.

5. Conclusions

In summary, we have demonstrated wavelength-selective reflectors using microdisk resonators integrated with Y-branch splitters. A high Q of 88,000 (Q_i over 10⁵) has been measured for a 2.5-μm-radius device. With small footprints, high quality factors, and wide FSRs, these devices are promising for next-generation, on-chip applications. In particular, they can be used as high-sensitivity, wide-range sensors for harsh or special circumstances where a single input/output fiber is preferred [6

H. Sun, A. Chen, and L. R. Dalton, “A reflective microring notch filter and sensor,” Opt. Express 17, 10731–10737 (2009). [CrossRef] [PubMed]

, 7

]. We have also demonstrated a technique, using microring resonators, for accurate loss measurement of photonic components, that is insensitive to fiber-waveguide coupling errors. Using the demonstrated high-Q, wide-FSR microdisk reflectors, we have proposed a cascaded-resonator system that is promising for multichannel sensing applications.

Acknowledgments

We acknowledge S. Grist and M. Greenberg for the SEM images, CMC Microsystems for the fabrication support, Lumerical Solutions Inc. for the design softwares (MODE Solutions and FDTD Solutions), Design Workshop Technologies Inc. for the mask layout software, and the Natural Sciences and Engineering Research Council of Canada for their financial support.

References and links

1.	Y. Chung, D.-G. Kim, and N. Dagli, “Reflection properties of coupled-ring reflectors,” J. Lightwave Technol. 24, 1865–1874 (2006). [CrossRef]
2.	G. T. Paloczi, J. Scheuer, and A. Yariv, “Compact microring-based wavelength-selective inline optical reflector,” IEEE Photon. Technol. Lett. 17, 390–392 (2005). [CrossRef]
3.	J. K. S. Poon, J. Scheuer, and A. Yariv, “Wavelength-selective reflector based on a circular array of coupled microring resonators,” IEEE Photon. Technol. Lett. 16, 1331–1333 (2004). [CrossRef]
4.	A. Arbabi, Y. M. Kang, C.-Y. Lu, E. Chow, and L. L. Goddard, “Realization of a narrowband single wavelength microring mirror,” Appl. Phys. Lett. 99, 091105–091105–3 (2011). [CrossRef]
5.	I. Chremmos and N. Uzunoglu, “Reflective properties of double-ring resonator system coupled to a waveguide,” IEEE Photon. Technol. Lett. 17, 2110–2112 (2005). [CrossRef]
6.	H. Sun, A. Chen, and L. R. Dalton, “A reflective microring notch filter and sensor,” Opt. Express 17, 10731–10737 (2009). [CrossRef] [PubMed]
7.	W. Shi, R. Vafaei, M. Á. G. Torres, N. A. F. Jaeger, and L. Chrostowski, “Design and characterization of microring reflectors with a waveguide crossing,” Opt. Lett. 35, 2901–2903 (2010). [CrossRef] [PubMed]
8.	T. Chu, N. Fujioka, and M. Ishizaka, “Compact, lower-power-consumption wavelength tunable laser fabricated with silicon photonic-wire waveguide micro-ring resonators,” Opt. Express 17, 14063–14068 (2009). [CrossRef] [PubMed]
9.	J. Scheuer, G. T. Paloczi, and A. Yariv, “All optically tunable wavelength-selective reflector consisting of coupled polymeric microring resonators,” Appl. Phys. Lett. 87, 251102–251102–3 (2005). [CrossRef]
10.	V. Van, “Dual-mode microring reflection filters,” J. Lightwave Technol. 25, 3142–3150 (2007). [CrossRef]
11.	W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert, B. Luyssaert, J. V. Campenhout, P. Bienstman, and D. V. Thourhout, “Nanophotonic waveguides in silicon-on-insulator fabricated with CMOS technology,” J. Lightwave Technol. 23, 401–412 (2005). [CrossRef]
12.	L. Chrostowski, S. Grist, J. Flueckiger, W. Shi, X. Wang, E. Ouellet, H. Yun, M. Webb, B. Nie, Z. Liang, K. C. Cheung, A. S. S, D. M. Ratner, and N. A. F. Jaeger, “Silicon photonic resonator sensors and devices,” Proceedings of SPIE 8236, 823620 (2012). [CrossRef]
13.	M. Soltani, Q. Li, S. Yegnanarayanan, and A. Adibi, “Toward ultimate miniaturization of high Q silicon traveling-wave microresonators,” Opt. Express 18, 19541–19557 (2010). [CrossRef] [PubMed]
14.	G. Yoffe, T. Nguyen, J. Heanue, and B. Pezeshki, “Efficient compact tunable laser for access networks using silicon ring resonators,” OFC/NFOEC, Los Angeles, CA, USA OW1G.4 (2012).
15.	J. E. Cunningham, I. Shubin, X. Zheng, T. Pinguet, A. Mekis, Y. Luo, H. Thacker, G. Li, J. Yao, K. Raj, and A. V. Krishnamoorthy, “Highly-efficient thermally-tuned resonant optical filters,” Opt. Express 18, 19055–19063 (2010). [CrossRef] [PubMed]
16.	D. G. Rabus, Integrated Ring Resonators (Springer, 2007).
17.	A. Yariv, “Critical coupling and its control in optical waveguide-ring resonator systems,” IEEE Photon. Technol. Lett. 14, 483–485 (2002). [CrossRef]
18.	M. Soltani, S. Yegnanarayanan, Q. Li, and A. Adibi, “Systematic engineering of waveguide-resonator coupling for silicon microring/microdisk/racetrack resonators: theory and experiment,” IEEE J. Quantum Electron. 46, 1158–1169 (2010). [CrossRef]

