Abstract

We report on the transmission spectra of a sausage-like microresonator (SLM) in aqueous environment, where a fiber taper is used as a light coupler. The transmission spectra show an interesting dependence on the coupling position between the SLM and the fiber taper. When the SLM is moved along the fiber taper, the line shape can evolve periodically among symmetric dips, asymmetric Fano-like resonance line shapes, and symmetric peaks. A coupled-mode theory with feedback is developed to explain the observation. The observation of Fano-like resonance in aqueous environment holds great potential in biochemical sensing.

© 2017 Chinese Laser Press

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2017 (1)

2016 (11)

X.-F. Liu, F. Lei, M. Gao, X. Yang, G.-Q. Qin, and G.-L. Long, “Fabrication of a microtoroidal resonator with picometer precise resonant wavelength,” Opt. Lett. 41, 3603–3606 (2016).
[Crossref]

Y.-F. Xiao and Q. Gong, “Optical microcavity: from fundamental physics to functional photonics devices,” Sci. Bull. 61, 185–186 (2016).
[Crossref]

F. Wan, G. Qian, R. Li, J. Tang, and T. Zhang, “High sensitivity optical waveguide accelerometer based on Fano resonance,” Appl. Opt. 55, 6644–6648 (2016).
[Crossref]

S. Zhu, Y. Liu, L. Shi, X. Xu, and X. Zhang, “Extinction ratio and resonant wavelength tuning using three dimensions of silica microresonators,” Photon. Res. 4, 191–196 (2016).
[Crossref]

Y. Wang, K. Zhang, S. Zhou, Y.-H. Wu, M.-B. Chi, and P. Hao, “Coupled-mode induced transparency in a bottle whispering-gallery-mode resonator,” Opt. Lett. 41, 1825–1828 (2016).
[Crossref]

C. Zhao, X. Gan, L. Fang, L. Han, K. Chang, D. Li, and J. Zhao, “Tunable Fano-like resonance enabled by coupling a microsphere with a fiber Mach–Zehnder interferometer,” Appl. Opt. 55, 5756–5760 (2016).
[Crossref]

X.-F. Liu, F. Lei, M. Gao, X. Yang, C. Wang, Ş. K. Özdemir, L. Yang, and G.-L. Long, “Gain competition induced mode evolution and resonance control in erbium-doped whispering-gallery microresonators,” Opt. Express 24, 9550–9560 (2016).
[Crossref]

J. Li, R. Yu, C. Ding, and Y. Wu, “PT-symmetry-induced evolution of sharp asymmetric line shapes and high-sensitivity refractive index sensors in a three-cavity array,” Phys. Rev. A 93, 023814 (2016).
[Crossref]

Z. Shen, C.-H. Dong, Y. Chen, Y.-F. Xiao, F.-W. Sun, and G. C. Guo, “Compensation of the Kerr effect for transient optomechanically induced transparency in a silica microsphere,” Opt. Lett. 41, 1249–1252 (2016).
[Crossref]

J. Liao, X. Wu, L. Liu, and L. Xu, “Fano resonance and improved sensing performance in a spectral-simplified optofluidic micro-bubble resonator by introducing selective modal losses,” Opt. Express 24, 8574–8580 (2016).
[Crossref]

Y. Miao, Y. Peng, Y. Xiang, M. Li, Y. Lu, and Y. Song, “Dynamic Fano resonance in thin fiber taper coupled cylindrical microcavity,” IEEE Photon. J. 8, 1–6 (2016).
[Crossref]

2015 (6)

C.-H. Dong, Z. Shen, C.-L. Zou, Y.-L. Zhang, W. Fu, and G.-C. Guo, “Brillouin-scattering-induced transparency and non-reciprocal light storage,” Nat. Commun. 6, 6193 (2015).
[Crossref]

Y. Yang, S. Saurabh, J. Ward, and S. N. Chormaic, “Coupled-mode-induced transparency in aerostatically tuned microbubble whispering-gallery resonators,” Opt. Lett. 40, 1834–1837 (2015).
[Crossref]

F. Bo, X. Wang, Y. Li, F. Gao, G. Zhang, and J. Xu, “Mode characteristics of silver-coated inverted-wedge silica microdisks,” Sci. Chin. Phys. Mech. Astron. 58, 114207 (2015).
[Crossref]

J. Lin, Y. Xu, Z. Fang, M. Wang, N. Wang, L. Qiao, W. Fang, and Y. Cheng, “Second harmonic generation in a high-Q lithium niobate microresonator fabricated by femtosecond laser micromachining,” Sci. Chin. Phys. Mech. Astron. 58, 114209 (2015).
[Crossref]

Z. Shen, Z.-H. Zhou, C.-L. Zou, F.-W. Sun, G.-P. Guo, C.-H. Dong, and G.-C. Guo, “Observation of high-Q optomechanical modes in the mounted silica microspheres,” Photon. Res. 3, 243–247 (2015).
[Crossref]

