Abstract

Ultra-high Q whispering-gallery mode resonators pumped by a continuous-wave laser are known to enhance stimulated Brillouin scattering when optimal resonance and phase-matching conditions are met. In crystalline resonators, this process depends critically on the crystal orientation and family, which impose the elastic constants defining the velocity of the acoustic waves. In this article, we investigate the effect of crystalline orientation and family on this velocity which is proportional to the Brillouin frequency down-shift. In particular, the study is based on the development of a model and numerical simulations of acoustic wave velocities that propagate along the periphery of four fluoride crystals, namely calcium, magnesium, lithium and barium fluoride. We find that depending on the crystal and its orientation, the frequency excursion around the Brillouin offset can vary from few tens of kHz to more than a GHz.

© 2017 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 (2)

K. Saleh and Y. K. Chembo, “Phase noise performance comparison between microwaves generated with Kerr optical frequency combs and optoelectronic oscillators,” Electron. Lett. 53, 264–265 (2017).
[Crossref]

J. Li, M. G. Suh, and K. Vahala, “Microresonator Brillouin gyroscope,” Optica 4, 346–348 (2017).
[Crossref]

2016 (8)

W. Loh, J. Becker, D. C. Cole, A. Coillet, F. N. Baynes, S. B. Papp, and S. A. Diddams, “A microrod-resonator Brillouin laser with 240 Hz absolute linewidth,” New J. Phys. 18, 045001 (2016).
[Crossref]

G. Lin and Y. K. Chembo, “Phase-locking transition in Raman combs generated with whispering gallery mode resonators,” Opt. Lett. 41, 3718–3721 (2016).
[Crossref] [PubMed]

Y. K. Chembo, “Quantum dynamics of Kerr optical frequency combs below and above threshold: Spontaneous four-wave mixing, entanglement, and squeezed states of light,” Phys. Rev. A 93, 033820 (2016).
[Crossref]

Y. K. Chembo, “Kerr optical frequency combs: theory, applications and perspectives,” Nanophotonics 5, 214–230 (2016).
[Crossref]

S. Diallo, G. Lin, R. Martinenghi, L. Furfaro, M. Jacquot, and Y. K. Chembo, “Brillouin Lasing in Ultra-High Q Lithium Fluoride Disk-Resonators,” IEEE Photon. Technol. Lett. 28, 955–958(2016).

G. Lin, S. Diallo, J. M. Dudley, and Y. K. Chembo, “Universal scattering in ultra-high Q whispering gallery mode resonators,” Opt. Express 24, 14880 (2016).
[Crossref] [PubMed]

D. V. Strekalov, C. Marquardt, A. B. Matsko, H. G. L. Schwefel, and G. Leuchs, “Nonlinear and quantum optics with whispering gallery resonators,” J. Opt. 18, 123002 (2016).
[Crossref]

K. Saleh and Y. K. Chembo, “On the phase noise performance of microwave and millimeter-wave signals generated with versatile Kerr optical frequency combs,” Opt. Express 24, 25043–25056 (2016).
[Crossref] [PubMed]

2015 (3)

R. Henriet, G. Lin, A. Coillet, M. Jacquot, L. Furfaro, L. Larger, and Y. K. Chembo, “Kerr optical frequency comb generation in strontium fluoride whispering-gallery mode resonators with billion quality factor,” Opt. Lett. 40, 1567–1570 (2015).
[Crossref] [PubMed]

K. Saleh, G. Lin, and Y. K. Chembo, “Effect of laser coupling and active stabilization on the phase noise performance of optoelectronic microwave oscillators based on whispering-gallery-mode resonators,” IEEE Photon. J. 7, 1–11 (2015).
[Crossref]

Y. K. Chembo, I. S. Grudinin, and N. Yu, “Spatiotemporal dynamics of Kerr-Raman optical frequency combs,” Phys. Rev. A 92, 043818 (2015).
[Crossref]

2014 (3)

2013 (4)

A. Coillet, R. Henriet, K. P. Huy, M. Jacquot, L. Furfaro, I. Balakireva, L. Larger, and Y. K. Chembo, “Microwave photonics systems based on whispering-gallery-mode resonators,” J. Vis. Exp 78, e50423 (2013).

S. B. Papp, P. DelHaye, and S. A. Diddams, “Mechanical control of a microrod-resonator optical frequency comb”, Phys. Rev. X 3, 031003 (2013).

J. Li, H. Lee, and K. J. Vahala, “Microwave synthesizer using an on-chip Brillouin oscillator,” Nat. Commun. 4, 2097 (2013).
[Crossref]

H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson, A. Starbuck, Z. Wang, and P. T. Rakich, “Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides,” Nat. Commun. 4, 1944 (2013).
[Crossref]

2012 (1)

H. Lee, T. Chen, J. Li, K. Y. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics 6, 369–373 (2012).
[Crossref]

2011 (1)

2009 (1)

I. S. Grudinin, A. B. Matsko, and L. Maleki, “Brillouin lasing with a CaF2 whispering gallery mode resonator,” Phys. Rev. Lett. 102, 043902 (2009).
[Crossref]

2007 (2)

2006 (1)

I. S. Grudinin, V. S. Ilchenko, and L. Maleki, “Ultrahigh optical Q factors of crystalline resonators in the linear regime,” Phys. Rev. A 74, 063806 (2006).
[Crossref]

2002 (1)

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] [PubMed]

1993 (1)

1991 (1)

1990 (2)

1943 (1)

W. L. Bond, “The mathematics of the physical properties of crystals,” Bell Syst. Tech. J. 22, 1–72 (1943).
[Crossref]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2007).

