Abstract

We report on the experimental study of phase noise properties of a high frequency photonic microwave oscillator based on four wave mixing in calcium fluoride whispering gallery mode resonators. Specifically, the oscillator generates ~ 8.5 GHz signals with -120 dBc/Hz at 100 kHz from the carrier. The floor of the phase noise is limited by the shot noise of the signal received at the photodetector. We argue that the performance of the oscillator can be significantly improved if one uses extremely high finesse resonators, increases the input optical power, supersaturates the oscillator, and suppresses the residual stimulated Raman scattering in the resonator. We also disclose a method of extremely sensitive measurement of the integral dispersion of millimeter scale dielectric resonators.

© 2008 Optical Society of America

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    [CrossRef]
  2. B. A. Floyd, S. K. Reynolds, U. R. Pfeiffer, T. Zwick, T. Beukema, and B. Gaucher, "SiGe bipolar transceiver circuits operating at 60 GHz," IEEE J. Solid-State Circuits 40, 156-167 (2005).
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    [CrossRef]
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    [CrossRef] [PubMed]
  11. A. B. Matsko, A. A. Savchenkov, N. Yu, and L. Maleki, "Whispering-gallery-mode resonators as frequency references: I. Fundamental limitations," J. Opt. Soc. Am. B 24, 1324-1335 (2007).
    [CrossRef]
  12. A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, N. Yu, and L. Maleki, "Whispering-gallery-mode resonators as frequency references. II. Stabilization," J. Opt. Soc. Am. B 24, 2988-2997 (2007).
    [CrossRef]
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2007

2006

E. N. Ivanov and M. E. Tobar, "Low phase-noise microwave oscillators with interferometric signal processing," IEEE Trans. Microwave Theory Tech. 54, 3284-3294 (2006).
[CrossRef]

J. F. Gravel and J. S. Wight, "On the conception and analysis of a 12-GHz push-push phase-locked DRO," IEEE Trans. Microwave Theory Tech. 54, 153-159 (2006).
[CrossRef]

2005

B. A. Floyd, S. K. Reynolds, U. R. Pfeiffer, T. Zwick, T. Beukema, and B. Gaucher, "SiGe bipolar transceiver circuits operating at 60 GHz," IEEE J. Solid-State Circuits 40, 156-167 (2005).
[CrossRef]

J. J. McFerran, E. N. Ivanov, A. Bartels, G. Wilpers, C. W. Oates, S. A. Diddams, and Hollberg, "Low-noise synthesis of microwave signals from an optical source," Electron. Lett. 41, 650-651 (2005).
[CrossRef]

A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, "Optical hyper-parametric oscillations in a whispering gallery mode resonator: threshold and phase diffusion," Phys. Rev. A 71, 033804 (2005).
[CrossRef]

N. Yu, E. Salik, and L. Maleki, "Ultralow-noise mode-locked laser with coupled optoelectronic oscillator configuration," Opt. Lett. 30, 1231-1233 (2005).
[CrossRef] [PubMed]

2004

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Kerr-Nonlinearity Optical Parametric Oscillation in an Ultrahigh-Q Toroid Microcavity," Phys. Rev. Lett. 93, 083904 (2004).
[CrossRef] [PubMed]

A. A. Savchenkov, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, "Low Threshold Optical Oscillations in a Whispering Gallery Mode CaF2 Resonator," Phys. Rev. Lett. 93, 243905 (2004).
[CrossRef]

2003

K. Hosoya, K. Ohata, M. Funabashi, T. Inoue, and M. Kuzuhara, "V-band HJFET MMIC DROs with low phase noise, high power, and excellent temperature stability," IEEE Trans. Microwave Theory Tech. 51, 2250-2258 (2003).
[CrossRef]

2002

2001

1999

Y. Ji, X. S. Yao, and L. Maleki, "Compact optoelectronic oscillator with ultralow phase noise performance," Electron. Lett. 35, 1554-1555 (1999).
[CrossRef]

1998

V. V. Vassiliev, V. L. Velichansky, V. S. Ilchenko, M. L. Gorodetsky, L. Hollberg, and A. V. Yarovitsky, "Narrowline-width diode laser with a high-Q microsphere resonator," Opt. Commun. 158, 305312 (1998).
[CrossRef]

1997

S. Coen and M. Haelterman, "Modulational instability induced by cavity boundary conditions in a normally dispersive optical fiber," Phys. Rev. Lett. 79, 4139-4142 (1997).
[CrossRef]

1992

1966

D. B. Leeson, "A simple model of feed back oscillator noise spectrum," Proc. IEEE 54, 329330 (1966).
[CrossRef]

1958

A. L. Schawlow and C. H. Townes, "Infrared and optical masers," Phys. Rev. 112, 1940-1949 (1958).
[CrossRef]

Arcizet, O.

