Abstract

We propose and demonstrate a new type of electro-optic polymeric microring resonators, where the shape of the transmission spectrum is controlled by losses and phase shifts induced at the asymmetric directional coupler between the cavity and the bus waveguide. The theoretical analysis of such Charon microresonators shows, depending on the coupler design, three different transmission characteristics: normal Lorentzian dips, asymmetric Fano resonances, and Lorentzian peaks. The combination of the active azo-stilbene based polyimide SANDM2 surrounded by the hybrid polymer Ormocomp allowed the first experimental demonstration of electro-optic modulation in Charon microresonators. The low-loss modulators (down to 0.6 dB per round trip), with a radius of 50µm, were produced by micro-embossing and exhibit either highly asymmetric and steep Fano resonances with large 43-GHz modulation bandwidth or strong resonances with 11-dB extinction ratio. We show that Charon microresonators can lead to 1-V half wave voltage all-polymer micrometer-scale devices with larger tolerances to coupler fabrication limitations and wider modulation bandwidths than classical ring resonators.

© 2008 Optical Society of America

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  1. M. Lee, H. E. Katz, Ch. Erben, D. M. Gill, P. Gopalan, J. D. Heber, and D. J. McGee, "Broadband modulation of light by using an electro-optic polymer," Science 298, 1401-1403 (2002).
    [CrossRef] [PubMed]
  2. Y. Q. Shi, C. Zhang, H. Zhang, J. H. Bechtel, L. R. Dalton, B. H. Robinson, and W. H. Steier, "Low (sub-1-volt) halfwave voltage polymeric electro-optic modulators achieved by controlling chromophore shape," Science 288, 119-122 (2000).
    [CrossRef]
  3. Y. Enami, C. T. Derose, D. Mathine, C. Loychik, G. Greenlee, R. A. Norwood, T. D. Kim, J. Luo, Y. Tian, A. K. Y. Jen, and N. Peyghambarian, "Hybrid polymer/sol-gel waveguide modulators with exceptionally large electro-optic coefficients," Nat. Photonics 1, 180-185 (2007).
    [CrossRef]
  4. H. Tazawa and W. H. Steier, "Analysis of ring resonator-based traveling-wave modulators," IEEE Photon. Technol. Lett. 18, 211-213 (2006).
    [CrossRef]
  5. B. Bortnik, Y. C. Hung, H. Tazawa, B. J. Seo, J. D. Luo, A. K.-Y. Jen, W. H. Steier, and H. R. Fetterman, "Electrooptic polymer ring resonator modulation up to 165 GHz," IEEE J. Sel. Top. Quantum Electron. 13, 104-110 (2007).
    [CrossRef]
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    [CrossRef]
  7. H. Tazawa, Y.-H. Kuo, I. Dunayevskiy, J. D. Luo, A. K.-Y. Jen, H. R. Fetterman, and W. H. Steier, "Ring resonatorbased electrooptic polymer traveling-wave modulator," J. Lightwave Technol. 24, 3514-3519 (2006).
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  9. D. Rezzonico, A. Guarino, C. Herzog, M. Jazbinsek, P. Günter, "High-finesse laterally coupled organic-inorganic hybrid polymer microring resonators for VLSI photonics," IEEE Photon. Technol. Lett. 18,865-867 (2006).
    [CrossRef]
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  14. T. D. Kim, J. Luo, J. W. Ka, S. Hau, Y. Tian, Z. Shi, N. M. Tucker, S. H. Jang, J. W. Kang, and A. K. Y. Jen, "Ultralarge and thermally stable electro-optic activities from DielsAlder crosslinkable polymers containing binary chromophore Systems," Adv. Mater. 18, 3038-3042 (2006)
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  16. Y. Lu, J. Yao, X. Li, and P. Wang, "Tunable asymmetrical Fano resonance and bistability in a microcavity-resonatorcoupled Mach-Zehnder interferometer," Opt. Lett. 30, 3069-3071 (2005).
    [CrossRef] [PubMed]
  17. P. P. Absil, J. V. Hryniewicz, B. E. Little, R. A. Wilson, L. G. Joneckis, and P. T. Ho, "Compact microring notch filters," IEEE Photon. Technol. Lett. 12, 398-400 (2000).
    [CrossRef]
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    [CrossRef]
  22. A. Galvan-Gonzalez, M. Canva, G. I. Stegeman, L. Sukhomlinova, R. J. Twieg, K. P. Chan, T. C. Kowalczyk, and H. S. Lackritz, "Photodegradation of azobenzene nonlinear optical chromophores: the influence of structure and environment," J. Opt. Soc. Am. B 17, 1992-2000 (2000).
    [CrossRef]
  23. P. Prêtre, P. Kaatz, A. Bohren, P. Günter, B. Zysset, M. Ahlheim, M. Stähelin, and F. Fehr, "Modified polyimide side-chain polymers for electrooptics," Macromolecules 27, 5476-5486 (1994).
    [CrossRef]
  24. A. Guarino, G. Poberaj, D. Rezzonico, R. Degl’Innocenti, and P. Günter, "Electro-optically tunable microring resonators in lithium niobate," Nat. Photonics 1, 407-410 (2007).
    [CrossRef]

2007 (4)

Y. Enami, C. T. Derose, D. Mathine, C. Loychik, G. Greenlee, R. A. Norwood, T. D. Kim, J. Luo, Y. Tian, A. K. Y. Jen, and N. Peyghambarian, "Hybrid polymer/sol-gel waveguide modulators with exceptionally large electro-optic coefficients," Nat. Photonics 1, 180-185 (2007).
[CrossRef]

B. Bortnik, Y. C. Hung, H. Tazawa, B. J. Seo, J. D. Luo, A. K.-Y. Jen, W. H. Steier, and H. R. Fetterman, "Electrooptic polymer ring resonator modulation up to 165 GHz," IEEE J. Sel. Top. Quantum Electron. 13, 104-110 (2007).
[CrossRef]

D. Rezzonico, M. Jazbinsek, P. Günter, Ch. Bosshard, D. H. Bale, Y. Liao, L. R. Dalton, P. J. Reid, "Photostability studies of p-conjugated chromophores with resonant and nonresonant light excitation for long-life polymeric telecommunication devices," J. Opt. Soc. Am. B 24, 2199-2207 (2007).
[CrossRef]

A. Guarino, G. Poberaj, D. Rezzonico, R. Degl’Innocenti, and P. Günter, "Electro-optically tunable microring resonators in lithium niobate," Nat. Photonics 1, 407-410 (2007).
[CrossRef]

2006 (4)