M.-Y. Ye, M.-X. Shen, and X.-M. Lin, “Transmission spectra of sausage-like microresonators,” Opt. Express 23, 25846–25853 (2015).
[Crossref]

2014 (4)

L.-X. Zou, Y.-Z. Huang, X.-M. Lv, B.-W. Liu, H. Long, Y.-D. Yang, J.-L. Xiao, and Y. Du, “Modulation characteristics and microwave generation for AlGaInAs/InP microring lasers under four-wave mixing,” Photon. Res. 2, 177–181 (2014).
[Crossref]

B. Peng, Ş. K. Özdemir, W. Chen, F. Nori, and L. Yang, “What is and what is not electromagnetically induced transparency in whispering-gallery microcavities,” Nat. Commun. 5, 5082 (2014).
[Crossref]

F. Lei, B. Peng, Ş. K. Özdemir, G. L. Long, and L. Yang, “Dynamic Fano-like resonances in erbium-doped whispering-gallery-mode microresonators,” Appl. Phys. Lett. 105, 101112 (2014).
[Crossref]

F. Nazari, N. Bender, H. Ramezani, M. K. Moravvej-Farshi, D. N. Christodoulides, and T. Kottos, “Optical isolation via PT-symmetric nonlinear Fano resonances,” Opt. Express 22, 9574–9584 (2014).
[Crossref]

2013 (2)

Y.-F. Xiao, X.-F. Jiang, Q.-F. Yang, L. Wang, K. Shi, Y. Li, and Q. Gong, “Tunneling-induced transparency in a chaotic microcavity,” Laser Photon. Rev. 7, L51-L54 (2013).
[Crossref]

Y. Zhou, D. Zhu, X. Yu, W. Ding, and F. Luan, “Fano resonances in metallic grating coupled whispering gallery mode resonator,” Appl. Phys. Lett. 103, 151108 (2013).
[Crossref]

2012 (2)

C. Zheng, X. Jiang, S. Hua, L. Chang, G. Li, H. Fan, and M. Xiao, “Controllable optical analog to electromagnetically induced transparency in coupled high-Q microtoroid cavities,” Opt. Express 20, 18319–18325 (2012).
[Crossref]

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

2011 (2)

G. C. Righini, Y. Dumeige, P. Féron, M. Ferrari, G. N. Conti, D. Ristic, and S. Soria, “Whispering gallery mode microresonators: fundamentals and applications,” Riv. Nuovo Cimento Soc. Ital. Fis. 34, 435–488 (2011).
[Crossref]

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

2010 (3)

Q. Li, T. Wang, Y. Su, M. Yan, and M. Qiu, “Coupled mode theory analysis of mode-splitting in coupled cavity system,” Opt. Express 18, 8367–8382 (2010).
[Crossref]

Y.-F. Xiao, M. Li, Y. C. Liu, Y. Li, X. Sun, and Q. Gong, “Asymmetric Fano resonance analysis in indirectly coupled microresonators,” Phys. Rev. A 82, 065804 (2010).
[Crossref]

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82, 2257–2298 (2010).
[Crossref]

2009 (2)

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

C.-H. Dong, C.-L. Zou, Y.-F. Xiao, J.-M. Cui, Z.-F. Han, and G.-C. Guo, “Modified transmission spectrum induced by two-mode interference in a single silica microsphere,” J. Phys. B 42, 215401 (2009).
[Crossref]

2007 (1)

K. Totsuka, N. Kobayashi, and M. Tomita, “Slow light in coupled-resonator-induced transparency,” Phys. Rev. Lett. 98, 213904 (2007).
[Crossref]

2006 (2)

2005 (1)

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

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 (1)

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

1997 (1)

1961 (1)

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866–1878 (1961).
[Crossref]

Bai, H.

Bender, N.

Birks, T. A.

Bo, F.

F. Bo, X. Wang, Y. Li, F. Gao, G. Zhang, and J. Xu, “Mode characteristics of silver-coated inverted-wedge silica microdisks,” Sci. Chin. Phys. Mech. Astron. 58, 114207 (2015).
[Crossref]

Chang, K.

Chang, L.

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]

Chen, W.

B. Peng, Ş. K. Özdemir, W. Chen, F. Nori, and L. Yang, “What is and what is not electromagnetically induced transparency in whispering-gallery microcavities,” Nat. Commun. 5, 5082 (2014).
[Crossref]

Chen, Y.

Chen, Y.-L.

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

Cheng, Y.

J. Lin, Y. Xu, Z. Fang, M. Wang, N. Wang, L. Qiao, W. Fang, and Y. Cheng, “Second harmonic generation in a high-Q lithium niobate microresonator fabricated by femtosecond laser micromachining,” Sci. Chin. Phys. Mech. Astron. 58, 114209 (2015).
[Crossref]

Cheung, G.

Chi, M.-B.

Chiba, A.

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

Chormaic, S. N.

Christodoulides, D. N.

Conti, G. N.