P. Del Haye, A. Schliesser, O. Arcizet, T. Wilkins, R. Holzwarth, T. J. Kippenberg, "Optical frequency comb generation from a monolithic microresonator," Nature 450, 1214-1217 (2007).
[CrossRef]

Bartels, A.

J. J. McFerran, E. N. Ivanov, A. Bartels, G. Wilpers, C. W. Oates, S. A. Diddams, and Hollberg, "Low-noise synthesis of microwave signals from an optical source," Electron. Lett. 41, 650-651 (2005).
[CrossRef]

Beukema, T.

B. A. Floyd, S. K. Reynolds, U. R. Pfeiffer, T. Zwick, T. Beukema, and B. Gaucher, "SiGe bipolar transceiver circuits operating at 60 GHz," IEEE J. Solid-State Circuits 40, 156-167 (2005).
[CrossRef]

Coen, S.

S. Coen and M. Haelterman, "Continuous-wave ultrahigh-repetition-rate pulse-train generation through modulational instability in a passive fiber cavity," Opt. Lett. 26, 39-41 (2001).
[CrossRef]

S. Coen and M. Haelterman, "Modulational instability induced by cavity boundary conditions in a normally dispersive optical fiber," Phys. Rev. Lett. 79, 4139-4142 (1997).
[CrossRef]

Daimon, M.

Del Haye, P.

P. Del Haye, A. Schliesser, O. Arcizet, T. Wilkins, R. Holzwarth, T. J. Kippenberg, "Optical frequency comb generation from a monolithic microresonator," Nature 450, 1214-1217 (2007).
[CrossRef]

Diddams, S. A.

J. J. McFerran, E. N. Ivanov, A. Bartels, G. Wilpers, C. W. Oates, S. A. Diddams, and Hollberg, "Low-noise synthesis of microwave signals from an optical source," Electron. Lett. 41, 650-651 (2005).
[CrossRef]

Floyd, B. A.

B. A. Floyd, S. K. Reynolds, U. R. Pfeiffer, T. Zwick, T. Beukema, and B. Gaucher, "SiGe bipolar transceiver circuits operating at 60 GHz," IEEE J. Solid-State Circuits 40, 156-167 (2005).
[CrossRef]

Funabashi, M.

K. Hosoya, K. Ohata, M. Funabashi, T. Inoue, and M. Kuzuhara, "V-band HJFET MMIC DROs with low phase noise, high power, and excellent temperature stability," IEEE Trans. Microwave Theory Tech. 51, 2250-2258 (2003).
[CrossRef]

Gaucher, B.

B. A. Floyd, S. K. Reynolds, U. R. Pfeiffer, T. Zwick, T. Beukema, and B. Gaucher, "SiGe bipolar transceiver circuits operating at 60 GHz," IEEE J. Solid-State Circuits 40, 156-167 (2005).
[CrossRef]

Gorodetsky, M. L.

V. V. Vassiliev, V. L. Velichansky, V. S. Ilchenko, M. L. Gorodetsky, L. Hollberg, and A. V. Yarovitsky, "Narrowline-width diode laser with a high-Q microsphere resonator," Opt. Commun. 158, 305312 (1998).
[CrossRef]

Haelterman, M.

Hollberg, L.

V. V. Vassiliev, V. L. Velichansky, V. S. Ilchenko, M. L. Gorodetsky, L. Hollberg, and A. V. Yarovitsky, "Narrowline-width diode laser with a high-Q microsphere resonator," Opt. Commun. 158, 305312 (1998).
[CrossRef]

Hollberg, S. A.

J. J. McFerran, E. N. Ivanov, A. Bartels, G. Wilpers, C. W. Oates, S. A. Diddams, and Hollberg, "Low-noise synthesis of microwave signals from an optical source," Electron. Lett. 41, 650-651 (2005).
[CrossRef]

Holzwarth, R.

