Abstract

The relative intensity noise (RIN) of a solid state whispering-gallery-mode class-B laser is studied both theoretically and experimentally under different pumping regimes. In particular, we show that harmonics of the spiking frequency are observed in the RIN spectrum. A rate equation model including Langevin forces and the nonlinear coupling between inverted ion and photon number fluctuations has been developed to reproduce the experimental results and to extract relevant physical parameters from the fitting of the RIN spectrum.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2017 (2)

2016 (3)

G. Palma, M. C. Falconi, F. Starecki, V. Nazabal, T. Yano, T. Kishi, T. Kumagai, and F. Prudenzano, “Novel double step approach for optical sensing via microsphere WGM resonance,” Opt. Express 24, 26956–26971 (2016).
[Crossref] [PubMed]

D. Ristić, S. Berneschi, M. Camerini, D. Farnesi, S. Pelli, C. Trono, A. Chiappini, A. Chiasera, M. Ferrari, A. Lukowiak, Y. Dumeige, P. Féron, G. Righini, S. Soria, and G. Nunzi Conti, “Photoluminescence and lasing in whispering gallery mode glass microspherical resonators,” J. Lumin. 170, 755–760 (2016).
[Crossref]

V. Huet, A. Rasoloniaina, P. Guillemé, P. Rochard, P. Féron, M. Mortier, A. Levenson, K. Bencheikh, A. Yacomotti, and Y. Dumeige, “Millisecond photon lifetime in a slow-light microcavity,” Phys. Rev. Lett. 116, 133902 (2016).
[Crossref] [PubMed]

2015 (3)

W. Liang, V. S. Ilchenko, D. Eliyahu, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “Ultralow noise miniature external cavity semiconductor laser,” Nat. Commun. 6, 7371 (2015).
[Crossref] [PubMed]

W. Loh, S. B. Papp, and S. A. Diddams, “Noise and dynamics of stimulated-brillouin-scattering microresonator lasers,” Phys. Rev. A 91, 053843 (2015).
[Crossref]

A. Rasoloniaina, V. Huet, M. Thual, S. Balac, P. Féron, and Y. Dumeige, “Analysis of third-order nonlinearity effects in very high-Q WGM resonator cavity ringdown spectroscopy,” J. Opt. Soc. Am. B 32, 370–378 (2015).
[Crossref]

2014 (3)

2013 (7)

S. De, V. Pal, A. E. Amili, G. Pillet, G. Baili, M. Alouini, I. Sagnes, R. Ghosh, and F. Bretenaker, “Intensity noise correlations in a two-frequency VECSEL,” Opt. Express 21, 2538–2550 (2013).
[Crossref] [PubMed]

A. J. Maker and A. M. Armani, “Nanowatt threshold, alumina sensitized neodymium laser integrated on silicon,” Opt. Express 21, 27238–27245 (2013).
[Crossref] [PubMed]

F. Tan, M. K. Wu, M. Liu, M. Feng, and N. Holonyak, “Relative intensity noise in high speed microcavity laser,” Appl. Phys. Lett. 103, 141116 (2013).
[Crossref]

A. Lebreton, I. Abram, R. Braive, I. Sagnes, I. Robert-Philip, and A. Beveratos, “Unequivocal differentiation of coherent and chaotic light through interferometric photon correlation measurements,” Phys. Rev. Lett. 110, 163603 (2013).
[Crossref] [PubMed]

L. He, a. K. Özdemir, and L. Yang, “Whispering gallery microcavity lasers,” Laser Photonics Rev. 7, 60–82 (2013).
[Crossref]

A. J. Maker and A. M. Armani, “Heterodyned toroidal microlaser sensor,” Appl. Phys. Lett. 103, 123302 (2013).
[Crossref]

E. H. Bernhardi, K. O. van der Werf, A. J. F. Hollink, K. Wörhoff, R. M. de Ridder, V. Subramaniam, and M. Pollnau, “Intra-laser-cavity microparticle sensing with a dual-wavelength distributed-feedback laser,” Laser Photonics Rev. 7, 589–598 (2013).
[Crossref]

2012 (2)

2010 (4)

L. He, S. K. Ozdemir, Y. F. Xiao, and L. Yang, “Gain-induced evolution of mode splitting spectra in a high-Q active microresonator,” IEEE J. Quantum Electron. 46, 1626–1633 (2010).
[Crossref]

A. Chiasera, Y. Dumeige, P. Féron, M. Ferrari, Y. Jestin, G. Nunzi Conti, S. Pelli, S. Soria, and G. Righini, “Spherical whispering-gallery-mode microresonators,” Laser Photonics Rev. 4, 457–482 (2010).
[Crossref]

L. Xiao, S. Trebaol, Y. Dumeige, Z. Cai, M. Mortier, and P. Feron, “Miniaturized optical microwave source using a dual-wavelength whispering gallery mode laser,” IEEE Photonics Technol. Lett. 22, 559–561 (2010).
[Crossref]

L. He, S. K. Özdemir, J. Zhu, and L. Yang, “Ultrasensitive detection of mode splitting in active optical microcavities,” Phys. Rev. A 82, 053810 (2010).
[Crossref]

2009 (1)

G. Baili, M. Alouini, T. Malherbe, D. Dolfi, I. Sagnes, and F. Bretenaker, “Direct observation of the class-B to class-A transition in the dynamical behavior of a semiconductor laser,” EPL (Europhysics Letters) 87, 44005 (2009).
[Crossref]

2008 (1)

2007 (2)

D. G. O’Shea, J. M. Ward, B. J. Shortt, M. Mortier, P. Féron, and S. Nic Chormaic, “Upconversion channels in Er3+:ZBLALiP fluoride glass microspheres,” Eur. Phys. J. Appl. Phys. 40, 181–188 (2007).
[Crossref]

S. Schwartz, G. Feugnet, E. Lariontsev, and J.-P. Pocholle, “Oscillation regimes of a solid-state ring laser with active beat-note stabilization: From a chaotic device to a ring-laser gyroscope,” Phys. Rev. A 76, 023807 (2007).
[Crossref]

2006 (2)

V. S. Ilchenko and A. B. Matsko, “Optical resonators with whispering-gallery modes-part II: applications,” IEEE J. Sel. Top. Quantum. Electron. 12, 15–32 (2006).
[Crossref]

T. J. Kippenberg, J. Kalkman, A. Polman, and K. J. Vahala, “Demonstration of an erbium-doped microdisk laser on a silicon chip,” Phys. Rev. A 74, 051802 (2006).
[Crossref]

2003 (1)

2001 (2)

F. Lissillour, D. Messager, G. Stéphan, and P. Féron, “Whispering-gallery-mode laser at 1.56μm excited by a fiber taper,” Opt. Lett. 26, 1051–1053 (2001).
[Crossref]

F. Lissillour, R. Gabet, P. Féron, P. Besnard, and G. Stéphan, “Linewidth narrowing of a DFB semiconductor laser at 1.55μm by optical injection of an Er:ZBLAN microspherical laser,” EPL (Europhysics Letters) 55, 499–504 (2001).
[Crossref]

1999 (1)

S. M. Dutra, K. Joosten, G. Nienhuis, N. J. van Druten, A. M. van der Lee, M. P. van Exter, and J. P. Woerdman, “Maxwell-Bloch approach to excess quantum noise,” Phys. Rev. A 59, 4699–4702 (1999).
[Crossref]

1998 (1)

1997 (1)

D. C. Kilper, P. A. Roos, J. L. Carlsten, and K. L. Lear, “Squeezed light generated by a microcavity laser,” Phys. Rev. A 55, R3323–R3326 (1997).
[Crossref]

1996 (1)

V. Sandoghdar, F. Treussart, J. Hare, V. Lefèvre-Seguin, J. M. Raimond, and S. Haroche, “Very low threshold whispering-gallery-mode microsphere laser,” Phys. Rev. A 54, R1777–R1780 (1996).
[Crossref] [PubMed]

1994 (1)

G. Björk, A. Karlsson, and Y. Yamamoto, “Definition of a laser threshold,” Phys. Rev. A 50, 1675–1680 (1994).
[Crossref] [PubMed]

1993 (1)

L. Collot, V. Lefèvre-Seguin, M. Brune, J. M. Raimond, and S. Haroche, “Very high-Q whispering-gallery mode resonances observed on fused silica microspheres,” EPL (Europhysics Letters) 23, 327 (1993).
[Crossref]

Abram, I.

A. Lebreton, I. Abram, R. Braive, I. Sagnes, I. Robert-Philip, and A. Beveratos, “Unequivocal differentiation of coherent and chaotic light through interferometric photon correlation measurements,” Phys. Rev. Lett. 110, 163603 (2013).
[Crossref] [PubMed]

Alouini, M.

Amili, A. E.

Ari, J.

Armani, A. M.

Baili, G.

Balac, S.

Baudet, E.

Bencheikh, K.

V. Huet, A. Rasoloniaina, P. Guillemé, P. Rochard, P. Féron, M. Mortier, A. Levenson, K. Bencheikh, A. Yacomotti, and Y. Dumeige, “Millisecond photon lifetime in a slow-light microcavity,” Phys. Rev. Lett. 116, 133902 (2016).
[Crossref] [PubMed]

Berneschi, S.

D. Ristić, S. Berneschi, M. Camerini, D. Farnesi, S. Pelli, C. Trono, A. Chiappini, A. Chiasera, M. Ferrari, A. Lukowiak, Y. Dumeige, P. Féron, G. Righini, S. Soria, and G. Nunzi Conti, “Photoluminescence and lasing in whispering gallery mode glass microspherical resonators,” J. Lumin. 170, 755–760 (2016).
[Crossref]

Bernhardi, E. H.

