Abstract

Recently, a high efficiency, narrow-linewidth, chip-based stimulated Brillouin laser (SBL) was demonstrated using an ultra-high-Q, silica-on-silicon resonator. In this work, this novel laser is more fully characterized. The Schawlow Townes linewidth formula for Brillouin laser operation is derived and compared to linewidth data, and the fitting is used to measure the mechanical thermal quanta contribution to the Brillouin laser linewidth. A study of laser mode pulling by the Brillouin optical gain spectrum is also presented, and high-order, cascaded operation of the SBL is demonstrated. Potential application of these devices to microwave sources and phase-coherent communication is discussed.

© 2012 OSA

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    [CrossRef] [PubMed]

2012

H. Lee, T. Chen, J. Li, K. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics6, 369–373 (2012).
[CrossRef]

2011

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science332, 555–559 (2011).
[CrossRef] [PubMed]

T. Fortier, M. Kirchner, F. Quinlan, J. Taylor, J. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. Oates, and S. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics5, 425–429 (2011).
[CrossRef]

R. Pant, C. G. Poulton, D. Choi, H. Mcfarlane, S. Hile, E. Li, L. Thevenaz, B. Luther-Davies, S. J. Madden, and B. J. Eggleton, “On-chip stimulated Brillouin scattering,” Opt. Express19, 8285–8290 (2011)
[CrossRef] [PubMed]

Z. Wu, L. Zhan, Q. Shen, J. Liu, X. Hu, and P. Xiao, “Ultrafine optical-frequency tunable Brillouin fiber laser based on fiber strain,” Opt. Lett.36, 3837–3839 (2011).
[CrossRef] [PubMed]

2010

M. C. Gross, P. T. Callahan, T. R. Clark, D. Novak, R. B. Waterhouse, and M. L. Dennis, “Tunable millimeter-wave frequency synthesis up to 100 GHz by dual-wavelength Brillouin fiber laser,” Opt. Express18, 13321–13330 (2010).
[CrossRef] [PubMed]

W. Liang, V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “Whispering-gallery-mode-resonator-based ultranarrow linewidth external-cavity semiconductor laser,” Opt. Lett.352822–2824 (2010).
[CrossRef] [PubMed]

I. S. Grudinin, H. Lee, O. Painter, and K. J. Vahala, “Phonon laser action in a tunable two-level system,” Phys. Rev. Lett.104, 083901 (2010).
[CrossRef] [PubMed]

M. Nakazawa, S. Okamoto, T. Omiya, K. Kasai, and M. Yoshida, “256-QAM (64 Gb/s) coherent optical transmission over 160 km with an optical bandwidth of 5.4 GHz,” IEEE Photon. Technol. Lett.22, 185–187 (2010).
[CrossRef]

2009

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

M. Tomes and T. Carmon, “Photonic micro-electromechanical systems vibrating at X-band (11-GHz) rates,” Phys. Rev. Lett.102, 113601 (2009).
[CrossRef] [PubMed]

2008

A. Schliesser, R. Riviere, G. Anetsberger, O. Arcizet, and T. J. Kippenberg, “Resolved-sideband cooling of a micromechanical oscillator,” Nat. Phys.4, 415–419 (2008).
[CrossRef]

K. J. Vahala, “Back-action limit of linewidth in an optomechnical oscillator,” Phys. Rev. A78, 023832 (2008).
[CrossRef]

E. IP, A. Lau, D. Barros, and J. Kahn, “Coherent detection in optical fiber systems,” Opt. Express16, 753–791 (2008).
[CrossRef] [PubMed]

2007

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature450, 1214–1217 (2007).
[CrossRef]

2005

Y. Okawachi, M. Bigelgow, J. Sharping, Z. Zhu, A. Schweinsberg, D. Gauthier, R. Boyd, and A. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett.94, 153902 (2005).
[CrossRef] [PubMed]

2004

T. J. Kippenberg, S. M. Spillane, B. Min, and K. J. Vahala, “Theoretical and experimental study of stimulated and cascaded Raman scattering in ultrahigh-Q optical microcavities,” IEEE J. Quantum Electron.10, 1219–1228 (2004).
[CrossRef]

2003

S. M. Spillane, T. J. Kippenberg, O. Painter, and K. J. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett.91, 043902 (2003).
[CrossRef] [PubMed]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature421, 925–928 (2003).
[CrossRef] [PubMed]

B. Min, T. J. Kippenberg, and K. J. Vahala, “Compact, fiber-compatible, cascaded Raman laser,” Opt. Lett.28, 1507–1509 (2003).
[CrossRef] [PubMed]

2002

A. B. Matsko, V. S. Ilchenko, A. A. Savchenkov, and L. Maleki, “Highly nondegenerate all-resonant optical parametric oscillator,” Phys. Rev. A66, 043814 (2002).
[CrossRef]

