Abstract

Silicon nitride (Si3N4) optical ring resonators provide exceptional opportunities for low-loss integrated optics. Here we study the transmission through a multimode waveguide coupled to a Si3N4 ring resonator. By coupling single-mode fibers to both input and output ports of the waveguide we selectively excite and probe combinations of modes in the waveguide. Strong asymmetric Fano resonances are observed and the degree of asymmetry can be tuned through the positions of the input and output fibers. The Fano resonance results from the interference between modes of the waveguide and light that couples resonantly to the ring resonator. We develop a theoretical model based on the coupled mode theory to describe the experimental results. The large extension of the optical modes out of the Si3N4 core makes this system promising for sensing applications.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. F. Xia, L. Sekaric, Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1, 65–71 (2007).
    [CrossRef]
  2. B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, E. Ippen, “Vertically coupled glass microring resonator channel dropping filters,” IEEE Photon. Technol. Lett. 11, 215–217 (1999).
    [CrossRef]
  3. V. R. Almeida, C. A. Barrios, R. R. Panepucci, M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
    [CrossRef] [PubMed]
  4. A. Ksendzov, Y. Lin, “Integrated optics ring-resonator sensors for protein detection,” Opt. Lett. 30, 3344–3346 (2005).
    [CrossRef]
  5. S. Fan, “Sharp asymmetric line shapes in side-coupled waveguide-cavity systems,” Appl. Phys. Lett. 80, 908–910 (2002).
    [CrossRef]
  6. C.-Y. Chao, L. J. Guo, “Biochemical sensors based on polymer microrings with sharp asymmetrical resonance,” Appl. Phys. Lett. 83, 1527–1529 (2003).
    [CrossRef]
  7. A. Chiba, H. Fujiwara, J. Hotta, S. Takeuchi, K. Sasaki, “Fano resonance in a multimode tapered fiber coupled with a microspherical cavity,” Appl. Phys. Lett. 86, 261106 (2005).
    [CrossRef]
  8. A. C. Ruege, R. M. Reano, “Sharp Fano resonances from a two-mode waveguide coupled to a single-mode ring resonator,” J. Lightwave Technol. 28, 2964–2968 (2010).
    [CrossRef]
  9. A. C. Ruege, R. M. Reano, “Multimode waveguide-cavity sensor based on fringe visibility detection,” Opt. Express 17, 4295–4305 (2009).
    [CrossRef] [PubMed]
  10. B.-B. Li, Y.-F. Xiao, C.-L. Zou, Y.-C. Liu, X.-F. Jiang, Y.-L. Chen, Y. Li, Q. Gong, “Experimental observation of Fano resonance in a single whispering-gallery microresonator,” Appl. Phys. Lett. 98, 021116 (2011).
    [CrossRef]
  11. Y.-F. Xiao, L. He, J. Zhu, L. Yang, “Electromagnetically induced transparency-like effect in a single polydimethylsiloxane-coated silica microtoroid,” Appl. Phys. Lett. 94, 231115 (2009).
    [CrossRef]
  12. B.-B. Li, Y.-F. Xiao, C.-L. Zou, X.-F. Jiang, Y.-C. Liu, F.-W. Sun, Y. Li, Q. Gong, “Experimental controlling of Fano resonance in indirectly coupled whispering-gallery microresonators,” Appl. Phys. Lett. 100, 021108 (2012).
    [CrossRef]
  13. P. Rabiei, W. H. Steier, “Polymer microring resonators,” in Optical Microcavities, K. Vahala, eds. (World Scientific, 2005), pp. 321–324.
  14. S. Fan, W. Suh, J. D. Joannopoulos, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A 20, 569–572 (2003).
    [CrossRef]
  15. J. F. Bauters, M. J. R. Heck, D. John, D. Dai, M.-C. Tien, J. S. Barton, A. Leinse, R. G. Heideman, D. J. Blumenthal, J. E. Bowers, “Ultra-low-loss high-aspect-ratio Si3N4 waveguides,” Opt. Express 19, 3163–3174 (2011).
    [CrossRef] [PubMed]
  16. M.-C. Tien, J. F. Bauters, M. J. R. Heck, D. T. Spencer, D. J. Blumenthal, J. E. Bowers, “Ultra-high quality factor planar Si3N4 ring resonators on Si substrates,” Opt. Express 19, 13551–13556 (2011).
    [CrossRef] [PubMed]
  17. R. M. Knox, P. P. Toulios, “Integrated circuits for the millimeter through optical frequency range,” in Proceedings of the Symposium on Submillimeter Waves, (Polytechnic Press, 1970), pp. 497–516.
  18. J. F. Bauters, M. J. R. Heck, D. D. John, J. S. Barton, C. M. Bruinink, A. Leinse, R. G. Heideman, D. J. Blumenthal, J. E. Bowers, “Planar waveguides with less than 0.1 dB/m propagation loss fabricated with wafer bonding,” Opt. Express 19, 24090–24101 (2011).
    [CrossRef] [PubMed]