E. H. Bernhardi, K. O. van der Werf, A. J. F. Hollink, K. Wörhoff, R. M. de Ridder, V. Subramaniam, and M. Pollnau, “Intra-laser-cavity microparticle sensing with a dual-wavelength distributed-feedback laser,” Laser Photonics Rev. 7, 589–598 (2013).
[Crossref]

Besnard, P.

F. Lissillour, R. Gabet, P. Féron, P. Besnard, and G. Stéphan, “Linewidth narrowing of a DFB semiconductor laser at 1.55μm by optical injection of an Er:ZBLAN microspherical laser,” EPL (Europhysics Letters) 55, 499–504 (2001).
[Crossref]

Beveratos, A.

A. Lebreton, I. Abram, R. Braive, I. Sagnes, I. Robert-Philip, and A. Beveratos, “Unequivocal differentiation of coherent and chaotic light through interferometric photon correlation measurements,” Phys. Rev. Lett. 110, 163603 (2013).
[Crossref] [PubMed]

Björk, G.

G. Björk, A. Karlsson, and Y. Yamamoto, “Definition of a laser threshold,” Phys. Rev. A 50, 1675–1680 (1994).
[Crossref] [PubMed]

Bodiou, L.

Braive, R.

A. Lebreton, I. Abram, R. Braive, I. Sagnes, I. Robert-Philip, and A. Beveratos, “Unequivocal differentiation of coherent and chaotic light through interferometric photon correlation measurements,” Phys. Rev. Lett. 110, 163603 (2013).
[Crossref] [PubMed]

Bretenaker, F.

Brune, M.

L. Collot, V. Lefèvre-Seguin, M. Brune, J. M. Raimond, and S. Haroche, “Very high-Q whispering-gallery mode resonances observed on fused silica microspheres,” EPL (Europhysics Letters) 23, 327 (1993).
[Crossref]

Cai, Z.

L. Xiao, S. Trebaol, Y. Dumeige, Z. Cai, M. Mortier, and P. Feron, “Miniaturized optical microwave source using a dual-wavelength whispering gallery mode laser,” IEEE Photonics Technol. Lett. 22, 559–561 (2010).
[Crossref]

Camerini, M.

D. Ristić, S. Berneschi, M. Camerini, D. Farnesi, S. Pelli, C. Trono, A. Chiappini, A. Chiasera, M. Ferrari, A. Lukowiak, Y. Dumeige, P. Féron, G. Righini, S. Soria, and G. Nunzi Conti, “Photoluminescence and lasing in whispering gallery mode glass microspherical resonators,” J. Lumin. 170, 755–760 (2016).
[Crossref]

Carlsten, J. L.

D. C. Kilper, P. A. Roos, J. L. Carlsten, and K. L. Lear, “Squeezed light generated by a microcavity laser,” Phys. Rev. A 55, R3323–R3326 (1997).
[Crossref]

Charrier, J.

Chiappini, A.

D. Ristić, S. Berneschi, M. Camerini, D. Farnesi, S. Pelli, C. Trono, A. Chiappini, A. Chiasera, M. Ferrari, A. Lukowiak, Y. Dumeige, P. Féron, G. Righini, S. Soria, and G. Nunzi Conti, “Photoluminescence and lasing in whispering gallery mode glass microspherical resonators,” J. Lumin. 170, 755–760 (2016).
[Crossref]

Chiasera, A.

D. Ristić, S. Berneschi, M. Camerini, D. Farnesi, S. Pelli, C. Trono, A. Chiappini, A. Chiasera, M. Ferrari, A. Lukowiak, Y. Dumeige, P. Féron, G. Righini, S. Soria, and G. Nunzi Conti, “Photoluminescence and lasing in whispering gallery mode glass microspherical resonators,” J. Lumin. 170, 755–760 (2016).
[Crossref]

A. Chiasera, Y. Dumeige, P. Féron, M. Ferrari, Y. Jestin, G. Nunzi Conti, S. Pelli, S. Soria, and G. Righini, “Spherical whispering-gallery-mode microresonators,” Laser Photonics Rev. 4, 457–482 (2010).
[Crossref]

Collodo, M. C.

Collot, L.

L. Collot, V. Lefèvre-Seguin, M. Brune, J. M. Raimond, and S. Haroche, “Very high-Q whispering-gallery mode resonances observed on fused silica microspheres,” EPL (Europhysics Letters) 23, 327 (1993).
[Crossref]

Cowle, G. J.

De, S.

de Ridder, R. M.

E. H. Bernhardi, K. O. van der Werf, A. J. F. Hollink, K. Wörhoff, R. M. de Ridder, V. Subramaniam, and M. Pollnau, “Intra-laser-cavity microparticle sensing with a dual-wavelength distributed-feedback laser,” Laser Photonics Rev. 7, 589–598 (2013).
[Crossref]

Deng, Y.

Diddams, S. A.

W. Loh, S. B. Papp, and S. A. Diddams, “Noise and dynamics of stimulated-brillouin-scattering microresonator lasers,” Phys. Rev. A 91, 053843 (2015).
[Crossref]

Dolfi, D.

G. Baili, M. Alouini, T. Malherbe, D. Dolfi, I. Sagnes, and F. Bretenaker, “Direct observation of the class-B to class-A transition in the dynamical behavior of a semiconductor laser,” EPL (Europhysics Letters) 87, 44005 (2009).
[Crossref]

G. Baili, F. Bretenaker, M. Alouini, L. Morvan, D. Dolfi, and I. Sagnes, “Experimental investigation and analytical modeling of excess intensity noise in semiconductor class-A lasers,” J. Lightwave Technol. 26, 952–961 (2008).
[Crossref]

Dong, L.

Dumeige, Y.

G. Palma, M. C. Falconi, F. Starecki, V. Nazabal, J. Ari, L. Bodiou, J. Charrier, Y. Dumeige, E. Baudet, and F. Prudenzano, “Design of praseodymium-doped chalcogenide micro-disk emitting at 4.7 μm,” Opt. Express 25, 7014–7030 (2017).
[Crossref] [PubMed]

V. Huet, A. Rasoloniaina, P. Guillemé, P. Rochard, P. Féron, M. Mortier, A. Levenson, K. Bencheikh, A. Yacomotti, and Y. Dumeige, “Millisecond photon lifetime in a slow-light microcavity,” Phys. Rev. Lett. 116, 133902 (2016).
[Crossref] [PubMed]

D. Ristić, S. Berneschi, M. Camerini, D. Farnesi, S. Pelli, C. Trono, A. Chiappini, A. Chiasera, M. Ferrari, A. Lukowiak, Y. Dumeige, P. Féron, G. Righini, S. Soria, and G. Nunzi Conti, “Photoluminescence and lasing in whispering gallery mode glass microspherical resonators,” J. Lumin. 170, 755–760 (2016).
[Crossref]

A. Rasoloniaina, V. Huet, M. Thual, S. Balac, P. Féron, and Y. Dumeige, “Analysis of third-order nonlinearity effects in very high-Q WGM resonator cavity ringdown spectroscopy,” J. Opt. Soc. Am. B 32, 370–378 (2015).
[Crossref]

A. Rasoloniaina, V. Huet, T. K. N. Nguyên, E. Le Cren, M. Mortier, L. Michely, Y. Dumeige, and P. Féron, “Controling the coupling properties of active ultrahigh-Q WGM microcavities from undercoupling to selective amplification,” Sci. Rep. 4, 4023 (2014).
[Crossref] [PubMed]

A. Rasoloniaina, S. Trebaol, V. Huet, E. Le Cren, G. Nunzi Conti, H. Serier-Brault, M. Mortier, Y. Dumeige, and P. Féron, “High-gain wavelength-selective amplification and cavity ring down spectroscopy in a fluoride glass erbium-doped microsphere,” Opt. Lett. 37, 4735–4737 (2012).
[Crossref] [PubMed]

A. Chiasera, Y. Dumeige, P. Féron, M. Ferrari, Y. Jestin, G. Nunzi Conti, S. Pelli, S. Soria, and G. Righini, “Spherical whispering-gallery-mode microresonators,” Laser Photonics Rev. 4, 457–482 (2010).
[Crossref]

L. Xiao, S. Trebaol, Y. Dumeige, Z. Cai, M. Mortier, and P. Feron, “Miniaturized optical microwave source using a dual-wavelength whispering gallery mode laser,” IEEE Photonics Technol. Lett. 22, 559–561 (2010).
[Crossref]

Dutra, S. M.

S. M. Dutra, K. Joosten, G. Nienhuis, N. J. van Druten, A. M. van der Lee, M. P. van Exter, and J. P. Woerdman, “Maxwell-Bloch approach to excess quantum noise,” Phys. Rev. A 59, 4699–4702 (1999).
[Crossref]

Eliyahu, D.

W. Liang, V. S. Ilchenko, D. Eliyahu, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “Ultralow noise miniature external cavity semiconductor laser,” Nat. Commun. 6, 7371 (2015).
[Crossref] [PubMed]

Falconi, M. C.

Farnesi, D.

D. Ristić, S. Berneschi, M. Camerini, D. Farnesi, S. Pelli, C. Trono, A. Chiappini, A. Chiasera, M. Ferrari, A. Lukowiak, Y. Dumeige, P. Féron, G. Righini, S. Soria, and G. Nunzi Conti, “Photoluminescence and lasing in whispering gallery mode glass microspherical resonators,” J. Lumin. 170, 755–760 (2016).
[Crossref]

Feng, M.

F. Tan, M. K. Wu, M. Liu, M. Feng, and N. Holonyak, “Relative intensity noise in high speed microcavity laser,” Appl. Phys. Lett. 103, 141116 (2013).
[Crossref]

Feron, P.

L. Xiao, S. Trebaol, Y. Dumeige, Z. Cai, M. Mortier, and P. Feron, “Miniaturized optical microwave source using a dual-wavelength whispering gallery mode laser,” IEEE Photonics Technol. Lett. 22, 559–561 (2010).
[Crossref]

Féron, P.