G. C. Righini, Y. Dumeige, P. Féron, M. Ferrari, G. N. Conti, D. Ristic, and S. Soria, “Whispering gallery mode microresonators: fundamentals and applications,” Riv. Nuovo Cimento Soc. Ital. Fis. 34, 435–488 (2011).
[Crossref]

Cui, J.-M.

C.-H. Dong, C.-L. Zou, Y.-F. Xiao, J.-M. Cui, Z.-F. Han, and G.-C. Guo, “Modified transmission spectrum induced by two-mode interference in a single silica microsphere,” J. Phys. B 42, 215401 (2009).
[Crossref]

Ding, C.

J. Li, R. Yu, C. Ding, and Y. Wu, “PT-symmetry-induced evolution of sharp asymmetric line shapes and high-sensitivity refractive index sensors in a three-cavity array,” Phys. Rev. A 93, 023814 (2016).
[Crossref]

Ding, W.

Y. Zhou, D. Zhu, X. Yu, W. Ding, and F. Luan, “Fano resonances in metallic grating coupled whispering gallery mode resonator,” Appl. Phys. Lett. 103, 151108 (2013).
[Crossref]

Dong, C.-H.

Z. Shen, C.-H. Dong, Y. Chen, Y.-F. Xiao, F.-W. Sun, and G. C. Guo, “Compensation of the Kerr effect for transient optomechanically induced transparency in a silica microsphere,” Opt. Lett. 41, 1249–1252 (2016).
[Crossref]

Z. Shen, Z.-H. Zhou, C.-L. Zou, F.-W. Sun, G.-P. Guo, C.-H. Dong, and G.-C. Guo, “Observation of high-Q optomechanical modes in the mounted silica microspheres,” Photon. Res. 3, 243–247 (2015).
[Crossref]

C.-H. Dong, Z. Shen, C.-L. Zou, Y.-L. Zhang, W. Fu, and G.-C. Guo, “Brillouin-scattering-induced transparency and non-reciprocal light storage,” Nat. Commun. 6, 6193 (2015).
[Crossref]

C.-H. Dong, C.-L. Zou, Y.-F. Xiao, J.-M. Cui, Z.-F. Han, and G.-C. Guo, “Modified transmission spectrum induced by two-mode interference in a single silica microsphere,” J. Phys. B 42, 215401 (2009).
[Crossref]

Du, Y.

Dumeige, Y.

G. C. Righini, Y. Dumeige, P. Féron, M. Ferrari, G. N. Conti, D. Ristic, and S. Soria, “Whispering gallery mode microresonators: fundamentals and applications,” Riv. Nuovo Cimento Soc. Ital. Fis. 34, 435–488 (2011).
[Crossref]

Fan, H.

Fan, S.

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

Fang, L.

Fang, W.

J. Lin, Y. Xu, Z. Fang, M. Wang, N. Wang, L. Qiao, W. Fang, and Y. Cheng, “Second harmonic generation in a high-Q lithium niobate microresonator fabricated by femtosecond laser micromachining,” Sci. Chin. Phys. Mech. Astron. 58, 114209 (2015).
[Crossref]

Fang, Z.

J. Lin, Y. Xu, Z. Fang, M. Wang, N. Wang, L. Qiao, W. Fang, and Y. Cheng, “Second harmonic generation in a high-Q lithium niobate microresonator fabricated by femtosecond laser micromachining,” Sci. Chin. Phys. Mech. Astron. 58, 114209 (2015).
[Crossref]

Fano, U.

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866–1878 (1961).
[Crossref]

Féron, P.

G. C. Righini, Y. Dumeige, P. Féron, M. Ferrari, G. N. Conti, D. Ristic, and S. Soria, “Whispering gallery mode microresonators: fundamentals and applications,” Riv. Nuovo Cimento Soc. Ital. Fis. 34, 435–488 (2011).
[Crossref]

Ferrari, M.

G. C. Righini, Y. Dumeige, P. Féron, M. Ferrari, G. N. Conti, D. Ristic, and S. Soria, “Whispering gallery mode microresonators: fundamentals and applications,” Riv. Nuovo Cimento Soc. Ital. Fis. 34, 435–488 (2011).
[Crossref]

Flach, S.

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82, 2257–2298 (2010).
[Crossref]

Fu, W.

C.-H. Dong, Z. Shen, C.-L. Zou, Y.-L. Zhang, W. Fu, and G.-C. Guo, “Brillouin-scattering-induced transparency and non-reciprocal light storage,” Nat. Commun. 6, 6193 (2015).
[Crossref]

Fujiwara, H.

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

Gan, X.

Gao, F.

F. Bo, X. Wang, Y. Li, F. Gao, G. Zhang, and J. Xu, “Mode characteristics of silver-coated inverted-wedge silica microdisks,” Sci. Chin. Phys. Mech. Astron. 58, 114207 (2015).
[Crossref]

Gao, M.

Gong, Q.