2001

2000

C. Karlsson, F. Olsson, D. Letalick, and M. Harris, “All-fiber multifunction CW coherent laser radar at 1.55 μm for range, speed, vibration, and wind measurements,” Appl. Opt.39, 3716–3726 (2000).
[CrossRef]

A. Debut, S. Randoux, and J. Zemmouri, “Linewidth narrowing in Brillouin lasers: theoretical analysis,” Phys. Rev. A62023803 (2000).
[CrossRef]

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

R. Rafac, B. Young, J. Beall, W. Itano, D. Wineland, and J. Berquist, “Sub-dekahertz Ultraviolet Spectroscopy of 199Hg+”, Phys. Rev. Lett.85, 2462–2465 (2000).
[CrossRef] [PubMed]

1999

B. Young, F. Cruz, W. Itano, and J. Bergquist, “Visible lasers with aubhertz linewidths,” Phys. Rev. Lett.82, 3799–3802 (1999).
[CrossRef]

1993

M. Okai, M. Suzuki, and T. Taniwatari, “Strained multiquantum-well corrugation-pitch-modulated distributed feedback laser with ultranarrow (3.6 kHz) spectral linewidth,” Electron. Lett.29, 1696–1697 (1993).
[CrossRef]

1991

1990

R. W. Boyd, K. Rzaewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A42, 5514 (1990).
[CrossRef] [PubMed]

1980

T. W. Hänsch and B. Couillaud, “Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity.” Opt. Commun.35, 441–444 (1980).
[CrossRef]

1965

Y. R. Shen and N. Bloembergen, “Theory of stimulated Brillouin and Raman scattering,” Phys. Rev.137, A1787–A1805 (1965).
[CrossRef]

Anetsberger, G.

A. Schliesser, R. Riviere, G. Anetsberger, O. Arcizet, and T. J. Kippenberg, “Resolved-sideband cooling of a micromechanical oscillator,” Nat. Phys.4, 415–419 (2008).
[CrossRef]

Arcizet, O.

A. Schliesser, R. Riviere, G. Anetsberger, O. Arcizet, and T. J. Kippenberg, “Resolved-sideband cooling of a micromechanical oscillator,” Nat. Phys.4, 415–419 (2008).
[CrossRef]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature450, 1214–1217 (2007).
[CrossRef]

Armani, D. K.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature421, 925–928 (2003).
[CrossRef] [PubMed]

Barros, D.

Beall, J.

R. Rafac, B. Young, J. Beall, W. Itano, D. Wineland, and J. Berquist, “Sub-dekahertz Ultraviolet Spectroscopy of 199Hg+”, Phys. Rev. Lett.85, 2462–2465 (2000).
[CrossRef] [PubMed]

Bergquist, J.

T. Fortier, M. Kirchner, F. Quinlan, J. Taylor, J. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. Oates, and S. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics5, 425–429 (2011).
[CrossRef]

B. Young, F. Cruz, W. Itano, and J. Bergquist, “Visible lasers with aubhertz linewidths,” Phys. Rev. Lett.82, 3799–3802 (1999).
[CrossRef]

Berquist, J.

R. Rafac, B. Young, J. Beall, W. Itano, D. Wineland, and J. Berquist, “Sub-dekahertz Ultraviolet Spectroscopy of 199Hg+”, Phys. Rev. Lett.85, 2462–2465 (2000).
[CrossRef] [PubMed]

Bigelgow, M.

Y. Okawachi, M. Bigelgow, J. Sharping, Z. Zhu, A. Schweinsberg, D. Gauthier, R. Boyd, and A. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett.94, 153902 (2005).
[CrossRef] [PubMed]

Bloembergen, N.

Y. R. Shen and N. Bloembergen, “Theory of stimulated Brillouin and Raman scattering,” Phys. Rev.137, A1787–A1805 (1965).
[CrossRef]

Boyd, R.

Y. Okawachi, M. Bigelgow, J. Sharping, Z. Zhu, A. Schweinsberg, D. Gauthier, R. Boyd, and A. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett.94, 153902 (2005).
[CrossRef] [PubMed]

Boyd, R. W.

R. W. Boyd, K. Rzaewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A42, 5514 (1990).
[CrossRef] [PubMed]

Cai, M.

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

Callahan, P. T.

Carmon, T.

M. Tomes and T. Carmon, “Photonic micro-electromechanical systems vibrating at X-band (11-GHz) rates,” Phys. Rev. Lett.102, 113601 (2009).
[CrossRef] [PubMed]

L. Yang, T. Lu, T. Carmon, B. Min, and K. J. Vahala, “A 4-Hz fundamental linewidth on-chip microlaser,” Conference on Lasers and Electro-Optics (CLEO), Technical Digest Series (CD) (Optical Society of America, 2007), paper CMR2.

