Abstract

We present a novel and simple method to obtain an ultrawide free spectral range (FSR) silicon ring resonator together with a tuning range covering the entire spectrum from 1500 to 1600 nm. A ring resonator with a large FSR together with a high Q factor, high tuning efficiency, and low fabrication cost and complexity is desired for many applications. In this paper, we introduce a novel way to make such a ring resonator, which takes advantage of the well-known resonance-splitting phenomenon. It is a single ring resonator with an FSR of more than 150 nm around 1550 nm and which has an easy thermo-optic tunability that can produce a tuning range around 90 nm or even more. Moreover, the device is simple to implement and can be fabricated in standard complementary metal-oxide semiconductor technology without requiring any kind of complicated processing or extra materials. The potential applications include single mode laser cavities, wavelength division multiplexing filters, (de)multiplexers, optical sensors, and integrated reflectors.

Journal © 2016 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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2015 (3)

2014 (3)

2012 (2)

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6, 47–73 (2012).
[Crossref]

M. Fiers, T. V. Vaerenbergh, K. Caluwaerts, D. V. Ginste, B. Schrauwen, J. Dambre, and P. Bienstman, “Time-domain and frequency-domain modeling of nonlinear optical components at the circuit-level using a node-based approach,” J. Opt. Soc. Am. B 29, 896–900 (2012).
[Crossref]

2011 (1)

S. K. Selvaraja, W. Bogaerts, and D. Van Thourhout, “Loss reduction in silicon nanophotonic waveguide micro-bends through etch profile improvement,” Opt. Commun. 284, 2141–2144 (2011).
[Crossref]

2010 (2)

H. Shen, L. Fan, J. Wang, J. C. Wirth, and M. Qi, “A taper to reduce the straight-to-bend transition loss in compact silicon waveguides,” IEEE Photon. Technol. Lett. 22, 1174–1176 (2010).
[Crossref]

F. Morichetti, A. Canciamilla, and A. Melloni, “Statistics of backscattering in optical waveguides,” Opt. Lett. 35, 1777–1779 (2010).
[Crossref]

2007 (1)

2006 (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, 71110 (2006).
[Crossref]

M. A. Popovíc, T. Barwicz, M. R. Watts, P. T. Rakich, L. Socci, E. P. Ippen, F. X. Kärtner, and H. I. Smith, “Multistage high-order microring-resonator add–drop filters,” Opt. Lett. 31, 2571–2573 (2006).
[Crossref]

W. Bogaerts, P. Dumon, D. Van Thourhout, D. Taillaert, P. Jaenen, J. Wouters, S. Beckx, V. Wiaux, and R. G. Baets, “Compact wavelength-selective functions in silicon-on-insulator photonic wires,” IEEE J. Sel. Top. Quantum Electron. 12, 1394–1401 (2006).
[Crossref]

2005 (1)

1997 (2)

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[Crossref]

B. Little, S. Chu, H. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[Crossref]

1991 (1)

K. Oda, N. Takato, and H. Toba, “A wide-FSR waveguide double-ring resonator for optical FDM transmission systems,” J. Lightwave Technol. 9, 728–736 (1991).
[Crossref]

Baets, R.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6, 47–73 (2012).
[Crossref]

Baets, R. G.

W. Bogaerts, P. Dumon, D. Van Thourhout, D. Taillaert, P. Jaenen, J. Wouters, S. Beckx, V. Wiaux, and R. G. Baets, “Compact wavelength-selective functions in silicon-on-insulator photonic wires,” IEEE J. Sel. Top. Quantum Electron. 12, 1394–1401 (2006).
[Crossref]

Balcytis, A.

Barwicz, T.

Beckx, S.

W. Bogaerts, P. Dumon, D. Van Thourhout, D. Taillaert, P. Jaenen, J. Wouters, S. Beckx, V. Wiaux, and R. G. Baets, “Compact wavelength-selective functions in silicon-on-insulator photonic wires,” IEEE J. Sel. Top. Quantum Electron. 12, 1394–1401 (2006).
[Crossref]

Bickford, J.

Bienstman, P.

J.-W. Hoste, S. Werquin, T. Claes, and P. Bienstman, “Conformational analysis of proteins with a dual polarisation silicon microring,” Opt. Express 22, 2807–2820 (2014).
[Crossref]

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6, 47–73 (2012).
[Crossref]

M. Fiers, T. V. Vaerenbergh, K. Caluwaerts, D. V. Ginste, B. Schrauwen, J. Dambre, and P. Bienstman, “Time-domain and frequency-domain modeling of nonlinear optical components at the circuit-level using a node-based approach,” J. Opt. Soc. Am. B 29, 896–900 (2012).
[Crossref]

A. Li, T. V. Vaerenbergh, P. De Heyn, Y. Xing, P. Bienstman, and W. Bogaerts, “Experimentally demonstrate the origin for asymmetric resonance splitting and contributions from couplers to backscattering in SOI microrings,” in Advanced Photonics (Optical Society of America, 2015), paper IM2B.6.