Y.-F. Xiao and Q. Gong, “Optical microcavity: from fundamental physics to functional photonics devices,” Sci. Bull. 61, 185–186 (2016).
[Crossref]

Y.-F. Xiao, X.-F. Jiang, Q.-F. Yang, L. Wang, K. Shi, Y. Li, and Q. Gong, “Tunneling-induced transparency in a chaotic microcavity,” Laser Photon. Rev. 7, L51-L54 (2013).
[Crossref]

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

Y.-F. Xiao, M. Li, Y. C. Liu, Y. Li, X. Sun, and Q. Gong, “Asymmetric Fano resonance analysis in indirectly coupled microresonators,” Phys. Rev. A 82, 065804 (2010).
[Crossref]

Guo, G. C.

Guo, G.-C.

Z. Shen, Z.-H. Zhou, C.-L. Zou, F.-W. Sun, G.-P. Guo, C.-H. Dong, and G.-C. Guo, “Observation of high-Q optomechanical modes in the mounted silica microspheres,” Photon. Res. 3, 243–247 (2015).
[Crossref]

C.-H. Dong, Z. Shen, C.-L. Zou, Y.-L. Zhang, W. Fu, and G.-C. Guo, “Brillouin-scattering-induced transparency and non-reciprocal light storage,” Nat. Commun. 6, 6193 (2015).
[Crossref]

C.-H. Dong, C.-L. Zou, Y.-F. Xiao, J.-M. Cui, Z.-F. Han, and G.-C. Guo, “Modified transmission spectrum induced by two-mode interference in a single silica microsphere,” J. Phys. B 42, 215401 (2009).
[Crossref]

Guo, G.-P.

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]

Han, L.

Han, Z.-F.

C.-H. Dong, C.-L. Zou, Y.-F. Xiao, J.-M. Cui, Z.-F. Han, and G.-C. Guo, “Modified transmission spectrum induced by two-mode interference in a single silica microsphere,” J. Phys. B 42, 215401 (2009).
[Crossref]

Hao, P.

He, L.

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

Hotta, J.

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

Hua, S.

Huang, Y.

Huang, Y.-Z.

Jacques, F.

Jiang, X.

Jiang, X.-F.

Y.-F. Xiao, X.-F. Jiang, Q.-F. Yang, L. Wang, K. Shi, Y. Li, and Q. Gong, “Tunneling-induced transparency in a chaotic microcavity,” Laser Photon. Rev. 7, L51-L54 (2013).
[Crossref]

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

Kivshar, Y. S.

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82, 2257–2298 (2010).
[Crossref]

Knight, J. C.

Kobayashi, N.

K. Totsuka, N. Kobayashi, and M. Tomita, “Slow light in coupled-resonator-induced transparency,” Phys. Rev. Lett. 98, 213904 (2007).
[Crossref]

Kottos, T.

Lei, F.

Li, B.-B.

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

Li, D.

Li, G.

Li, J.

J. Li, R. Yu, C. Ding, and Y. Wu, “PT-symmetry-induced evolution of sharp asymmetric line shapes and high-sensitivity refractive index sensors in a three-cavity array,” Phys. Rev. A 93, 023814 (2016).
[Crossref]

Li, M.

Y. Miao, Y. Peng, Y. Xiang, M. Li, Y. Lu, and Y. Song, “Dynamic Fano resonance in thin fiber taper coupled cylindrical microcavity,” IEEE Photon. J. 8, 1–6 (2016).
[Crossref]

Y.-F. Xiao, M. Li, Y. C. Liu, Y. Li, X. Sun, and Q. Gong, “Asymmetric Fano resonance analysis in indirectly coupled microresonators,” Phys. Rev. A 82, 065804 (2010).
[Crossref]

Li, Q.

Li, R.

Li, Y.

F. Bo, X. Wang, Y. Li, F. Gao, G. Zhang, and J. Xu, “Mode characteristics of silver-coated inverted-wedge silica microdisks,” Sci. Chin. Phys. Mech. Astron. 58, 114207 (2015).
[Crossref]

Y.-F. Xiao, X.-F. Jiang, Q.-F. Yang, L. Wang, K. Shi, Y. Li, and Q. Gong, “Tunneling-induced transparency in a chaotic microcavity,” Laser Photon. Rev. 7, L51-L54 (2013).
[Crossref]

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

Y.-F. Xiao, M. Li, Y. C. Liu, Y. Li, X. Sun, and Q. Gong, “Asymmetric Fano resonance analysis in indirectly coupled microresonators,” Phys. Rev. A 82, 065804 (2010).
[Crossref]

Liang, W.

Liao, J.

Lin, J.

J. Lin, Y. Xu, Z. Fang, M. Wang, N. Wang, L. Qiao, W. Fang, and Y. Cheng, “Second harmonic generation in a high-Q lithium niobate microresonator fabricated by femtosecond laser micromachining,” Sci. Chin. Phys. Mech. Astron. 58, 114209 (2015).
[Crossref]

Lin, X.-M.

Liu, B.-W.

Liu, L.

Liu, X.-F.

Liu, Y.

Liu, Y. C.