2012 (1)

B.-B. Li, Y.-F. Xiao, C.-L. Zou, X.-F. Jiang, Y.-C. Liu, F.-W. Sun, Y. Li, Q. Gong, “Experimental controlling of Fano resonance in indirectly coupled whispering-gallery microresonators,” Appl. Phys. Lett. 100, 021108 (2012).
[CrossRef]

2011 (4)

2010 (1)

2009 (2)

A. C. Ruege, R. M. Reano, “Multimode waveguide-cavity sensor based on fringe visibility detection,” Opt. Express 17, 4295–4305 (2009).
[CrossRef] [PubMed]

Y.-F. Xiao, L. He, J. Zhu, L. Yang, “Electromagnetically induced transparency-like effect in a single polydimethylsiloxane-coated silica microtoroid,” Appl. Phys. Lett. 94, 231115 (2009).
[CrossRef]

2007 (1)

F. Xia, L. Sekaric, Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1, 65–71 (2007).
[CrossRef]

2005 (2)

A. Chiba, H. Fujiwara, J. Hotta, S. Takeuchi, K. Sasaki, “Fano resonance in a multimode tapered fiber coupled with a microspherical cavity,” Appl. Phys. Lett. 86, 261106 (2005).
[CrossRef]

A. Ksendzov, Y. Lin, “Integrated optics ring-resonator sensors for protein detection,” Opt. Lett. 30, 3344–3346 (2005).
[CrossRef]

2004 (1)

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

2003 (2)

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

S. Fan, W. Suh, J. D. Joannopoulos, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A 20, 569–572 (2003).
[CrossRef]

2002 (1)

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

1999 (1)

B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, E. Ippen, “Vertically coupled glass microring resonator channel dropping filters,” IEEE Photon. Technol. Lett. 11, 215–217 (1999).
[CrossRef]

Almeida, V. R.

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

Barrios, C. A.

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

Barton, J. S.

Bauters, J. F.

Blumenthal, D. J.

Bowers, J. E.

Bruinink, C. M.

Chao, C.-Y.

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

Chen, Y.-L.

B.-B. Li, Y.-F. Xiao, C.-L. Zou, Y.-C. Liu, X.-F. Jiang, Y.-L. Chen, Y. Li, Q. Gong, “Experimental observation of Fano resonance in a single whispering-gallery microresonator,” Appl. Phys. Lett. 98, 021116 (2011).
[CrossRef]

Chiba, A.

A. Chiba, H. Fujiwara, J. Hotta, S. Takeuchi, K. Sasaki, “Fano resonance in a multimode tapered fiber coupled with a microspherical cavity,” Appl. Phys. Lett. 86, 261106 (2005).
[CrossRef]

Chu, S. T.

B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, E. Ippen, “Vertically coupled glass microring resonator channel dropping filters,” IEEE Photon. Technol. Lett. 11, 215–217 (1999).
[CrossRef]

Dai, D.

Fan, S.

S. Fan, W. Suh, J. D. Joannopoulos, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A 20, 569–572 (2003).
[CrossRef]

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

Fujiwara, H.

A. Chiba, H. Fujiwara, J. Hotta, S. Takeuchi, K. Sasaki, “Fano resonance in a multimode tapered fiber coupled with a microspherical cavity,” Appl. Phys. Lett. 86, 261106 (2005).
[CrossRef]

Gong, Q.

B.-B. Li, Y.-F. Xiao, C.-L. Zou, X.-F. Jiang, Y.-C. Liu, F.-W. Sun, Y. Li, Q. Gong, “Experimental controlling of Fano resonance in indirectly coupled whispering-gallery microresonators,” Appl. Phys. Lett. 100, 021108 (2012).
[CrossRef]

B.-B. Li, Y.-F. Xiao, C.-L. Zou, Y.-C. Liu, X.-F. Jiang, Y.-L. Chen, Y. Li, Q. Gong, “Experimental observation of Fano resonance in a single whispering-gallery microresonator,” Appl. Phys. Lett. 98, 021116 (2011).
[CrossRef]

Guo, L. J.

