Abstract

Microresonators offer an attractive combination of high quality factors and small optical mode volume. They have emerged as a unique platform for the study of fundamental physics and for applications ranging from exquisite sensors to miniature optical combs. Characterizing the linear and nonlinear properties of a microresonator is the first step toward new applications. Here, we present a novel in situ method to measure the nonlinear refractive index and absorption coefficient in microresonators. Laser-scanned transmission spectra are fitted by a comprehensive theoretical model that includes the thermo-optic effect, Kerr effect, and back-coupling of counter-propagating modes. The effectiveness of our technique is demonstrated by evaluating the nonlinear indices and optical absorption of silica and chalcogenide (As2S3) microspheres at 1.55 μm. Significantly, our method also quantifies important parameters including the quality factor, thermal relaxation time, and back-coupling coefficient at the same time. Our findings provide a powerful new approach for characterization of microresonators and optical materials and pave the way for new opportunities in the area.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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References

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2017 (1)

L. Del Bino, J. M. Silver, S. L. Stebbings, and P. Del’Haye, “Symmetry breaking of counter-propagating light in a nonlinear resonator,” Sci. Rep.-Uk 7, 43142 (2017).
[Crossref]

2016 (2)

W. Chen, J. Zhu, Ş. K. Özdemir, B. Peng, and L. Yang, “A simple method for characterizing and engineering thermal relaxation of an optical microcavity,” Appl. Phys. Lett. 109, 061103 (2016).
[Crossref]

M. R. Krogstad, S. Ahn, W. Park, and J. T. Gopinath, “Optical characterization of chalcogenide Ge-Sb–Se waveguides at telecom wavelengths,” IEEE Photon. Technol. Lett. 28, 2720–2723 (2016).
[Crossref]

2015 (2)

2014 (3)

2012 (1)

F. Vollmer and L. Yang, “Review Label-free detection with high-Q microcavities: a review of biosensing mechanisms for integrated devices,” Nanophotonics (Berlin) 1, 267–291 (2012).
[Crossref]

2011 (2)

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332, 555–559 (2011).
[Crossref]

R. Ahmad and M. Rochette, “Photosensitivity at 1550 nm and Bragg grating inscription in As2Se3 chalcogenide microwires,” Appl. Phys. Lett. 99, 061109 (2011).
[Crossref]

2010 (3)

J. Hu, M. Torregiani, F. Morichetti, N. Carlie, A. Agarwal, K. Richardson, L. C. Kimerling, and A. Melloni, “Resonant cavity-enhanced photosensitivity in As 2 S 3 chalcogenide glass at 1550 nm telecommunication wavelength,” Opt. Lett. 35, 874–876 (2010).
[Crossref]

J. G. Zhu, S. K. Ozdemir, Y. F. Xiao, L. Li, L. N. He, D. R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4, 46–49 (2010).
[Crossref]

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, P. Emplit, and M. Haelterman, “Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer,” Nat. Photonics 4, 471–476 (2010).
[Crossref]

2007 (2)

2005 (4)

2004 (2)

T. Carmon, L. Yang, and K. J. Vahala, “Dynamical thermal behavior and thermal self-stability of microcavities,” Opt. Express 12, 4742–4750 (2004).
[Crossref]

T. Kippenberg, S. Spillane, and K. Vahala, “Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity,” Phys. Rev. Lett. 93, 083904 (2004).
[Crossref]

2003 (2)

L. Yang, D. Armani, and K. Vahala, “Fiber-coupled erbium microlasers on a chip,” Appl. Phys. Lett. 83, 825–826 (2003).
[Crossref]

K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003).
[Crossref]

2002 (3)

2000 (1)

M. Cai, O. Painter, and K. J. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85, 74–77 (2000).
[Crossref]

1998 (1)

1994 (1)

1993 (1)

M. Asobe, H. Itoh, T. Miyazawa, and T. Kanamori, “Efficient and ultrafast all-optical switching using high Delta n, small core chalcogenide glass fibre,” Electron Lett. 29, 1966–1968 (1993).
[Crossref]

1990 (1)

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[Crossref]

Agarwal, A.

Aggarwal, I.

Ahmad, R.

R. Ahmad and M. Rochette, “Photosensitivity at 1550 nm and Bragg grating inscription in As2Se3 chalcogenide microwires,” Appl. Phys. Lett. 99, 061109 (2011).
[Crossref]

Ahn, S.

M. R. Krogstad, S. Ahn, W. Park, and J. T. Gopinath, “Optical characterization of chalcogenide Ge-Sb–Se waveguides at telecom wavelengths,” IEEE Photon. Technol. Lett. 28, 2720–2723 (2016).
[Crossref]

Armani, D.

L. Yang, D. Armani, and K. Vahala, “Fiber-coupled erbium microlasers on a chip,” Appl. Phys. Lett. 83, 825–826 (2003).
[Crossref]

Asobe, M.