P. Del Haye, A. Schliesser, O. Arcizet, T. Wilkins, R. Holzwarth, T. J. Kippenberg, "Optical frequency comb generation from a monolithic microresonator," Nature 450, 1214-1217 (2007).
[CrossRef]

Hosoya, K.

K. Hosoya, K. Ohata, M. Funabashi, T. Inoue, and M. Kuzuhara, "V-band HJFET MMIC DROs with low phase noise, high power, and excellent temperature stability," IEEE Trans. Microwave Theory Tech. 51, 2250-2258 (2003).
[CrossRef]

Ilchenko, V. S.

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, and L. Maleki, "Optical resonators with ten million finesse," Opt. Express 15, 6768-6773 (2007).
[CrossRef] [PubMed]

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, N. Yu, and L. Maleki, "Whispering-gallery-mode resonators as frequency references. II. Stabilization," J. Opt. Soc. Am. B 24, 2988-2997 (2007).
[CrossRef]

A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, "Optical hyper-parametric oscillations in a whispering gallery mode resonator: threshold and phase diffusion," Phys. Rev. A 71, 033804 (2005).
[CrossRef]

A. A. Savchenkov, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, "Low Threshold Optical Oscillations in a Whispering Gallery Mode CaF2 Resonator," Phys. Rev. Lett. 93, 243905 (2004).
[CrossRef]

V. V. Vassiliev, V. L. Velichansky, V. S. Ilchenko, M. L. Gorodetsky, L. Hollberg, and A. V. Yarovitsky, "Narrowline-width diode laser with a high-Q microsphere resonator," Opt. Commun. 158, 305312 (1998).
[CrossRef]

Inoue, T.

K. Hosoya, K. Ohata, M. Funabashi, T. Inoue, and M. Kuzuhara, "V-band HJFET MMIC DROs with low phase noise, high power, and excellent temperature stability," IEEE Trans. Microwave Theory Tech. 51, 2250-2258 (2003).
[CrossRef]

Ivanov, E. N.

J. J. McFerran, E. N. Ivanov, A. Bartels, G. Wilpers, C. W. Oates, S. A. Diddams, and Hollberg, "Low-noise synthesis of microwave signals from an optical source," Electron. Lett. 41, 650-651 (2005).
[CrossRef]

Ji, Y.

Y. Ji, X. S. Yao, and L. Maleki, "Compact optoelectronic oscillator with ultralow phase noise performance," Electron. Lett. 35, 1554-1555 (1999).
[CrossRef]

Kippenberg, T. J.

P. Del Haye, A. Schliesser, O. Arcizet, T. Wilkins, R. Holzwarth, T. J. Kippenberg, "Optical frequency comb generation from a monolithic microresonator," Nature 450, 1214-1217 (2007).
[CrossRef]

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Kerr-Nonlinearity Optical Parametric Oscillation in an Ultrahigh-Q Toroid Microcavity," Phys. Rev. Lett. 93, 083904 (2004).
[CrossRef] [PubMed]

Kuzuhara, M.

K. Hosoya, K. Ohata, M. Funabashi, T. Inoue, and M. Kuzuhara, "V-band HJFET MMIC DROs with low phase noise, high power, and excellent temperature stability," IEEE Trans. Microwave Theory Tech. 51, 2250-2258 (2003).
[CrossRef]

Leeson, D. B.

D. B. Leeson, "A simple model of feed back oscillator noise spectrum," Proc. IEEE 54, 329330 (1966).
[CrossRef]

Maleki, L.

A. B. Matsko, A. A. Savchenkov, N. Yu, and L. Maleki, "Whispering-gallery-mode resonators as frequency references: I. Fundamental limitations," J. Opt. Soc. Am. B 24, 1324-1335 (2007).
[CrossRef]

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, N. Yu, and L. Maleki, "Whispering-gallery-mode resonators as frequency references. II. Stabilization," J. Opt. Soc. Am. B 24, 2988-2997 (2007).
[CrossRef]

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, and L. Maleki, "Optical resonators with ten million finesse," Opt. Express 15, 6768-6773 (2007).
[CrossRef] [PubMed]

N. Yu, E. Salik, and L. Maleki, "Ultralow-noise mode-locked laser with coupled optoelectronic oscillator configuration," Opt. Lett. 30, 1231-1233 (2005).
[CrossRef] [PubMed]

A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, "Optical hyper-parametric oscillations in a whispering gallery mode resonator: threshold and phase diffusion," Phys. Rev. A 71, 033804 (2005).
[CrossRef]

A. A. Savchenkov, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, "Low Threshold Optical Oscillations in a Whispering Gallery Mode CaF2 Resonator," Phys. Rev. Lett. 93, 243905 (2004).
[CrossRef]

Y. Ji, X. S. Yao, and L. Maleki, "Compact optoelectronic oscillator with ultralow phase noise performance," Electron. Lett. 35, 1554-1555 (1999).
[CrossRef]

Masumura, A.