H. Tazawa, Y.-H. Kuo, I. Dunayevskiy, J. D. Luo, A. K.-Y. Jen, H. R. Fetterman, and W. H. Steier, "Ring resonatorbased electrooptic polymer traveling-wave modulator," J. Lightwave Technol. 24, 3514-3519 (2006).
[CrossRef]

H. Tazawa and W. H. Steier, "Analysis of ring resonator-based traveling-wave modulators," IEEE Photon. Technol. Lett. 18, 211-213 (2006).
[CrossRef]

D. Rezzonico, A. Guarino, C. Herzog, M. Jazbinsek, P. Günter, "High-finesse laterally coupled organic-inorganic hybrid polymer microring resonators for VLSI photonics," IEEE Photon. Technol. Lett. 18,865-867 (2006).
[CrossRef]

T. D. Kim, J. Luo, J. W. Ka, S. Hau, Y. Tian, Z. Shi, N. M. Tucker, S. H. Jang, J. W. Kang, and A. K. Y. Jen, "Ultralarge and thermally stable electro-optic activities from DielsAlder crosslinkable polymers containing binary chromophore Systems," Adv. Mater. 18, 3038-3042 (2006)
[CrossRef]

2005 (3)

Y. Lu, J. Yao, X. Li, and P. Wang, "Tunable asymmetrical Fano resonance and bistability in a microcavity-resonatorcoupled Mach-Zehnder interferometer," Opt. Lett. 30, 3069-3071 (2005).
[CrossRef] [PubMed]

A. Leinse, M. B. J. Diemeer, A. Rousseau, and A. Driessen, "A novel high-speed polymeric EO modulator based on a combination of a microring resonator and an MZI," IEEE Photon. Technol. Lett. 17, 2074-2076 (2005).
[CrossRef]

Q. F. Xu, B. Schmidt, S. Pradhan, and M. Lipson, "Micrometre-scale silicon electro-optic modulator," Nature 435, 325-327 (2005).
[CrossRef] [PubMed]

2003 (1)

C. Y. Chao and L. J. Guo, "Biochemical sensors based on polymer microrings with sharp asymmetrical resonance," Appl. Phys. Lett. 83, 1527-1529 (2003).
[CrossRef]

2002 (4)

P. Rabiei, W. H. Steier, Z. Cheng, and L. R. Dalton, "Polymer microring filters and modulators," J. Lightwave Technol. 20, 1968-1975 (2002).
[CrossRef]

M. Lee, H. E. Katz, Ch. Erben, D. M. Gill, P. Gopalan, J. D. Heber, and D. J. McGee, "Broadband modulation of light by using an electro-optic polymer," Science 298, 1401-1403 (2002).
[CrossRef] [PubMed]

S. H. Fan, "Sharp asymmetric line shapes in side-coupled waveguide-cavity systems," Appl. Phys. Lett. 80, 908-910 (2002).
[CrossRef]

I. L. Gheorma and R. M. Osgood, "Fundamental limitations of optical resonator based on high-speed EO modulators," IEEE Photon. Technol. Lett. 14, 795-797 (2002).
[CrossRef]

2000 (3)

P. P. Absil, J. V. Hryniewicz, B. E. Little, R. A. Wilson, L. G. Joneckis, and P. T. Ho, "Compact microring notch filters," IEEE Photon. Technol. Lett. 12, 398-400 (2000).
[CrossRef]

Y. Q. Shi, C. Zhang, H. Zhang, J. H. Bechtel, L. R. Dalton, B. H. Robinson, and W. H. Steier, "Low (sub-1-volt) halfwave voltage polymeric electro-optic modulators achieved by controlling chromophore shape," Science 288, 119-122 (2000).
[CrossRef]

A. Galvan-Gonzalez, M. Canva, G. I. Stegeman, L. Sukhomlinova, R. J. Twieg, K. P. Chan, T. C. Kowalczyk, and H. S. Lackritz, "Photodegradation of azobenzene nonlinear optical chromophores: the influence of structure and environment," J. Opt. Soc. Am. B 17, 1992-2000 (2000).
[CrossRef]

1994 (1)

P. Prêtre, P. Kaatz, A. Bohren, P. Günter, B. Zysset, M. Ahlheim, M. Stähelin, and F. Fehr, "Modified polyimide side-chain polymers for electrooptics," Macromolecules 27, 5476-5486 (1994).
[CrossRef]

1993 (1)

M. K. Smit, E. C. M. Pennings, and H. Blok, "A normalized approach to the design of low-loss optical wave-guide bends," J. Lightwave Technol. 11, 1737-1742 (1993).
[CrossRef]

1961 (1)

U. Fano, "Effects of configuration interaction on intensities and phase shifts," Phys. Rev. 124, 1866-1878 (1961).
[CrossRef]

Absil, P. P.

P. P. Absil, J. V. Hryniewicz, B. E. Little, R. A. Wilson, L. G. Joneckis, and P. T. Ho, "Compact microring notch filters," IEEE Photon. Technol. Lett. 12, 398-400 (2000).
[CrossRef]

Ahlheim, M.

P. Prêtre, P. Kaatz, A. Bohren, P. Günter, B. Zysset, M. Ahlheim, M. Stähelin, and F. Fehr, "Modified polyimide side-chain polymers for electrooptics," Macromolecules 27, 5476-5486 (1994).
[CrossRef]

Bale, D. H.

Bechtel, J. H.

Y. Q. Shi, C. Zhang, H. Zhang, J. H. Bechtel, L. R. Dalton, B. H. Robinson, and W. H. Steier, "Low (sub-1-volt) halfwave voltage polymeric electro-optic modulators achieved by controlling chromophore shape," Science 288, 119-122 (2000).
[CrossRef]

Blok, H.

M. K. Smit, E. C. M. Pennings, and H. Blok, "A normalized approach to the design of low-loss optical wave-guide bends," J. Lightwave Technol. 11, 1737-1742 (1993).
[CrossRef]

Bohren, A.

P. Prêtre, P. Kaatz, A. Bohren, P. Günter, B. Zysset, M. Ahlheim, M. Stähelin, and F. Fehr, "Modified polyimide side-chain polymers for electrooptics," Macromolecules 27, 5476-5486 (1994).
[CrossRef]

Bortnik, B.

B. Bortnik, Y. C. Hung, H. Tazawa, B. J. Seo, J. D. Luo, A. K.-Y. Jen, W. H. Steier, and H. R. Fetterman, "Electrooptic polymer ring resonator modulation up to 165 GHz," IEEE J. Sel. Top. Quantum Electron. 13, 104-110 (2007).
[CrossRef]

Bosshard, Ch.

Canva, M.

Chan, K. P.

Chao, C. Y.

