Abstract

We present experimental results of photonic crystal ring resonators (PhCRRs) fabricated on the CMOS-compatible, silicon-on-insulator platform via 193-nm deep-UV lithography. Our dispersion-engineering design approach is compared to experimental results, showing very good agreement between theory and measurements. Specifically, we report a mean photonic band-edge wavelength of 1546.2 ± 5.8 nm, a 0.2% variation from our targeted band-edge wavelength of 1550 nm. Methods for the direct calculation of the experimental, discrete dispersion relation and extraction of intrinsic quality factors for a highly-dispersive resonator are discussed. A maximum intrinsic quality factor of ≈83,800 is reported, substantiating our design method and indicating that high-throughput optical lithography is a viable candidate for PhCRR fabrication. Finally, through comparison of the mean intrinsic quality and slowdown factors of the PhCRRs and standard ring resonators, we present evidence of an increase in light-matter interaction strength with simultaneous preservation of microcavity lifetimes.

© 2017 Optical Society of America

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2016 (5)

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip-based optical frequency comb using soliton Cherenkov radiation,” Science 351, 357–360 (2016).
[Crossref] [PubMed]

C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351, 1176–1180 (2016).
[Crossref]

K. Y. Yang, K. Beha, D. Cole, X. Yi, P. Del’Haye, H. Lee, J. Li, D. Oh, S. A. Diddams, S.B. Papp, and K.J. Vahala, “Broadband dispersion-engineered microresonator on a chip,” Nat. Photon. 10, 316–320 (2016).
[Crossref]

G. Gao, Y. Zhang, H. Zhang, Y. Wang, Q. Huang, and J. Xia, “Air-mode photonic crystal ring resonator on silicon-on-insulator,” Sci. Rep. 6, 19999 (2016).
[Crossref] [PubMed]

D. Urbonas, A. Balčytis, K. Vaškevičius, M. Gabalis, and R. Petruškevičius, “Air and dielectric bands photonic crystal microringresonator for refractive index sensing,” Opt. Lett. 41, 3655–3658 (2016).
[Crossref] [PubMed]

2015 (2)

2014 (2)

2012 (3)

2009 (1)

2007 (3)

2006 (1)

2005 (2)

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72, 161318 (2005).
[Crossref]

M. Soljacić, E. Lidorikis, L. V. Hau, and J. D. Joannopoulos, “Enhancement of microcavity lifetimes using highly dispersive materials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71, 026602 (2005).
[Crossref]

2004 (2)

A. Y. Petrov and M. Eich, “Zero dispersion at small group velocities in photonic crystal waveguides,” Appl. Phys. Lett. 85, 4866 (2004).
[Crossref]

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[Crossref] [PubMed]

2001 (1)

1997 (1)

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]

Almeida, V. R.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[Crossref] [PubMed]

Bailey, R. C.

M. S. McClellan, L. L. Domier, and R. C. Bailey, “Label-free virus detection using silicon photonic microring resonators,” Biosens. Bioelectron. 31, 388–392 (2012).
[Crossref]

Balcytis, A.

Barrios, C. A.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[Crossref] [PubMed]

Beha, K.

K. Y. Yang, K. Beha, D. Cole, X. Yi, P. Del’Haye, H. Lee, J. Li, D. Oh, S. A. Diddams, S.B. Papp, and K.J. Vahala, “Broadband dispersion-engineered microresonator on a chip,” Nat. Photon. 10, 316–320 (2016).
[Crossref]

Bianucci, P.

Brasch, V.

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip-based optical frequency comb using soliton Cherenkov radiation,” Science 351, 357–360 (2016).
[Crossref] [PubMed]

Bromberg, Y.

C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351, 1176–1180 (2016).
[Crossref]

Campanella, C. E.

Caspani, L.

C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351, 1176–1180 (2016).
[Crossref]

Cheben, P.

Chen, S.

Chin, S.

L. Thévenaz, I. Dicaire, and S. Chin, “Enhancing the light-matter interaction using slow light: towards the concept of dense light,” in “SPIE OPTO,” S. M. Shahriar and F. A. Narducci, eds. (International Society for Optics and Photonics, 2012), pp. 82731D.

Chu, S.

Chu, S. T.

C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351, 1176–1180 (2016).
[Crossref]

Cole, D.

K. Y. Yang, K. Beha, D. Cole, X. Yi, P. Del’Haye, H. Lee, J. Li, D. Oh, S. A. Diddams, S.B. Papp, and K.J. Vahala, “Broadband dispersion-engineered microresonator on a chip,” Nat. Photon. 10, 316–320 (2016).
[Crossref]

De Leonardis, F.