M. Asobe, H. Itoh, T. Miyazawa, and T. Kanamori, “Efficient and ultrafast all-optical switching using high Delta n, small core chalcogenide glass fibre,” Electron Lett. 29, 1966–1968 (1993).
[Crossref]

Bahl, G.

J. Kim, M. C. Kuzyk, K. Han, H. Wang, and G. Bahl, “Non-reciprocal Brillouin scattering induced transparency,” Nat. Phys. 11, 275–280 (2015).
[Crossref]

Balac, S.

Bender, C. M.

B. Peng, Ş. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

Bianucci, P.

F. Vanier, P. Bianucci, N. Godbout, M. Rochette, and Y.-A. Peter, “As 2 S 3 microspheres with near absorption-limited quality factor,” in International Conference on Optical MEMS and Nanophotonics (OMN) (IEEE, 2012), pp. 45–46.

Birks, T. A.

Borselli, M.

Cai, M.

M. Cai, O. Painter, and K. J. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85, 74–77 (2000).
[Crossref]

Carlie, N.

Carmon, T.

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94, 223902 (2005).
[Crossref]

T. Carmon, L. Yang, and K. J. Vahala, “Dynamical thermal behavior and thermal self-stability of microcavities,” Opt. Express 12, 4742–4750 (2004).
[Crossref]

Chen, D. R.

J. G. Zhu, S. K. Ozdemir, Y. F. Xiao, L. Li, L. N. He, D. R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4, 46–49 (2010).
[Crossref]

Chen, W.

W. Chen, J. Zhu, Ş. K. Özdemir, B. Peng, and L. Yang, “A simple method for characterizing and engineering thermal relaxation of an optical microcavity,” Appl. Phys. Lett. 109, 061103 (2016).
[Crossref]

Coen, S.

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, P. Emplit, and M. Haelterman, “Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer,” Nat. Photonics 4, 471–476 (2010).
[Crossref]

Del Bino, L.

L. Del Bino, J. M. Silver, S. L. Stebbings, and P. Del’Haye, “Symmetry breaking of counter-propagating light in a nonlinear resonator,” Sci. Rep.-Uk 7, 43142 (2017).
[Crossref]

Del’Haye, P.

L. Del Bino, J. M. Silver, S. L. Stebbings, and P. Del’Haye, “Symmetry breaking of counter-propagating light in a nonlinear resonator,” Sci. Rep.-Uk 7, 43142 (2017).
[Crossref]

Diddams, S. A.

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332, 555–559 (2011).
[Crossref]

Dumeige, Y.

Emplit, P.

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, P. Emplit, and M. Haelterman, “Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer,” Nat. Photonics 4, 471–476 (2010).
[Crossref]

Fan, S.

B. Peng, Ş. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

Féron, P.

Fomin, A. E.

Gianfreda, M.

B. Peng, Ş. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

Godbout, N.

F. Vanier, P. Bianucci, N. Godbout, M. Rochette, and Y.-A. Peter, “As 2 S 3 microspheres with near absorption-limited quality factor,” in International Conference on Optical MEMS and Nanophotonics (OMN) (IEEE, 2012), pp. 45–46.

Gopinath, J. T.

M. R. Krogstad, S. Ahn, W. Park, and J. T. Gopinath, “Optical characterization of chalcogenide Ge-Sb–Se waveguides at telecom wavelengths,” IEEE Photon. Technol. Lett. 28, 2720–2723 (2016).
[Crossref]

Gorodetsky, M. L.

Gorza, S.-P.

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, P. Emplit, and M. Haelterman, “Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer,” Nat. Photonics 4, 471–476 (2010).
[Crossref]

Grudinin, I. S.

Haelterman, M.

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, P. Emplit, and M. Haelterman, “Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer,” Nat. Photonics 4, 471–476 (2010).
[Crossref]

Hagan, D. J.

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[Crossref]

Han, K.

J. Kim, M. C. Kuzyk, K. Han, H. Wang, and G. Bahl, “Non-reciprocal Brillouin scattering induced transparency,” Nat. Phys. 11, 275–280 (2015).
[Crossref]

Harbold, J.

He, L. N.

J. G. Zhu, S. K. Ozdemir, Y. F. Xiao, L. Li, L. N. He, D. R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4, 46–49 (2010).
[Crossref]

Hô, N.

Holzwarth, R.

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332, 555–559 (2011).
[Crossref]

Hu, J.

Huet, V.

Ilchenko, V. S.

Ilday, F.

Itoh, H.

M. Asobe, H. Itoh, T. Miyazawa, and T. Kanamori, “Efficient and ultrafast all-optical switching using high Delta n, small core chalcogenide glass fibre,” Electron Lett. 29, 1966–1968 (1993).
[Crossref]

Johnson, T. J.