C. Y. Chao and L. J. Guo, "Biochemical sensors based on polymer microrings with sharp asymmetrical resonance," Appl. Phys. Lett. 83, 1527-1529 (2003).
[CrossRef]

Cheng, Z.

Dalton, L. R.

Derose, C. T.

Y. Enami, C. T. Derose, D. Mathine, C. Loychik, G. Greenlee, R. A. Norwood, T. D. Kim, J. Luo, Y. Tian, A. K. Y. Jen, and N. Peyghambarian, "Hybrid polymer/sol-gel waveguide modulators with exceptionally large electro-optic coefficients," Nat. Photonics 1, 180-185 (2007).
[CrossRef]

Diemeer, M. B. J.

A. Leinse, M. B. J. Diemeer, A. Rousseau, and A. Driessen, "A novel high-speed polymeric EO modulator based on a combination of a microring resonator and an MZI," IEEE Photon. Technol. Lett. 17, 2074-2076 (2005).
[CrossRef]

Driessen, A.

A. Leinse, M. B. J. Diemeer, A. Rousseau, and A. Driessen, "A novel high-speed polymeric EO modulator based on a combination of a microring resonator and an MZI," IEEE Photon. Technol. Lett. 17, 2074-2076 (2005).
[CrossRef]

Dunayevskiy, I.

Enami, Y.

Y. Enami, C. T. Derose, D. Mathine, C. Loychik, G. Greenlee, R. A. Norwood, T. D. Kim, J. Luo, Y. Tian, A. K. Y. Jen, and N. Peyghambarian, "Hybrid polymer/sol-gel waveguide modulators with exceptionally large electro-optic coefficients," Nat. Photonics 1, 180-185 (2007).
[CrossRef]

Erben, Ch.

M. Lee, H. E. Katz, Ch. Erben, D. M. Gill, P. Gopalan, J. D. Heber, and D. J. McGee, "Broadband modulation of light by using an electro-optic polymer," Science 298, 1401-1403 (2002).
[CrossRef] [PubMed]

Fan, S. H.

S. H. Fan, "Sharp asymmetric line shapes in side-coupled waveguide-cavity systems," Appl. Phys. Lett. 80, 908-910 (2002).
[CrossRef]

Fano, U.

U. Fano, "Effects of configuration interaction on intensities and phase shifts," Phys. Rev. 124, 1866-1878 (1961).
[CrossRef]

Fehr, F.

P. Prêtre, P. Kaatz, A. Bohren, P. Günter, B. Zysset, M. Ahlheim, M. Stähelin, and F. Fehr, "Modified polyimide side-chain polymers for electrooptics," Macromolecules 27, 5476-5486 (1994).
[CrossRef]

Fetterman, H. R.

B. Bortnik, Y. C. Hung, H. Tazawa, B. J. Seo, J. D. Luo, A. K.-Y. Jen, W. H. Steier, and H. R. Fetterman, "Electrooptic polymer ring resonator modulation up to 165 GHz," IEEE J. Sel. Top. Quantum Electron. 13, 104-110 (2007).
[CrossRef]

H. Tazawa, Y.-H. Kuo, I. Dunayevskiy, J. D. Luo, A. K.-Y. Jen, H. R. Fetterman, and W. H. Steier, "Ring resonatorbased electrooptic polymer traveling-wave modulator," J. Lightwave Technol. 24, 3514-3519 (2006).
[CrossRef]

Galvan-Gonzalez, A.

Gheorma, I. L.

I. L. Gheorma and R. M. Osgood, "Fundamental limitations of optical resonator based on high-speed EO modulators," IEEE Photon. Technol. Lett. 14, 795-797 (2002).
[CrossRef]

Gill, D. M.

M. Lee, H. E. Katz, Ch. Erben, D. M. Gill, P. Gopalan, J. D. Heber, and D. J. McGee, "Broadband modulation of light by using an electro-optic polymer," Science 298, 1401-1403 (2002).
[CrossRef] [PubMed]

Gopalan, P.

M. Lee, H. E. Katz, Ch. Erben, D. M. Gill, P. Gopalan, J. D. Heber, and D. J. McGee, "Broadband modulation of light by using an electro-optic polymer," Science 298, 1401-1403 (2002).
[CrossRef] [PubMed]

Greenlee, G.

Y. Enami, C. T. Derose, D. Mathine, C. Loychik, G. Greenlee, R. A. Norwood, T. D. Kim, J. Luo, Y. Tian, A. K. Y. Jen, and N. Peyghambarian, "Hybrid polymer/sol-gel waveguide modulators with exceptionally large electro-optic coefficients," Nat. Photonics 1, 180-185 (2007).
[CrossRef]

Guarino, A.

A. Guarino, G. Poberaj, D. Rezzonico, R. Degl’Innocenti, and P. Günter, "Electro-optically tunable microring resonators in lithium niobate," Nat. Photonics 1, 407-410 (2007).
[CrossRef]

D. Rezzonico, A. Guarino, C. Herzog, M. Jazbinsek, P. Günter, "High-finesse laterally coupled organic-inorganic hybrid polymer microring resonators for VLSI photonics," IEEE Photon. Technol. Lett. 18,865-867 (2006).
[CrossRef]

Günter, P.

D. Rezzonico, M. Jazbinsek, P. Günter, Ch. Bosshard, D. H. Bale, Y. Liao, L. R. Dalton, P. J. Reid, "Photostability studies of p-conjugated chromophores with resonant and nonresonant light excitation for long-life polymeric telecommunication devices," J. Opt. Soc. Am. B 24, 2199-2207 (2007).
[CrossRef]

D. Rezzonico, A. Guarino, C. Herzog, M. Jazbinsek, P. Günter, "High-finesse laterally coupled organic-inorganic hybrid polymer microring resonators for VLSI photonics," IEEE Photon. Technol. Lett. 18,865-867 (2006).
[CrossRef]

P. Prêtre, P. Kaatz, A. Bohren, P. Günter, B. Zysset, M. Ahlheim, M. Stähelin, and F. Fehr, "Modified polyimide side-chain polymers for electrooptics," Macromolecules 27, 5476-5486 (1994).
[CrossRef]

Guo, L. J.

C. Y. Chao and L. J. Guo, "Biochemical sensors based on polymer microrings with sharp asymmetrical resonance," Appl. Phys. Lett. 83, 1527-1529 (2003).
[CrossRef]

Hau, S.

T. D. Kim, J. Luo, J. W. Ka, S. Hau, Y. Tian, Z. Shi, N. M. Tucker, S. H. Jang, J. W. Kang, and A. K. Y. Jen, "Ultralarge and thermally stable electro-optic activities from DielsAlder crosslinkable polymers containing binary chromophore Systems," Adv. Mater. 18, 3038-3042 (2006)
[CrossRef]

Heber, J. D.