T. Lu, L. Yang, T. Carmon, B. Min, and K. J. Vahala, “Frequency noise of a microchip raman laser,” Conference on Lasers and Electro-Optics (CLEO), Technical Digest Series (CD) (Optical Society of America, 2009), paper CTuB3.

Chen, T.

H. Lee, T. Chen, J. Li, K. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics6, 369–373 (2012).
[CrossRef]

Choi, D.

Clark, T. R.

Couillaud, B.

T. W. Hänsch and B. Couillaud, “Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity.” Opt. Commun.35, 441–444 (1980).
[CrossRef]

Cruz, F.

B. Young, F. Cruz, W. Itano, and J. Bergquist, “Visible lasers with aubhertz linewidths,” Phys. Rev. Lett.82, 3799–3802 (1999).
[CrossRef]

Debut, A.

A. Debut, S. Randoux, and J. Zemmouri, “Experimental and theoretical study of linewidth narrowing in Brillouin fiber ring lasers,” J. Opt. Soc. Am. B18, 556–567 (2001).
[CrossRef]

A. Debut, S. Randoux, and J. Zemmouri, “Linewidth narrowing in Brillouin lasers: theoretical analysis,” Phys. Rev. A62023803 (2000).
[CrossRef]

Del’Haye, P.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature450, 1214–1217 (2007).
[CrossRef]

Dennis, M. L.

Diddams, S.

T. Fortier, M. Kirchner, F. Quinlan, J. Taylor, J. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. Oates, and S. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics5, 425–429 (2011).
[CrossRef]

Diddams, S. A.

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science332, 555–559 (2011).
[CrossRef] [PubMed]

Eggleton, B. J.

Ezekiel, S.

Fortier, T.

T. Fortier, M. Kirchner, F. Quinlan, J. Taylor, J. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. Oates, and S. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics5, 425–429 (2011).
[CrossRef]

Gaeta, A.

Y. Okawachi, M. Bigelgow, J. Sharping, Z. Zhu, A. Schweinsberg, D. Gauthier, R. Boyd, and A. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett.94, 153902 (2005).
[CrossRef] [PubMed]

Gauthier, D.

Y. Okawachi, M. Bigelgow, J. Sharping, Z. Zhu, A. Schweinsberg, D. Gauthier, R. Boyd, and A. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett.94, 153902 (2005).
[CrossRef] [PubMed]

Gross, M. C.

Grudinin, I.

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

Grudinin, I. S.

I. S. Grudinin, H. Lee, O. Painter, and K. J. Vahala, “Phonon laser action in a tunable two-level system,” Phys. Rev. Lett.104, 083901 (2010).
[CrossRef] [PubMed]

Hänsch, T. W.

T. W. Hänsch and B. Couillaud, “Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity.” Opt. Commun.35, 441–444 (1980).
[CrossRef]

Harris, M.

Hile, S.

Holzwarth, R.

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science332, 555–559 (2011).
[CrossRef] [PubMed]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature450, 1214–1217 (2007).
[CrossRef]

Hu, X.

Ilchenko, V. S.

IP, E.

Itano, W.

R. Rafac, B. Young, J. Beall, W. Itano, D. Wineland, and J. Berquist, “Sub-dekahertz Ultraviolet Spectroscopy of 199Hg+”, Phys. Rev. Lett.85, 2462–2465 (2000).
[CrossRef] [PubMed]

B. Young, F. Cruz, W. Itano, and J. Bergquist, “Visible lasers with aubhertz linewidths,” Phys. Rev. Lett.82, 3799–3802 (1999).
[CrossRef]

Jeon, S.

H. Lee, T. Chen, J. Li, K. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics6, 369–373 (2012).
[CrossRef]

Jiang, Y.

T. Fortier, M. Kirchner, F. Quinlan, J. Taylor, J. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. Oates, and S. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics5, 425–429 (2011).
[CrossRef]

Kahn, J.

Karlsson, C.

Kasai, K.

M. Nakazawa, S. Okamoto, T. Omiya, K. Kasai, and M. Yoshida, “256-QAM (64 Gb/s) coherent optical transmission over 160 km with an optical bandwidth of 5.4 GHz,” IEEE Photon. Technol. Lett.22, 185–187 (2010).
[CrossRef]

Kippenberg, T. J.

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science332, 555–559 (2011).
[CrossRef] [PubMed]

A. Schliesser, R. Riviere, G. Anetsberger, O. Arcizet, and T. J. Kippenberg, “Resolved-sideband cooling of a micromechanical oscillator,” Nat. Phys.4, 415–419 (2008).
[CrossRef]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature450, 1214–1217 (2007).
[CrossRef]

T. J. Kippenberg, S. M. Spillane, B. Min, and K. J. Vahala, “Theoretical and experimental study of stimulated and cascaded Raman scattering in ultrahigh-Q optical microcavities,” IEEE J. Quantum Electron.10, 1219–1228 (2004).
[CrossRef]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature421, 925–928 (2003).
[CrossRef] [PubMed]

S. M. Spillane, T. J. Kippenberg, O. Painter, and K. J. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett.91, 043902 (2003).
[CrossRef] [PubMed]

B. Min, T. J. Kippenberg, and K. J. Vahala, “Compact, fiber-compatible, cascaded Raman laser,” Opt. Lett.28, 1507–1509 (2003).
[CrossRef] [PubMed]

Kirchner, M.