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

He, L.

Y.-F. Xiao, L. He, J. Zhu, L. Yang, “Electromagnetically induced transparency-like effect in a single polydimethylsiloxane-coated silica microtoroid,” Appl. Phys. Lett. 94, 231115 (2009).
[CrossRef]

Heck, M. J. R.

Heideman, R. G.

Hotta, J.

A. Chiba, H. Fujiwara, J. Hotta, S. Takeuchi, K. Sasaki, “Fano resonance in a multimode tapered fiber coupled with a microspherical cavity,” Appl. Phys. Lett. 86, 261106 (2005).
[CrossRef]

Ippen, E.

B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, E. Ippen, “Vertically coupled glass microring resonator channel dropping filters,” IEEE Photon. Technol. Lett. 11, 215–217 (1999).
[CrossRef]

Jiang, X.-F.

B.-B. Li, Y.-F. Xiao, C.-L. Zou, X.-F. Jiang, Y.-C. Liu, F.-W. Sun, Y. Li, Q. Gong, “Experimental controlling of Fano resonance in indirectly coupled whispering-gallery microresonators,” Appl. Phys. Lett. 100, 021108 (2012).
[CrossRef]

B.-B. Li, Y.-F. Xiao, C.-L. Zou, Y.-C. Liu, X.-F. Jiang, Y.-L. Chen, Y. Li, Q. Gong, “Experimental observation of Fano resonance in a single whispering-gallery microresonator,” Appl. Phys. Lett. 98, 021116 (2011).
[CrossRef]

Joannopoulos, J. D.

John, D.

John, D. D.

Kaneko, T.

B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, E. Ippen, “Vertically coupled glass microring resonator channel dropping filters,” IEEE Photon. Technol. Lett. 11, 215–217 (1999).
[CrossRef]

Knox, R. M.

R. M. Knox, P. P. Toulios, “Integrated circuits for the millimeter through optical frequency range,” in Proceedings of the Symposium on Submillimeter Waves, (Polytechnic Press, 1970), pp. 497–516.

Kokubun, Y.

B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, E. Ippen, “Vertically coupled glass microring resonator channel dropping filters,” IEEE Photon. Technol. Lett. 11, 215–217 (1999).
[CrossRef]

Ksendzov, A.

Leinse, A.

Li, B.-B.

B.-B. Li, Y.-F. Xiao, C.-L. Zou, X.-F. Jiang, Y.-C. Liu, F.-W. Sun, Y. Li, Q. Gong, “Experimental controlling of Fano resonance in indirectly coupled whispering-gallery microresonators,” Appl. Phys. Lett. 100, 021108 (2012).
[CrossRef]

B.-B. Li, Y.-F. Xiao, C.-L. Zou, Y.-C. Liu, X.-F. Jiang, Y.-L. Chen, Y. Li, Q. Gong, “Experimental observation of Fano resonance in a single whispering-gallery microresonator,” Appl. Phys. Lett. 98, 021116 (2011).
[CrossRef]

Li, Y.

B.-B. Li, Y.-F. Xiao, C.-L. Zou, X.-F. Jiang, Y.-C. Liu, F.-W. Sun, Y. Li, Q. Gong, “Experimental controlling of Fano resonance in indirectly coupled whispering-gallery microresonators,” Appl. Phys. Lett. 100, 021108 (2012).
[CrossRef]

B.-B. Li, Y.-F. Xiao, C.-L. Zou, Y.-C. Liu, X.-F. Jiang, Y.-L. Chen, Y. Li, Q. Gong, “Experimental observation of Fano resonance in a single whispering-gallery microresonator,” Appl. Phys. Lett. 98, 021116 (2011).
[CrossRef]

Lin, Y.

Lipson, M.

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

Little, B. E.

B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, E. Ippen, “Vertically coupled glass microring resonator channel dropping filters,” IEEE Photon. Technol. Lett. 11, 215–217 (1999).
[CrossRef]

Liu, Y.-C.