M. Lee, H. E. Katz, Ch. Erben, D. M. Gill, P. Gopalan, J. D. Heber, and D. J. McGee, "Broadband modulation of light by using an electro-optic polymer," Science 298, 1401-1403 (2002).
[CrossRef] [PubMed]

Herzog, C.

D. Rezzonico, A. Guarino, C. Herzog, M. Jazbinsek, P. Günter, "High-finesse laterally coupled organic-inorganic hybrid polymer microring resonators for VLSI photonics," IEEE Photon. Technol. Lett. 18,865-867 (2006).
[CrossRef]

Ho, P. T.

P. P. Absil, J. V. Hryniewicz, B. E. Little, R. A. Wilson, L. G. Joneckis, and P. T. Ho, "Compact microring notch filters," IEEE Photon. Technol. Lett. 12, 398-400 (2000).
[CrossRef]

Hryniewicz, J. V.

P. P. Absil, J. V. Hryniewicz, B. E. Little, R. A. Wilson, L. G. Joneckis, and P. T. Ho, "Compact microring notch filters," IEEE Photon. Technol. Lett. 12, 398-400 (2000).
[CrossRef]

Hung, Y. C.

B. Bortnik, Y. C. Hung, H. Tazawa, B. J. Seo, J. D. Luo, A. K.-Y. Jen, W. H. Steier, and H. R. Fetterman, "Electrooptic polymer ring resonator modulation up to 165 GHz," IEEE J. Sel. Top. Quantum Electron. 13, 104-110 (2007).
[CrossRef]

Jang, S. H.

T. D. Kim, J. Luo, J. W. Ka, S. Hau, Y. Tian, Z. Shi, N. M. Tucker, S. H. Jang, J. W. Kang, and A. K. Y. Jen, "Ultralarge and thermally stable electro-optic activities from DielsAlder crosslinkable polymers containing binary chromophore Systems," Adv. Mater. 18, 3038-3042 (2006)
[CrossRef]

Jazbinsek, M.

D. Rezzonico, M. Jazbinsek, P. Günter, Ch. Bosshard, D. H. Bale, Y. Liao, L. R. Dalton, P. J. Reid, "Photostability studies of p-conjugated chromophores with resonant and nonresonant light excitation for long-life polymeric telecommunication devices," J. Opt. Soc. Am. B 24, 2199-2207 (2007).
[CrossRef]

D. Rezzonico, A. Guarino, C. Herzog, M. Jazbinsek, P. Günter, "High-finesse laterally coupled organic-inorganic hybrid polymer microring resonators for VLSI photonics," IEEE Photon. Technol. Lett. 18,865-867 (2006).
[CrossRef]

Jen, A. K. Y.

Y. Enami, C. T. Derose, D. Mathine, C. Loychik, G. Greenlee, R. A. Norwood, T. D. Kim, J. Luo, Y. Tian, A. K. Y. Jen, and N. Peyghambarian, "Hybrid polymer/sol-gel waveguide modulators with exceptionally large electro-optic coefficients," Nat. Photonics 1, 180-185 (2007).
[CrossRef]

T. D. Kim, J. Luo, J. W. Ka, S. Hau, Y. Tian, Z. Shi, N. M. Tucker, S. H. Jang, J. W. Kang, and A. K. Y. Jen, "Ultralarge and thermally stable electro-optic activities from DielsAlder crosslinkable polymers containing binary chromophore Systems," Adv. Mater. 18, 3038-3042 (2006)
[CrossRef]

Jen, A. K.-Y.

B. Bortnik, Y. C. Hung, H. Tazawa, B. J. Seo, J. D. Luo, A. K.-Y. Jen, W. H. Steier, and H. R. Fetterman, "Electrooptic polymer ring resonator modulation up to 165 GHz," IEEE J. Sel. Top. Quantum Electron. 13, 104-110 (2007).
[CrossRef]

H. Tazawa, Y.-H. Kuo, I. Dunayevskiy, J. D. Luo, A. K.-Y. Jen, H. R. Fetterman, and W. H. Steier, "Ring resonatorbased electrooptic polymer traveling-wave modulator," J. Lightwave Technol. 24, 3514-3519 (2006).
[CrossRef]

Joneckis, L. G.

P. P. Absil, J. V. Hryniewicz, B. E. Little, R. A. Wilson, L. G. Joneckis, and P. T. Ho, "Compact microring notch filters," IEEE Photon. Technol. Lett. 12, 398-400 (2000).
[CrossRef]

Ka, J. W.

T. D. Kim, J. Luo, J. W. Ka, S. Hau, Y. Tian, Z. Shi, N. M. Tucker, S. H. Jang, J. W. Kang, and A. K. Y. Jen, "Ultralarge and thermally stable electro-optic activities from DielsAlder crosslinkable polymers containing binary chromophore Systems," Adv. Mater. 18, 3038-3042 (2006)
[CrossRef]

Kaatz, P.

P. Prêtre, P. Kaatz, A. Bohren, P. Günter, B. Zysset, M. Ahlheim, M. Stähelin, and F. Fehr, "Modified polyimide side-chain polymers for electrooptics," Macromolecules 27, 5476-5486 (1994).
[CrossRef]

Kang, J. W.

T. D. Kim, J. Luo, J. W. Ka, S. Hau, Y. Tian, Z. Shi, N. M. Tucker, S. H. Jang, J. W. Kang, and A. K. Y. Jen, "Ultralarge and thermally stable electro-optic activities from DielsAlder crosslinkable polymers containing binary chromophore Systems," Adv. Mater. 18, 3038-3042 (2006)
[CrossRef]

Katz, H. E.

M. Lee, H. E. Katz, Ch. Erben, D. M. Gill, P. Gopalan, J. D. Heber, and D. J. McGee, "Broadband modulation of light by using an electro-optic polymer," Science 298, 1401-1403 (2002).
[CrossRef] [PubMed]

Kim, T. D.

Y. Enami, C. T. Derose, D. Mathine, C. Loychik, G. Greenlee, R. A. Norwood, T. D. Kim, J. Luo, Y. Tian, A. K. Y. Jen, and N. Peyghambarian, "Hybrid polymer/sol-gel waveguide modulators with exceptionally large electro-optic coefficients," Nat. Photonics 1, 180-185 (2007).
[CrossRef]

T. D. Kim, J. Luo, J. W. Ka, S. Hau, Y. Tian, Z. Shi, N. M. Tucker, S. H. Jang, J. W. Kang, and A. K. Y. Jen, "Ultralarge and thermally stable electro-optic activities from DielsAlder crosslinkable polymers containing binary chromophore Systems," Adv. Mater. 18, 3038-3042 (2006)
[CrossRef]

Kowalczyk, T. C.