Boeck, R.

Bogaerts, W.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6, 47–73 (2012).
[Crossref]

S. K. Selvaraja, W. Bogaerts, and D. Van Thourhout, “Loss reduction in silicon nanophotonic waveguide micro-bends through etch profile improvement,” Opt. Commun. 284, 2141–2144 (2011).
[Crossref]

W. Bogaerts, P. Dumon, D. Van Thourhout, D. Taillaert, P. Jaenen, J. Wouters, S. Beckx, V. Wiaux, and R. G. Baets, “Compact wavelength-selective functions in silicon-on-insulator photonic wires,” IEEE J. Sel. Top. Quantum Electron. 12, 1394–1401 (2006).
[Crossref]

A. Li, T. V. Vaerenbergh, P. De Heyn, Y. Xing, P. Bienstman, and W. Bogaerts, “Experimentally demonstrate the origin for asymmetric resonance splitting and contributions from couplers to backscattering in SOI microrings,” in Advanced Photonics (Optical Society of America, 2015), paper IM2B.6.

Caluwaerts, K.

Canciamilla, A.

Caverley, M.

Chrostowski, L.

Chu, S.

B. Little, S. Chu, H. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[Crossref]

Chu, S. T.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[Crossref]

Claes, T.

J.-W. Hoste, S. Werquin, T. Claes, and P. Bienstman, “Conformational analysis of proteins with a dual polarisation silicon microring,” Opt. Express 22, 2807–2820 (2014).
[Crossref]

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6, 47–73 (2012).
[Crossref]

Cunningham, J. E.

Dambre, J.

De Heyn, P.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6, 47–73 (2012).
[Crossref]

A. Li, T. V. Vaerenbergh, P. De Heyn, Y. Xing, P. Bienstman, and W. Bogaerts, “Experimentally demonstrate the origin for asymmetric resonance splitting and contributions from couplers to backscattering in SOI microrings,” in Advanced Photonics (Optical Society of America, 2015), paper IM2B.6.

De Vos, K.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6, 47–73 (2012).
[Crossref]

Djordjevic, S. S.

Driessen, A.

D. Geuzebroek, E. Klein, H. Kelderman, F. Tan, D. Klunder, and A. Driessen, “Thermally tuneable, wide FSR switch based on micro-ring resonators,” in IEEE/LEOS Benelux Chapter 2002 Annual Symposium (2002), pp. 155–158.

Dumon, P.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6, 47–73 (2012).
[Crossref]

W. Bogaerts, P. Dumon, D. Van Thourhout, D. Taillaert, P. Jaenen, J. Wouters, S. Beckx, V. Wiaux, and R. G. Baets, “Compact wavelength-selective functions in silicon-on-insulator photonic wires,” IEEE J. Sel. Top. Quantum Electron. 12, 1394–1401 (2006).
[Crossref]

Emelett, S. J.

Fan, L.

H. Shen, L. Fan, J. Wang, J. C. Wirth, and M. Qi, “A taper to reduce the straight-to-bend transition loss in compact silicon waveguides,” IEEE Photon. Technol. Lett. 22, 1174–1176 (2010).
[Crossref]

Faralli, S.

A. Malacarne, F. Gambini, S. Faralli, J. Klamkin, and L. Poti, “High-speed silicon electro-optic microring modulator for optical interconnects,” IEEE Photon. Technol. Lett. 26, 1042–1044 (2014).
[Crossref]

Fiers, M.

Foresi, J.

B. Little, S. Chu, H. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[Crossref]

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[Crossref]

Gabalis, M.

Gambini, F.

A. Malacarne, F. Gambini, S. Faralli, J. Klamkin, and L. Poti, “High-speed silicon electro-optic microring modulator for optical interconnects,” IEEE Photon. Technol. Lett. 26, 1042–1044 (2014).
[Crossref]

Geuzebroek, D.

D. Geuzebroek, E. Klein, H. Kelderman, F. Tan, D. Klunder, and A. Driessen, “Thermally tuneable, wide FSR switch based on micro-ring resonators,” in IEEE/LEOS Benelux Chapter 2002 Annual Symposium (2002), pp. 155–158.

Ginste, D. V.

Haus, H.