Kanamori, T.

M. Asobe, H. Itoh, T. Miyazawa, and T. Kanamori, “Efficient and ultrafast all-optical switching using high Delta n, small core chalcogenide glass fibre,” Electron Lett. 29, 1966–1968 (1993).
[Crossref]

Kim, J.

J. Kim, M. C. Kuzyk, K. Han, H. Wang, and G. Bahl, “Non-reciprocal Brillouin scattering induced transparency,” Nat. Phys. 11, 275–280 (2015).
[Crossref]

Kim, K.

Kimerling, L. C.

Kippenberg, T.

T. Kippenberg, S. Spillane, and K. Vahala, “Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity,” Phys. Rev. Lett. 93, 083904 (2004).
[Crossref]

Kippenberg, T. J.

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332, 555–559 (2011).
[Crossref]

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94, 223902 (2005).
[Crossref]

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” Nature 415, 621–623 (2002).
[Crossref]

Knight, J. C.

Kockaert, P.

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, P. Emplit, and M. Haelterman, “Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer,” Nat. Photonics 4, 471–476 (2010).
[Crossref]

Krogstad, M. R.

M. R. Krogstad, S. Ahn, W. Park, and J. T. Gopinath, “Optical characterization of chalcogenide Ge-Sb–Se waveguides at telecom wavelengths,” IEEE Photon. Technol. Lett. 28, 2720–2723 (2016).
[Crossref]

Kuzyk, M. C.

J. Kim, M. C. Kuzyk, K. Han, H. Wang, and G. Bahl, “Non-reciprocal Brillouin scattering induced transparency,” Nat. Phys. 11, 275–280 (2015).
[Crossref]

Laniel, J. M.

Lee, J. Y.

Lei, F.

B. Peng, Ş. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

Leo, F.

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, P. Emplit, and M. Haelterman, “Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer,” Nat. Photonics 4, 471–476 (2010).
[Crossref]

Li, L.

J. G. Zhu, S. K. Ozdemir, Y. F. Xiao, L. Li, L. N. He, D. R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4, 46–49 (2010).
[Crossref]

Lin, Q.

Long, G. L.

B. Peng, Ş. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

Lu, X.

Man, T.-P. M.

Melloni, A.

Milam, D.

Miyazawa, T.

M. Asobe, H. Itoh, T. Miyazawa, and T. Kanamori, “Efficient and ultrafast all-optical switching using high Delta n, small core chalcogenide glass fibre,” Electron Lett. 29, 1966–1968 (1993).
[Crossref]

Monifi, F.

B. Peng, Ş. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

Morichetti, F.

Nguyen, V.

Nori, F.

B. Peng, Ş. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

Ortigosa-Blanch, A.

Ozdemir, S. K.

J. G. Zhu, S. K. Ozdemir, Y. F. Xiao, L. Li, L. N. He, D. R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4, 46–49 (2010).
[Crossref]

Özdemir, S. K.

W. Chen, J. Zhu, Ş. K. Özdemir, B. Peng, and L. Yang, “A simple method for characterizing and engineering thermal relaxation of an optical microcavity,” Appl. Phys. Lett. 109, 061103 (2016).
[Crossref]

B. Peng, Ş. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

Painter, O.

M. Borselli, T. J. Johnson, and O. Painter, “Accurate measurement of scattering and absorption loss in microphotonic devices,” Opt. Lett. 32, 2954–2956 (2007).
[Crossref]

M. Cai, O. Painter, and K. J. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85, 74–77 (2000).
[Crossref]

Park, W.

M. R. Krogstad, S. Ahn, W. Park, and J. T. Gopinath, “Optical characterization of chalcogenide Ge-Sb–Se waveguides at telecom wavelengths,” IEEE Photon. Technol. Lett. 28, 2720–2723 (2016).
[Crossref]

Park, Y. S.

Peng, B.

W. Chen, J. Zhu, Ş. K. Özdemir, B. Peng, and L. Yang, “A simple method for characterizing and engineering thermal relaxation of an optical microcavity,” Appl. Phys. Lett. 109, 061103 (2016).
[Crossref]

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B. Peng, Ş. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
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Nature (2)

K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003).
[Crossref]

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” Nature 415, 621–623 (2002).
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Opt. Express (3)

Opt. Lett. (6)

Phys. Rev. Lett. (3)

T. Kippenberg, S. Spillane, and K. Vahala, “Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity,” Phys. Rev. Lett. 93, 083904 (2004).
[Crossref]

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94, 223902 (2005).
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Sci. Rep.-Uk (1)

L. Del Bino, J. M. Silver, S. L. Stebbings, and P. Del’Haye, “Symmetry breaking of counter-propagating light in a nonlinear resonator,” Sci. Rep.-Uk 7, 43142 (2017).
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Science (1)

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332, 555–559 (2011).
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Other (1)

F. Vanier, P. Bianucci, N. Godbout, M. Rochette, and Y.-A. Peter, “As 2 S 3 microspheres with near absorption-limited quality factor,” in International Conference on Optical MEMS and Nanophotonics (OMN) (IEEE, 2012), pp. 45–46.