Kuo, Y.-H.

Lackritz, H. S.

Lee, M.

M. Lee, H. E. Katz, Ch. Erben, D. M. Gill, P. Gopalan, J. D. Heber, and D. J. McGee, "Broadband modulation of light by using an electro-optic polymer," Science 298, 1401-1403 (2002).
[CrossRef] [PubMed]

Leinse, A.

A. Leinse, M. B. J. Diemeer, A. Rousseau, and A. Driessen, "A novel high-speed polymeric EO modulator based on a combination of a microring resonator and an MZI," IEEE Photon. Technol. Lett. 17, 2074-2076 (2005).
[CrossRef]

Li, X.

Liao, Y.

Lipson, M.

Q. F. Xu, B. Schmidt, S. Pradhan, and M. Lipson, "Micrometre-scale silicon electro-optic modulator," Nature 435, 325-327 (2005).
[CrossRef] [PubMed]

Little, B. E.

P. P. Absil, J. V. Hryniewicz, B. E. Little, R. A. Wilson, L. G. Joneckis, and P. T. Ho, "Compact microring notch filters," IEEE Photon. Technol. Lett. 12, 398-400 (2000).
[CrossRef]

Loychik, C.

Y. Enami, C. T. Derose, D. Mathine, C. Loychik, G. Greenlee, R. A. Norwood, T. D. Kim, J. Luo, Y. Tian, A. K. Y. Jen, and N. Peyghambarian, "Hybrid polymer/sol-gel waveguide modulators with exceptionally large electro-optic coefficients," Nat. Photonics 1, 180-185 (2007).
[CrossRef]

Lu, Y.

Luo, J.

Y. Enami, C. T. Derose, D. Mathine, C. Loychik, G. Greenlee, R. A. Norwood, T. D. Kim, J. Luo, Y. Tian, A. K. Y. Jen, and N. Peyghambarian, "Hybrid polymer/sol-gel waveguide modulators with exceptionally large electro-optic coefficients," Nat. Photonics 1, 180-185 (2007).
[CrossRef]

T. D. Kim, J. Luo, J. W. Ka, S. Hau, Y. Tian, Z. Shi, N. M. Tucker, S. H. Jang, J. W. Kang, and A. K. Y. Jen, "Ultralarge and thermally stable electro-optic activities from DielsAlder crosslinkable polymers containing binary chromophore Systems," Adv. Mater. 18, 3038-3042 (2006)
[CrossRef]

Luo, J. D.

B. Bortnik, Y. C. Hung, H. Tazawa, B. J. Seo, J. D. Luo, A. K.-Y. Jen, W. H. Steier, and H. R. Fetterman, "Electrooptic polymer ring resonator modulation up to 165 GHz," IEEE J. Sel. Top. Quantum Electron. 13, 104-110 (2007).
[CrossRef]

H. Tazawa, Y.-H. Kuo, I. Dunayevskiy, J. D. Luo, A. K.-Y. Jen, H. R. Fetterman, and W. H. Steier, "Ring resonatorbased electrooptic polymer traveling-wave modulator," J. Lightwave Technol. 24, 3514-3519 (2006).
[CrossRef]

Mathine, D.

Y. Enami, C. T. Derose, D. Mathine, C. Loychik, G. Greenlee, R. A. Norwood, T. D. Kim, J. Luo, Y. Tian, A. K. Y. Jen, and N. Peyghambarian, "Hybrid polymer/sol-gel waveguide modulators with exceptionally large electro-optic coefficients," Nat. Photonics 1, 180-185 (2007).
[CrossRef]

McGee, D. J.

M. Lee, H. E. Katz, Ch. Erben, D. M. Gill, P. Gopalan, J. D. Heber, and D. J. McGee, "Broadband modulation of light by using an electro-optic polymer," Science 298, 1401-1403 (2002).
[CrossRef] [PubMed]

Norwood, R. A.

Y. Enami, C. T. Derose, D. Mathine, C. Loychik, G. Greenlee, R. A. Norwood, T. D. Kim, J. Luo, Y. Tian, A. K. Y. Jen, and N. Peyghambarian, "Hybrid polymer/sol-gel waveguide modulators with exceptionally large electro-optic coefficients," Nat. Photonics 1, 180-185 (2007).
[CrossRef]

Osgood, R. M.

I. L. Gheorma and R. M. Osgood, "Fundamental limitations of optical resonator based on high-speed EO modulators," IEEE Photon. Technol. Lett. 14, 795-797 (2002).
[CrossRef]

Pennings, E. C. M.

M. K. Smit, E. C. M. Pennings, and H. Blok, "A normalized approach to the design of low-loss optical wave-guide bends," J. Lightwave Technol. 11, 1737-1742 (1993).
[CrossRef]

Peyghambarian, N.

Y. Enami, C. T. Derose, D. Mathine, C. Loychik, G. Greenlee, R. A. Norwood, T. D. Kim, J. Luo, Y. Tian, A. K. Y. Jen, and N. Peyghambarian, "Hybrid polymer/sol-gel waveguide modulators with exceptionally large electro-optic coefficients," Nat. Photonics 1, 180-185 (2007).
[CrossRef]

Poberaj, G.

A. Guarino, G. Poberaj, D. Rezzonico, R. Degl’Innocenti, and P. Günter, "Electro-optically tunable microring resonators in lithium niobate," Nat. Photonics 1, 407-410 (2007).
[CrossRef]

Pradhan, S.

Q. F. Xu, B. Schmidt, S. Pradhan, and M. Lipson, "Micrometre-scale silicon electro-optic modulator," Nature 435, 325-327 (2005).
[CrossRef] [PubMed]

Prêtre, P.

P. Prêtre, P. Kaatz, A. Bohren, P. Günter, B. Zysset, M. Ahlheim, M. Stähelin, and F. Fehr, "Modified polyimide side-chain polymers for electrooptics," Macromolecules 27, 5476-5486 (1994).
[CrossRef]

Rabiei, P.

Reid, P. J.

Rezzonico, D.

D. Rezzonico, M. Jazbinsek, P. Günter, Ch. Bosshard, D. H. Bale, Y. Liao, L. R. Dalton, P. J. Reid, "Photostability studies of p-conjugated chromophores with resonant and nonresonant light excitation for long-life polymeric telecommunication devices," J. Opt. Soc. Am. B 24, 2199-2207 (2007).
[CrossRef]

A. Guarino, G. Poberaj, D. Rezzonico, R. Degl’Innocenti, and P. Günter, "Electro-optically tunable microring resonators in lithium niobate," Nat. Photonics 1, 407-410 (2007).
[CrossRef]

D. Rezzonico, A. Guarino, C. Herzog, M. Jazbinsek, P. Günter, "High-finesse laterally coupled organic-inorganic hybrid polymer microring resonators for VLSI photonics," IEEE Photon. Technol. Lett. 18,865-867 (2006).
[CrossRef]

Robinson, B. H.