Alasia, D.

Arcizet, O.

P. DelHaye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[Crossref]

Auld, B. A.

B. A. Auld, Acoustic Fields and Waves in Solids (Krieger, 1990).

Balakireva, I.

A. Coillet, R. Henriet, K. P. Huy, M. Jacquot, L. Furfaro, I. Balakireva, L. Larger, and Y. K. Chembo, “Microwave photonics systems based on whispering-gallery-mode resonators,” J. Vis. Exp 78, e50423 (2013).

Balakireva, I. V.

Baynes, F. N.

W. Loh, J. Becker, D. C. Cole, A. Coillet, F. N. Baynes, S. B. Papp, and S. A. Diddams, “A microrod-resonator Brillouin laser with 240 Hz absolute linewidth,” New J. Phys. 18, 045001 (2016).
[Crossref]

Becker, J.

W. Loh, J. Becker, D. C. Cole, A. Coillet, F. N. Baynes, S. B. Papp, and S. A. Diddams, “A microrod-resonator Brillouin laser with 240 Hz absolute linewidth,” New J. Phys. 18, 045001 (2016).
[Crossref]

Beugnot, J. C.

Bond, W. L.

W. L. Bond, “The mathematics of the physical properties of crystals,” Bell Syst. Tech. J. 22, 1–72 (1943).
[Crossref]

Boyd, R.

R. Boyd, Nonlinear Optics (Academic Press, 2003).

Campillo, A. J.

Cantrell, C. D.

Chembo, Y. K.

K. Saleh and Y. K. Chembo, “Phase noise performance comparison between microwaves generated with Kerr optical frequency combs and optoelectronic oscillators,” Electron. Lett. 53, 264–265 (2017).
[Crossref]

Y. K. Chembo, “Kerr optical frequency combs: theory, applications and perspectives,” Nanophotonics 5, 214–230 (2016).
[Crossref]

S. Diallo, G. Lin, R. Martinenghi, L. Furfaro, M. Jacquot, and Y. K. Chembo, “Brillouin Lasing in Ultra-High Q Lithium Fluoride Disk-Resonators,” IEEE Photon. Technol. Lett. 28, 955–958(2016).

Y. K. Chembo, “Quantum dynamics of Kerr optical frequency combs below and above threshold: Spontaneous four-wave mixing, entanglement, and squeezed states of light,” Phys. Rev. A 93, 033820 (2016).
[Crossref]

G. Lin, S. Diallo, J. M. Dudley, and Y. K. Chembo, “Universal scattering in ultra-high Q whispering gallery mode resonators,” Opt. Express 24, 14880 (2016).
[Crossref] [PubMed]

G. Lin and Y. K. Chembo, “Phase-locking transition in Raman combs generated with whispering gallery mode resonators,” Opt. Lett. 41, 3718–3721 (2016).
[Crossref] [PubMed]

K. Saleh and Y. K. Chembo, “On the phase noise performance of microwave and millimeter-wave signals generated with versatile Kerr optical frequency combs,” Opt. Express 24, 25043–25056 (2016).
[Crossref] [PubMed]

R. Henriet, G. Lin, A. Coillet, M. Jacquot, L. Furfaro, L. Larger, and Y. K. Chembo, “Kerr optical frequency comb generation in strontium fluoride whispering-gallery mode resonators with billion quality factor,” Opt. Lett. 40, 1567–1570 (2015).
[Crossref] [PubMed]

Y. K. Chembo, I. S. Grudinin, and N. Yu, “Spatiotemporal dynamics of Kerr-Raman optical frequency combs,” Phys. Rev. A 92, 043818 (2015).
[Crossref]

K. Saleh, G. Lin, and Y. K. Chembo, “Effect of laser coupling and active stabilization on the phase noise performance of optoelectronic microwave oscillators based on whispering-gallery-mode resonators,” IEEE Photon. J. 7, 1–11 (2015).
[Crossref]

G. Lin, S. Diallo, R. Henriet, M. Jacquot, and Y. K. Chembo, “Barium fluoride whispering-gallery-mode disk-resonator with one billion quality-factor,” Opt. Lett 39, 6009–6012 (2014).
[Crossref] [PubMed]

K. Saleh, R. Henriet, S. Diallo, G. Lin, R Martinenghi, I. V. Balakireva, P. Salzenstein, A Coillet, and Y. K. Chembo, “Phase noise performance comparison between optoelectronic oscillators based on optical delay lines and whispering gallery mode resonators,” Opt. Express 22, 32158–32173 (2014).
[Crossref]

A. Coillet, R. Henriet, K. P. Huy, M. Jacquot, L. Furfaro, I. Balakireva, L. Larger, and Y. K. Chembo, “Microwave photonics systems based on whispering-gallery-mode resonators,” J. Vis. Exp 78, e50423 (2013).

Chen, T.

H. Lee, T. Chen, J. Li, K. Y. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics 6, 369–373 (2012).
[Crossref]

Ching, S. C.

S. C. Ching, P. T. Leung, and K. Young, “Spontaneous Brillouin scattering in a microdroplet,” Phys. Rev. A 41, 5026 (1990).
[Crossref] [PubMed]

Coillet, A

Coillet, A.