Supplementary Material (1)

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» Supplement 1       Additional details on experiments and theory

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Figures (7)

Fig. 1.
Fig. 1. Schematic of the microresonator coupled to a waveguide. Two counter-propagating modes, A c w and A c c w , are excited by a waveguide coupler. A c w and A c c w are coupled through scatterers with coupling rate of g . The material of the microresonator has nonlinear index of n 2 , and the thermo-optic mode volume related to direct optical heating is designated as H . Two circulators are used to separate the counter-propagating modes coupled back to the waveguide.
Fig. 2.
Fig. 2. Calculated transmission spectrum of a theoretical microresonator for (a) different α during wavelength upscan, (b) for different n 2 during wavelength upscan, (c) for different α during wavelength downscan, and (d) for different n 2 during wavelength downscan. Parameters for calculation: input power: 5 mW; resonator radius: 50 μm; effective mode area: 15 μm 2 ; intrinsic Q factor: 2 × 10 7 ; n 2 : 1 × 10 20 m 2 / W ; α : 0.0015/m; specific heat: 700 J/(kgK); density: 2400 kg / m 3 .
Fig. 3.
Fig. 3. Calculated transmission spectrum of a theoretical microresonator: (a) during wavelength upscan for different thermal time constant τ = H / G , (b) during wavelength downscan for different τ , (c) during wavelength upscan for different g , and (d) during wavelength downscan for different g . Parameters for calculation: input power: 5 mW; resonator radius: 50 μm; effective mode area: 15 μm 2 ; intrinsic Q factor: 2 × 10 7 ; n 2 : 1 × 10 20 m 2 / W ; α : 0.0015/m; specific heat: 700 J/(kgK); density: 2400 kg / m 3 .
Fig. 4.
Fig. 4. Calculated transmission spectra of a theoretical microresonator showing ringing effect during (a) wavelength upscan and (b) during wavelength downscan. The oscillations at the beginning of the spectra are due to noise in the numerical integration (sensitivity to initial values). Parameters for calculation: input power: 5 mW; resonator radius: 50 μm; effective mode area: 15 μm 2 ; intrinsic Q factor: 8 × 10 7 ; α : 10 4 / m ; specific heat: 700 J/(kgK); density: 2400 kg / m 3 .
Fig. 5.
Fig. 5. Individually fitted experimentally measured transmission spectra of a silica microsphere resonator during (a) upscan and (b) downscan at five different coupling conditions. The inset shows the image of the silica microsphere with a radius of 46.4 μm. The input laser power is 6.83 mW.
Fig. 6.
Fig. 6. Example of experiment (group 1 in Table 1) and group fitted transmission spectra of the silica microsphere resonator during (a) upscan and (b) downscan at five different coupling conditions. The resulting n 2 value is 1.86 × 10 20 m 2 / W .
Fig. 7.
Fig. 7. (a) Image of the As 2 S 3 microsphere and its transmission spectrum at low power. The radius of the As 2 S 3 microsphere is 51.5 μm, and Q factor estimated from low power, deeply under-coupled resonance linewidth is 3.5 × 10 6 . (b) Experiment and group fitted transmission spectra of an As 2 S 3 microsphere resonator during wavelength upscan and (c) during wavelength downscan at six different coupling conditions. The input laser power is 0.21 mW, and resulting n 2 value is 2.82 × 10 18 m 2 / W .

Tables (2)

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Table 1. Measured n 2 and α Values of a Silica Microsphere for Four Independent Groups of Spectra

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Table 2. Measured n 2 and α Values of an As 2 S 3 Microsphere for a Group of 12 Spectra

Equations (7)

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d A c w d t = ( γ tot ( Δ ω c w g ) ) A c w i g A c c w i η τ 0 B c w in ,
d A c c w d t = ( γ tot ( Δ ω c c w g ) ) A c c w i g A c w i η τ 0 B c c w in ,
d T d t = G H ( T T 0 ) + α c τ 0 H ( | A c w | 2 + | A c c w | 2 ) ,
Δ ω c w = ω p ω 0 ( 1 n 2 n 0 A eff ( | A c w | 2 + 2 | A c c w | 2 ) d n d T T n 0 ) ,
Δ ω c c w = ω p ω 0 ( 1 n 2 n 0 A eff ( | A c c w | 2 + 2 | A c w | 2 ) d n d T T n 0 ) ,
P c w = B c w in i η A c w ,
P c c w = B c c w in i η A c c w ,

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