Del’Haye, P.

K. Y. Yang, K. Beha, D. Cole, X. Yi, P. Del’Haye, H. Lee, J. Li, D. Oh, S. A. Diddams, S.B. Papp, and K.J. Vahala, “Broadband dispersion-engineered microresonator on a chip,” Nat. Photon. 10, 316–320 (2016).
[Crossref]

Dicaire, I.

L. Thévenaz, I. Dicaire, and S. Chin, “Enhancing the light-matter interaction using slow light: towards the concept of dense light,” in “SPIE OPTO,” S. M. Shahriar and F. A. Narducci, eds. (International Society for Optics and Photonics, 2012), pp. 82731D.

Diddams, S. A.

K. Y. Yang, K. Beha, D. Cole, X. Yi, P. Del’Haye, H. Lee, J. Li, D. Oh, S. A. Diddams, S.B. Papp, and K.J. Vahala, “Broadband dispersion-engineered microresonator on a chip,” Nat. Photon. 10, 316–320 (2016).
[Crossref]

Domier, L. L.

M. S. McClellan, L. L. Domier, and R. C. Bailey, “Label-free virus detection using silicon photonic microring resonators,” Biosens. Bioelectron. 31, 388–392 (2012).
[Crossref]

Duchesne, D.

Dulashko, Y.

Eich, M.

A. Y. Petrov and M. Eich, “Zero dispersion at small group velocities in photonic crystal waveguides,” Appl. Phys. Lett. 85, 4866 (2004).
[Crossref]

Fan, X.

Fauchet, P. M.

Ferrera, 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]

Foster, M. A.

Gabalis, M.

Gaeta, A. L.

Gagliardi, G.

Gao, G.

G. Gao, Y. Zhang, H. Zhang, Y. Wang, Q. Huang, and J. Xia, “Air-mode photonic crystal ring resonator on silicon-on-insulator,” Sci. Rep. 6, 19999 (2016).
[Crossref] [PubMed]

Geiselmann, M.

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip-based optical frequency comb using soliton Cherenkov radiation,” Science 351, 357–360 (2016).
[Crossref] [PubMed]

Goldring, D.

Gorodetsky, M. L.

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip-based optical frequency comb using soliton Cherenkov radiation,” Science 351, 357–360 (2016).
[Crossref] [PubMed]

Grazioso, F.

C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351, 1176–1180 (2016).
[Crossref]

Grudinin, I.S.

I.S. Grudinin and N. Yu, “Dispersion engineering of crystalline resonators via microstructuring,” Optica 3, 221–224 (2015).
[Crossref]

Hau, L. V.

M. Soljacić, E. Lidorikis, L. V. Hau, and J. D. Joannopoulos, “Enhancement of microcavity lifetimes using highly dispersive materials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71, 026602 (2005).
[Crossref]

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]

Herr, T.

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip-based optical frequency comb using soliton Cherenkov radiation,” Science 351, 357–360 (2016).
[Crossref] [PubMed]

Huang, Q.

G. Gao, Y. Zhang, H. Zhang, Y. Wang, Q. Huang, and J. Xia, “Air-mode photonic crystal ring resonator on silicon-on-insulator,” Sci. Rep. 6, 19999 (2016).
[Crossref] [PubMed]

Hughes, S.

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72, 161318 (2005).
[Crossref]

Janz, S.

Joannopoulos, J.

Joannopoulos, J. D.

M. Soljacić, E. Lidorikis, L. V. Hau, and J. D. Joannopoulos, “Enhancement of microcavity lifetimes using highly dispersive materials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71, 026602 (2005).
[Crossref]

Johnson, S.

Johnston, T.

C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351, 1176–1180 (2016).
[Crossref]

Kippenberg, T. J.

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip-based optical frequency comb using soliton Cherenkov radiation,” Science 351, 357–360 (2016).
[Crossref] [PubMed]

Krauss, T. F.

Kues, M.

C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351, 1176–1180 (2016).
[Crossref]

Kuramochi, E.

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72, 161318 (2005).
[Crossref]

Laine, J.-P.

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]

Lau, R. K. W.

Leaird, D. E.

Lee, H.

K. Y. Yang, K. Beha, D. Cole, X. Yi, P. Del’Haye, H. Lee, J. Li, D. Oh, S. A. Diddams, S.B. Papp, and K.J. Vahala, “Broadband dispersion-engineered microresonator on a chip,” Nat. Photon. 10, 316–320 (2016).
[Crossref]

Lee, J. Y.