B.-B. Li, Y.-F. Xiao, C.-L. Zou, X.-F. Jiang, Y.-C. Liu, F.-W. Sun, Y. Li, Q. Gong, “Experimental controlling of Fano resonance in indirectly coupled whispering-gallery microresonators,” Appl. Phys. Lett. 100, 021108 (2012).
[CrossRef]

B.-B. Li, Y.-F. Xiao, C.-L. Zou, Y.-C. Liu, X.-F. Jiang, Y.-L. Chen, Y. Li, Q. Gong, “Experimental observation of Fano resonance in a single whispering-gallery microresonator,” Appl. Phys. Lett. 98, 021116 (2011).
[CrossRef]

Pan, W.

B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, E. Ippen, “Vertically coupled glass microring resonator channel dropping filters,” IEEE Photon. Technol. Lett. 11, 215–217 (1999).
[CrossRef]

Panepucci, R. R.

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

Rabiei, P.

P. Rabiei, W. H. Steier, “Polymer microring resonators,” in Optical Microcavities, K. Vahala, eds. (World Scientific, 2005), pp. 321–324.

Reano, R. M.

Ripin, D.

B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, E. Ippen, “Vertically coupled glass microring resonator channel dropping filters,” IEEE Photon. Technol. Lett. 11, 215–217 (1999).
[CrossRef]

Ruege, A. C.

Sasaki, K.

A. Chiba, H. Fujiwara, J. Hotta, S. Takeuchi, K. Sasaki, “Fano resonance in a multimode tapered fiber coupled with a microspherical cavity,” Appl. Phys. Lett. 86, 261106 (2005).
[CrossRef]

Sekaric, L.

F. Xia, L. Sekaric, Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1, 65–71 (2007).
[CrossRef]

Spencer, D. T.

Steier, W. H.

P. Rabiei, W. H. Steier, “Polymer microring resonators,” in Optical Microcavities, K. Vahala, eds. (World Scientific, 2005), pp. 321–324.

Suh, W.

Sun, F.-W.

B.-B. Li, Y.-F. Xiao, C.-L. Zou, X.-F. Jiang, Y.-C. Liu, F.-W. Sun, Y. Li, Q. Gong, “Experimental controlling of Fano resonance in indirectly coupled whispering-gallery microresonators,” Appl. Phys. Lett. 100, 021108 (2012).
[CrossRef]

Takeuchi, S.

A. Chiba, H. Fujiwara, J. Hotta, S. Takeuchi, K. Sasaki, “Fano resonance in a multimode tapered fiber coupled with a microspherical cavity,” Appl. Phys. Lett. 86, 261106 (2005).
[CrossRef]

Tien, M.-C.

Toulios, P. P.

R. M. Knox, P. P. Toulios, “Integrated circuits for the millimeter through optical frequency range,” in Proceedings of the Symposium on Submillimeter Waves, (Polytechnic Press, 1970), pp. 497–516.

Vlasov, Y.

F. Xia, L. Sekaric, Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1, 65–71 (2007).
[CrossRef]

Xia, F.

F. Xia, L. Sekaric, Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1, 65–71 (2007).
[CrossRef]

Xiao, Y.-F.

B.-B. Li, Y.-F. Xiao, C.-L. Zou, X.-F. Jiang, Y.-C. Liu, F.-W. Sun, Y. Li, Q. Gong, “Experimental controlling of Fano resonance in indirectly coupled whispering-gallery microresonators,” Appl. Phys. Lett. 100, 021108 (2012).
[CrossRef]

B.-B. Li, Y.-F. Xiao, C.-L. Zou, Y.-C. Liu, X.-F. Jiang, Y.-L. Chen, Y. Li, Q. Gong, “Experimental observation of Fano resonance in a single whispering-gallery microresonator,” Appl. Phys. Lett. 98, 021116 (2011).
[CrossRef]

Y.-F. Xiao, L. He, J. Zhu, L. Yang, “Electromagnetically induced transparency-like effect in a single polydimethylsiloxane-coated silica microtoroid,” Appl. Phys. Lett. 94, 231115 (2009).
[CrossRef]

Yang, L.

Y.-F. Xiao, L. He, J. Zhu, L. Yang, “Electromagnetically induced transparency-like effect in a single polydimethylsiloxane-coated silica microtoroid,” Appl. Phys. Lett. 94, 231115 (2009).
[CrossRef]

Zhu, J.

Y.-F. Xiao, L. He, J. Zhu, L. Yang, “Electromagnetically induced transparency-like effect in a single polydimethylsiloxane-coated silica microtoroid,” Appl. Phys. Lett. 94, 231115 (2009).
[CrossRef]

Zou, C.-L.