D. Ristić, S. Berneschi, M. Camerini, D. Farnesi, S. Pelli, C. Trono, A. Chiappini, A. Chiasera, M. Ferrari, A. Lukowiak, Y. Dumeige, P. Féron, G. Righini, S. Soria, and G. Nunzi Conti, “Photoluminescence and lasing in whispering gallery mode glass microspherical resonators,” J. Lumin. 170, 755–760 (2016).
[Crossref]

V. Huet, A. Rasoloniaina, P. Guillemé, P. Rochard, P. Féron, M. Mortier, A. Levenson, K. Bencheikh, A. Yacomotti, and Y. Dumeige, “Millisecond photon lifetime in a slow-light microcavity,” Phys. Rev. Lett. 116, 133902 (2016).
[Crossref] [PubMed]

A. Rasoloniaina, V. Huet, M. Thual, S. Balac, P. Féron, and Y. Dumeige, “Analysis of third-order nonlinearity effects in very high-Q WGM resonator cavity ringdown spectroscopy,” J. Opt. Soc. Am. B 32, 370–378 (2015).
[Crossref]

A. Rasoloniaina, V. Huet, T. K. N. Nguyên, E. Le Cren, M. Mortier, L. Michely, Y. Dumeige, and P. Féron, “Controling the coupling properties of active ultrahigh-Q WGM microcavities from undercoupling to selective amplification,” Sci. Rep. 4, 4023 (2014).
[Crossref] [PubMed]

A. Rasoloniaina, S. Trebaol, V. Huet, E. Le Cren, G. Nunzi Conti, H. Serier-Brault, M. Mortier, Y. Dumeige, and P. Féron, “High-gain wavelength-selective amplification and cavity ring down spectroscopy in a fluoride glass erbium-doped microsphere,” Opt. Lett. 37, 4735–4737 (2012).
[Crossref] [PubMed]

A. Chiasera, Y. Dumeige, P. Féron, M. Ferrari, Y. Jestin, G. Nunzi Conti, S. Pelli, S. Soria, and G. Righini, “Spherical whispering-gallery-mode microresonators,” Laser Photonics Rev. 4, 457–482 (2010).
[Crossref]

D. G. O’Shea, J. M. Ward, B. J. Shortt, M. Mortier, P. Féron, and S. Nic Chormaic, “Upconversion channels in Er3+:ZBLALiP fluoride glass microspheres,” Eur. Phys. J. Appl. Phys. 40, 181–188 (2007).
[Crossref]

F. Lissillour, R. Gabet, P. Féron, P. Besnard, and G. Stéphan, “Linewidth narrowing of a DFB semiconductor laser at 1.55μm by optical injection of an Er:ZBLAN microspherical laser,” EPL (Europhysics Letters) 55, 499–504 (2001).
[Crossref]

F. Lissillour, D. Messager, G. Stéphan, and P. Féron, “Whispering-gallery-mode laser at 1.56μm excited by a fiber taper,” Opt. Lett. 26, 1051–1053 (2001).
[Crossref]

Ferrari, M.

D. Ristić, S. Berneschi, M. Camerini, D. Farnesi, S. Pelli, C. Trono, A. Chiappini, A. Chiasera, M. Ferrari, A. Lukowiak, Y. Dumeige, P. Féron, G. Righini, S. Soria, and G. Nunzi Conti, “Photoluminescence and lasing in whispering gallery mode glass microspherical resonators,” J. Lumin. 170, 755–760 (2016).
[Crossref]

A. Chiasera, Y. Dumeige, P. Féron, M. Ferrari, Y. Jestin, G. Nunzi Conti, S. Pelli, S. Soria, and G. Righini, “Spherical whispering-gallery-mode microresonators,” Laser Photonics Rev. 4, 457–482 (2010).
[Crossref]

Feugnet, G.

S. Schwartz, G. Feugnet, E. Lariontsev, and J.-P. Pocholle, “Oscillation regimes of a solid-state ring laser with active beat-note stabilization: From a chaotic device to a ring-laser gyroscope,” Phys. Rev. A 76, 023807 (2007).
[Crossref]

Gabet, R.

F. Lissillour, R. Gabet, P. Féron, P. Besnard, and G. Stéphan, “Linewidth narrowing of a DFB semiconductor laser at 1.55μm by optical injection of an Er:ZBLAN microspherical laser,” EPL (Europhysics Letters) 55, 499–504 (2001).
[Crossref]

Ghosh, R.

Guillemé, P.

V. Huet, A. Rasoloniaina, P. Guillemé, P. Rochard, P. Féron, M. Mortier, A. Levenson, K. Bencheikh, A. Yacomotti, and Y. Dumeige, “Millisecond photon lifetime in a slow-light microcavity,” Phys. Rev. Lett. 116, 133902 (2016).
[Crossref] [PubMed]

Hare, J.

V. Sandoghdar, F. Treussart, J. Hare, V. Lefèvre-Seguin, J. M. Raimond, and S. Haroche, “Very low threshold whispering-gallery-mode microsphere laser,” Phys. Rev. A 54, R1777–R1780 (1996).
[Crossref] [PubMed]

Haroche, S.

V. Sandoghdar, F. Treussart, J. Hare, V. Lefèvre-Seguin, J. M. Raimond, and S. Haroche, “Very low threshold whispering-gallery-mode microsphere laser,” Phys. Rev. A 54, R1777–R1780 (1996).
[Crossref] [PubMed]

L. Collot, V. Lefèvre-Seguin, M. Brune, J. M. Raimond, and S. Haroche, “Very high-Q whispering-gallery mode resonances observed on fused silica microspheres,” EPL (Europhysics Letters) 23, 327 (1993).
[Crossref]

He, L.

L. He, a. K. Özdemir, and L. Yang, “Whispering gallery microcavity lasers,” Laser Photonics Rev. 7, 60–82 (2013).
[Crossref]

L. He, S. K. Özdemir, J. Zhu, and L. Yang, “Ultrasensitive detection of mode splitting in active optical microcavities,” Phys. Rev. A 82, 053810 (2010).
[Crossref]

L. He, S. K. Ozdemir, Y. F. Xiao, and L. Yang, “Gain-induced evolution of mode splitting spectra in a high-Q active microresonator,” IEEE J. Quantum Electron. 46, 1626–1633 (2010).
[Crossref]

Hollink, A. J. F.

E. H. Bernhardi, K. O. van der Werf, A. J. F. Hollink, K. Wörhoff, R. M. de Ridder, V. Subramaniam, and M. Pollnau, “Intra-laser-cavity microparticle sensing with a dual-wavelength distributed-feedback laser,” Laser Photonics Rev. 7, 589–598 (2013).
[Crossref]

Holonyak, N.

F. Tan, M. K. Wu, M. Liu, M. Feng, and N. Holonyak, “Relative intensity noise in high speed microcavity laser,” Appl. Phys. Lett. 103, 141116 (2013).
[Crossref]

Hossein-Zadeh, M.

Hsu, K.

Huet, V.

V. Huet, A. Rasoloniaina, P. Guillemé, P. Rochard, P. Féron, M. Mortier, A. Levenson, K. Bencheikh, A. Yacomotti, and Y. Dumeige, “Millisecond photon lifetime in a slow-light microcavity,” Phys. Rev. Lett. 116, 133902 (2016).
[Crossref] [PubMed]

A. Rasoloniaina, V. Huet, M. Thual, S. Balac, P. Féron, and Y. Dumeige, “Analysis of third-order nonlinearity effects in very high-Q WGM resonator cavity ringdown spectroscopy,” J. Opt. Soc. Am. B 32, 370–378 (2015).
[Crossref]

A. Rasoloniaina, V. Huet, T. K. N. Nguyên, E. Le Cren, M. Mortier, L. Michely, Y. Dumeige, and P. Féron, “Controling the coupling properties of active ultrahigh-Q WGM microcavities from undercoupling to selective amplification,” Sci. Rep. 4, 4023 (2014).
[Crossref] [PubMed]

A. Rasoloniaina, S. Trebaol, V. Huet, E. Le Cren, G. Nunzi Conti, H. Serier-Brault, M. Mortier, Y. Dumeige, and P. Féron, “High-gain wavelength-selective amplification and cavity ring down spectroscopy in a fluoride glass erbium-doped microsphere,” Opt. Lett. 37, 4735–4737 (2012).
[Crossref] [PubMed]

Ilchenko, V. S.

W. Liang, V. S. Ilchenko, D. Eliyahu, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “Ultralow noise miniature external cavity semiconductor laser,” Nat. Commun. 6, 7371 (2015).
[Crossref] [PubMed]

V. S. Ilchenko and A. B. Matsko, “Optical resonators with whispering-gallery modes-part II: applications,” IEEE J. Sel. Top. Quantum. Electron. 12, 15–32 (2006).
[Crossref]

Jain, R. K.

Jestin, Y.

A. Chiasera, Y. Dumeige, P. Féron, M. Ferrari, Y. Jestin, G. Nunzi Conti, S. Pelli, S. Soria, and G. Righini, “Spherical whispering-gallery-mode microresonators,” Laser Photonics Rev. 4, 457–482 (2010).
[Crossref]

Joosten, K.

S. M. Dutra, K. Joosten, G. Nienhuis, N. J. van Druten, A. M. van der Lee, M. P. van Exter, and J. P. Woerdman, “Maxwell-Bloch approach to excess quantum noise,” Phys. Rev. A 59, 4699–4702 (1999).
[Crossref]

Kalkman, J.