Y.-F. Xiao, M. Li, Y. C. Liu, Y. Li, X. Sun, and Q. Gong, “Asymmetric Fano resonance analysis in indirectly coupled microresonators,” Phys. Rev. A 82, 065804 (2010).
[Crossref]

Liu, Y.-C.

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

Long, G. L.

F. Lei, B. Peng, Ş. K. Özdemir, G. L. Long, and L. Yang, “Dynamic Fano-like resonances in erbium-doped whispering-gallery-mode microresonators,” Appl. Phys. Lett. 105, 101112 (2014).
[Crossref]

Long, G.-L.

Long, H.

Lu, Y.

Y. Miao, Y. Peng, Y. Xiang, M. Li, Y. Lu, and Y. Song, “Dynamic Fano resonance in thin fiber taper coupled cylindrical microcavity,” IEEE Photon. J. 8, 1–6 (2016).
[Crossref]

Y. Lu, L. Xu, Y. Yu, P. Wang, and J. Yao, “Double-wavelength Fano resonance and enhanced coupled-resonator-induced transparency in a double-microcavity resonator system,” J. Opt. Soc. Am. A 23, 1718–1721 (2006).
[Crossref]

Luan, F.

Y. Zhou, D. Zhu, X. Yu, W. Ding, and F. Luan, “Fano resonances in metallic grating coupled whispering gallery mode resonator,” Appl. Phys. Lett. 103, 151108 (2013).
[Crossref]

Lv, X.-M.

Miao, Y.

Y. Miao, Y. Peng, Y. Xiang, M. Li, Y. Lu, and Y. Song, “Dynamic Fano resonance in thin fiber taper coupled cylindrical microcavity,” IEEE Photon. J. 8, 1–6 (2016).
[Crossref]

Miroshnichenko, A. E.

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82, 2257–2298 (2010).
[Crossref]

Moravvej-Farshi, M. K.

Nazari, F.

Nori, F.

B. Peng, Ş. K. Özdemir, W. Chen, F. Nori, and L. Yang, “What is and what is not electromagnetically induced transparency in whispering-gallery microcavities,” Nat. Commun. 5, 5082 (2014).
[Crossref]

Özdemir, S. K.

X.-F. Liu, F. Lei, M. Gao, X. Yang, C. Wang, Ş. K. Özdemir, L. Yang, and G.-L. Long, “Gain competition induced mode evolution and resonance control in erbium-doped whispering-gallery microresonators,” Opt. Express 24, 9550–9560 (2016).
[Crossref]

B. Peng, Ş. K. Özdemir, W. Chen, F. Nori, and L. Yang, “What is and what is not electromagnetically induced transparency in whispering-gallery microcavities,” Nat. Commun. 5, 5082 (2014).
[Crossref]

F. Lei, B. Peng, Ş. K. Özdemir, G. L. Long, and L. Yang, “Dynamic Fano-like resonances in erbium-doped whispering-gallery-mode microresonators,” Appl. Phys. Lett. 105, 101112 (2014).
[Crossref]

Pang, F.

Peng, B.

B. Peng, Ş. K. Özdemir, W. Chen, F. Nori, and L. Yang, “What is and what is not electromagnetically induced transparency in whispering-gallery microcavities,” Nat. Commun. 5, 5082 (2014).
[Crossref]

F. Lei, B. Peng, Ş. K. Özdemir, G. L. Long, and L. Yang, “Dynamic Fano-like resonances in erbium-doped whispering-gallery-mode microresonators,” Appl. Phys. Lett. 105, 101112 (2014).
[Crossref]

Peng, Y.

Y. Miao, Y. Peng, Y. Xiang, M. Li, Y. Lu, and Y. Song, “Dynamic Fano resonance in thin fiber taper coupled cylindrical microcavity,” IEEE Photon. J. 8, 1–6 (2016).
[Crossref]

Poon, J. K. S.

Qian, G.

Qiao, L.

J. Lin, Y. Xu, Z. Fang, M. Wang, N. Wang, L. Qiao, W. Fang, and Y. Cheng, “Second harmonic generation in a high-Q lithium niobate microresonator fabricated by femtosecond laser micromachining,” Sci. Chin. Phys. Mech. Astron. 58, 114209 (2015).
[Crossref]

Qin, G.-Q.

Qiu, M.

Ramezani, H.

Righini, G. C.

G. C. Righini, Y. Dumeige, P. Féron, M. Ferrari, G. N. Conti, D. Ristic, and S. Soria, “Whispering gallery mode microresonators: fundamentals and applications,” Riv. Nuovo Cimento Soc. Ital. Fis. 34, 435–488 (2011).
[Crossref]

Ristic, D.

G. C. Righini, Y. Dumeige, P. Féron, M. Ferrari, G. N. Conti, D. Ristic, and S. Soria, “Whispering gallery mode microresonators: fundamentals and applications,” Riv. Nuovo Cimento Soc. Ital. Fis. 34, 435–488 (2011).
[Crossref]

Sasaki, K.

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

Saurabh, S.

Shao, H.

Shen, M.-X.

Shen, Z.

Shi, K.