W. Loh, J. Becker, D. C. Cole, A. Coillet, F. N. Baynes, S. B. Papp, and S. A. Diddams, “A microrod-resonator Brillouin laser with 240 Hz absolute linewidth,” New J. Phys. 18, 045001 (2016).
[Crossref]

R. Henriet, G. Lin, A. Coillet, M. Jacquot, L. Furfaro, L. Larger, and Y. K. Chembo, “Kerr optical frequency comb generation in strontium fluoride whispering-gallery mode resonators with billion quality factor,” Opt. Lett. 40, 1567–1570 (2015).
[Crossref] [PubMed]

A. Coillet, R. Henriet, K. P. Huy, M. Jacquot, L. Furfaro, I. Balakireva, L. Larger, and Y. K. Chembo, “Microwave photonics systems based on whispering-gallery-mode resonators,” J. Vis. Exp 78, e50423 (2013).

Cole, D. C.

W. Loh, J. Becker, D. C. Cole, A. Coillet, F. N. Baynes, S. B. Papp, and S. A. Diddams, “A microrod-resonator Brillouin laser with 240 Hz absolute linewidth,” New J. Phys. 18, 045001 (2016).
[Crossref]

Cox, J. A.

H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson, A. Starbuck, Z. Wang, and P. T. Rakich, “Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides,” Nat. Commun. 4, 1944 (2013).
[Crossref]

DelHaye, P.

S. B. Papp, P. DelHaye, and S. A. Diddams, “Mechanical control of a microrod-resonator optical frequency comb”, Phys. Rev. X 3, 031003 (2013).

P. DelHaye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[Crossref]

Diallo, S.

S. Diallo, G. Lin, R. Martinenghi, L. Furfaro, M. Jacquot, and Y. K. Chembo, “Brillouin Lasing in Ultra-High Q Lithium Fluoride Disk-Resonators,” IEEE Photon. Technol. Lett. 28, 955–958(2016).

G. Lin, S. Diallo, J. M. Dudley, and Y. K. Chembo, “Universal scattering in ultra-high Q whispering gallery mode resonators,” Opt. Express 24, 14880 (2016).
[Crossref] [PubMed]

K. Saleh, R. Henriet, S. Diallo, G. Lin, R Martinenghi, I. V. Balakireva, P. Salzenstein, A Coillet, and Y. K. Chembo, “Phase noise performance comparison between optoelectronic oscillators based on optical delay lines and whispering gallery mode resonators,” Opt. Express 22, 32158–32173 (2014).
[Crossref]

G. Lin, S. Diallo, R. Henriet, M. Jacquot, and Y. K. Chembo, “Barium fluoride whispering-gallery-mode disk-resonator with one billion quality-factor,” Opt. Lett 39, 6009–6012 (2014).
[Crossref] [PubMed]

Diddams, S. A.

W. Loh, J. Becker, D. C. Cole, A. Coillet, F. N. Baynes, S. B. Papp, and S. A. Diddams, “A microrod-resonator Brillouin laser with 240 Hz absolute linewidth,” New J. Phys. 18, 045001 (2016).
[Crossref]

S. B. Papp, P. DelHaye, and S. A. Diddams, “Mechanical control of a microrod-resonator optical frequency comb”, Phys. Rev. X 3, 031003 (2013).

Dieulesaint, E.

E. Dieulesaint and D. Royer, Ondes Élastiques dans les Solides : Application au Traitement du Signal (Masson, 1974).

Dudley, J. M.

Eversole, J. D.

Furfaro, L.

S. Diallo, G. Lin, R. Martinenghi, L. Furfaro, M. Jacquot, and Y. K. Chembo, “Brillouin Lasing in Ultra-High Q Lithium Fluoride Disk-Resonators,” IEEE Photon. Technol. Lett. 28, 955–958(2016).

R. Henriet, G. Lin, A. Coillet, M. Jacquot, L. Furfaro, L. Larger, and Y. K. Chembo, “Kerr optical frequency comb generation in strontium fluoride whispering-gallery mode resonators with billion quality factor,” Opt. Lett. 40, 1567–1570 (2015).
[Crossref] [PubMed]

A. Coillet, R. Henriet, K. P. Huy, M. Jacquot, L. Furfaro, I. Balakireva, L. Larger, and Y. K. Chembo, “Microwave photonics systems based on whispering-gallery-mode resonators,” J. Vis. Exp 78, e50423 (2013).

Grudinin, I. S.

Y. K. Chembo, I. S. Grudinin, and N. Yu, “Spatiotemporal dynamics of Kerr-Raman optical frequency combs,” Phys. Rev. A 92, 043818 (2015).
[Crossref]

I. S. Grudinin, A. B. Matsko, and L. Maleki, “Brillouin lasing with a CaF2 whispering gallery mode resonator,” Phys. Rev. Lett. 102, 043902 (2009).
[Crossref]

I. S. Grudinin, V. S. Ilchenko, and L. Maleki, “Ultrahigh optical Q factors of crystalline resonators in the linear regime,” Phys. Rev. A 74, 063806 (2006).
[Crossref]

Hahn, T.

V. Janovec, T. Hahn, H. Klapper, and J. Privratska, International Tables for Crystallography. Volume D : Physical Properties of Crystals (International Union of Crystallography and Kluwer Academic Publishers, 2003).

Henriet, R.