T. Fortier, M. Kirchner, F. Quinlan, J. Taylor, J. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. Oates, and S. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics5, 425–429 (2011).
[CrossRef]

Lau, A.

Lee, H.

H. Lee, T. Chen, J. Li, K. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics6, 369–373 (2012).
[CrossRef]

I. S. Grudinin, H. Lee, O. Painter, and K. J. Vahala, “Phonon laser action in a tunable two-level system,” Phys. Rev. Lett.104, 083901 (2010).
[CrossRef] [PubMed]

Lemke, N.

T. Fortier, M. Kirchner, F. Quinlan, J. Taylor, J. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. Oates, and S. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics5, 425–429 (2011).
[CrossRef]

Letalick, D.

Li, E.

Li, J.

H. Lee, T. Chen, J. Li, K. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics6, 369–373 (2012).
[CrossRef]

Liang, W.

Liu, J.

Lu, T.

T. Lu, L. Yang, T. Carmon, B. Min, and K. J. Vahala, “Frequency noise of a microchip raman laser,” Conference on Lasers and Electro-Optics (CLEO), Technical Digest Series (CD) (Optical Society of America, 2009), paper CTuB3.

L. Yang, T. Lu, T. Carmon, B. Min, and K. J. Vahala, “A 4-Hz fundamental linewidth on-chip microlaser,” Conference on Lasers and Electro-Optics (CLEO), Technical Digest Series (CD) (Optical Society of America, 2007), paper CMR2.

Ludlow, A.

T. Fortier, M. Kirchner, F. Quinlan, J. Taylor, J. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. Oates, and S. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics5, 425–429 (2011).
[CrossRef]

Luther-Davies, B.

Madden, S. J.

Maleki, L.

W. Liang, V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “Whispering-gallery-mode-resonator-based ultranarrow linewidth external-cavity semiconductor laser,” Opt. Lett.352822–2824 (2010).
[CrossRef] [PubMed]

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

A. B. Matsko, V. S. Ilchenko, A. A. Savchenkov, and L. Maleki, “Highly nondegenerate all-resonant optical parametric oscillator,” Phys. Rev. A66, 043814 (2002).
[CrossRef]

Matsko, A.

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

Matsko, A. B.

Mcfarlane, H.

Min, B.

T. J. Kippenberg, S. M. Spillane, B. Min, and K. J. Vahala, “Theoretical and experimental study of stimulated and cascaded Raman scattering in ultrahigh-Q optical microcavities,” IEEE J. Quantum Electron.10, 1219–1228 (2004).
[CrossRef]

B. Min, T. J. Kippenberg, and K. J. Vahala, “Compact, fiber-compatible, cascaded Raman laser,” Opt. Lett.28, 1507–1509 (2003).
[CrossRef] [PubMed]

L. Yang, T. Lu, T. Carmon, B. Min, and K. J. Vahala, “A 4-Hz fundamental linewidth on-chip microlaser,” Conference on Lasers and Electro-Optics (CLEO), Technical Digest Series (CD) (Optical Society of America, 2007), paper CMR2.

T. Lu, L. Yang, T. Carmon, B. Min, and K. J. Vahala, “Frequency noise of a microchip raman laser,” Conference on Lasers and Electro-Optics (CLEO), Technical Digest Series (CD) (Optical Society of America, 2009), paper CTuB3.

Nakazawa, M.

M. Nakazawa, S. Okamoto, T. Omiya, K. Kasai, and M. Yoshida, “256-QAM (64 Gb/s) coherent optical transmission over 160 km with an optical bandwidth of 5.4 GHz,” IEEE Photon. Technol. Lett.22, 185–187 (2010).
[CrossRef]

Narum, P.

R. W. Boyd, K. Rzaewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A42, 5514 (1990).
[CrossRef] [PubMed]

Novak, D.

Oates, C.

T. Fortier, M. Kirchner, F. Quinlan, J. Taylor, J. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. Oates, and S. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics5, 425–429 (2011).
[CrossRef]

Okai, M.

M. Okai, M. Suzuki, and T. Taniwatari, “Strained multiquantum-well corrugation-pitch-modulated distributed feedback laser with ultranarrow (3.6 kHz) spectral linewidth,” Electron. Lett.29, 1696–1697 (1993).
[CrossRef]

Okamoto, S.