B. Little, S. Chu, H. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[Crossref]

H. Haus, Waves and Fields in Optoelectronics, Prentice-Hall Series in Solid State Physical Electronics (Prentice-Hall, 1984).

Haus, H. A.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[Crossref]

He, S.

Q. Huang, K. Ma, and S. He, “Experimental demonstration of single mode-splitting in microring with Bragg gratings,” IEEE Photon. Technol. Lett. 27, 1402–1405 (2015).
[Crossref]

Hoste, J.-W.

Huang, Q.

Q. Huang, K. Ma, and S. He, “Experimental demonstration of single mode-splitting in microring with Bragg gratings,” IEEE Photon. Technol. Lett. 27, 1402–1405 (2015).
[Crossref]

Ippen, E. P.

Jaeger, N. A. F.

Jaenen, P.

W. Bogaerts, P. Dumon, D. Van Thourhout, D. Taillaert, P. Jaenen, J. Wouters, S. Beckx, V. Wiaux, and R. G. Baets, “Compact wavelength-selective functions in silicon-on-insulator photonic wires,” IEEE J. Sel. Top. Quantum Electron. 12, 1394–1401 (2006).
[Crossref]

Juodkazis, S.

Kärtner, F. X.

Kelderman, H.

D. Geuzebroek, E. Klein, H. Kelderman, F. Tan, D. Klunder, and A. Driessen, “Thermally tuneable, wide FSR switch based on micro-ring resonators,” in IEEE/LEOS Benelux Chapter 2002 Annual Symposium (2002), pp. 155–158.

Klamkin, J.

A. Malacarne, F. Gambini, S. Faralli, J. Klamkin, and L. Poti, “High-speed silicon electro-optic microring modulator for optical interconnects,” IEEE Photon. Technol. Lett. 26, 1042–1044 (2014).
[Crossref]

Klein, E.

D. Geuzebroek, E. Klein, H. Kelderman, F. Tan, D. Klunder, and A. Driessen, “Thermally tuneable, wide FSR switch based on micro-ring resonators,” in IEEE/LEOS Benelux Chapter 2002 Annual Symposium (2002), pp. 155–158.

Klunder, D.

D. Geuzebroek, E. Klein, H. Kelderman, F. Tan, D. Klunder, and A. Driessen, “Thermally tuneable, wide FSR switch based on micro-ring resonators,” in IEEE/LEOS Benelux Chapter 2002 Annual Symposium (2002), pp. 155–158.

Krishnamoorthy, A. K.

Kumar Selvaraja, S.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6, 47–73 (2012).
[Crossref]

Laine, J.-P.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[Crossref]

B. Little, S. Chu, H. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[Crossref]

Lee, J. H.

Li, A.

A. Li, T. V. Vaerenbergh, P. De Heyn, Y. Xing, P. Bienstman, and W. Bogaerts, “Experimentally demonstrate the origin for asymmetric resonance splitting and contributions from couplers to backscattering in SOI microrings,” in Advanced Photonics (Optical Society of America, 2015), paper IM2B.6.

Lin, S.

Lipson, M.

Little, B.

B. Little, S. Chu, H. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[Crossref]

Little, B. E.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[Crossref]

Liu, T.

M. S. Nawrocka, T. Liu, X. Wang, and R. R. Panepucci, “Tunable silicon microring resonator with wide free spectral range,” Appl. Phys. Lett. 89, 71110 (2006).
[Crossref]

Luo, Y.

Ma, K.

Q. Huang, K. Ma, and S. He, “Experimental demonstration of single mode-splitting in microring with Bragg gratings,” IEEE Photon. Technol. Lett. 27, 1402–1405 (2015).
[Crossref]

Malacarne, A.

A. Malacarne, F. Gambini, S. Faralli, J. Klamkin, and L. Poti, “High-speed silicon electro-optic microring modulator for optical interconnects,” IEEE Photon. Technol. Lett. 26, 1042–1044 (2014).
[Crossref]

Melloni, A.

Morichetti, F.

Naujokaite, G.

Nawrocka, M. S.

M. S. Nawrocka, T. Liu, X. Wang, and R. R. Panepucci, “Tunable silicon microring resonator with wide free spectral range,” Appl. Phys. Lett. 89, 71110 (2006).
[Crossref]

Oda, K.

K. Oda, N. Takato, and H. Toba, “A wide-FSR waveguide double-ring resonator for optical FDM transmission systems,” J. Lightwave Technol. 9, 728–736 (1991).
[Crossref]

Panepucci, R. R.