Levy, J. S.

Levy, U.

Li, J.

K. Y. Yang, K. Beha, D. Cole, X. Yi, P. Del’Haye, H. Lee, J. Li, D. Oh, S. A. Diddams, S.B. Papp, and K.J. Vahala, “Broadband dispersion-engineered microresonator on a chip,” Nat. Photon. 10, 316–320 (2016).
[Crossref]

Lidorikis, E.

M. Soljacić, E. Lidorikis, L. V. Hau, and J. D. Joannopoulos, “Enhancement of microcavity lifetimes using highly dispersive materials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71, 026602 (2005).
[Crossref]

Lihachev, G.

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip-based optical frequency comb using soliton Cherenkov radiation,” Science 351, 357–360 (2016).
[Crossref] [PubMed]

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.

C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351, 1176–1180 (2016).
[Crossref]

M. Ferrera, D. Duchesne, L. Razzari, M. Peccianti, R. Morandotti, P. Cheben, S. Janz, D.-X. Xu, B. E. Little, S. Chu, and D. J. Moss, “Low power four wave mixing in an integrated, micro-ring resonator with Q = 12 million,” Opt. Express 17, 14098 (2009).
[Crossref] [PubMed]

Liu, Y.

Luke, K.

Malara, P.

Mastronardi, L.

McClellan, M. S.

M. S. McClellan, L. L. Domier, and R. C. Bailey, “Label-free virus detection using silicon photonic microring resonators,” Biosens. Bioelectron. 31, 388–392 (2012).
[Crossref]

McGarvey-Lechable, K.

Mendlovic, D.

Metcalf, A. J.

Michaeli, A.

Morandotti, R.

C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351, 1176–1180 (2016).
[Crossref]

M. Ferrera, D. Duchesne, L. Razzari, M. Peccianti, R. Morandotti, P. Cheben, S. Janz, D.-X. Xu, B. E. Little, S. Chu, and D. J. Moss, “Low power four wave mixing in an integrated, micro-ring resonator with Q = 12 million,” Opt. Express 17, 14098 (2009).
[Crossref] [PubMed]

Moss, D. J.

C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351, 1176–1180 (2016).
[Crossref]

M. Ferrera, D. Duchesne, L. Razzari, M. Peccianti, R. Morandotti, P. Cheben, S. Janz, D.-X. Xu, B. E. Little, S. Chu, and D. J. Moss, “Low power four wave mixing in an integrated, micro-ring resonator with Q = 12 million,” Opt. Express 17, 14098 (2009).
[Crossref] [PubMed]

Notomi, M.

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72, 161318 (2005).
[Crossref]

Oh, D.

K. Y. Yang, K. Beha, D. Cole, X. Yi, P. Del’Haye, H. Lee, J. Li, D. Oh, S. A. Diddams, S.B. Papp, and K.J. Vahala, “Broadband dispersion-engineered microresonator on a chip,” Nat. Photon. 10, 316–320 (2016).
[Crossref]

Okawachi, Y.

Panepucci, R. R.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[Crossref] [PubMed]

Papp, S.B.

K. Y. Yang, K. Beha, D. Cole, X. Yi, P. Del’Haye, H. Lee, J. Li, D. Oh, S. A. Diddams, S.B. Papp, and K.J. Vahala, “Broadband dispersion-engineered microresonator on a chip,” Nat. Photon. 10, 316–320 (2016).
[Crossref]

Passaro, V. M. N.

Peccianti, M.

Petrov, A. Y.

A. Y. Petrov and M. Eich, “Zero dispersion at small group velocities in photonic crystal waveguides,” Appl. Phys. Lett. 85, 4866 (2004).
[Crossref]

Petruškevicius, R.

Pfeiffer, M. H. P.

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip-based optical frequency comb using soliton Cherenkov radiation,” Science 351, 357–360 (2016).
[Crossref] [PubMed]

Qi, M.

Ramunno, L.

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72, 161318 (2005).
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C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351, 1176–1180 (2016).
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E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72, 161318 (2005).
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L. Thévenaz, I. Dicaire, and S. Chin, “Enhancing the light-matter interaction using slow light: towards the concept of dense light,” in “SPIE OPTO,” S. M. Shahriar and F. A. Narducci, eds. (International Society for Optics and Photonics, 2012), pp. 82731D.