R. Henriet, G. Lin, A. Coillet, M. Jacquot, L. Furfaro, L. Larger, and Y. K. Chembo, “Kerr optical frequency comb generation in strontium fluoride whispering-gallery mode resonators with billion quality factor,” Opt. Lett. 40, 1567–1570 (2015).
[Crossref] [PubMed]

K. Saleh, R. Henriet, S. Diallo, G. Lin, R Martinenghi, I. V. Balakireva, P. Salzenstein, A Coillet, and Y. K. Chembo, “Phase noise performance comparison between optoelectronic oscillators based on optical delay lines and whispering gallery mode resonators,” Opt. Express 22, 32158–32173 (2014).
[Crossref]

G. Lin, S. Diallo, R. Henriet, M. Jacquot, and Y. K. Chembo, “Barium fluoride whispering-gallery-mode disk-resonator with one billion quality-factor,” Opt. Lett 39, 6009–6012 (2014).
[Crossref] [PubMed]

A. Coillet, R. Henriet, K. P. Huy, M. Jacquot, L. Furfaro, I. Balakireva, L. Larger, and Y. K. Chembo, “Microwave photonics systems based on whispering-gallery-mode resonators,” J. Vis. Exp 78, e50423 (2013).

Holzwarth, R.

P. DelHaye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[Crossref]

Huston, A. L.

Huy, K. P.

A. Coillet, R. Henriet, K. P. Huy, M. Jacquot, L. Furfaro, I. Balakireva, L. Larger, and Y. K. Chembo, “Microwave photonics systems based on whispering-gallery-mode resonators,” J. Vis. Exp 78, e50423 (2013).

Ilchenko, V. S.

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Seidel, and L. Maleki, “Surface acoustic wave opto-mechanical oscillator and frequency comb generator,” Opt. Lett. 36, 3338–3340 (2011).
[Crossref] [PubMed]

I. S. Grudinin, V. S. Ilchenko, and L. Maleki, “Ultrahigh optical Q factors of crystalline resonators in the linear regime,” Phys. Rev. A 74, 063806 (2006).
[Crossref]

Jacquot, M.

S. Diallo, G. Lin, R. Martinenghi, L. Furfaro, M. Jacquot, and Y. K. Chembo, “Brillouin Lasing in Ultra-High Q Lithium Fluoride Disk-Resonators,” IEEE Photon. Technol. Lett. 28, 955–958(2016).

R. Henriet, G. Lin, A. Coillet, M. Jacquot, L. Furfaro, L. Larger, and Y. K. Chembo, “Kerr optical frequency comb generation in strontium fluoride whispering-gallery mode resonators with billion quality factor,” Opt. Lett. 40, 1567–1570 (2015).
[Crossref] [PubMed]

G. Lin, S. Diallo, R. Henriet, M. Jacquot, and Y. K. Chembo, “Barium fluoride whispering-gallery-mode disk-resonator with one billion quality-factor,” Opt. Lett 39, 6009–6012 (2014).
[Crossref] [PubMed]

A. Coillet, R. Henriet, K. P. Huy, M. Jacquot, L. Furfaro, I. Balakireva, L. Larger, and Y. K. Chembo, “Microwave photonics systems based on whispering-gallery-mode resonators,” J. Vis. Exp 78, e50423 (2013).

Janovec, V.

V. Janovec, T. Hahn, H. Klapper, and J. Privratska, International Tables for Crystallography. Volume D : Physical Properties of Crystals (International Union of Crystallography and Kluwer Academic Publishers, 2003).

Jarecki, R.

H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson, A. Starbuck, Z. Wang, and P. T. Rakich, “Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides,” Nat. Commun. 4, 1944 (2013).
[Crossref]

Jeon, S.

H. Lee, T. Chen, J. Li, K. Y. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics 6, 369–373 (2012).
[Crossref]

Kippenberg, T. J.

P. DelHaye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[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] [PubMed]

Kittel, C.

C. Kittel, Introduction to Solid State Physics (Wiley, 2004).

Klapper, H.

V. Janovec, T. Hahn, H. Klapper, and J. Privratska, International Tables for Crystallography. Volume D : Physical Properties of Crystals (International Union of Crystallography and Kluwer Academic Publishers, 2003).

Lai, H. M.

Larger, L.

R. Henriet, G. Lin, A. Coillet, M. Jacquot, L. Furfaro, L. Larger, and Y. K. Chembo, “Kerr optical frequency comb generation in strontium fluoride whispering-gallery mode resonators with billion quality factor,” Opt. Lett. 40, 1567–1570 (2015).
[Crossref] [PubMed]

A. Coillet, R. Henriet, K. P. Huy, M. Jacquot, L. Furfaro, I. Balakireva, L. Larger, and Y. K. Chembo, “Microwave photonics systems based on whispering-gallery-mode resonators,” J. Vis. Exp 78, e50423 (2013).

Laude, V.

Lee, H.

J. Li, H. Lee, and K. J. Vahala, “Low-noise Brillouin laser on a chip at 1064 nm,” Opt. Lett. 39, 287–290 (2014).
[Crossref] [PubMed]

J. Li, H. Lee, and K. J. Vahala, “Microwave synthesizer using an on-chip Brillouin oscillator,” Nat. Commun. 4, 2097 (2013).
[Crossref]

H. Lee, T. Chen, J. Li, K. Y. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics 6, 369–373 (2012).
[Crossref]

Leuchs, G.

D. V. Strekalov, C. Marquardt, A. B. Matsko, H. G. L. Schwefel, and G. Leuchs, “Nonlinear and quantum optics with whispering gallery resonators,” J. Opt. 18, 123002 (2016).
[Crossref]

Leung, P. T.

Li, J.