B.-B. Li, Y.-F. Xiao, C.-L. Zou, X.-F. Jiang, Y.-C. Liu, F.-W. Sun, Y. Li, Q. Gong, “Experimental controlling of Fano resonance in indirectly coupled whispering-gallery microresonators,” Appl. Phys. Lett. 100, 021108 (2012).
[CrossRef]

B.-B. Li, Y.-F. Xiao, C.-L. Zou, Y.-C. Liu, X.-F. Jiang, Y.-L. Chen, Y. Li, Q. Gong, “Experimental observation of Fano resonance in a single whispering-gallery microresonator,” Appl. Phys. Lett. 98, 021116 (2011).
[CrossRef]

Appl. Phys. Lett. (6)

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

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

A. Chiba, H. Fujiwara, J. Hotta, S. Takeuchi, K. Sasaki, “Fano resonance in a multimode tapered fiber coupled with a microspherical cavity,” Appl. Phys. Lett. 86, 261106 (2005).
[CrossRef]

B.-B. Li, Y.-F. Xiao, C.-L. Zou, Y.-C. Liu, X.-F. Jiang, Y.-L. Chen, Y. Li, Q. Gong, “Experimental observation of Fano resonance in a single whispering-gallery microresonator,” Appl. Phys. Lett. 98, 021116 (2011).
[CrossRef]

Y.-F. Xiao, L. He, J. Zhu, L. Yang, “Electromagnetically induced transparency-like effect in a single polydimethylsiloxane-coated silica microtoroid,” Appl. Phys. Lett. 94, 231115 (2009).
[CrossRef]

B.-B. Li, Y.-F. Xiao, C.-L. Zou, X.-F. Jiang, Y.-C. Liu, F.-W. Sun, Y. Li, Q. Gong, “Experimental controlling of Fano resonance in indirectly coupled whispering-gallery microresonators,” Appl. Phys. Lett. 100, 021108 (2012).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, E. Ippen, “Vertically coupled glass microring resonator channel dropping filters,” IEEE Photon. Technol. Lett. 11, 215–217 (1999).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. A (1)

Nat. Photonics (1)

F. Xia, L. Sekaric, Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1, 65–71 (2007).
[CrossRef]

Nature (1)

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

Opt. Express (4)

Opt. Lett. (1)

Other (2)

P. Rabiei, W. H. Steier, “Polymer microring resonators,” in Optical Microcavities, K. Vahala, eds. (World Scientific, 2005), pp. 321–324.

R. M. Knox, P. P. Toulios, “Integrated circuits for the millimeter through optical frequency range,” in Proceedings of the Symposium on Submillimeter Waves, (Polytechnic Press, 1970), pp. 497–516.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

Schematic drawing of a multimode waveguide coupled to a multimode ring resonator via a coupling region (CR). Light is coupled into and out of the waveguide using single-mode fibers (SM) with optical powers Pin and Pout through the fibers, respectively. Both the input and output fiber positions are tunable with respect to the center of the waveguide. The length of the waveguide section from the input (output) to the coupling region is L1 (L2). The electric fields at different positions are denoted by E1E5. The radius of the ring resonator is R.

Fig. 2
Fig. 2

Cross-sectional drawing (a) of a Si3N4 waveguide with a width of 5.25 μm and a thickness of 50 nm in SiO2 cladding and calculated TM ((b) TM0 and (c) TM1, y-component electric field or Ey) and TE ((d) TE0, (e) TE1 and (f) TE2, x-component electric field or Ex) mode profiles of this waveguide at 978 nm wavelength. The refractive indices of the Si3N4 core and SiO2 cladding are assumed to be 1.9885 and 1.4507, respectively. The simulation is implemented by the finite element method (FEM) using COMSOL.

Fig. 3
Fig. 3

Schematic of the experimental setup for measuring the transmission of the multimode waveguide and ring resonator system. Abbreviations: ECDL (External Cavity Diode Laser), FBS (Fiber Beamsplitter), FPI (Fabry-Perot Interferometer), PD (Photodetector), DAQ (Data Acquisition) and HV-Amp (High Voltage Amplifier). Black lines denote single mode optical fibers and purple lines denote electrical wirings.

Fig. 4
Fig. 4

Measured transmission as a function of laser frequency detuning over a 20 GHz range. The free spectral range (FSR) of the ring resonator is approximately 5.3 GHz and the measurement range includes four sets of three resonances spaced by one FSR.