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K. Y. Yang, K. Beha, D. Cole, X. Yi, P. Del’Haye, H. Lee, J. Li, D. Oh, S. A. Diddams, S.B. Papp, and K.J. Vahala, “Broadband dispersion-engineered microresonator on a chip,” Nat. Photon. 10, 316–320 (2016).
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K. Y. Yang, K. Beha, D. Cole, X. Yi, P. Del’Haye, H. Lee, J. Li, D. Oh, S. A. Diddams, S.B. Papp, and K.J. Vahala, “Broadband dispersion-engineered microresonator on a chip,” Nat. Photon. 10, 316–320 (2016).
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Opt. Lett. (2)

Optica (2)

Phys. Rev. B (1)

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72, 161318 (2005).
[Crossref]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

M. Soljacić, E. Lidorikis, L. V. Hau, and J. D. Joannopoulos, “Enhancement of microcavity lifetimes using highly dispersive materials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71, 026602 (2005).
[Crossref]

Sci. Rep. (1)

G. Gao, Y. Zhang, H. Zhang, Y. Wang, Q. Huang, and J. Xia, “Air-mode photonic crystal ring resonator on silicon-on-insulator,” Sci. Rep. 6, 19999 (2016).
[Crossref] [PubMed]

Science (2)

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip-based optical frequency comb using soliton Cherenkov radiation,” Science 351, 357–360 (2016).
[Crossref] [PubMed]

C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351, 1176–1180 (2016).
[Crossref]

Other (1)

L. Thévenaz, I. Dicaire, and S. Chin, “Enhancing the light-matter interaction using slow light: towards the concept of dense light,” in “SPIE OPTO,” S. M. Shahriar and F. A. Narducci, eds. (International Society for Optics and Photonics, 2012), pp. 82731D.

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Figures (7)

Fig. 1
Fig. 1 (a) The geometry of a PhCRR. The high refractive index material is indicated in black and the low-index, background material is indicated in white. (b) A scanning electron microscope image of a 10-µm-diameter PhCRR evanescently coupled to a 0.450 µm wide strip waveguide.
Fig. 2
Fig. 2 (a) The dispersion relation of the first photonic band of an infinitely-long SOI PhC waveguide of width w = 1.3a, and f = 0.243. The photonic band edge is denoted as the dotted vertical line. (b,c,d) The electric field energy densities of the fundamental, two-fold, and four-fold PhCRR modes, respectively.
Fig. 3
Fig. 3 The experimental setup utilized for the characterization of the devices. Each PhCRR is evanescently coupled to an input waveguide and the transmission spectrum is monitored via an output waveguide coupled to an optical fiber (figure not to scale).
Fig. 4
Fig. 4 The spectra of a 20-µm-diameter PhCRR (left) and an equivalently sized standard ring resonator (right). The photonic band gap of the PhCRR is indicated by the shaded region. The wavelengths of the fundamental, two-fold, and four-fold modes of the PhCRR predicted using the design prescription discussed in [14] are indicated by the blue, green, and purple lines, respectively.
Fig. 5
Fig. 5 (a) The experimental dispersion relation of a 10-µm-diameter PhCRR as compared to the simulated dispersion relation of the PhCRR computed via MPB. (b) The experimental group index of a 10-µm-diameter PhCRR as compared to the simulated group relation of the PhCRR computed via MPB. The inset shows the transmission spectrum of the PhCRR in question.
Fig. 6
Fig. 6 An example illustrating our peak fitting technique for the split two-fold mode of a 20-µm PhCRR. Each peak was fit using the parameters and known constants detailed in the inset table. The highest intrinsic quality factor of the thirty measured PhCRRs was found at Peak 2.
Fig. 7
Fig. 7 The mean intrinsic quality factors of the 10 µm diameter PhCRRs’ two-fold, and four-fold modes as compared to the mean intrinsic quality factors of their equivalently sized standard RRs as a function of the slowdown factor. The vertical and horizontal error bars indicate the range of values of the intrinsic quality factors and slowdown factors, respectively, for the thirty measured devices.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

1 Q t o t a l = 1 Q C + 1 Q I
1 | T | 2 = ( a 2 1 ) ( r 2 1 ) 1 + r 2 a 2 2 a r cos ( φ )
φ = ω 0 n g e f f L c
Q C = ω 0 τ r t 2 | ln ( r ) | Q I = ω 0 τ r t 2 | ln ( a ) |
ω ˜ 0 = ω 0 [ 1 n g e f f ( ω ) n g e f f ( ω 0 ) n g e f f ( ω 0 ) ]
φ ( ω ) = τ r t ω 0 n g e f f ( ω 0 ) [ 1 n g e f f ( ω ) ]

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