J. Li, M. G. Suh, and K. Vahala, “Microresonator Brillouin gyroscope,” Optica 4, 346–348 (2017).
[Crossref]

J. Li, H. Lee, and K. J. Vahala, “Low-noise Brillouin laser on a chip at 1064 nm,” Opt. Lett. 39, 287–290 (2014).
[Crossref] [PubMed]

J. Li, H. Lee, and K. J. Vahala, “Microwave synthesizer using an on-chip Brillouin oscillator,” Nat. Commun. 4, 2097 (2013).
[Crossref]

H. Lee, T. Chen, J. Li, K. Y. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics 6, 369–373 (2012).
[Crossref]

Lin, G.

S. Diallo, G. Lin, R. Martinenghi, L. Furfaro, M. Jacquot, and Y. K. Chembo, “Brillouin Lasing in Ultra-High Q Lithium Fluoride Disk-Resonators,” IEEE Photon. Technol. Lett. 28, 955–958(2016).

G. Lin and Y. K. Chembo, “Phase-locking transition in Raman combs generated with whispering gallery mode resonators,” Opt. Lett. 41, 3718–3721 (2016).
[Crossref] [PubMed]

G. Lin, S. Diallo, J. M. Dudley, and Y. K. Chembo, “Universal scattering in ultra-high Q whispering gallery mode resonators,” Opt. Express 24, 14880 (2016).
[Crossref] [PubMed]

R. Henriet, G. Lin, A. Coillet, M. Jacquot, L. Furfaro, L. Larger, and Y. K. Chembo, “Kerr optical frequency comb generation in strontium fluoride whispering-gallery mode resonators with billion quality factor,” Opt. Lett. 40, 1567–1570 (2015).
[Crossref] [PubMed]

K. Saleh, G. Lin, and Y. K. Chembo, “Effect of laser coupling and active stabilization on the phase noise performance of optoelectronic microwave oscillators based on whispering-gallery-mode resonators,” IEEE Photon. J. 7, 1–11 (2015).
[Crossref]

G. Lin, S. Diallo, R. Henriet, M. Jacquot, and Y. K. Chembo, “Barium fluoride whispering-gallery-mode disk-resonator with one billion quality-factor,” Opt. Lett 39, 6009–6012 (2014).
[Crossref] [PubMed]

K. Saleh, R. Henriet, S. Diallo, G. Lin, R Martinenghi, I. V. Balakireva, P. Salzenstein, A Coillet, and Y. K. Chembo, “Phase noise performance comparison between optoelectronic oscillators based on optical delay lines and whispering gallery mode resonators,” Opt. Express 22, 32158–32173 (2014).
[Crossref]

Lin, H. B.

Loh, W.

W. Loh, J. Becker, D. C. Cole, A. Coillet, F. N. Baynes, S. B. Papp, and S. A. Diddams, “A microrod-resonator Brillouin laser with 240 Hz absolute linewidth,” New J. Phys. 18, 045001 (2016).
[Crossref]

Mafang, S. F.

Maillotte, H.

Maleki, L.

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Seidel, and L. Maleki, “Surface acoustic wave opto-mechanical oscillator and frequency comb generator,” Opt. Lett. 36, 3338–3340 (2011).
[Crossref] [PubMed]

I. S. Grudinin, A. B. Matsko, and L. Maleki, “Brillouin lasing with a CaF2 whispering gallery mode resonator,” Phys. Rev. Lett. 102, 043902 (2009).
[Crossref]

I. S. Grudinin, V. S. Ilchenko, and L. Maleki, “Ultrahigh optical Q factors of crystalline resonators in the linear regime,” Phys. Rev. A 74, 063806 (2006).
[Crossref]

Marquardt, C.

D. V. Strekalov, C. Marquardt, A. B. Matsko, H. G. L. Schwefel, and G. Leuchs, “Nonlinear and quantum optics with whispering gallery resonators,” J. Opt. 18, 123002 (2016).
[Crossref]

Martinenghi, R

Martinenghi, R.

S. Diallo, G. Lin, R. Martinenghi, L. Furfaro, M. Jacquot, and Y. K. Chembo, “Brillouin Lasing in Ultra-High Q Lithium Fluoride Disk-Resonators,” IEEE Photon. Technol. Lett. 28, 955–958(2016).

Matsko, A. B.

D. V. Strekalov, C. Marquardt, A. B. Matsko, H. G. L. Schwefel, and G. Leuchs, “Nonlinear and quantum optics with whispering gallery resonators,” J. Opt. 18, 123002 (2016).
[Crossref]

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Seidel, and L. Maleki, “Surface acoustic wave opto-mechanical oscillator and frequency comb generator,” Opt. Lett. 36, 3338–3340 (2011).
[Crossref] [PubMed]

I. S. Grudinin, A. B. Matsko, and L. Maleki, “Brillouin lasing with a CaF2 whispering gallery mode resonator,” Phys. Rev. Lett. 102, 043902 (2009).
[Crossref]

Monteville, A.

Ng, C. K.

Olsson, R. H.

H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson, A. Starbuck, Z. Wang, and P. T. Rakich, “Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides,” Nat. Commun. 4, 1944 (2013).
[Crossref]

Painter, O.

H. Lee, T. Chen, J. Li, K. Y. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics 6, 369–373 (2012).
[Crossref]

Papp, S. B.

W. Loh, J. Becker, D. C. Cole, A. Coillet, F. N. Baynes, S. B. Papp, and S. A. Diddams, “A microrod-resonator Brillouin laser with 240 Hz absolute linewidth,” New J. Phys. 18, 045001 (2016).
[Crossref]

S. B. Papp, P. DelHaye, and S. A. Diddams, “Mechanical control of a microrod-resonator optical frequency comb”, Phys. Rev. X 3, 031003 (2013).