Y. Q. Shi, C. Zhang, H. Zhang, J. H. Bechtel, L. R. Dalton, B. H. Robinson, and W. H. Steier, "Low (sub-1-volt) halfwave voltage polymeric electro-optic modulators achieved by controlling chromophore shape," Science 288, 119-122 (2000).
[CrossRef]

Rousseau, A.

A. Leinse, M. B. J. Diemeer, A. Rousseau, and A. Driessen, "A novel high-speed polymeric EO modulator based on a combination of a microring resonator and an MZI," IEEE Photon. Technol. Lett. 17, 2074-2076 (2005).
[CrossRef]

Schmidt, B.

Q. F. Xu, B. Schmidt, S. Pradhan, and M. Lipson, "Micrometre-scale silicon electro-optic modulator," Nature 435, 325-327 (2005).
[CrossRef] [PubMed]

Seo, B. J.

B. Bortnik, Y. C. Hung, H. Tazawa, B. J. Seo, J. D. Luo, A. K.-Y. Jen, W. H. Steier, and H. R. Fetterman, "Electrooptic polymer ring resonator modulation up to 165 GHz," IEEE J. Sel. Top. Quantum Electron. 13, 104-110 (2007).
[CrossRef]

Shi, Y. Q.

Y. Q. Shi, C. Zhang, H. Zhang, J. H. Bechtel, L. R. Dalton, B. H. Robinson, and W. H. Steier, "Low (sub-1-volt) halfwave voltage polymeric electro-optic modulators achieved by controlling chromophore shape," Science 288, 119-122 (2000).
[CrossRef]

Shi, Z.

T. D. Kim, J. Luo, J. W. Ka, S. Hau, Y. Tian, Z. Shi, N. M. Tucker, S. H. Jang, J. W. Kang, and A. K. Y. Jen, "Ultralarge and thermally stable electro-optic activities from DielsAlder crosslinkable polymers containing binary chromophore Systems," Adv. Mater. 18, 3038-3042 (2006)
[CrossRef]

Smit, M. K.

M. K. Smit, E. C. M. Pennings, and H. Blok, "A normalized approach to the design of low-loss optical wave-guide bends," J. Lightwave Technol. 11, 1737-1742 (1993).
[CrossRef]

Stähelin, M.

P. Prêtre, P. Kaatz, A. Bohren, P. Günter, B. Zysset, M. Ahlheim, M. Stähelin, and F. Fehr, "Modified polyimide side-chain polymers for electrooptics," Macromolecules 27, 5476-5486 (1994).
[CrossRef]

Stegeman, G. I.

Steier, W. H.

B. Bortnik, Y. C. Hung, H. Tazawa, B. J. Seo, J. D. Luo, A. K.-Y. Jen, W. H. Steier, and H. R. Fetterman, "Electrooptic polymer ring resonator modulation up to 165 GHz," IEEE J. Sel. Top. Quantum Electron. 13, 104-110 (2007).
[CrossRef]

H. Tazawa and W. H. Steier, "Analysis of ring resonator-based traveling-wave modulators," IEEE Photon. Technol. Lett. 18, 211-213 (2006).
[CrossRef]

H. Tazawa, Y.-H. Kuo, I. Dunayevskiy, J. D. Luo, A. K.-Y. Jen, H. R. Fetterman, and W. H. Steier, "Ring resonatorbased electrooptic polymer traveling-wave modulator," J. Lightwave Technol. 24, 3514-3519 (2006).
[CrossRef]

P. Rabiei, W. H. Steier, Z. Cheng, and L. R. Dalton, "Polymer microring filters and modulators," J. Lightwave Technol. 20, 1968-1975 (2002).
[CrossRef]

Y. Q. Shi, C. Zhang, H. Zhang, J. H. Bechtel, L. R. Dalton, B. H. Robinson, and W. H. Steier, "Low (sub-1-volt) halfwave voltage polymeric electro-optic modulators achieved by controlling chromophore shape," Science 288, 119-122 (2000).
[CrossRef]

Sukhomlinova, L.

Tazawa, H.

B. Bortnik, Y. C. Hung, H. Tazawa, B. J. Seo, J. D. Luo, A. K.-Y. Jen, W. H. Steier, and H. R. Fetterman, "Electrooptic polymer ring resonator modulation up to 165 GHz," IEEE J. Sel. Top. Quantum Electron. 13, 104-110 (2007).
[CrossRef]

H. Tazawa and W. H. Steier, "Analysis of ring resonator-based traveling-wave modulators," IEEE Photon. Technol. Lett. 18, 211-213 (2006).
[CrossRef]

H. Tazawa, Y.-H. Kuo, I. Dunayevskiy, J. D. Luo, A. K.-Y. Jen, H. R. Fetterman, and W. H. Steier, "Ring resonatorbased electrooptic polymer traveling-wave modulator," J. Lightwave Technol. 24, 3514-3519 (2006).
[CrossRef]

Tian, Y.

Y. Enami, C. T. Derose, D. Mathine, C. Loychik, G. Greenlee, R. A. Norwood, T. D. Kim, J. Luo, Y. Tian, A. K. Y. Jen, and N. Peyghambarian, "Hybrid polymer/sol-gel waveguide modulators with exceptionally large electro-optic coefficients," Nat. Photonics 1, 180-185 (2007).
[CrossRef]

T. D. Kim, J. Luo, J. W. Ka, S. Hau, Y. Tian, Z. Shi, N. M. Tucker, S. H. Jang, J. W. Kang, and A. K. Y. Jen, "Ultralarge and thermally stable electro-optic activities from DielsAlder crosslinkable polymers containing binary chromophore Systems," Adv. Mater. 18, 3038-3042 (2006)
[CrossRef]

Tucker, N. M.

T. D. Kim, J. Luo, J. W. Ka, S. Hau, Y. Tian, Z. Shi, N. M. Tucker, S. H. Jang, J. W. Kang, and A. K. Y. Jen, "Ultralarge and thermally stable electro-optic activities from DielsAlder crosslinkable polymers containing binary chromophore Systems," Adv. Mater. 18, 3038-3042 (2006)
[CrossRef]

Twieg, R. J.

Wang, P.

Wilson, R. A.