Y.-F. Xiao, X.-F. Jiang, Q.-F. Yang, L. Wang, K. Shi, Y. Li, and Q. Gong, “Tunneling-induced transparency in a chaotic microcavity,” Laser Photon. Rev. 7, L51-L54 (2013).
[Crossref]

Shi, L.

Song, Y.

Y. Miao, Y. Peng, Y. Xiang, M. Li, Y. Lu, and Y. Song, “Dynamic Fano resonance in thin fiber taper coupled cylindrical microcavity,” IEEE Photon. J. 8, 1–6 (2016).
[Crossref]

Soria, S.

G. C. Righini, Y. Dumeige, P. Féron, M. Ferrari, G. N. Conti, D. Ristic, and S. Soria, “Whispering gallery mode microresonators: fundamentals and applications,” Riv. Nuovo Cimento Soc. Ital. Fis. 34, 435–488 (2011).
[Crossref]

Su, Y.

Sun, F.-W.

Sun, X.

Y.-F. Xiao, M. Li, Y. C. Liu, Y. Li, X. Sun, and Q. Gong, “Asymmetric Fano resonance analysis in indirectly coupled microresonators,” Phys. Rev. A 82, 065804 (2010).
[Crossref]

Takeuchi, S.

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

Tang, J.

Tomita, M.

K. Totsuka, N. Kobayashi, and M. Tomita, “Slow light in coupled-resonator-induced transparency,” Phys. Rev. Lett. 98, 213904 (2007).
[Crossref]

Totsuka, K.

K. Totsuka, N. Kobayashi, and M. Tomita, “Slow light in coupled-resonator-induced transparency,” Phys. Rev. Lett. 98, 213904 (2007).
[Crossref]

Vahala, K. J.

Wan, F.

Wang, C.

Wang, L.

Y.-F. Xiao, X.-F. Jiang, Q.-F. Yang, L. Wang, K. Shi, Y. Li, and Q. Gong, “Tunneling-induced transparency in a chaotic microcavity,” Laser Photon. Rev. 7, L51-L54 (2013).
[Crossref]

Wang, M.

J. Lin, Y. Xu, Z. Fang, M. Wang, N. Wang, L. Qiao, W. Fang, and Y. Cheng, “Second harmonic generation in a high-Q lithium niobate microresonator fabricated by femtosecond laser micromachining,” Sci. Chin. Phys. Mech. Astron. 58, 114209 (2015).
[Crossref]

Wang, N.

J. Lin, Y. Xu, Z. Fang, M. Wang, N. Wang, L. Qiao, W. Fang, and Y. Cheng, “Second harmonic generation in a high-Q lithium niobate microresonator fabricated by femtosecond laser micromachining,” Sci. Chin. Phys. Mech. Astron. 58, 114209 (2015).
[Crossref]

Wang, P.

Wang, T.

Wang, X.

F. Bo, X. Wang, Y. Li, F. Gao, G. Zhang, and J. Xu, “Mode characteristics of silver-coated inverted-wedge silica microdisks,” Sci. Chin. Phys. Mech. Astron. 58, 114207 (2015).
[Crossref]

Wang, Y.

Ward, J.

Wu, X.

Wu, Y.

J. Li, R. Yu, C. Ding, and Y. Wu, “PT-symmetry-induced evolution of sharp asymmetric line shapes and high-sensitivity refractive index sensors in a three-cavity array,” Phys. Rev. A 93, 023814 (2016).
[Crossref]

Wu, Y.-H.

Xiang, Y.

Y. Miao, Y. Peng, Y. Xiang, M. Li, Y. Lu, and Y. Song, “Dynamic Fano resonance in thin fiber taper coupled cylindrical microcavity,” IEEE Photon. J. 8, 1–6 (2016).
[Crossref]

Xiao, H.

Xiao, J.-L.

Xiao, M.

Xiao, Y.-F.

Y.-F. Xiao and Q. Gong, “Optical microcavity: from fundamental physics to functional photonics devices,” Sci. Bull. 61, 185–186 (2016).
[Crossref]

Z. Shen, C.-H. Dong, Y. Chen, Y.-F. Xiao, F.-W. Sun, and G. C. Guo, “Compensation of the Kerr effect for transient optomechanically induced transparency in a silica microsphere,” Opt. Lett. 41, 1249–1252 (2016).
[Crossref]

Y.-F. Xiao, X.-F. Jiang, Q.-F. Yang, L. Wang, K. Shi, Y. Li, and Q. Gong, “Tunneling-induced transparency in a chaotic microcavity,” Laser Photon. Rev. 7, L51-L54 (2013).
[Crossref]

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

Y.-F. Xiao, M. Li, Y. C. Liu, Y. Li, X. Sun, and Q. Gong, “Asymmetric Fano resonance analysis in indirectly coupled microresonators,” Phys. Rev. A 82, 065804 (2010).
[Crossref]

C.-H. Dong, C.-L. Zou, Y.-F. Xiao, J.-M. Cui, Z.-F. Han, and G.-C. Guo, “Modified transmission spectrum induced by two-mode interference in a single silica microsphere,” J. Phys. B 42, 215401 (2009).
[Crossref]

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

Xu, J.