Privratska, J.

V. Janovec, T. Hahn, H. Klapper, and J. Privratska, International Tables for Crystallography. Volume D : Physical Properties of Crystals (International Union of Crystallography and Kluwer Academic Publishers, 2003).

Provino, L.

Qiu, W.

H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson, A. Starbuck, Z. Wang, and P. T. Rakich, “Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides,” Nat. Commun. 4, 1944 (2013).
[Crossref]

Rakich, P. T.

H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson, A. Starbuck, Z. Wang, and P. T. Rakich, “Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides,” Nat. Commun. 4, 1944 (2013).
[Crossref]

Royer, D.

E. Dieulesaint and D. Royer, Ondes Élastiques dans les Solides : Application au Traitement du Signal (Masson, 1974).

Saleh, K.

K. Saleh and Y. K. Chembo, “Phase noise performance comparison between microwaves generated with Kerr optical frequency combs and optoelectronic oscillators,” Electron. Lett. 53, 264–265 (2017).
[Crossref]

K. Saleh and Y. K. Chembo, “On the phase noise performance of microwave and millimeter-wave signals generated with versatile Kerr optical frequency combs,” Opt. Express 24, 25043–25056 (2016).
[Crossref] [PubMed]

K. Saleh, G. Lin, and Y. K. Chembo, “Effect of laser coupling and active stabilization on the phase noise performance of optoelectronic microwave oscillators based on whispering-gallery-mode resonators,” IEEE Photon. J. 7, 1–11 (2015).
[Crossref]

K. Saleh, R. Henriet, S. Diallo, G. Lin, R Martinenghi, I. V. Balakireva, P. Salzenstein, A Coillet, and Y. K. Chembo, “Phase noise performance comparison between optoelectronic oscillators based on optical delay lines and whispering gallery mode resonators,” Opt. Express 22, 32158–32173 (2014).
[Crossref]

Salzenstein, P.

Savchenkov, A. A.

Schliesser, A.

P. DelHaye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[Crossref]

Schwefel, H. G. L.

D. V. Strekalov, C. Marquardt, A. B. Matsko, H. G. L. Schwefel, and G. Leuchs, “Nonlinear and quantum optics with whispering gallery resonators,” J. Opt. 18, 123002 (2016).
[Crossref]

Seidel, D.

Shin, H.

H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson, A. Starbuck, Z. Wang, and P. T. Rakich, “Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides,” Nat. Commun. 4, 1944 (2013).
[Crossref]

Spillane, S. M.

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] [PubMed]

Starbuck, A.

H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson, A. Starbuck, Z. Wang, and P. T. Rakich, “Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides,” Nat. Commun. 4, 1944 (2013).
[Crossref]

Strekalov, D. V.

D. V. Strekalov, C. Marquardt, A. B. Matsko, H. G. L. Schwefel, and G. Leuchs, “Nonlinear and quantum optics with whispering gallery resonators,” J. Opt. 18, 123002 (2016).
[Crossref]

Suh, M. G.

Sylvestre, T.

Thevenaz, L.

Traynor, N.

Vahala, K.

Vahala, K. J.

J. Li, H. Lee, and K. J. Vahala, “Low-noise Brillouin laser on a chip at 1064 nm,” Opt. Lett. 39, 287–290 (2014).
[Crossref] [PubMed]

J. Li, H. Lee, and K. J. Vahala, “Microwave synthesizer using an on-chip Brillouin oscillator,” Nat. Commun. 4, 2097 (2013).
[Crossref]

H. Lee, T. Chen, J. Li, K. Y. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics 6, 369–373 (2012).
[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] [PubMed]

Wang, Z.

H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson, A. Starbuck, Z. Wang, and P. T. Rakich, “Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides,” Nat. Commun. 4, 1944 (2013).
[Crossref]

Weber, M. J.

M. J. Weber, Handbook of Optical Materials (CRC press, 2002).
[Crossref]

Wilken, T.

P. DelHaye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[Crossref]

Yang, K. Y.

H. Lee, T. Chen, J. Li, K. Y. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics 6, 369–373 (2012).
[Crossref]

Young, K

Young, K.

S. C. Ching, P. T. Leung, and K. Young, “Spontaneous Brillouin scattering in a microdroplet,” Phys. Rev. A 41, 5026 (1990).
[Crossref] [PubMed]

Yu, N.

Y. K. Chembo, I. S. Grudinin, and N. Yu, “Spatiotemporal dynamics of Kerr-Raman optical frequency combs,” Phys. Rev. A 92, 043818 (2015).
[Crossref]

Bell Syst. Tech. J. (1)

W. L. Bond, “The mathematics of the physical properties of crystals,” Bell Syst. Tech. J. 22, 1–72 (1943).
[Crossref]

Electron. Lett. (1)

K. Saleh and Y. K. Chembo, “Phase noise performance comparison between microwaves generated with Kerr optical frequency combs and optoelectronic oscillators,” Electron. Lett. 53, 264–265 (2017).
[Crossref]

IEEE Photon. J. (1)

K. Saleh, G. Lin, and Y. K. Chembo, “Effect of laser coupling and active stabilization on the phase noise performance of optoelectronic microwave oscillators based on whispering-gallery-mode resonators,” IEEE Photon. J. 7, 1–11 (2015).
[Crossref]

IEEE Photon. Technol. Lett. (1)

S. Diallo, G. Lin, R. Martinenghi, L. Furfaro, M. Jacquot, and Y. K. Chembo, “Brillouin Lasing in Ultra-High Q Lithium Fluoride Disk-Resonators,” IEEE Photon. Technol. Lett. 28, 955–958(2016).