P. P. Absil, J. V. Hryniewicz, B. E. Little, R. A. Wilson, L. G. Joneckis, and P. T. Ho, "Compact microring notch filters," IEEE Photon. Technol. Lett. 12, 398-400 (2000).
[CrossRef]

Xu, Q. F.

Q. F. Xu, B. Schmidt, S. Pradhan, and M. Lipson, "Micrometre-scale silicon electro-optic modulator," Nature 435, 325-327 (2005).
[CrossRef] [PubMed]

Yao, J.

Zhang, C.

Y. Q. Shi, C. Zhang, H. Zhang, J. H. Bechtel, L. R. Dalton, B. H. Robinson, and W. H. Steier, "Low (sub-1-volt) halfwave voltage polymeric electro-optic modulators achieved by controlling chromophore shape," Science 288, 119-122 (2000).
[CrossRef]

Zhang, H.

Y. Q. Shi, C. Zhang, H. Zhang, J. H. Bechtel, L. R. Dalton, B. H. Robinson, and W. H. Steier, "Low (sub-1-volt) halfwave voltage polymeric electro-optic modulators achieved by controlling chromophore shape," Science 288, 119-122 (2000).
[CrossRef]

Zysset, B.

P. Prêtre, P. Kaatz, A. Bohren, P. Günter, B. Zysset, M. Ahlheim, M. Stähelin, and F. Fehr, "Modified polyimide side-chain polymers for electrooptics," Macromolecules 27, 5476-5486 (1994).
[CrossRef]

Adv. Mater. (1)

T. D. Kim, J. Luo, J. W. Ka, S. Hau, Y. Tian, Z. Shi, N. M. Tucker, S. H. Jang, J. W. Kang, and A. K. Y. Jen, "Ultralarge and thermally stable electro-optic activities from DielsAlder crosslinkable polymers containing binary chromophore Systems," Adv. Mater. 18, 3038-3042 (2006)
[CrossRef]

Appl. Phys. Lett. (2)

S. H. Fan, "Sharp asymmetric line shapes in side-coupled waveguide-cavity systems," Appl. Phys. Lett. 80, 908-910 (2002).
[CrossRef]

C. Y. Chao and L. J. Guo, "Biochemical sensors based on polymer microrings with sharp asymmetrical resonance," Appl. Phys. Lett. 83, 1527-1529 (2003).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

H. Tazawa and W. H. Steier, "Analysis of ring resonator-based traveling-wave modulators," IEEE Photon. Technol. Lett. 18, 211-213 (2006).
[CrossRef]

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

B. Bortnik, Y. C. Hung, H. Tazawa, B. J. Seo, J. D. Luo, A. K.-Y. Jen, W. H. Steier, and H. R. Fetterman, "Electrooptic polymer ring resonator modulation up to 165 GHz," IEEE J. Sel. Top. Quantum Electron. 13, 104-110 (2007).
[CrossRef]

IEEE Photon. Technol. Lett. (4)

D. Rezzonico, A. Guarino, C. Herzog, M. Jazbinsek, P. Günter, "High-finesse laterally coupled organic-inorganic hybrid polymer microring resonators for VLSI photonics," IEEE Photon. Technol. Lett. 18,865-867 (2006).
[CrossRef]

I. L. Gheorma and R. M. Osgood, "Fundamental limitations of optical resonator based on high-speed EO modulators," IEEE Photon. Technol. Lett. 14, 795-797 (2002).
[CrossRef]

P. P. Absil, J. V. Hryniewicz, B. E. Little, R. A. Wilson, L. G. Joneckis, and P. T. Ho, "Compact microring notch filters," IEEE Photon. Technol. Lett. 12, 398-400 (2000).
[CrossRef]

A. Leinse, M. B. J. Diemeer, A. Rousseau, and A. Driessen, "A novel high-speed polymeric EO modulator based on a combination of a microring resonator and an MZI," IEEE Photon. Technol. Lett. 17, 2074-2076 (2005).
[CrossRef]

J. Lightwave Technol. (3)

J. Opt. Soc. Am. B (2)

Macromolecules (1)

P. Prêtre, P. Kaatz, A. Bohren, P. Günter, B. Zysset, M. Ahlheim, M. Stähelin, and F. Fehr, "Modified polyimide side-chain polymers for electrooptics," Macromolecules 27, 5476-5486 (1994).
[CrossRef]

Nat. Photonics (2)

A. Guarino, G. Poberaj, D. Rezzonico, R. Degl’Innocenti, and P. Günter, "Electro-optically tunable microring resonators in lithium niobate," Nat. Photonics 1, 407-410 (2007).
[CrossRef]

Y. Enami, C. T. Derose, D. Mathine, C. Loychik, G. Greenlee, R. A. Norwood, T. D. Kim, J. Luo, Y. Tian, A. K. Y. Jen, and N. Peyghambarian, "Hybrid polymer/sol-gel waveguide modulators with exceptionally large electro-optic coefficients," Nat. Photonics 1, 180-185 (2007).
[CrossRef]

Nature (1)

Q. F. Xu, B. Schmidt, S. Pradhan, and M. Lipson, "Micrometre-scale silicon electro-optic modulator," Nature 435, 325-327 (2005).
[CrossRef] [PubMed]

Opt. Lett. (1)

Phys. Rev. (1)

U. Fano, "Effects of configuration interaction on intensities and phase shifts," Phys. Rev. 124, 1866-1878 (1961).
[CrossRef]

Science (2)

M. Lee, H. E. Katz, Ch. Erben, D. M. Gill, P. Gopalan, J. D. Heber, and D. J. McGee, "Broadband modulation of light by using an electro-optic polymer," Science 298, 1401-1403 (2002).
[CrossRef] [PubMed]

Y. Q. Shi, C. Zhang, H. Zhang, J. H. Bechtel, L. R. Dalton, B. H. Robinson, and W. H. Steier, "Low (sub-1-volt) halfwave voltage polymeric electro-optic modulators achieved by controlling chromophore shape," Science 288, 119-122 (2000).
[CrossRef]

Other (2)

B. E. A. Saleh and M. C. Teich, Fundamental of Photonics (Wiley, 1991).
[CrossRef]

K. Okamoto, Fundamentals of Optical Waveguides (Academic, 2000).

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Figures (12)

Fig. 1.
Fig. 1.

Left:Scheme of a traveling wave resonator with lossless coupler. κ tw is the amplitude coupling constant and τ tw is the amplitude transmission constant, where κ 2 tw+τ 2 tw=1. Right: Operation principle of a resonator-based EO modulation. ΔT is the resonator signal extinction, while Δφ is the EO induced round-trip phase modulation amplitude.