Fig. 5
Fig. 5

Detailed transmission measurement as a function of laser frequency detuning (blue dots) showing three resonances. The red curve through the data is a fit to Eq. (12). The three resonances labeled by 1, 2 and 3 correspond to the three resonances in Fig. 4 with the same labels. Inset: magnified plot of the main figure for resonance 2.

Fig. 6
Fig. 6

Measured transmission of resonance 1 as a function of frequency detuning (blue dots). The red curves through the data are fits to Eq. (17) for four different input-output fiber positions. The Fano parameter θ obtained from the fit is shown for each transmission curve. A value of θ close to unity corresponds to a transmission dip (a), while θ close to zero corresponds to a transmission peak (d). θ close to ± 2 / 2 ( 0.707 ) gives maximum negative (b) and positive (c) asymmetry. The slope responsivity defined as |dT/dν|max are 4.23, 4.90, 5.35 and 0.22 GHz−1, respectively.

Fig. 7
Fig. 7

Contour plot of the measured log10 Toff as a function of the input and output fiber positions. The two dashed lines are symmetry axes of the Toff data. The origin of the plot is defined as the intersection of the two symmetry axes. The points marked by (a) – (d) are positions where the transmission (a) – (d) in Fig. 6 are measured, respectively.

Fig. 8
Fig. 8

Contour plot of the measured absolute value of the Fano parameter θ as a function of the input and output fiber positions. The points marked by (a) – (d) are positions where the transmission (a) – (d) in Fig. 6 are measured, respectively. The four valleys III and IV yield symmetric transmission peaks with |θ| close to zero.

Equations (23)

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

E 1 ( x , y ) = j A j f j ( x , y ) , E 2 ( x , y ) = j B j f j ( x , y ) , E 3 ( x , y ) = j C j g j ( x , y ) , E 4 ( x , y ) = j D j g j ( x , y ) ,
B j = t j A j + i k r k j C k ,
D j = t j C j + i k r k j A k ,
C j = D j a j exp ( i 2 π β j R ) ,
β j = 2 π n p j ( ν ) ν c ,
B j = t j A j k a k r k j l r l k A l exp ( i 2 π β k R ) a k t k .
η j ( x , y ) = f j ( x , y ) h ( x x , y y ) d x d y ,
A j ( x , y ) = η j ( x , y ) P in exp ( i β j L 1 ) ,
E 5 ( x , y , x , y ) = j B j ( x , y ) exp ( i β j L 2 ) f j ( x , y ) ,
P out ( x , y , x , y ) = | E 5 ( x , y , x , y ) h ( x x , y y ) d x d y | 2 | j S j ( x , y ) B j | 2 ,
T ( x , y , x , y ) = P out P in = | j S j B j | 2 1 P in .
T ( Δ ν , x , y , x , y ) = | j S j t j A j k a k j , l S j r k j r l k A l exp [ i e k ( ν 0 + Δ ν ) ] a k t k | 2 1 P in ,
e j ( ν 0 + Δ ν ) = 2 m π ,
Δ ν 0 j = 2 m π e j ν 0 = m c 2 π n p j ( ν ) R ν 0 .
FSR j = c 2 π n g j ( ν ) R ,
T ( Δ ν , x , y , x , y ) | q b j exp [ i e j ( ν 0 + Δ ν ) ] a j t j | 2 ,
T ( Δ ν , x , y , x , y ) ζ j + α j [ ϕ j 2 ( Δ ν Δ ν 0 j ) 2 + 2 ϕ j θ j γ j ( Δ ν Δ ν 0 j ) + θ j 2 γ j 2 ( Δ ν Δ ν 0 j ) 2 + γ j 2 ] ,
γ j = 1 a j t j e j a j t j .
ϕ j = 1 θ j 2 and α j , ζ j > 0 ,
Q j = ν 0 + Δ ν 0 j 2 γ j = e j a j t j ( ν 0 + Δ ν 0 j ) 2 ( 1 a j t j ) ,
T off ( x , y , x , y ) = | j f j ( x , y ) h ( x x , y y ) d x d y f j ( x , y ) h ( x x , y y ) d x d y exp [ i β j ( L 1 + L 2 ) ] | 2 .
T ( Δ ν ) = | p j = 1 3 b j exp [ i e j ( Δ ν + ν 0 j ) ] d j | 2 ,
T off = ζ + α ϕ 2 .

Metrics