F. Bo, X. Wang, Y. Li, F. Gao, G. Zhang, and J. Xu, “Mode characteristics of silver-coated inverted-wedge silica microdisks,” Sci. Chin. Phys. Mech. Astron. 58, 114207 (2015).
[Crossref]

Xu, L.

Xu, X.

Xu, Y.

J. Lin, Y. Xu, Z. Fang, M. Wang, N. Wang, L. Qiao, W. Fang, and Y. Cheng, “Second harmonic generation in a high-Q lithium niobate microresonator fabricated by femtosecond laser micromachining,” Sci. Chin. Phys. Mech. Astron. 58, 114209 (2015).
[Crossref]

Yan, M.

Yang, L.

X.-F. Liu, F. Lei, M. Gao, X. Yang, C. Wang, Ş. K. Özdemir, L. Yang, and G.-L. Long, “Gain competition induced mode evolution and resonance control in erbium-doped whispering-gallery microresonators,” Opt. Express 24, 9550–9560 (2016).
[Crossref]

F. Lei, B. Peng, Ş. K. Özdemir, G. L. Long, and L. Yang, “Dynamic Fano-like resonances in erbium-doped whispering-gallery-mode microresonators,” Appl. Phys. Lett. 105, 101112 (2014).
[Crossref]

B. Peng, Ş. K. Özdemir, W. Chen, F. Nori, and L. Yang, “What is and what is not electromagnetically induced transparency in whispering-gallery microcavities,” Nat. Commun. 5, 5082 (2014).
[Crossref]

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

W. Liang, L. Yang, J. K. S. Poon, Y. Huang, K. J. Vahala, and A. Yariv, “Transmission characteristics of a Fabry–Perot etalon-microtoroid resonator coupled system,” Opt. Lett. 31, 510–512 (2006).
[Crossref]

Yang, Q.-F.

Y.-F. Xiao, X.-F. Jiang, Q.-F. Yang, L. Wang, K. Shi, Y. Li, and Q. Gong, “Tunneling-induced transparency in a chaotic microcavity,” Laser Photon. Rev. 7, L51-L54 (2013).
[Crossref]

Yang, X.

Yang, Y.

Yang, Y.-D.

Yao, J.

Yariv, A.

Ye, M.-Y.

Yu, R.

J. Li, R. Yu, C. Ding, and Y. Wu, “PT-symmetry-induced evolution of sharp asymmetric line shapes and high-sensitivity refractive index sensors in a three-cavity array,” Phys. Rev. A 93, 023814 (2016).
[Crossref]

Yu, X.

Y. Zhou, D. Zhu, X. Yu, W. Ding, and F. Luan, “Fano resonances in metallic grating coupled whispering gallery mode resonator,” Appl. Phys. Lett. 103, 151108 (2013).
[Crossref]

Yu, Y.

Zhang, G.

F. Bo, X. Wang, Y. Li, F. Gao, G. Zhang, and J. Xu, “Mode characteristics of silver-coated inverted-wedge silica microdisks,” Sci. Chin. Phys. Mech. Astron. 58, 114207 (2015).
[Crossref]

Zhang, K.

Zhang, T.

Zhang, X.

Zhang, Y.-L.

C.-H. Dong, Z. Shen, C.-L. Zou, Y.-L. Zhang, W. Fu, and G.-C. Guo, “Brillouin-scattering-induced transparency and non-reciprocal light storage,” Nat. Commun. 6, 6193 (2015).
[Crossref]

Zhao, C.

Zhao, J.

Zheng, C.

Zhou, S.

Zhou, Y.

Y. Zhou, D. Zhu, X. Yu, W. Ding, and F. Luan, “Fano resonances in metallic grating coupled whispering gallery mode resonator,” Appl. Phys. Lett. 103, 151108 (2013).
[Crossref]

Zhou, Z.-H.

Zhu, D.

Y. Zhou, D. Zhu, X. Yu, W. Ding, and F. Luan, “Fano resonances in metallic grating coupled whispering gallery mode resonator,” Appl. Phys. Lett. 103, 151108 (2013).
[Crossref]

Zhu, J.

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

Zhu, S.

Zou, C.-L.

Z. Shen, Z.-H. Zhou, C.-L. Zou, F.-W. Sun, G.-P. Guo, C.-H. Dong, and G.-C. Guo, “Observation of high-Q optomechanical modes in the mounted silica microspheres,” Photon. Res. 3, 243–247 (2015).
[Crossref]

C.-H. Dong, Z. Shen, C.-L. Zou, Y.-L. Zhang, W. Fu, and G.-C. Guo, “Brillouin-scattering-induced transparency and non-reciprocal light storage,” Nat. Commun. 6, 6193 (2015).
[Crossref]

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

C.-H. Dong, C.-L. Zou, Y.-F. Xiao, J.-M. Cui, Z.-F. Han, and G.-C. Guo, “Modified transmission spectrum induced by two-mode interference in a single silica microsphere,” J. Phys. B 42, 215401 (2009).
[Crossref]

Zou, L.-X.