T. J. Kippenberg, J. Kalkman, A. Polman, and K. J. Vahala, “Demonstration of an erbium-doped microdisk laser on a silicon chip,” Phys. Rev. A 74, 051802 (2006).
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G. Björk, A. Karlsson, and Y. Yamamoto, “Definition of a laser threshold,” Phys. Rev. A 50, 1675–1680 (1994).
[Crossref] [PubMed]

Kilper, D. C.

D. C. Kilper, P. A. Roos, J. L. Carlsten, and K. L. Lear, “Squeezed light generated by a microcavity laser,” Phys. Rev. A 55, R3323–R3326 (1997).
[Crossref]

Kippenberg, T. J.

T. J. Kippenberg, J. Kalkman, A. Polman, and K. J. Vahala, “Demonstration of an erbium-doped microdisk laser on a silicon chip,” Phys. Rev. A 74, 051802 (2006).
[Crossref]

Kishi, T.

Kumagai, T.

Kuwata-Gonokami, M.

N. Takemura, J. Omachi, and M. Kuwata-Gonokami, “Fast periodic modulations in the photon correlation of single-mode vertical-cavity surface-emitting lasers,” Phys. Rev. A 85, 053811 (2012).
[Crossref]

Lariontsev, E.

S. Schwartz, G. Feugnet, E. Lariontsev, and J.-P. Pocholle, “Oscillation regimes of a solid-state ring laser with active beat-note stabilization: From a chaotic device to a ring-laser gyroscope,” Phys. Rev. A 76, 023807 (2007).
[Crossref]

Le Cren, E.

A. Rasoloniaina, V. Huet, T. K. N. Nguyên, E. Le Cren, M. Mortier, L. Michely, Y. Dumeige, and P. Féron, “Controling the coupling properties of active ultrahigh-Q WGM microcavities from undercoupling to selective amplification,” Sci. Rep. 4, 4023 (2014).
[Crossref] [PubMed]

A. Rasoloniaina, S. Trebaol, V. Huet, E. Le Cren, G. Nunzi Conti, H. Serier-Brault, M. Mortier, Y. Dumeige, and P. Féron, “High-gain wavelength-selective amplification and cavity ring down spectroscopy in a fluoride glass erbium-doped microsphere,” Opt. Lett. 37, 4735–4737 (2012).
[Crossref] [PubMed]

Lear, K. L.

D. C. Kilper, P. A. Roos, J. L. Carlsten, and K. L. Lear, “Squeezed light generated by a microcavity laser,” Phys. Rev. A 55, R3323–R3326 (1997).
[Crossref]

Lebreton, A.

A. Lebreton, I. Abram, R. Braive, I. Sagnes, I. Robert-Philip, and A. Beveratos, “Unequivocal differentiation of coherent and chaotic light through interferometric photon correlation measurements,” Phys. Rev. Lett. 110, 163603 (2013).
[Crossref] [PubMed]

Lefèvre-Seguin, V.

V. Sandoghdar, F. Treussart, J. Hare, V. Lefèvre-Seguin, J. M. Raimond, and S. Haroche, “Very low threshold whispering-gallery-mode microsphere laser,” Phys. Rev. A 54, R1777–R1780 (1996).
[Crossref] [PubMed]

L. Collot, V. Lefèvre-Seguin, M. Brune, J. M. Raimond, and S. Haroche, “Very high-Q whispering-gallery mode resonances observed on fused silica microspheres,” EPL (Europhysics Letters) 23, 327 (1993).
[Crossref]

Levenson, A.

V. Huet, A. Rasoloniaina, P. Guillemé, P. Rochard, P. Féron, M. Mortier, A. Levenson, K. Bencheikh, A. Yacomotti, and Y. Dumeige, “Millisecond photon lifetime in a slow-light microcavity,” Phys. Rev. Lett. 116, 133902 (2016).
[Crossref] [PubMed]

Li, J.

Liang, W.

W. Liang, V. S. Ilchenko, D. Eliyahu, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “Ultralow noise miniature external cavity semiconductor laser,” Nat. Commun. 6, 7371 (2015).
[Crossref] [PubMed]

Lissillour, F.

F. Lissillour, R. Gabet, P. Féron, P. Besnard, and G. Stéphan, “Linewidth narrowing of a DFB semiconductor laser at 1.55μm by optical injection of an Er:ZBLAN microspherical laser,” EPL (Europhysics Letters) 55, 499–504 (2001).
[Crossref]

F. Lissillour, D. Messager, G. Stéphan, and P. Féron, “Whispering-gallery-mode laser at 1.56μm excited by a fiber taper,” Opt. Lett. 26, 1051–1053 (2001).
[Crossref]

Liu, M.

F. Tan, M. K. Wu, M. Liu, M. Feng, and N. Holonyak, “Relative intensity noise in high speed microcavity laser,” Appl. Phys. Lett. 103, 141116 (2013).
[Crossref]

Loh, W.

W. Loh, S. B. Papp, and S. A. Diddams, “Noise and dynamics of stimulated-brillouin-scattering microresonator lasers,” Phys. Rev. A 91, 053843 (2015).
[Crossref]

Loh, W. H.

Lukowiak, A.

D. Ristić, S. Berneschi, M. Camerini, D. Farnesi, S. Pelli, C. Trono, A. Chiappini, A. Chiasera, M. Ferrari, A. Lukowiak, Y. Dumeige, P. Féron, G. Righini, S. Soria, and G. Nunzi Conti, “Photoluminescence and lasing in whispering gallery mode glass microspherical resonators,” J. Lumin. 170, 755–760 (2016).
[Crossref]

Maker, A. J.

Maleki, L.

W. Liang, V. S. Ilchenko, D. Eliyahu, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “Ultralow noise miniature external cavity semiconductor laser,” Nat. Commun. 6, 7371 (2015).
[Crossref] [PubMed]

Malherbe, T.

G. Baili, M. Alouini, T. Malherbe, D. Dolfi, I. Sagnes, and F. Bretenaker, “Direct observation of the class-B to class-A transition in the dynamical behavior of a semiconductor laser,” EPL (Europhysics Letters) 87, 44005 (2009).
[Crossref]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).
[Crossref]

Matsko, A. B.

W. Liang, V. S. Ilchenko, D. Eliyahu, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “Ultralow noise miniature external cavity semiconductor laser,” Nat. Commun. 6, 7371 (2015).
[Crossref] [PubMed]

V. S. Ilchenko and A. B. Matsko, “Optical resonators with whispering-gallery modes-part II: applications,” IEEE J. Sel. Top. Quantum. Electron. 12, 15–32 (2006).
[Crossref]

Messager, D.

Michely, L.

A. Rasoloniaina, V. Huet, T. K. N. Nguyên, E. Le Cren, M. Mortier, L. Michely, Y. Dumeige, and P. Féron, “Controling the coupling properties of active ultrahigh-Q WGM microcavities from undercoupling to selective amplification,” Sci. Rep. 4, 4023 (2014).
[Crossref] [PubMed]

Mortier, M.

V. Huet, A. Rasoloniaina, P. Guillemé, P. Rochard, P. Féron, M. Mortier, A. Levenson, K. Bencheikh, A. Yacomotti, and Y. Dumeige, “Millisecond photon lifetime in a slow-light microcavity,” Phys. Rev. Lett. 116, 133902 (2016).
[Crossref] [PubMed]

A. Rasoloniaina, V. Huet, T. K. N. Nguyên, E. Le Cren, M. Mortier, L. Michely, Y. Dumeige, and P. Féron, “Controling the coupling properties of active ultrahigh-Q WGM microcavities from undercoupling to selective amplification,” Sci. Rep. 4, 4023 (2014).
[Crossref] [PubMed]

A. Rasoloniaina, S. Trebaol, V. Huet, E. Le Cren, G. Nunzi Conti, H. Serier-Brault, M. Mortier, Y. Dumeige, and P. Féron, “High-gain wavelength-selective amplification and cavity ring down spectroscopy in a fluoride glass erbium-doped microsphere,” Opt. Lett. 37, 4735–4737 (2012).
[Crossref] [PubMed]

L. Xiao, S. Trebaol, Y. Dumeige, Z. Cai, M. Mortier, and P. Feron, “Miniaturized optical microwave source using a dual-wavelength whispering gallery mode laser,” IEEE Photonics Technol. Lett. 22, 559–561 (2010).
[Crossref]

D. G. O’Shea, J. M. Ward, B. J. Shortt, M. Mortier, P. Féron, and S. Nic Chormaic, “Upconversion channels in Er3+:ZBLALiP fluoride glass microspheres,” Eur. Phys. J. Appl. Phys. 40, 181–188 (2007).
[Crossref]

Morvan, L.

Nazabal, V.

Nguyên, T. K. N.

A. Rasoloniaina, V. Huet, T. K. N. Nguyên, E. Le Cren, M. Mortier, L. Michely, Y. Dumeige, and P. Féron, “Controling the coupling properties of active ultrahigh-Q WGM microcavities from undercoupling to selective amplification,” Sci. Rep. 4, 4023 (2014).
[Crossref] [PubMed]

Nic Chormaic, S.

D. G. O’Shea, J. M. Ward, B. J. Shortt, M. Mortier, P. Féron, and S. Nic Chormaic, “Upconversion channels in Er3+:ZBLALiP fluoride glass microspheres,” Eur. Phys. J. Appl. Phys. 40, 181–188 (2007).
[Crossref]

Nienhuis, G.

S. M. Dutra, K. Joosten, G. Nienhuis, N. J. van Druten, A. M. van der Lee, M. P. van Exter, and J. P. Woerdman, “Maxwell-Bloch approach to excess quantum noise,” Phys. Rev. A 59, 4699–4702 (1999).
[Crossref]

Nunzi Conti, G.