M. Nakazawa, S. Okamoto, T. Omiya, K. Kasai, and M. Yoshida, “256-QAM (64 Gb/s) coherent optical transmission over 160 km with an optical bandwidth of 5.4 GHz,” IEEE Photon. Technol. Lett.22, 185–187 (2010).
[CrossRef]

Okawachi, Y.

Y. Okawachi, M. Bigelgow, J. Sharping, Z. Zhu, A. Schweinsberg, D. Gauthier, R. Boyd, and A. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett.94, 153902 (2005).
[CrossRef] [PubMed]

Olsson, F.

Omiya, T.

M. Nakazawa, S. Okamoto, T. Omiya, K. Kasai, and M. Yoshida, “256-QAM (64 Gb/s) coherent optical transmission over 160 km with an optical bandwidth of 5.4 GHz,” IEEE Photon. Technol. Lett.22, 185–187 (2010).
[CrossRef]

Painter, O.

H. Lee, T. Chen, J. Li, K. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics6, 369–373 (2012).
[CrossRef]

I. S. Grudinin, H. Lee, O. Painter, and K. J. Vahala, “Phonon laser action in a tunable two-level system,” Phys. Rev. Lett.104, 083901 (2010).
[CrossRef] [PubMed]

S. M. Spillane, T. J. Kippenberg, O. Painter, and K. J. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett.91, 043902 (2003).
[CrossRef] [PubMed]

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

Pant, R.

Poulton, C. G.

Quinlan, F.

T. Fortier, M. Kirchner, F. Quinlan, J. Taylor, J. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. Oates, and S. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics5, 425–429 (2011).
[CrossRef]

Rafac, R.

R. Rafac, B. Young, J. Beall, W. Itano, D. Wineland, and J. Berquist, “Sub-dekahertz Ultraviolet Spectroscopy of 199Hg+”, Phys. Rev. Lett.85, 2462–2465 (2000).
[CrossRef] [PubMed]

Randoux, S.

A. Debut, S. Randoux, and J. Zemmouri, “Experimental and theoretical study of linewidth narrowing in Brillouin fiber ring lasers,” J. Opt. Soc. Am. B18, 556–567 (2001).
[CrossRef]

A. Debut, S. Randoux, and J. Zemmouri, “Linewidth narrowing in Brillouin lasers: theoretical analysis,” Phys. Rev. A62023803 (2000).
[CrossRef]

Riviere, R.

A. Schliesser, R. Riviere, G. Anetsberger, O. Arcizet, and T. J. Kippenberg, “Resolved-sideband cooling of a micromechanical oscillator,” Nat. Phys.4, 415–419 (2008).
[CrossRef]

Rosenband, T.

T. Fortier, M. Kirchner, F. Quinlan, J. Taylor, J. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. Oates, and S. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics5, 425–429 (2011).
[CrossRef]

Rzaewski, K.

R. W. Boyd, K. Rzaewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A42, 5514 (1990).
[CrossRef] [PubMed]

Savchenkov, A. A.

Schliesser, A.

A. Schliesser, R. Riviere, G. Anetsberger, O. Arcizet, and T. J. Kippenberg, “Resolved-sideband cooling of a micromechanical oscillator,” Nat. Phys.4, 415–419 (2008).
[CrossRef]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature450, 1214–1217 (2007).
[CrossRef]

Schweinsberg, A.

Y. Okawachi, M. Bigelgow, J. Sharping, Z. Zhu, A. Schweinsberg, D. Gauthier, R. Boyd, and A. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett.94, 153902 (2005).
[CrossRef] [PubMed]

Seidel, D.

Sharping, J.

Y. Okawachi, M. Bigelgow, J. Sharping, Z. Zhu, A. Schweinsberg, D. Gauthier, R. Boyd, and A. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett.94, 153902 (2005).
[CrossRef] [PubMed]

Shen, Q.

Shen, Y. R.

Y. R. Shen and N. Bloembergen, “Theory of stimulated Brillouin and Raman scattering,” Phys. Rev.137, A1787–A1805 (1965).
[CrossRef]

Smith, S. P.

Spillane, S. M.

T. J. Kippenberg, S. M. Spillane, B. Min, and K. J. Vahala, “Theoretical and experimental study of stimulated and cascaded Raman scattering in ultrahigh-Q optical microcavities,” IEEE J. Quantum Electron.10, 1219–1228 (2004).
[CrossRef]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature421, 925–928 (2003).
[CrossRef] [PubMed]

S. M. Spillane, T. J. Kippenberg, O. Painter, and K. J. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett.91, 043902 (2003).
[CrossRef] [PubMed]

Suzuki, M.

M. Okai, M. Suzuki, and T. Taniwatari, “Strained multiquantum-well corrugation-pitch-modulated distributed feedback laser with ultranarrow (3.6 kHz) spectral linewidth,” Electron. Lett.29, 1696–1697 (1993).
[CrossRef]

Taniwatari, T.