J. Opt. (1)

D. V. Strekalov, C. Marquardt, A. B. Matsko, H. G. L. Schwefel, and G. Leuchs, “Nonlinear and quantum optics with whispering gallery resonators,” J. Opt. 18, 123002 (2016).
[Crossref]

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

J. Vis. Exp (1)

A. Coillet, R. Henriet, K. P. Huy, M. Jacquot, L. Furfaro, I. Balakireva, L. Larger, and Y. K. Chembo, “Microwave photonics systems based on whispering-gallery-mode resonators,” J. Vis. Exp 78, e50423 (2013).

Nanophotonics (1)

Y. K. Chembo, “Kerr optical frequency combs: theory, applications and perspectives,” Nanophotonics 5, 214–230 (2016).
[Crossref]

Nat. Commun. (2)

J. Li, H. Lee, and K. J. Vahala, “Microwave synthesizer using an on-chip Brillouin oscillator,” Nat. Commun. 4, 2097 (2013).
[Crossref]

H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson, A. Starbuck, Z. Wang, and P. T. Rakich, “Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides,” Nat. Commun. 4, 1944 (2013).
[Crossref]

Nat. Photonics (1)

H. Lee, T. Chen, J. Li, K. Y. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics 6, 369–373 (2012).
[Crossref]

Nature (2)

P. DelHaye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[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] [PubMed]

New J. Phys. (1)

W. Loh, J. Becker, D. C. Cole, A. Coillet, F. N. Baynes, S. B. Papp, and S. A. Diddams, “A microrod-resonator Brillouin laser with 240 Hz absolute linewidth,” New J. Phys. 18, 045001 (2016).
[Crossref]

Opt. Express (4)

Opt. Lett (1)

G. Lin, S. Diallo, R. Henriet, M. Jacquot, and Y. K. Chembo, “Barium fluoride whispering-gallery-mode disk-resonator with one billion quality-factor,” Opt. Lett 39, 6009–6012 (2014).
[Crossref] [PubMed]

Opt. Lett. (5)

Optica (1)

Phys. Rev. A (4)

S. C. Ching, P. T. Leung, and K. Young, “Spontaneous Brillouin scattering in a microdroplet,” Phys. Rev. A 41, 5026 (1990).
[Crossref] [PubMed]

Y. K. Chembo, “Quantum dynamics of Kerr optical frequency combs below and above threshold: Spontaneous four-wave mixing, entanglement, and squeezed states of light,” Phys. Rev. A 93, 033820 (2016).
[Crossref]

Y. K. Chembo, I. S. Grudinin, and N. Yu, “Spatiotemporal dynamics of Kerr-Raman optical frequency combs,” Phys. Rev. A 92, 043818 (2015).
[Crossref]

I. S. Grudinin, V. S. Ilchenko, and L. Maleki, “Ultrahigh optical Q factors of crystalline resonators in the linear regime,” Phys. Rev. A 74, 063806 (2006).
[Crossref]

Phys. Rev. Lett. (1)

I. S. Grudinin, A. B. Matsko, and L. Maleki, “Brillouin lasing with a CaF2 whispering gallery mode resonator,” Phys. Rev. Lett. 102, 043902 (2009).
[Crossref]

Phys. Rev. X (1)

S. B. Papp, P. DelHaye, and S. A. Diddams, “Mechanical control of a microrod-resonator optical frequency comb”, Phys. Rev. X 3, 031003 (2013).

Other (7)

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2007).

R. Boyd, Nonlinear Optics (Academic Press, 2003).

E. Dieulesaint and D. Royer, Ondes Élastiques dans les Solides : Application au Traitement du Signal (Masson, 1974).

B. A. Auld, Acoustic Fields and Waves in Solids (Krieger, 1990).

C. Kittel, Introduction to Solid State Physics (Wiley, 2004).

M. J. Weber, Handbook of Optical Materials (CRC press, 2002).
[Crossref]

V. Janovec, T. Hahn, H. Klapper, and J. Privratska, International Tables for Crystallography. Volume D : Physical Properties of Crystals (International Union of Crystallography and Kluwer Academic Publishers, 2003).

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Figures (5)

Fig. 1
Fig. 1 Illustration of the normal vector n and angle ψ characterizing the propagation of the acoustic wave in the plan of the crystalline WGM disk.
Fig. 2
Fig. 2 Illustration of the orientation of a crystal as a function of the direction of its normal vector n. Figures (a), (b), and (c) correspond respectively to so-called z-cut, y-cut and x-cut, while (d) correspond to the [111] orientation.
Fig. 3
Fig. 3 Illustration of the longitudinal acoustic waves velocities VL and corresponding Brillouin sifts ΩL for particular directions, in accordance with longitudinal acoustic wave velocities expressions given by Eq. (26), and for a crystal oriented along 001 which corresponds to a z-cut.
Fig. 4
Fig. 4 Longitudinal acoustic mode frequency variations along the periphery of CaF2 oriented along 111 at a wavelength of 1064 nm. The calculation reveals a longitudinal acoustic mode at a frequency of 17.7 GHz with a peak-to-peak frequency variation along the disk of 112 MHz. This is in agreement with the results reported by Grudinin et al. in [16].
Fig. 5
Fig. 5 Numerical simulations for the Brillouin shifts at 1550 nm, for different crystals oriented along 111. Figures (a), (c), (e), and (g) (in blue) correspond respectively to transverse longitudinal acoustic waves for a crystal of BaF2, CaF2, LiF, and MgF2. Figures (b), (d), (f), (h) represent respectively the fast transverse acoustic waves (or FT, in green) and slow transverse acoustic waves (or ST, in red) for the aforementioned crystals.