D. Ristić, S. Berneschi, M. Camerini, D. Farnesi, S. Pelli, C. Trono, A. Chiappini, A. Chiasera, M. Ferrari, A. Lukowiak, Y. Dumeige, P. Féron, G. Righini, S. Soria, and G. Nunzi Conti, “Photoluminescence and lasing in whispering gallery mode glass microspherical resonators,” J. Lumin. 170, 755–760 (2016).
[Crossref]

A. Rasoloniaina, S. Trebaol, V. Huet, E. Le Cren, G. Nunzi Conti, H. Serier-Brault, M. Mortier, Y. Dumeige, and P. Féron, “High-gain wavelength-selective amplification and cavity ring down spectroscopy in a fluoride glass erbium-doped microsphere,” Opt. Lett. 37, 4735–4737 (2012).
[Crossref] [PubMed]

A. Chiasera, Y. Dumeige, P. Féron, M. Ferrari, Y. Jestin, G. Nunzi Conti, S. Pelli, S. Soria, and G. Righini, “Spherical whispering-gallery-mode microresonators,” Laser Photonics Rev. 4, 457–482 (2010).
[Crossref]

O’Shea, D. G.

D. G. O’Shea, J. M. Ward, B. J. Shortt, M. Mortier, P. Féron, and S. Nic Chormaic, “Upconversion channels in Er3+:ZBLALiP fluoride glass microspheres,” Eur. Phys. J. Appl. Phys. 40, 181–188 (2007).
[Crossref]

Omachi, J.

N. Takemura, J. Omachi, and M. Kuwata-Gonokami, “Fast periodic modulations in the photon correlation of single-mode vertical-cavity surface-emitting lasers,” Phys. Rev. A 85, 053811 (2012).
[Crossref]

Ozdemir, S. K.

L. He, S. K. Ozdemir, Y. F. Xiao, and L. Yang, “Gain-induced evolution of mode splitting spectra in a high-Q active microresonator,” IEEE J. Quantum Electron. 46, 1626–1633 (2010).
[Crossref]

Özdemir, a. K.

L. He, a. K. Özdemir, and L. Yang, “Whispering gallery microcavity lasers,” Laser Photonics Rev. 7, 60–82 (2013).
[Crossref]

Özdemir, S. K.

L. He, S. K. Özdemir, J. Zhu, and L. Yang, “Ultrasensitive detection of mode splitting in active optical microcavities,” Phys. Rev. A 82, 053810 (2010).
[Crossref]

Pal, V.

Palma, G.

Papp, S. B.

W. Loh, S. B. Papp, and S. A. Diddams, “Noise and dynamics of stimulated-brillouin-scattering microresonator lasers,” Phys. Rev. A 91, 053843 (2015).
[Crossref]

Pelli, S.

D. Ristić, S. Berneschi, M. Camerini, D. Farnesi, S. Pelli, C. Trono, A. Chiappini, A. Chiasera, M. Ferrari, A. Lukowiak, Y. Dumeige, P. Féron, G. Righini, S. Soria, and G. Nunzi Conti, “Photoluminescence and lasing in whispering gallery mode glass microspherical resonators,” J. Lumin. 170, 755–760 (2016).
[Crossref]

A. Chiasera, Y. Dumeige, P. Féron, M. Ferrari, Y. Jestin, G. Nunzi Conti, S. Pelli, S. Soria, and G. Righini, “Spherical whispering-gallery-mode microresonators,” Laser Photonics Rev. 4, 457–482 (2010).
[Crossref]

Pillet, G.

Pocholle, J.-P.

S. Schwartz, G. Feugnet, E. Lariontsev, and J.-P. Pocholle, “Oscillation regimes of a solid-state ring laser with active beat-note stabilization: From a chaotic device to a ring-laser gyroscope,” Phys. Rev. A 76, 023807 (2007).
[Crossref]

Pollnau, M.

E. H. Bernhardi, K. O. van der Werf, A. J. F. Hollink, K. Wörhoff, R. M. de Ridder, V. Subramaniam, and M. Pollnau, “Intra-laser-cavity microparticle sensing with a dual-wavelength distributed-feedback laser,” Laser Photonics Rev. 7, 589–598 (2013).
[Crossref]

Polman, A.

T. J. Kippenberg, J. Kalkman, A. Polman, and K. J. Vahala, “Demonstration of an erbium-doped microdisk laser on a silicon chip,” Phys. Rev. A 74, 051802 (2006).
[Crossref]

Prudenzano, F.

Raimond, J. M.

V. Sandoghdar, F. Treussart, J. Hare, V. Lefèvre-Seguin, J. M. Raimond, and S. Haroche, “Very low threshold whispering-gallery-mode microsphere laser,” Phys. Rev. A 54, R1777–R1780 (1996).
[Crossref] [PubMed]

L. Collot, V. Lefèvre-Seguin, M. Brune, J. M. Raimond, and S. Haroche, “Very high-Q whispering-gallery mode resonances observed on fused silica microspheres,” EPL (Europhysics Letters) 23, 327 (1993).
[Crossref]

Rasoloniaina, A.

V. Huet, A. Rasoloniaina, P. Guillemé, P. Rochard, P. Féron, M. Mortier, A. Levenson, K. Bencheikh, A. Yacomotti, and Y. Dumeige, “Millisecond photon lifetime in a slow-light microcavity,” Phys. Rev. Lett. 116, 133902 (2016).
[Crossref] [PubMed]

A. Rasoloniaina, V. Huet, M. Thual, S. Balac, P. Féron, and Y. Dumeige, “Analysis of third-order nonlinearity effects in very high-Q WGM resonator cavity ringdown spectroscopy,” J. Opt. Soc. Am. B 32, 370–378 (2015).
[Crossref]

A. Rasoloniaina, V. Huet, T. K. N. Nguyên, E. Le Cren, M. Mortier, L. Michely, Y. Dumeige, and P. Féron, “Controling the coupling properties of active ultrahigh-Q WGM microcavities from undercoupling to selective amplification,” Sci. Rep. 4, 4023 (2014).
[Crossref] [PubMed]

A. Rasoloniaina, S. Trebaol, V. Huet, E. Le Cren, G. Nunzi Conti, H. Serier-Brault, M. Mortier, Y. Dumeige, and P. Féron, “High-gain wavelength-selective amplification and cavity ring down spectroscopy in a fluoride glass erbium-doped microsphere,” Opt. Lett. 37, 4735–4737 (2012).
[Crossref] [PubMed]

Righini, G.

D. Ristić, S. Berneschi, M. Camerini, D. Farnesi, S. Pelli, C. Trono, A. Chiappini, A. Chiasera, M. Ferrari, A. Lukowiak, Y. Dumeige, P. Féron, G. Righini, S. Soria, and G. Nunzi Conti, “Photoluminescence and lasing in whispering gallery mode glass microspherical resonators,” J. Lumin. 170, 755–760 (2016).
[Crossref]

A. Chiasera, Y. Dumeige, P. Féron, M. Ferrari, Y. Jestin, G. Nunzi Conti, S. Pelli, S. Soria, and G. Righini, “Spherical whispering-gallery-mode microresonators,” Laser Photonics Rev. 4, 457–482 (2010).
[Crossref]

Ristic, D.

D. Ristić, S. Berneschi, M. Camerini, D. Farnesi, S. Pelli, C. Trono, A. Chiappini, A. Chiasera, M. Ferrari, A. Lukowiak, Y. Dumeige, P. Féron, G. Righini, S. Soria, and G. Nunzi Conti, “Photoluminescence and lasing in whispering gallery mode glass microspherical resonators,” J. Lumin. 170, 755–760 (2016).
[Crossref]

Robert-Philip, I.

A. Lebreton, I. Abram, R. Braive, I. Sagnes, I. Robert-Philip, and A. Beveratos, “Unequivocal differentiation of coherent and chaotic light through interferometric photon correlation measurements,” Phys. Rev. Lett. 110, 163603 (2013).
[Crossref] [PubMed]

Rochard, P.

V. Huet, A. Rasoloniaina, P. Guillemé, P. Rochard, P. Féron, M. Mortier, A. Levenson, K. Bencheikh, A. Yacomotti, and Y. Dumeige, “Millisecond photon lifetime in a slow-light microcavity,” Phys. Rev. Lett. 116, 133902 (2016).
[Crossref] [PubMed]

Roos, P. A.

D. C. Kilper, P. A. Roos, J. L. Carlsten, and K. L. Lear, “Squeezed light generated by a microcavity laser,” Phys. Rev. A 55, R3323–R3326 (1997).
[Crossref]

Rosencher, E.

E. Rosencher and B. Vinter, Optoelectronics (Cambridge University Press, 2002).
[Crossref]

Sagnes, I.

A. Lebreton, I. Abram, R. Braive, I. Sagnes, I. Robert-Philip, and A. Beveratos, “Unequivocal differentiation of coherent and chaotic light through interferometric photon correlation measurements,” Phys. Rev. Lett. 110, 163603 (2013).
[Crossref] [PubMed]

S. De, V. Pal, A. E. Amili, G. Pillet, G. Baili, M. Alouini, I. Sagnes, R. Ghosh, and F. Bretenaker, “Intensity noise correlations in a two-frequency VECSEL,” Opt. Express 21, 2538–2550 (2013).
[Crossref] [PubMed]

G. Baili, M. Alouini, T. Malherbe, D. Dolfi, I. Sagnes, and F. Bretenaker, “Direct observation of the class-B to class-A transition in the dynamical behavior of a semiconductor laser,” EPL (Europhysics Letters) 87, 44005 (2009).
[Crossref]

G. Baili, F. Bretenaker, M. Alouini, L. Morvan, D. Dolfi, and I. Sagnes, “Experimental investigation and analytical modeling of excess intensity noise in semiconductor class-A lasers,” J. Lightwave Technol. 26, 952–961 (2008).
[Crossref]

Samson, B. N.

Sandoghdar, V.