M. Okai, M. Suzuki, and T. Taniwatari, “Strained multiquantum-well corrugation-pitch-modulated distributed feedback laser with ultranarrow (3.6 kHz) spectral linewidth,” Electron. Lett.29, 1696–1697 (1993).
[CrossRef]

Taylor, J.

T. Fortier, M. Kirchner, F. Quinlan, J. Taylor, J. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. Oates, and S. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics5, 425–429 (2011).
[CrossRef]

Thevenaz, L.

Tomes, M.

M. Tomes and T. Carmon, “Photonic micro-electromechanical systems vibrating at X-band (11-GHz) rates,” Phys. Rev. Lett.102, 113601 (2009).
[CrossRef] [PubMed]

Vahala, K. J.

H. Lee, T. Chen, J. Li, K. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics6, 369–373 (2012).
[CrossRef]

I. S. Grudinin, H. Lee, O. Painter, and K. J. Vahala, “Phonon laser action in a tunable two-level system,” Phys. Rev. Lett.104, 083901 (2010).
[CrossRef] [PubMed]

K. J. Vahala, “Back-action limit of linewidth in an optomechnical oscillator,” Phys. Rev. A78, 023832 (2008).
[CrossRef]

T. J. Kippenberg, S. M. Spillane, B. Min, and K. J. Vahala, “Theoretical and experimental study of stimulated and cascaded Raman scattering in ultrahigh-Q optical microcavities,” IEEE J. Quantum Electron.10, 1219–1228 (2004).
[CrossRef]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature421, 925–928 (2003).
[CrossRef] [PubMed]

S. M. Spillane, T. J. Kippenberg, O. Painter, and K. J. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett.91, 043902 (2003).
[CrossRef] [PubMed]

B. Min, T. J. Kippenberg, and K. J. Vahala, “Compact, fiber-compatible, cascaded Raman laser,” Opt. Lett.28, 1507–1509 (2003).
[CrossRef] [PubMed]

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

L. Yang, T. Lu, T. Carmon, B. Min, and K. J. Vahala, “A 4-Hz fundamental linewidth on-chip microlaser,” Conference on Lasers and Electro-Optics (CLEO), Technical Digest Series (CD) (Optical Society of America, 2007), paper CMR2.

T. Lu, L. Yang, T. Carmon, B. Min, and K. J. Vahala, “Frequency noise of a microchip raman laser,” Conference on Lasers and Electro-Optics (CLEO), Technical Digest Series (CD) (Optical Society of America, 2009), paper CTuB3.

Waterhouse, R. B.

Wilken, T.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature450, 1214–1217 (2007).
[CrossRef]

Wineland, D.

R. Rafac, B. Young, J. Beall, W. Itano, D. Wineland, and J. Berquist, “Sub-dekahertz Ultraviolet Spectroscopy of 199Hg+”, Phys. Rev. Lett.85, 2462–2465 (2000).
[CrossRef] [PubMed]

Wu, Z.

Xiao, P.

Yang, K.

H. Lee, T. Chen, J. Li, K. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics6, 369–373 (2012).
[CrossRef]

Yang, L.

T. Lu, L. Yang, T. Carmon, B. Min, and K. J. Vahala, “Frequency noise of a microchip raman laser,” Conference on Lasers and Electro-Optics (CLEO), Technical Digest Series (CD) (Optical Society of America, 2009), paper CTuB3.

L. Yang, T. Lu, T. Carmon, B. Min, and K. J. Vahala, “A 4-Hz fundamental linewidth on-chip microlaser,” Conference on Lasers and Electro-Optics (CLEO), Technical Digest Series (CD) (Optical Society of America, 2007), paper CMR2.

Yariv, A.

A. Yariv, Quantum Electronics (Wiley, 1989).

Yoshida, M.

M. Nakazawa, S. Okamoto, T. Omiya, K. Kasai, and M. Yoshida, “256-QAM (64 Gb/s) coherent optical transmission over 160 km with an optical bandwidth of 5.4 GHz,” IEEE Photon. Technol. Lett.22, 185–187 (2010).
[CrossRef]

Young, B.

R. Rafac, B. Young, J. Beall, W. Itano, D. Wineland, and J. Berquist, “Sub-dekahertz Ultraviolet Spectroscopy of 199Hg+”, Phys. Rev. Lett.85, 2462–2465 (2000).
[CrossRef] [PubMed]

B. Young, F. Cruz, W. Itano, and J. Bergquist, “Visible lasers with aubhertz linewidths,” Phys. Rev. Lett.82, 3799–3802 (1999).
[CrossRef]

Zarinetchi, F.

Zemmouri, J.