Fig. 2.
Fig. 2.

Vertical power coupling κ 2 tw between a straight and a 32λ-radius bent waveguide (corresponding to a radius of 50µm for a wavelength λ=1.55µm) as a function of the effective index difference Δn and the mode overlap coupling coefficient χ, expressed through the dimensionless parameter χ ˜ χλ. The calculations are made by perturbation theory assuming a homogeneous field interaction along the whole interaction length l=22λ.

Fig. 3.
Fig. 3.

Operation principle of a Charon microresonator. Out of resonance (left), most of the light entering the coupler is lost due to the distortion of the bus waveguide. In resonance (right), the ring “carries” the light across the lossy coupler leading to intensity maxima at the throughput port.

Fig. 4.
Fig. 4.

Scheme of a Charon coupler between a straight waveguide and a microring resonator. The model of the coupler consists of three parts: two lossless partial couplers along with a lossy propagation region. The amplitude coupling constant κ and the transmission factor τ at the two partial couplers are real and must guarantee energy conservation, κ 2+τ 2=1. The field loss factor of the cavity is ξ, while ϕ is the resonator round-trip phase change. The relations between the different optical field amplitudes are expressed in matrix form.

Fig. 5.
Fig. 5.

Throughput port transmission characteristics of Charon microresonators for partial coupler energy exchange coefficients κ 2=[0.05,0.1,0.5], energy coupler loss parameters r 2=[0.9,0.6,0.1] an phase asymmetry δ=[0,π/2,0], respectively. Slope, extinction and insertion loss for these curves are marked with the corresponding symbol in Fig. 7. All curves are calculated for an amplitude resonator loss factor ξ=0.9, ring radius R=50µm and effective refractive index n eff=1.7.

Fig. 6.
Fig. 6.

Charon transmission spectrum dependence on the coupler phase-shift δ for overcoupled microresonators (κ 2=0.35,ξ=0.9). The phase asymmetry δ=3π/4(◇) increases the maximum slope |dT/dλ|max by more than one order of magnitude as compared to δ=0(★). The photon lifetime of the lossy-coupler asymmetric resonator (r 2=0.6, ○) is reduced by 30% with respect to the lifetime of a lossless-coupler asymmetric cavity (r 2=1, ◇), but the maximum slopes are similar. Slope, extinction and insertion loss for these curves are marked with the corresponding symbol in Fig. 7.

Fig. 7.
Fig. 7.

Impact of the lossy Charon coupler on the slope |dT/dλ|max, the signal extinction ΔT=T max-T min and the insertion loss 1-T max for three different coupler phase asymmetries δ=[0,π/2,3π/4], varying energy coupling constants κ 2 and losses r 2, for a constant ξ=0.9. The symbols ⎔,★,*,○,□, and ◇ represent the parameters for the spectra depicted in Figs. 5 and 6.

Fig. 8.
Fig. 8.

Maximum spectral slope |dT/dλ|max and corresponding equivalent half wave voltage Veq π (see Eq. (5)) as a function of the energy coupling κ 2 for symmetric (δ=0) and strongly asymmetric (δ=3/4π) Charon couplers, respectively. The coupling acceptance for 1.3-V half wave voltage or better devices is increased from Δκ 2~0.013 (yellow shaded area) if δ=0 to Δκ 2~0.091 when δ=3π/4 (green shaded area). A nonlinear optical polymer with EO coefficient r 33~250pm/V [14] has been considered.

Fig. 9.
Fig. 9.

Structure of the azo-stilbene based polyimide SANDM2.

Fig. 10.
Fig. 10.

Schematic patterning procedure. (A) The straight bus waveguides of SU-8 were directly written by standard photolithography and covered by the cladding resin Ormocomp. (B) The quartz mold with the microrings was pressed against the sample, structuring the rings in form of grooves. Alternatively, either a deformation or a displacement of the bus waveguides occurred by slight shifting of the stamp in contact with the SU-8 structures and the patterns were fixed by UV exposure. The PPL-g-PEG coating allowed for clean removal of the stamp from the molded Ormocomp layer. (C) The sample was coated with the electro-optic polymer SANDM2 to fill the grooves. After vacuum drying, the excess layer was removed by RIE. (D) The devices were covered with a cladding layer and a gold top electrode.

Fig. 11.
Fig. 11.

Laterally coupled Charon microring. Left: Microscope picture of a lateral Charon microring’s coupler with front-view scheme. The lateral displacement of the bus waveguide is induced by a horizontal shift of the molding stamp. The rings had a radius of 50µm and a trapezoidal cross section with bases of 3 and 5µm, respectively, while their height was 2µm. Right: Measured TE transmitted intensity (solid line, left scale) and the corresponding analytical curve according to Eq. (9) (dotted line, right scale) showing high extinction peak-like resonances. The curve parameters are: δ=1.7rad,κ 2=0.4, r 2=0.03.

Fig. 12.
Fig. 12.

Vertically coupled Charon microring. Left: Microscope view of a vertical Charon microring’s coupler with front-view scheme. A deformation of the bus waveguide is produced by slightly excessive pressure of the mold. The 50-µm radius rings had a trapezoidal cross section with bases of 2 and 3µm, respectively, and height of 2.7µm. Right: Particular of the measured TE transmitted intensity (solid line, left scale) and the corresponding analytical curve according to Eq. (9) (dotted line, right scale), showing strongly asymmetric Fano resonances with approximately linear steepest resonance edge (blue straight line). The curve parameters are: δ=2.0rad,κ 2=0.07,r 2=0.4. A wider portion of the spectrum is depicted in the inset.

Equations (9)

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T ( ϕ ) = E out E in 2 = 1 ( 1 ξ 2 ) ( 1 τ tw 2 ) ( 1 τ tw ξ ) 2 + 4 τ tw ξ sin 2 ( ϕ 2 ) .
T ( ϕ ) = 1 T R 1 + ( 2 𝓕 π ) 2 sin 2 ( ϕ 2 ) ,
Δ ϕ = 2 π λ ( n 3 2 r eff V m d ) L ,
d T d ϕ max = 3 3 8 T R π 𝓕 ,
V π eq = π 2 1 d T d V max = π 2 1 δ ϕ δ V d T d ϕ max ,
τ cav nL 2 πc 𝓕 .
κ tw 2 ( l ) = P sin 2 ( ql ) ,
( D d ) = ( τ τ ) ( α 0 0 β ) ( τ τ ) ( A a ) .
T ( ϕ ) = α ( 1 κ 2 ) β κ 2 ( α + β ) 2 κ 2 ( 1 κ 2 ) ξ e 1 + ( α κ 2 β ( 1 κ 2 ) ) ξ e 2 .

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