V. Sandoghdar, F. Treussart, J. Hare, V. Lefèvre-Seguin, J. M. Raimond, and S. Haroche, “Very low threshold whispering-gallery-mode microsphere laser,” Phys. Rev. A 54, R1777–R1780 (1996).
[Crossref] [PubMed]

Savchenkov, A. A.

W. Liang, V. S. Ilchenko, D. Eliyahu, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “Ultralow noise miniature external cavity semiconductor laser,” Nat. Commun. 6, 7371 (2015).
[Crossref] [PubMed]

Schwartz, S.

S. Schwartz, G. Feugnet, E. Lariontsev, and J.-P. Pocholle, “Oscillation regimes of a solid-state ring laser with active beat-note stabilization: From a chaotic device to a ring-laser gyroscope,” Phys. Rev. A 76, 023807 (2007).
[Crossref]

Schwefel, H. G. L.

Sedlmeir, F.

Seidel, D.

W. Liang, V. S. Ilchenko, D. Eliyahu, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “Ultralow noise miniature external cavity semiconductor laser,” Nat. Commun. 6, 7371 (2015).
[Crossref] [PubMed]

Serier-Brault, H.

Shortt, B. J.

D. G. O’Shea, J. M. Ward, B. J. Shortt, M. Mortier, P. Féron, and S. Nic Chormaic, “Upconversion channels in Er3+:ZBLALiP fluoride glass microspheres,” Eur. Phys. J. Appl. Phys. 40, 181–188 (2007).
[Crossref]

Siegman, A. E.

A. E. Siegman, Lasers (University Science Books, 1986).

Soria, S.

D. Ristić, S. Berneschi, M. Camerini, D. Farnesi, S. Pelli, C. Trono, A. Chiappini, A. Chiasera, M. Ferrari, A. Lukowiak, Y. Dumeige, P. Féron, G. Righini, S. Soria, and G. Nunzi Conti, “Photoluminescence and lasing in whispering gallery mode glass microspherical resonators,” J. Lumin. 170, 755–760 (2016).
[Crossref]

A. Chiasera, Y. Dumeige, P. Féron, M. Ferrari, Y. Jestin, G. Nunzi Conti, S. Pelli, S. Soria, and G. Righini, “Spherical whispering-gallery-mode microresonators,” Laser Photonics Rev. 4, 457–482 (2010).
[Crossref]

Sprenger, B.

Starecki, F.

Stéphan, G.

F. Lissillour, D. Messager, G. Stéphan, and P. Féron, “Whispering-gallery-mode laser at 1.56μm excited by a fiber taper,” Opt. Lett. 26, 1051–1053 (2001).
[Crossref]

F. Lissillour, R. Gabet, P. Féron, P. Besnard, and G. Stéphan, “Linewidth narrowing of a DFB semiconductor laser at 1.55μm by optical injection of an Er:ZBLAN microspherical laser,” EPL (Europhysics Letters) 55, 499–504 (2001).
[Crossref]

Subramaniam, V.

E. H. Bernhardi, K. O. van der Werf, A. J. F. Hollink, K. Wörhoff, R. M. de Ridder, V. Subramaniam, and M. Pollnau, “Intra-laser-cavity microparticle sensing with a dual-wavelength distributed-feedback laser,” Laser Photonics Rev. 7, 589–598 (2013).
[Crossref]

Suh, M.-G.

Svitlov, S.

Takemura, N.

N. Takemura, J. Omachi, and M. Kuwata-Gonokami, “Fast periodic modulations in the photon correlation of single-mode vertical-cavity surface-emitting lasers,” Phys. Rev. A 85, 053811 (2012).
[Crossref]

Tan, F.

F. Tan, M. K. Wu, M. Liu, M. Feng, and N. Holonyak, “Relative intensity noise in high speed microcavity laser,” Appl. Phys. Lett. 103, 141116 (2013).
[Crossref]

Thual, M.

Trebaol, S.

A. Rasoloniaina, S. Trebaol, V. Huet, E. Le Cren, G. Nunzi Conti, H. Serier-Brault, M. Mortier, Y. Dumeige, and P. Féron, “High-gain wavelength-selective amplification and cavity ring down spectroscopy in a fluoride glass erbium-doped microsphere,” Opt. Lett. 37, 4735–4737 (2012).
[Crossref] [PubMed]

L. Xiao, S. Trebaol, Y. Dumeige, Z. Cai, M. Mortier, and P. Feron, “Miniaturized optical microwave source using a dual-wavelength whispering gallery mode laser,” IEEE Photonics Technol. Lett. 22, 559–561 (2010).
[Crossref]

Treussart, F.

V. Sandoghdar, F. Treussart, J. Hare, V. Lefèvre-Seguin, J. M. Raimond, and S. Haroche, “Very low threshold whispering-gallery-mode microsphere laser,” Phys. Rev. A 54, R1777–R1780 (1996).
[Crossref] [PubMed]

F. Treussart, Etude expérimentale de l’effet laser dans des microsphères de silice dopées avec des ions neodyme (Université Pierre et Marie Curie PhD Thesis, 1997).

Trono, C.

D. Ristić, S. Berneschi, M. Camerini, D. Farnesi, S. Pelli, C. Trono, A. Chiappini, A. Chiasera, M. Ferrari, A. Lukowiak, Y. Dumeige, P. Féron, G. Righini, S. Soria, and G. Nunzi Conti, “Photoluminescence and lasing in whispering gallery mode glass microspherical resonators,” J. Lumin. 170, 755–760 (2016).
[Crossref]

Vahala, K.

Vahala, K. J.

T. J. Kippenberg, J. Kalkman, A. Polman, and K. J. Vahala, “Demonstration of an erbium-doped microdisk laser on a silicon chip,” Phys. Rev. A 74, 051802 (2006).
[Crossref]

L. Yang and K. J. Vahala, “Gain functionalization of silica microresonators,” Opt. Lett. 28, 592–594 (2003).
[Crossref] [PubMed]

van der Lee, A. M.

S. M. Dutra, K. Joosten, G. Nienhuis, N. J. van Druten, A. M. van der Lee, M. P. van Exter, and J. P. Woerdman, “Maxwell-Bloch approach to excess quantum noise,” Phys. Rev. A 59, 4699–4702 (1999).
[Crossref]

van der Werf, K. O.

E. H. Bernhardi, K. O. van der Werf, A. J. F. Hollink, K. Wörhoff, R. M. de Ridder, V. Subramaniam, and M. Pollnau, “Intra-laser-cavity microparticle sensing with a dual-wavelength distributed-feedback laser,” Laser Photonics Rev. 7, 589–598 (2013).
[Crossref]

van Druten, N. J.

S. M. Dutra, K. Joosten, G. Nienhuis, N. J. van Druten, A. M. van der Lee, M. P. van Exter, and J. P. Woerdman, “Maxwell-Bloch approach to excess quantum noise,” Phys. Rev. A 59, 4699–4702 (1999).
[Crossref]

van Exter, M. P.

S. M. Dutra, K. Joosten, G. Nienhuis, N. J. van Druten, A. M. van der Lee, M. P. van Exter, and J. P. Woerdman, “Maxwell-Bloch approach to excess quantum noise,” Phys. Rev. A 59, 4699–4702 (1999).
[Crossref]

Vinter, B.

E. Rosencher and B. Vinter, Optoelectronics (Cambridge University Press, 2002).
[Crossref]

Wang, L. J.

Ward, J. M.

D. G. O’Shea, J. M. Ward, B. J. Shortt, M. Mortier, P. Féron, and S. Nic Chormaic, “Upconversion channels in Er3+:ZBLALiP fluoride glass microspheres,” Eur. Phys. J. Appl. Phys. 40, 181–188 (2007).
[Crossref]

Woerdman, J. P.

S. M. Dutra, K. Joosten, G. Nienhuis, N. J. van Druten, A. M. van der Lee, M. P. van Exter, and J. P. Woerdman, “Maxwell-Bloch approach to excess quantum noise,” Phys. Rev. A 59, 4699–4702 (1999).
[Crossref]

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).
[Crossref]

Wörhoff, K.

E. H. Bernhardi, K. O. van der Werf, A. J. F. Hollink, K. Wörhoff, R. M. de Ridder, V. Subramaniam, and M. Pollnau, “Intra-laser-cavity microparticle sensing with a dual-wavelength distributed-feedback laser,” Laser Photonics Rev. 7, 589–598 (2013).
[Crossref]

Wu, M. K.

F. Tan, M. K. Wu, M. Liu, M. Feng, and N. Holonyak, “Relative intensity noise in high speed microcavity laser,” Appl. Phys. Lett. 103, 141116 (2013).
[Crossref]

Xiao, L.

L. Xiao, S. Trebaol, Y. Dumeige, Z. Cai, M. Mortier, and P. Feron, “Miniaturized optical microwave source using a dual-wavelength whispering gallery mode laser,” IEEE Photonics Technol. Lett. 22, 559–561 (2010).
[Crossref]

Xiao, Y. F.

L. He, S. K. Ozdemir, Y. F. Xiao, and L. Yang, “Gain-induced evolution of mode splitting spectra in a high-Q active microresonator,” IEEE J. Quantum Electron. 46, 1626–1633 (2010).
[Crossref]

Yacomotti, A.

V. Huet, A. Rasoloniaina, P. Guillemé, P. Rochard, P. Féron, M. Mortier, A. Levenson, K. Bencheikh, A. Yacomotti, and Y. Dumeige, “Millisecond photon lifetime in a slow-light microcavity,” Phys. Rev. Lett. 116, 133902 (2016).
[Crossref] [PubMed]

Yamamoto, Y.

G. Björk, A. Karlsson, and Y. Yamamoto, “Definition of a laser threshold,” Phys. Rev. A 50, 1675–1680 (1994).
[Crossref] [PubMed]

Yang, L.