OCIS Codes
(120.5700) Instrumentation, measurement, and metrology : Reflection
(130.6010) Integrated optics : Sensors
(230.7020) Optical devices : Traveling-wave devices
(230.4555) Optical devices : Coupled resonators
(130.7408) Integrated optics : Wavelength filtering devices

ToC Category:
Integrated Optics

History
Original Manuscript: July 6, 2012
Revised Manuscript: August 14, 2012
Manuscript Accepted: August 23, 2012
Published: September 10, 2012

Citation
Wei Shi, Han Yun, Wen Zhang, Charlie Lin, Ting Kai Chang, Yun Wang, Nicolas A. F. Jaeger, and Lukas Chrostowski, "Ultra-compact, high-Q silicon microdisk reflectors," Opt. Express 20, 21840-21846 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-20-21840

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References

Y. Chung, D.-G. Kim, and N. Dagli, “Reflection properties of coupled-ring reflectors,” J. Lightwave Technol.24, 1865–1874 (2006). [CrossRef]
G. T. Paloczi, J. Scheuer, and A. Yariv, “Compact microring-based wavelength-selective inline optical reflector,” IEEE Photon. Technol. Lett.17, 390–392 (2005). [CrossRef]
J. K. S. Poon, J. Scheuer, and A. Yariv, “Wavelength-selective reflector based on a circular array of coupled microring resonators,” IEEE Photon. Technol. Lett.16, 1331–1333 (2004). [CrossRef]
A. Arbabi, Y. M. Kang, C.-Y. Lu, E. Chow, and L. L. Goddard, “Realization of a narrowband single wavelength microring mirror,” Appl. Phys. Lett.99, 091105–091105–3 (2011). [CrossRef]
I. Chremmos and N. Uzunoglu, “Reflective properties of double-ring resonator system coupled to a waveguide,” IEEE Photon. Technol. Lett.17, 2110–2112 (2005). [CrossRef]
H. Sun, A. Chen, and L. R. Dalton, “A reflective microring notch filter and sensor,” Opt. Express17, 10731–10737 (2009). [CrossRef] [PubMed]
W. Shi, R. Vafaei, M. Á. G. Torres, N. A. F. Jaeger, and L. Chrostowski, “Design and characterization of microring reflectors with a waveguide crossing,” Opt. Lett.35, 2901–2903 (2010). [CrossRef] [PubMed]
T. Chu, N. Fujioka, and M. Ishizaka, “Compact, lower-power-consumption wavelength tunable laser fabricated with silicon photonic-wire waveguide micro-ring resonators,” Opt. Express17, 14063–14068 (2009). [CrossRef] [PubMed]
J. Scheuer, G. T. Paloczi, and A. Yariv, “All optically tunable wavelength-selective reflector consisting of coupled polymeric microring resonators,” Appl. Phys. Lett.87, 251102–251102–3 (2005). [CrossRef]
V. Van, “Dual-mode microring reflection filters,” J. Lightwave Technol.25, 3142–3150 (2007). [CrossRef]
W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert, B. Luyssaert, J. V. Campenhout, P. Bienstman, and D. V. Thourhout, “Nanophotonic waveguides in silicon-on-insulator fabricated with CMOS technology,” J. Lightwave Technol.23, 401–412 (2005). [CrossRef]
L. Chrostowski, S. Grist, J. Flueckiger, W. Shi, X. Wang, E. Ouellet, H. Yun, M. Webb, B. Nie, Z. Liang, K. C. Cheung, A. S. S, D. M. Ratner, and N. A. F. Jaeger, “Silicon photonic resonator sensors and devices,” Proceedings of SPIE8236, 823620 (2012). [CrossRef]
M. Soltani, Q. Li, S. Yegnanarayanan, and A. Adibi, “Toward ultimate miniaturization of high Q silicon traveling-wave microresonators,” Opt. Express18, 19541–19557 (2010). [CrossRef] [PubMed]
G. Yoffe, T. Nguyen, J. Heanue, and B. Pezeshki, “Efficient compact tunable laser for access networks using silicon ring resonators,” OFC/NFOEC, Los Angeles, CA, USA OW1G.4 (2012).
J. E. Cunningham, I. Shubin, X. Zheng, T. Pinguet, A. Mekis, Y. Luo, H. Thacker, G. Li, J. Yao, K. Raj, and A. V. Krishnamoorthy, “Highly-efficient thermally-tuned resonant optical filters,” Opt. Express18, 19055–19063 (2010). [CrossRef] [PubMed]
D. G. Rabus, Integrated Ring Resonators (Springer, 2007).
A. Yariv, “Critical coupling and its control in optical waveguide-ring resonator systems,” IEEE Photon. Technol. Lett.14, 483–485 (2002). [CrossRef]
M. Soltani, S. Yegnanarayanan, Q. Li, and A. Adibi, “Systematic engineering of waveguide-resonator coupling for silicon microring/microdisk/racetrack resonators: theory and experiment,” IEEE J. Quantum Electron.46, 1158–1169 (2010). [CrossRef]

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