M. S. Nawrocka, T. Liu, X. Wang, and R. R. Panepucci, “Tunable silicon microring resonator with wide free spectral range,” Appl. Phys. Lett. 89, 71110 (2006).
[Crossref]

Petruškevicius, R.

Popovic, M. A.

M. A. Popović, “Theory and design of high-index-contrast microphotonic circuits,” Ph.D. thesis (Massachusetts Institute of Technology, 2008).

Popovíc, M. A.

Poti, L.

A. Malacarne, F. Gambini, S. Faralli, J. Klamkin, and L. Poti, “High-speed silicon electro-optic microring modulator for optical interconnects,” IEEE Photon. Technol. Lett. 26, 1042–1044 (2014).
[Crossref]

Qi, M.

H. Shen, L. Fan, J. Wang, J. C. Wirth, and M. Qi, “A taper to reduce the straight-to-bend transition loss in compact silicon waveguides,” IEEE Photon. Technol. Lett. 22, 1174–1176 (2010).
[Crossref]

Raj, K.

Rakich, P. T.

Schrauwen, B.

Selvaraja, S. K.

S. K. Selvaraja, W. Bogaerts, and D. Van Thourhout, “Loss reduction in silicon nanophotonic waveguide micro-bends through etch profile improvement,” Opt. Commun. 284, 2141–2144 (2011).
[Crossref]

Shen, H.

H. Shen, L. Fan, J. Wang, J. C. Wirth, and M. Qi, “A taper to reduce the straight-to-bend transition loss in compact silicon waveguides,” IEEE Photon. Technol. Lett. 22, 1174–1176 (2010).
[Crossref]

Shubin, I.

Smith, H. I.

Socci, L.

Soref, R.

Taillaert, D.

W. Bogaerts, P. Dumon, D. Van Thourhout, D. Taillaert, P. Jaenen, J. Wouters, S. Beckx, V. Wiaux, and R. G. Baets, “Compact wavelength-selective functions in silicon-on-insulator photonic wires,” IEEE J. Sel. Top. Quantum Electron. 12, 1394–1401 (2006).
[Crossref]

Takato, N.

K. Oda, N. Takato, and H. Toba, “A wide-FSR waveguide double-ring resonator for optical FDM transmission systems,” J. Lightwave Technol. 9, 728–736 (1991).
[Crossref]

Tan, F.

D. Geuzebroek, E. Klein, H. Kelderman, F. Tan, D. Klunder, and A. Driessen, “Thermally tuneable, wide FSR switch based on micro-ring resonators,” in IEEE/LEOS Benelux Chapter 2002 Annual Symposium (2002), pp. 155–158.

Thacker, H. D.

Toba, H.

K. Oda, N. Takato, and H. Toba, “A wide-FSR waveguide double-ring resonator for optical FDM transmission systems,” J. Lightwave Technol. 9, 728–736 (1991).
[Crossref]

Urbonas, D.

Vaerenbergh, T. V.

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W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6, 47–73 (2012).
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[Crossref]

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[Crossref]

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W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6, 47–73 (2012).
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W. Bogaerts, P. Dumon, D. Van Thourhout, D. Taillaert, P. Jaenen, J. Wouters, S. Beckx, V. Wiaux, and R. G. Baets, “Compact wavelength-selective functions in silicon-on-insulator photonic wires,” IEEE J. Sel. Top. Quantum Electron. 12, 1394–1401 (2006).
[Crossref]

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[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

W. Bogaerts, P. Dumon, D. Van Thourhout, D. Taillaert, P. Jaenen, J. Wouters, S. Beckx, V. Wiaux, and R. G. Baets, “Compact wavelength-selective functions in silicon-on-insulator photonic wires,” IEEE J. Sel. Top. Quantum Electron. 12, 1394–1401 (2006).
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W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6, 47–73 (2012).
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Figures (13)