L. He, a. K. Özdemir, and L. Yang, “Whispering gallery microcavity lasers,” Laser Photonics Rev. 7, 60–82 (2013).
[Crossref]

L. He, S. K. Özdemir, J. Zhu, and L. Yang, “Ultrasensitive detection of mode splitting in active optical microcavities,” Phys. Rev. A 82, 053810 (2010).
[Crossref]

L. He, S. K. Ozdemir, Y. F. Xiao, and L. Yang, “Gain-induced evolution of mode splitting spectra in a high-Q active microresonator,” IEEE J. Quantum Electron. 46, 1626–1633 (2010).
[Crossref]

L. Yang and K. J. Vahala, “Gain functionalization of silica microresonators,” Opt. Lett. 28, 592–594 (2003).
[Crossref] [PubMed]

Yano, T.

Zhu, J.

L. He, S. K. Özdemir, J. Zhu, and L. Yang, “Ultrasensitive detection of mode splitting in active optical microcavities,” Phys. Rev. A 82, 053810 (2010).
[Crossref]

Appl. Phys. Lett. (2)

A. J. Maker and A. M. Armani, “Heterodyned toroidal microlaser sensor,” Appl. Phys. Lett. 103, 123302 (2013).
[Crossref]

F. Tan, M. K. Wu, M. Liu, M. Feng, and N. Holonyak, “Relative intensity noise in high speed microcavity laser,” Appl. Phys. Lett. 103, 141116 (2013).
[Crossref]

EPL (Europhysics Letters) (3)

F. Lissillour, R. Gabet, P. Féron, P. Besnard, and G. Stéphan, “Linewidth narrowing of a DFB semiconductor laser at 1.55μm by optical injection of an Er:ZBLAN microspherical laser,” EPL (Europhysics Letters) 55, 499–504 (2001).
[Crossref]

G. Baili, M. Alouini, T. Malherbe, D. Dolfi, I. Sagnes, and F. Bretenaker, “Direct observation of the class-B to class-A transition in the dynamical behavior of a semiconductor laser,” EPL (Europhysics Letters) 87, 44005 (2009).
[Crossref]

L. Collot, V. Lefèvre-Seguin, M. Brune, J. M. Raimond, and S. Haroche, “Very high-Q whispering-gallery mode resonances observed on fused silica microspheres,” EPL (Europhysics Letters) 23, 327 (1993).
[Crossref]

Eur. Phys. J. Appl. Phys. (1)

D. G. O’Shea, J. M. Ward, B. J. Shortt, M. Mortier, P. Féron, and S. Nic Chormaic, “Upconversion channels in Er3+:ZBLALiP fluoride glass microspheres,” Eur. Phys. J. Appl. Phys. 40, 181–188 (2007).
[Crossref]

IEEE J. Quantum Electron. (1)

L. He, S. K. Ozdemir, Y. F. Xiao, and L. Yang, “Gain-induced evolution of mode splitting spectra in a high-Q active microresonator,” IEEE J. Quantum Electron. 46, 1626–1633 (2010).
[Crossref]

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

V. S. Ilchenko and A. B. Matsko, “Optical resonators with whispering-gallery modes-part II: applications,” IEEE J. Sel. Top. Quantum. Electron. 12, 15–32 (2006).
[Crossref]

IEEE Photonics Technol. Lett. (1)

L. Xiao, S. Trebaol, Y. Dumeige, Z. Cai, M. Mortier, and P. Feron, “Miniaturized optical microwave source using a dual-wavelength whispering gallery mode laser,” IEEE Photonics Technol. Lett. 22, 559–561 (2010).
[Crossref]

J. Lightwave Technol. (2)

J. Lumin. (1)

D. Ristić, S. Berneschi, M. Camerini, D. Farnesi, S. Pelli, C. Trono, A. Chiappini, A. Chiasera, M. Ferrari, A. Lukowiak, Y. Dumeige, P. Féron, G. Righini, S. Soria, and G. Nunzi Conti, “Photoluminescence and lasing in whispering gallery mode glass microspherical resonators,” J. Lumin. 170, 755–760 (2016).
[Crossref]

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

Laser Photonics Rev. (3)

E. H. Bernhardi, K. O. van der Werf, A. J. F. Hollink, K. Wörhoff, R. M. de Ridder, V. Subramaniam, and M. Pollnau, “Intra-laser-cavity microparticle sensing with a dual-wavelength distributed-feedback laser,” Laser Photonics Rev. 7, 589–598 (2013).
[Crossref]

A. Chiasera, Y. Dumeige, P. Féron, M. Ferrari, Y. Jestin, G. Nunzi Conti, S. Pelli, S. Soria, and G. Righini, “Spherical whispering-gallery-mode microresonators,” Laser Photonics Rev. 4, 457–482 (2010).
[Crossref]

L. He, a. K. Özdemir, and L. Yang, “Whispering gallery microcavity lasers,” Laser Photonics Rev. 7, 60–82 (2013).
[Crossref]

Nat. Commun. (1)

W. Liang, V. S. Ilchenko, D. Eliyahu, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “Ultralow noise miniature external cavity semiconductor laser,” Nat. Commun. 6, 7371 (2015).
[Crossref] [PubMed]

Opt. Express (5)

Opt. Lett. (4)

Optica (1)

Phys. Rev. A (9)

T. J. Kippenberg, J. Kalkman, A. Polman, and K. J. Vahala, “Demonstration of an erbium-doped microdisk laser on a silicon chip,” Phys. Rev. A 74, 051802 (2006).
[Crossref]

V. Sandoghdar, F. Treussart, J. Hare, V. Lefèvre-Seguin, J. M. Raimond, and S. Haroche, “Very low threshold whispering-gallery-mode microsphere laser,” Phys. Rev. A 54, R1777–R1780 (1996).
[Crossref] [PubMed]

L. He, S. K. Özdemir, J. Zhu, and L. Yang, “Ultrasensitive detection of mode splitting in active optical microcavities,” Phys. Rev. A 82, 053810 (2010).
[Crossref]

S. M. Dutra, K. Joosten, G. Nienhuis, N. J. van Druten, A. M. van der Lee, M. P. van Exter, and J. P. Woerdman, “Maxwell-Bloch approach to excess quantum noise,” Phys. Rev. A 59, 4699–4702 (1999).
[Crossref]

W. Loh, S. B. Papp, and S. A. Diddams, “Noise and dynamics of stimulated-brillouin-scattering microresonator lasers,” Phys. Rev. A 91, 053843 (2015).
[Crossref]

S. Schwartz, G. Feugnet, E. Lariontsev, and J.-P. Pocholle, “Oscillation regimes of a solid-state ring laser with active beat-note stabilization: From a chaotic device to a ring-laser gyroscope,” Phys. Rev. A 76, 023807 (2007).
[Crossref]

G. Björk, A. Karlsson, and Y. Yamamoto, “Definition of a laser threshold,” Phys. Rev. A 50, 1675–1680 (1994).
[Crossref] [PubMed]

D. C. Kilper, P. A. Roos, J. L. Carlsten, and K. L. Lear, “Squeezed light generated by a microcavity laser,” Phys. Rev. A 55, R3323–R3326 (1997).
[Crossref]

N. Takemura, J. Omachi, and M. Kuwata-Gonokami, “Fast periodic modulations in the photon correlation of single-mode vertical-cavity surface-emitting lasers,” Phys. Rev. A 85, 053811 (2012).
[Crossref]

Phys. Rev. Lett. (2)

A. Lebreton, I. Abram, R. Braive, I. Sagnes, I. Robert-Philip, and A. Beveratos, “Unequivocal differentiation of coherent and chaotic light through interferometric photon correlation measurements,” Phys. Rev. Lett. 110, 163603 (2013).
[Crossref] [PubMed]

V. Huet, A. Rasoloniaina, P. Guillemé, P. Rochard, P. Féron, M. Mortier, A. Levenson, K. Bencheikh, A. Yacomotti, and Y. Dumeige, “Millisecond photon lifetime in a slow-light microcavity,” Phys. Rev. Lett. 116, 133902 (2016).
[Crossref] [PubMed]

Sci. Rep. (1)

A. Rasoloniaina, V. Huet, T. K. N. Nguyên, E. Le Cren, M. Mortier, L. Michely, Y. Dumeige, and P. Féron, “Controling the coupling properties of active ultrahigh-Q WGM microcavities from undercoupling to selective amplification,” Sci. Rep. 4, 4023 (2014).
[Crossref] [PubMed]

Other (4)

E. Rosencher and B. Vinter, Optoelectronics (Cambridge University Press, 2002).
[Crossref]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).
[Crossref]

A. E. Siegman, Lasers (University Science Books, 1986).

F. Treussart, Etude expérimentale de l’effet laser dans des microsphères de silice dopées avec des ions neodyme (Université Pierre et Marie Curie PhD Thesis, 1997).

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Figures (3)

Fig. 1
Fig. 1 Experimental setups. a) tapered fiber setup, b) half tapered fiber setup. ISO : optical isolator, AV : variable attenuator, PC : polarization controller, WDM : wavelength multiplexer, PhD : InGaAs photodiode, TIA : transimpedance amplifier, V : voltmeter, ESA : electrical spectrum amplifier. i is the generated photo-current at the output of the photodiode.
Fig. 2
Fig. 2 RIN measurement for a broadband pumping. a) Half tapered fiber configuration and b) tapered fiber configuration. The physical and fit parameters are given in Table 1.
Fig. 3
Fig. 3 RIN measurement in the case of a narrow linewidth pump laser and a tapered fiber configuration. The physical and fit parameters are given in Table 1.

Tables (1)

Tables Icon

Table 1 Physical and fit parameters for the WGM laser shown in the three previous figures. a : radius of the sphere, PL : WGM laser power. We also give the deduced parameters Qe and Vm. The mode volume is calculated in TE since the theoretical resonance wavelength values match well with experimental data in this polarization.