Appl. Opt. (2)

Appl. Phys. Lett. (8)

Y. Zhou, D. Zhu, X. Yu, W. Ding, and F. Luan, “Fano resonances in metallic grating coupled whispering gallery mode resonator,” Appl. Phys. Lett. 103, 151108 (2013).
[Crossref]

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

F. Lei, B. Peng, Ş. K. Özdemir, G. L. Long, and L. Yang, “Dynamic Fano-like resonances in erbium-doped whispering-gallery-mode microresonators,” Appl. Phys. Lett. 105, 101112 (2014).
[Crossref]

S. 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]

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

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

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

IEEE Photon. J. (1)

Y. Miao, Y. Peng, Y. Xiang, M. Li, Y. Lu, and Y. Song, “Dynamic Fano resonance in thin fiber taper coupled cylindrical microcavity,” IEEE Photon. J. 8, 1–6 (2016).
[Crossref]

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

J. Phys. B (1)

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[Crossref]

Nat. Commun. (2)

B. Peng, Ş. K. Özdemir, W. Chen, F. Nori, and L. Yang, “What is and what is not electromagnetically induced transparency in whispering-gallery microcavities,” Nat. Commun. 5, 5082 (2014).
[Crossref]

C.-H. Dong, Z. Shen, C.-L. Zou, Y.-L. Zhang, W. Fu, and G.-C. Guo, “Brillouin-scattering-induced transparency and non-reciprocal light storage,” Nat. Commun. 6, 6193 (2015).
[Crossref]

Opt. Express (7)

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Phys. Rev. (1)

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[Crossref]

Phys. Rev. A (2)

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[Crossref]

J. Li, R. Yu, C. Ding, and Y. Wu, “PT-symmetry-induced evolution of sharp asymmetric line shapes and high-sensitivity refractive index sensors in a three-cavity array,” Phys. Rev. A 93, 023814 (2016).
[Crossref]

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Rev. Mod. Phys. (1)

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Riv. Nuovo Cimento Soc. Ital. Fis. (1)

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[Crossref]

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[Crossref]

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[Crossref]

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Figures (7)

Fig. 1.
Fig. 1. Micrograph of the SLM immersed in water. The fiber taper is placed under the SLM and some scattering points on it are clearly shown.
Fig. 2.
Fig. 2. Experimental transmission spectra with different positions of the SLM. From top to bottom, the SLM was moved to the left along the fiber taper.
Fig. 3.
Fig. 3. Microresonator side-coupled to a waveguide. The waveguide together with the embedded partially reflecting element simulates the function of the fiber taper in the experiment.
Fig. 4.
Fig. 4. Simulation of the dependence of the line shape of mode 1 on the position of the SLM. Increasing the value of θ means moving the SLM to the left. The simulation parameters are k o 1 / 2 π = 2.6    MHz , k e 1 / 2 π = 420.0    MHz , k 1 = k o 1 + k e 1 , k o 2 / 2 π = 2.5    MHz , k e 2 / 2 π = 19.8    MHz , g / 2 π = 19.2    MHz , and r = 0.42 .
Fig. 5.
Fig. 5. Simulation of the dependence of the line shape of mode 2 on the position of the SLM. Increasing the value of θ means moving the SLM to the left. The simulation parameters are k o 1 / 2 π = 2.3    MHz , k e 1 / 2 π = 260.0    MHz , k 1 = k o 1 + k e 1 , k o 2 / 2 π = 2.1    MHz , k e 2 / 2 π = 4.0    MHz , g / 2 π = 21.4    MHz , and r = 0.42 .
Fig. 6.
Fig. 6. Comparison between the experimental line shapes and simulated line shapes for mode 1. Experimental line shapes are normalized and shifted for clarity. Simulated line shapes are also shifted and they are plotted using the same parameters as those in Fig. 4.
Fig. 7.
Fig. 7. Comparison between the experimental and simulated line shapes for mode 2. Experimental line shapes are normalized and shifted for clarity. Simulated line shapes are also shifted and they are plotted using the same parameters as those in Fig. 5.

Equations (8)

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d E cw d t = ( i ω 1 κ o 1 κ e 1 ) E cw i g E ccw + 2 κ e 1 E t ,
d E ccw d t = ( i ω 2 κ o 2 κ e 2 ) E ccw i g E cw ,
E t = E in + 2 κ e 2 E ccw r e i θ ,
E out = E t + 2 κ e 1 E cw .
T = | E out E in | 2 ,
h r = 1 1 + i g 2 κ e 1 2 κ e 2 r e i θ ( i δ 1 κ o 1 κ e 1 ) ( i δ 2 κ o 2 κ e 2 ) + g 2 ,
h 0 = 1 2 κ e 1 i δ 1 κ o 1 κ e 1 + g 2 i δ 2 κ o 2 κ e 2 ,
T = | h r h 0 | 2 .

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