Fig. 1.
Fig. 1. Schematic of the tCMT model for ring resonators. (a) In an ideal ring resonator with no reflection inside, only one circulating mode is activated. (b) In a ring resonator with internal backreflection, the two modes are coupled and thus simultaneously active.
Fig. 2.
Fig. 2. At the critical coupling point, the extinction ratio drops dramatically with increasing reflection until it reaches an almost constant value.
Fig. 3.
Fig. 3. Extinction ratio still changes significantly with increasing reflectivity when the MRR is configured as κi=κo, which is the general case and easy to guarantee.
Fig. 4.
Fig. 4. These figures show how the extinction ratio as well as the side mode suppression changes with power coupling coefficient when the MRR is designed as κi=κo. (a) Extinction ratio as a function of coupling coefficient. (b) Side mode expression as a function of coupling coefficient.
Fig. 5.
Fig. 5. The ring resonator has a loop MZI tunable reflector inside, which introduces a wavelength-dependent intentional reflection that couples two circulating modes.
Fig. 6.
Fig. 6. Curves of the reflection spectra of the reflector. The directional couplers are designed to be a 50/50 splitter. (a) The directional coupler performance is wavelength independent. (b) A linear model for directional coupler extracted from FDTD simulation is added.
Fig. 7.
Fig. 7. Simulated throughport of our device. The order m is chosen to be 23, and the MRR is set at the normal coupling condition κi2=κo2.
Fig. 8.
Fig. 8. In common tuning configuration, the zero-reflection wavelength of the reflector and the resonance wavelength of the MRR shift at the same rate, and thus the MRR remains single mode. (a) The shift of the zero-reflection wavelength of the MZI based reflector induced by effective index neff change. (b) The shift of the resonance wavelength of the MRR induced by effective index neff change.
Fig. 9.
Fig. 9. Instead of using one common phase shifter, we can implement two separate phase shifters to achieve individual tuning of the zero-reflection wavelength of the reflector and the resonance wavelength of the ring.
Fig. 10.
Fig. 10. Two phase shifters are implemented, with PS1 responsible for the mode selection and PS2 in charge of comb tuning. With the same index change, we achieve a 4 times larger wavelength shift compared to common tuning. (a) Without PS2, the single mode resonance can only take place at some discrete wavelength points, as the zero-reflection wavelength of the reflector might not match the resonance of the ring. (b) With PS2 working, the single mode resonance can be tuned continuously, as the resonance of the ring resonator can now be aligned to the zero-reflection wavelength of the reflector.
Fig. 11.
Fig. 11. When optimizing for a larger tuning range (at the cost of smaller SMSR) we achieve a tuning range almost as wide as 100 nm with the same index change.
Fig. 12.
Fig. 12. Tuning maps for the two phase shifters PS1 and PS2 to achieve a continuous shift of the single mode resonance. (a), (c), and (e) give the results of the first design, where the SMSR of each wavelength is larger than 28 dB while the tuning range is only 30 nm, 4 times wider than that of a normal silicon ring resonator. The results of the modified design are illustrated in (b), (d), and (f) where the design parameters are changed to achieve a much wider tuning range around 90 nm at the price of a smaller SMSR, but still, at each wavelength, a SMSR larger than 14 dB can be guaranteed. (a) Wavelength of single mode ring 1. (b) Wavelength of single mode ring 2. (c) Extinction ratio of single mode ring 1. (d) Extinction ratio of single mode ring 2. (e) Side mode suppression of single mode ring 1. (f) Side mode suppression of single mode ring 2.
Fig. 13.
Fig. 13. Effect of unintentional backscattering on the performance of the MRR. The SMSR decreases with increasing length and backscattering. But it could be compensated by increasing m and ki.

Equations (18)

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ΔλΔneff=λ0ng.
dαccwdt=jω0αccw(1τi+1τo+1τl)αccwjμiSi,
St=SijμiαccwSd=jμoαccwSa=Sr=0.
μi2=κi2cngL=2τiμo2=κo2cngL=2τoal2cngL=2τl.
StSi=12τij(ωω0)+(1τi+1τo+1τl),
|St|2|Si|2=12τi(2τo+2τl)(ωω0)2+(1τi+1τo+1τl)2.
Pi=12τi(2τo+2τl)(1τi+1τo+1τl)2.
dαccwdt=jω0αccw(1τi+1τo+1τl)αccwjμiSijμrαcw,
dαcwdt=jω0αcw(1τi+1τo+1τl)αcwjμr*αccw.
μr2=r2(cngL)2.
Sa=jμoαcwSr=jμiαcw,
StSi=12τij(ωω0)+(1τi+1τo+1τl)[j(ωω0)+(1τi+1τo+1τl)]2+|μr|2=12τi(0.5j(ωω1)+(1τi+1τo+1τl)+0.5j(ωω2)+(1τi+1τo+1τl)).
Pr=(2τo+2τl2τi+2τo+2τl)2+(2τi)222τi(2τo+2τl)(2τi+2τo+2τl)2+16|μr|2=(κo2+al2κi2+κo2+al2)2+(κi2)22κi2(κo2+al2)(κi2+κo2+al2)2+16r2.
Pr|cp=14|κ|44|κ|4+16r2.
2πΔLneffλ=mπ.
Δλλ0=Δneffng.
Δλrefλ0=Δnps1ngLps1ΔL,
Δλringλ0=Δnps1Lps1+Δnps2Lps2ng(Lps1+Lps2)+neffLrest.

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