Equations (50)

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

f ( t ) = lim T + 1 T T / 2 T / 2 f ( t ) d t .
f ^ ( ω ) g ^ * ( ω ) = lim T + 1 T 𝔼 [ f ^ T ( ω ) g ^ T * ( ω ) ]
{ d Δ N d t = Δ N 0 Δ N τ r 2 κ F Δ N d F d t = F τ ph + κ F Δ N
κ = c σ e n 0 V m ,
Δ N 0 = N W P A W P + A ,
Δ N ¯ = Δ N th = 1 κ τ ph ,
F ¯ = η 1 2 κ τ r ,
W P , th = A N + Δ N th N Δ N th ,
Δ N ( t ) = Δ N ¯ + δ Δ N ( t )
F ( t ) = F ¯ + δ F ( t ) .
δ Δ N ( t ) = λ δ Δ N ( 1 ) ( t ) + λ 2 δ Δ N ( 2 ) ( t )
δ F ( t ) = λ δ F ( 1 ) ( t ) + λ 2 δ F ( 2 ) ( t ) ,
{ d δ Δ N ( 1 ) d t = η τ r δ Δ N ( 1 ) 2 τ ph δ F ( 1 ) + ξ N ( t ) d δ F ( 1 ) d t = η 1 2 τ r δ Δ N ( 1 ) + ξ F ( t ) ,
ξ N ( t ) ξ N * ( t + τ ) = D NN δ ( τ )
ξ F ( t ) ξ F * ( t + τ ) = D FF δ ( τ ) ,
ξ N ( t ) ξ F * ( t + τ ) = ξ F ( t ) ξ N * ( t + τ ) = 0 .
{ d δ Δ N ( 2 ) d t = η τ r δ Δ N ( 2 ) 2 τ ph δ F ( 2 ) 2 κ δ Δ N ( 1 ) ( t ) δ F ( 1 ) ( t ) d δ F ( 2 ) d t = η 1 2 τ r δ Δ N ( 2 ) + κ δ Δ N ( 1 ) ( t ) δ F ( 1 ) ( t ) ,
{ δ Δ N ^ ( 1 ) ( ω ) = 1 D ( ω ) [ 2 τ ph ξ ^ F ( ω ) + j ω ξ ^ N ( ω ) ] δ F ^ ( 1 ) ( ω ) = 1 D ( ω ) [ ( η τ r + j ω ) ξ ^ F ( ω ) + ( η 1 2 τ r ) ξ ^ N ( ω ) ]
D ( ω ) = η 1 τ r τ ph ω 2 + j ω η τ r .
{ δ Δ N ^ ( 2 ) ( ω ) = 2 κ 1 τ ph + j ω D ( ω ) ( δ F ^ ( 1 ) ( ω ) * δ Δ N ^ ( 1 ) ( ω ) ) = K N ( ω ) ( δ F ^ ( 1 ) ( ω ) * δ Δ N ^ ( 1 ) ( ω ) ) δ F ^ ( 2 ) ( ω ) = κ 1 τ r + j ω D ( ω ) ( δ F ^ ( 1 ) ( ω ) * δ Δ N ^ ( 1 ) ( ω ) ) = K F ( ω ) ( δ F ^ ( 1 ) ( ω ) * δ Δ N ^ ( 1 ) ( ω ) ) ,
RIN ( ω ) = FT [ δ F ( t ) δ F * ( t + τ ) ] F ¯ 2 .
FT [ δ F ( 1 ) ( t ) ( δ F ( 2 ) ( t + τ ) ) * ] = δ F ^ ( 1 ) ( ω ) ( δ F ^ ( 2 ) ( ω ) ) *
= K F * ( ω ) δ F ^ ( 1 ) ( ω ) ( δ F ^ ( 1 ) ( ω ) * δ Δ N ^ ( 1 ) ( ω ) ) * .
δ F ^ ( 1 ) ( ω ) * δ Δ N ^ ( 1 ) ( ω ) = FT [ δ F ( 1 ) ( t ) δ Δ N ( 1 ) ( t ) ]
FT [ δ F ( 1 ) ( t ) ( δ F ( 2 ) ( t + τ ) ) * ] = K F * ( ω ) FT [ δ F ( 1 ) ( t ) ( δ F ( 1 ) ( t + τ ) δ Δ N ( 1 ) ( t + τ ) ) * ] .
δ F ( 1 ) ( t ) ( δ F ( 1 ) ( t + τ ) δ Δ N ( 1 ) ( t + τ ) ) * = 0 ,
FT [ δ F ( 1 ) ( t ) ( δ F ( 2 ) ( t + τ ) ) * ] = 0 .
FT [ δ F ( 2 ) ( t ) ( δ F ( 1 ) ( t + τ ) ) * ] = 0 .
RIN ( ω ) = FT [ δ F ( 1 ) ( t ) ( δ F ( 1 ) ( t + τ ) ) * ] F ¯ 2 + FT [ δ F ( 2 ) ( t ) ( δ F ( 2 ) ( t + τ ) ) * ] F ¯ 2
= RIN ( 1 ) ( ω ) + RIN ( 2 ) ( ω ) .
RIN ( 1 ) ( ω ) = FT [ δ F ( 1 ) ( t ) ( δ F ( 1 ) ( t + τ ) ) * ] F ¯ 2 = | δ F ^ ( 1 ) ( ω ) | 2 F ¯ 2
RIN ( 1 ) ( ω ) = 1 F ¯ 2 | D ( ω ) | 2 [ ( η 1 2 τ r ) 2 D FF + [ ( η τ r ) 2 + ω 2 ] D NN ] ,
ξ ^ F ( ω ) ξ ^ N * ( ω ) = ξ ^ N ( ω ) ξ ^ F * ( ω ) = 0 .
RIN ( 2 ) ( ω ) = FT [ δ F ( 2 ) ( t ) ( δ F ( 2 ) ( t + τ ) ) * ] F ¯ 2 = | δ F ^ ( 2 ) ( ω ) | 2 F ¯ 2 ,
RIN ( 2 ) ( ω ) = | K F ( ω ) | 2 F ¯ 2 | δ F ^ ( 1 ) ( ω ) * δ Δ N ^ ( 1 ) ( ω ) | 2 ,
RIN ( 2 ) ( ω ) = | K F ( ω ) | 2 F ¯ 2 | A ^ 2 ( ω ) | 2 = | K F ( ω ) | 2 F ¯ 2 FT [ A 2 ( t ) A 2 * ( t + τ ) ] .
A 2 ( t ) A 2 * ( t + τ ) = δ F ( 1 ) ( t ) δ N ( 1 ) ( t ) ( δ F ( 1 ) ( t + τ ) δ N ( 1 ) ( t + τ ) ) *
A 2 ( t ) A 2 * ( t + τ ) = δ F ( 1 ) ( t ) δ N ( 1 ) ( t ) ( δ F ( 1 ) ( t + τ ) δ N ( 1 ) ( t + τ ) ) * + δ F ( 1 ) ( t ) ( δ F ( 1 ) ( t + τ ) ) * ( δ N ( 1 ) ( t ) δ N ( 1 ) ( t + τ ) ) * + δ F ( 1 ) ( t ) ( δ N ( 1 ) ( t + τ ) ) * δ N ( 1 ) ( t ) ( δ F ( 1 ) ( t + τ ) ) *
| A ^ 2 ( ω ) | 2 = C δ ( ω ) + ( FT [ δ F ( 1 ) ( t ) ( δ F ( 1 ) ( t + τ ) ) * ] ) * ( FT [ δ N ( 1 ) ( t ) ( δ N ( 1 ) ( t + τ ) ) * ] ) + ( FT [ δ F ( 1 ) ( t ) ( δ N ( 1 ) ( t + τ ) ) * ] ) * ( FT [ δ N ( 1 ) ( t ) ( δ F ( 1 ) ( t + τ ) ) * ] )
| A ^ 2 ( ω ) | 2 = C δ ( ω ) + | δ F ^ ( 1 ) ( ω ) | 2 * | δ N ^ ( 1 ) ( ω ) | 2 + δ F ^ ( 1 ) ( ω ) ( δ N ^ ( 1 ) ( ω ) ) * * δ N ^ ( 1 ) ( ω ) ( δ F ^ ( 1 ) ( ω ) ) * .
| A ^ 2 ( ω ) | 2 = C δ ( ω ) + U 1 ( ω ) [ ( η 1 τ r τ ph ) 2 D NN D FF + 2 ( η τ r ) 2 ( 2 τ ph ) 2 D FF 2 ] + U 2 ( ω ) [ ( η 1 2 τ r ) D NN + ( 2 τ ph ) D FF ] 2 + U 3 ( ω ) [ ( η 1 2 τ r ) 2 D NN 2 + ( 2 τ ph ) 2 D FF 2 + ( η τ r ) 2 D NN D FF ] + U 4 ( ω ) D NN D FF ,
U 1 ( ω ) = ( | D ( ω ) | 2 ) * ( | D ( ω ) | 2 )
U 2 ( ω ) = ( ω | D ( ω ) | 2 ) * ( ω | D ( ω ) | 2 )
U 3 ( ω ) = ( | D ( ω ) | 2 ) * ( ω 2 | D ( ω ) | 2 )
U 4 ( ω ) = ( ω 2 | D ( ω ) | 2 ) * ( ω 2 | D ( ω ) | 2 ) .
N tot = N kT + N sn + N RIN .
N sn = 2 | H ( ω ) | 2 Riq
N RIN = R | H ( ω ) | 2 i 2 × RIN ,
RIN = 2 q i ( N tot N kT N sn 1 ) ,
V m = 3 w ( r ) d 3 r max [ w ( r ) ]

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