A. Debut, S. Randoux, and J. Zemmouri, “Experimental and theoretical study of linewidth narrowing in Brillouin fiber ring lasers,” J. Opt. Soc. Am. B18, 556–567 (2001).
[CrossRef]

A. Debut, S. Randoux, and J. Zemmouri, “Linewidth narrowing in Brillouin lasers: theoretical analysis,” Phys. Rev. A62023803 (2000).
[CrossRef]

Zhan, L.

Zhu, Z.

Y. Okawachi, M. Bigelgow, J. Sharping, Z. Zhu, A. Schweinsberg, D. Gauthier, R. Boyd, and A. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett.94, 153902 (2005).
[CrossRef] [PubMed]

Appl. Opt.

Electron. Lett.

M. Okai, M. Suzuki, and T. Taniwatari, “Strained multiquantum-well corrugation-pitch-modulated distributed feedback laser with ultranarrow (3.6 kHz) spectral linewidth,” Electron. Lett.29, 1696–1697 (1993).
[CrossRef]

IEEE J. Quantum Electron.

T. J. Kippenberg, S. M. Spillane, B. Min, and K. J. Vahala, “Theoretical and experimental study of stimulated and cascaded Raman scattering in ultrahigh-Q optical microcavities,” IEEE J. Quantum Electron.10, 1219–1228 (2004).
[CrossRef]

IEEE Photon. Technol. Lett.

M. Nakazawa, S. Okamoto, T. Omiya, K. Kasai, and M. Yoshida, “256-QAM (64 Gb/s) coherent optical transmission over 160 km with an optical bandwidth of 5.4 GHz,” IEEE Photon. Technol. Lett.22, 185–187 (2010).
[CrossRef]

J. Opt. Soc. Am. B

Nat. Photonics

H. Lee, T. Chen, J. Li, K. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics6, 369–373 (2012).
[CrossRef]

T. Fortier, M. Kirchner, F. Quinlan, J. Taylor, J. Bergquist, T. Rosenband, N. Lemke, A. Ludlow, Y. Jiang, C. Oates, and S. Diddams, “Generation of ultrastable microwaves via optical frequency division,” Nat. Photonics5, 425–429 (2011).
[CrossRef]

Nat. Phys.

A. Schliesser, R. Riviere, G. Anetsberger, O. Arcizet, and T. J. Kippenberg, “Resolved-sideband cooling of a micromechanical oscillator,” Nat. Phys.4, 415–419 (2008).
[CrossRef]

Nature

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature421, 925–928 (2003).
[CrossRef] [PubMed]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature450, 1214–1217 (2007).
[CrossRef]

Opt. Commun.

T. W. Hänsch and B. Couillaud, “Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity.” Opt. Commun.35, 441–444 (1980).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev.

Y. R. Shen and N. Bloembergen, “Theory of stimulated Brillouin and Raman scattering,” Phys. Rev.137, A1787–A1805 (1965).
[CrossRef]

Phys. Rev. A

A. B. Matsko, V. S. Ilchenko, A. A. Savchenkov, and L. Maleki, “Highly nondegenerate all-resonant optical parametric oscillator,” Phys. Rev. A66, 043814 (2002).
[CrossRef]

K. J. Vahala, “Back-action limit of linewidth in an optomechnical oscillator,” Phys. Rev. A78, 023832 (2008).
[CrossRef]

R. W. Boyd, K. Rzaewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A42, 5514 (1990).
[CrossRef] [PubMed]

A. Debut, S. Randoux, and J. Zemmouri, “Linewidth narrowing in Brillouin lasers: theoretical analysis,” Phys. Rev. A62023803 (2000).
[CrossRef]

Phys. Rev. Lett.

I. S. Grudinin, H. Lee, O. Painter, and K. J. Vahala, “Phonon laser action in a tunable two-level system,” Phys. Rev. Lett.104, 083901 (2010).
[CrossRef] [PubMed]

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

S. M. Spillane, T. J. Kippenberg, O. Painter, and K. J. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett.91, 043902 (2003).
[CrossRef] [PubMed]

R. Rafac, B. Young, J. Beall, W. Itano, D. Wineland, and J. Berquist, “Sub-dekahertz Ultraviolet Spectroscopy of 199Hg+”, Phys. Rev. Lett.85, 2462–2465 (2000).
[CrossRef] [PubMed]

B. Young, F. Cruz, W. Itano, and J. Bergquist, “Visible lasers with aubhertz linewidths,” Phys. Rev. Lett.82, 3799–3802 (1999).
[CrossRef]

Y. Okawachi, M. Bigelgow, J. Sharping, Z. Zhu, A. Schweinsberg, D. Gauthier, R. Boyd, and A. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett.94, 153902 (2005).
[CrossRef] [PubMed]

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

M. Tomes and T. Carmon, “Photonic micro-electromechanical systems vibrating at X-band (11-GHz) rates,” Phys. Rev. Lett.102, 113601 (2009).
[CrossRef] [PubMed]

Science

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science332, 555–559 (2011).
[CrossRef] [PubMed]

Other

L. Yang, T. Lu, T. Carmon, B. Min, and K. J. Vahala, “A 4-Hz fundamental linewidth on-chip microlaser,” Conference on Lasers and Electro-Optics (CLEO), Technical Digest Series (CD) (Optical Society of America, 2007), paper CMR2.