Tables (1)

Tables Icon

Table 1 Summary of longitudinal Brillouin frequency shifts fL, fast transverses fFT and slow transverses fST with their respective variations ΔνL, ΔνFT, ΔνST, for ψ ranging from 0 to 2π, and for the following crystals in the 111 orientation: BaF2, CaF2, LiF, MgF2. The laser pump wavelength is 1550 nm.

Equations (36)

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

Δ ν B ν B = ν B max ν B min ν B = V a max V a min V a .
T i j = c i j k l S k l ,
ρ u i 2 t 2 = T i j x j ,
ρ 2 u i t 2 = c i j k l 2 u l x j x k
u i = U i f ( t n i x i V ) ,
ρ V 2 U i = c i j k l n j n k U l ,
Γ i l = c i j k l n j n k .
Γ i l ρ V 2 δ i l U l = 0
| Γ i l ρ V 2 δ i l | = 0 .
Γ 11 = C 11 n 1 2 + C 66 n 2 2 + C 55 n 3 2 + 2 C 16 n 1 n 2 + 2 C 15 n 1 n 3 + 2 C 56 n 2 n 3
Γ 22 = C 66 n 1 2 + C 22 n 2 2 + C 44 n 3 2 + 2 C 26 n 1 n 2 + 2 C 46 n 1 n 3 + 2 C 24 n 2 n 3
Γ 33 = C 55 n 1 2 + C 44 n 2 2 + C 33 n 3 2 + 2 C 45 n 1 n 2 + 2 C 35 n 1 n 3 + 2 C 34 n 2 n 3
Γ 12 = C 16 n 1 2 + C 26 n 2 2 + C 45 n 3 2 + C 12 + C 66 n 1 n 2 + C 14 + C 56 n 1 n 3 + C 46 + C 25 n 2 n 3
Γ 13 = C 15 n 1 2 + C 46 n 2 2 + C 55 n 3 2 + C 14 + C 56 n 1 n 2 + C 13 + C 55 n 1 n 3 + C 36 + C 45 n 2 n 3
Γ 23 = C 65 n 1 2 + C 24 n 2 2 + C 43 n 3 2 + C 46 + C 25 n 1 n 2 + C 36 + C 45 n 1 n 3 + C 23 + C 44 n 2 n 3 .
C α β = [ C 11 C 12 C 12 0 0 0 C 12 C 11 C 12 0 0 0 C 12 C 12 C 11 0 0 0 0 0 0 C 44 0 0 0 0 0 0 C 44 0 0 0 0 0 0 C 44 ] ,
Γ 11 = C 11 n 1 2 + C 44 n 2 2 + n 3 2
Γ 12 = Γ 21 = C 12 + C 44 n 1 n 2
Γ 13 = Γ 31 = C 12 + C 44 n 1 n 3
Γ 22 = C 44 n 1 2 + n 3 2 + C 11 n 2 2
Γ 23 = Γ 32 = C 12 + C 44 n 2 n 3
Γ 33 = C 44 n 1 2 + n 2 2 + C 11 n 3 2 .
| C 11 ρ V 2 0 0 0 C 44 ρ V 2 0 0 0 C 44 ρ V 2 | = 0 .
V L = C 11 ρ , V T 1 = C 44 ρ , V T 2 = C 44 ρ .
| 1 2 C 11 + C 44 ρ V 2 1 2 C 11 + C 44 0 1 2 C 11 + C 44 1 2 C 11 + C 44 ρ V 2 0 0 0 C 44 ρ V 2 | = 0 .
V L = C 11 + C 12 + 2 C 44 2 ρ , V T 1 = C 11 C 12 2 ρ , V T 2 = C 44 ρ .
T x x   = a x x 2 T x x + a x x a x y T x y + a x x a x z T x z + a x y a z x T y x + a x y 2 T y y + a x y a x z T y z + a x z a x x T z x + a x z a x y T z y + a x z 2 T zz ,
T x x   = a x x 2 T x x + a x y 2 T y y + a x z 2 T z z + 2 a x x a x y T x y + 2 a x x a x z T x z + 2 a x y a x z T y z ,
T 1   = a x x 2 T 1 + a x y 2 T 2 + a x z 2 T 3 + 2 a x x a x y T 6 + 2 a x x a x z T 5 + 2 a x y a x z T 4 .
M = [ B 1 2 B 2 B 3 B 4 ] and N = [ B 1 B 2 2 B 3 B 4 ]
B 1 = [ a x x 2 a x y 2 a x z 2 a y x 2 a y y 2 a y z 2 a z x 2 a z y 2 a z z 2 ]
B 2 = [ a x y a x z a x z a x x a x x a x y a y y a y z a y z a y x a y x a y y a z y a z z a z z a z x a z x a z y ]
B 3 = [ a y x a z x a y y a z y a y z a z z a z x a x x a z y a x y a z z a x z a x x a y x a x y a y y a x z a y z ]
B 4 = [ a y y a z z + a y z a z y a y x a z z + a y z a z x a y y a z x + a y x a z y a x y a z x + a x z a z y a x z a z x + a x x a z z a x x a z y + a x y a z x a x y a y z + a x z a y y a x z a y x + a x x a y z a x x a y y + a x y a y x ]
C = MC N 1 .
C = MC M T .

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