T. Lu, L. Yang, T. Carmon, B. Min, and K. J. Vahala, “Frequency noise of a microchip raman laser,” Conference on Lasers and Electro-Optics (CLEO), Technical Digest Series (CD) (Optical Society of America, 2009), paper CTuB3.

A. Yariv, Quantum Electronics (Wiley, 1989).

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Figures (5)

Fig. 1
Fig. 1

Experimental setup. (a) A tunable CW laser is amplified through an EDFA and coupled into the disk resonator using the taper-fiber technique. The SBL emission in the backward direction propagates through the fiber circulator, and is monitored by a photodetector (PD B) and an optical spectrum analyzer (OSA). The pump is monitored by a separate photodetector (PD A) and is also coupled to a balanced-homodyne detection setup (Hänsch-Couillaud technique) to generate an error signal for locking the pump laser to the cavity resonance. (b) A micrograph of the SBL disk resonator used in this experiment. The disk has a diameter of approximately 6.02 mm. (c) Experimental oscilloscope traces for transmitted pump, back-propagating SBL and Hänsch-Couillaud error signal.

Fig. 2
Fig. 2

SBL optical spectra and output power versus pump power for single-line operation. (a) A spectrum showing single-line SBL operation wherein only the 1st-order emission line is excited. (b) Spectrum showing cascaded SBL operation up to the 9th order. In both figures, the spectrum is collected in the backward direction with the pump and even order SBL emission lines suppressed on account of their propagation in the forward direction (i.e., the observed, weak level for these signals in the spectrum is a result of weak back-reflection in the experimental setup). (c) Output power of the 1st-order Stokes wave while adjusting the cavity loading so as to maintain critical coupling in each step. The differential efficiency is around 95%.

Fig. 3
Fig. 3

SBL output power dependence on pump power in cascaded operation. (a) Experimental output power of the 1st-order SBL versus the pump power. A threshold of 40 μW is obtained. The output power of the 1st-order SBL is clamped for pump power above 150 μW because the 2nd-order SBL begins oscillation. Also shown is the fitted curve using P t h ( P pump P t h 1 ). (b) Experimental output power of the 2nd-order SBL versus the pump power. Also shown is the linear fit with respect to the pump power.

Fig. 4
Fig. 4

SBL mode pulling measurement. The measured cold cavity FSR (circles), Brillouin beat frequency (squares) and SBL threshold power (triangles) are plotted versus the pump wavelength. The linear fit of the cold cavity FSR gives a slope of −2π × 0.02 MHz/nm and the fit of the Brillouin beat frequency gives a slope of −2π × 0.19 MHz/nm. The quadratic fit of the threshold power yields the Brillouin gain linewidth of 2π × 51 MHz.

Fig. 5
Fig. 5

Measurements of the SBL Schawlow-Townes-like, frequency noise characteristics (Original data appeared in the supplemental information of [12]). The dashed line is an inverse power fit to the data.

Equations (13)

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

A ˙ o = [ i ( ω p ω 0 ) γ / 2 ] A o + i γ ex s g c | α | 2 A o
α ˙ = [ i ( ω s ω 1 ) γ / 2 ] α + g c | A o | 2 α
g c = g 0 c 1 + 2 i [ ω p ω s Ω ] Γ = g 0 c ( 1 2 i Δ Ω Γ ) 1 + 4 Δ Ω 2 Γ 2
| A o | 2 = γ 2 1 + 4 Δ Ω 2 Γ 2 g 0 c
ω s ω 1 g 0 c 2 Δ Ω Γ 1 + 4 Δ Ω 2 Γ 2 | A o | 2 = 0
Δ ω beat = 1 1 + γ Γ ( Δ ω F S R + γ Γ Ω )
Δ ω beat Δ ω F S R = γ Γ ( Ω Δ ω F S R )
H = h ¯ ω 1 a a + h ¯ Ω b b + h ¯ μ 2 ( A ( t ) * b a + A ( t ) a b ) .
β ˙ = Γ 2 β + i μ 2 A o * α e i Δ Ω t + F ( t )
α ˙ = [ i ( ω s ω 1 ) γ 2 ] α i μ 2 A o β e i Δ Ω t + f ( t )
α ˙ = [ i ( ω s ω 1 ) γ 2 ] α + g c | A o | 2 α + h ( t )
Δ ν = γ 4 π N S ( n T + N T + 1 )
Δ ν = h ¯ ω 3 4 π P Q T Q E ( n T + N T + 1 )

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