Matsko, A. B.

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, and L. Maleki, "Optical resonators with ten million finesse," Opt. Express 15, 6768-6773 (2007).
[CrossRef] [PubMed]

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, N. Yu, and L. Maleki, "Whispering-gallery-mode resonators as frequency references. II. Stabilization," J. Opt. Soc. Am. B 24, 2988-2997 (2007).
[CrossRef]

A. B. Matsko, A. A. Savchenkov, N. Yu, and L. Maleki, "Whispering-gallery-mode resonators as frequency references: I. Fundamental limitations," J. Opt. Soc. Am. B 24, 1324-1335 (2007).
[CrossRef]

A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, "Optical hyper-parametric oscillations in a whispering gallery mode resonator: threshold and phase diffusion," Phys. Rev. A 71, 033804 (2005).
[CrossRef]

A. A. Savchenkov, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, "Low Threshold Optical Oscillations in a Whispering Gallery Mode CaF2 Resonator," Phys. Rev. Lett. 93, 243905 (2004).
[CrossRef]

McFerran, J. J.

J. J. McFerran, E. N. Ivanov, A. Bartels, G. Wilpers, C. W. Oates, S. A. Diddams, and Hollberg, "Low-noise synthesis of microwave signals from an optical source," Electron. Lett. 41, 650-651 (2005).
[CrossRef]

Mohageg, M.

A. A. Savchenkov, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, "Low Threshold Optical Oscillations in a Whispering Gallery Mode CaF2 Resonator," Phys. Rev. Lett. 93, 243905 (2004).
[CrossRef]

Oates, C. W.

J. J. McFerran, E. N. Ivanov, A. Bartels, G. Wilpers, C. W. Oates, S. A. Diddams, and Hollberg, "Low-noise synthesis of microwave signals from an optical source," Electron. Lett. 41, 650-651 (2005).
[CrossRef]

Ohata, K.

K. Hosoya, K. Ohata, M. Funabashi, T. Inoue, and M. Kuzuhara, "V-band HJFET MMIC DROs with low phase noise, high power, and excellent temperature stability," IEEE Trans. Microwave Theory Tech. 51, 2250-2258 (2003).
[CrossRef]

Pfeiffer, U. R.

B. A. Floyd, S. K. Reynolds, U. R. Pfeiffer, T. Zwick, T. Beukema, and B. Gaucher, "SiGe bipolar transceiver circuits operating at 60 GHz," IEEE J. Solid-State Circuits 40, 156-167 (2005).
[CrossRef]

Reynolds, S. K.

B. A. Floyd, S. K. Reynolds, U. R. Pfeiffer, T. Zwick, T. Beukema, and B. Gaucher, "SiGe bipolar transceiver circuits operating at 60 GHz," IEEE J. Solid-State Circuits 40, 156-167 (2005).
[CrossRef]

Salik, E.

Savchenkov, A. A.

A. B. Matsko, A. A. Savchenkov, N. Yu, and L. Maleki, "Whispering-gallery-mode resonators as frequency references: I. Fundamental limitations," J. Opt. Soc. Am. B 24, 1324-1335 (2007).
[CrossRef]

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, and L. Maleki, "Optical resonators with ten million finesse," Opt. Express 15, 6768-6773 (2007).
[CrossRef] [PubMed]

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, N. Yu, and L. Maleki, "Whispering-gallery-mode resonators as frequency references. II. Stabilization," J. Opt. Soc. Am. B 24, 2988-2997 (2007).
[CrossRef]

A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, "Optical hyper-parametric oscillations in a whispering gallery mode resonator: threshold and phase diffusion," Phys. Rev. A 71, 033804 (2005).
[CrossRef]

A. A. Savchenkov, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, "Low Threshold Optical Oscillations in a Whispering Gallery Mode CaF2 Resonator," Phys. Rev. Lett. 93, 243905 (2004).
[CrossRef]

Schawlow, A. L.

A. L. Schawlow and C. H. Townes, "Infrared and optical masers," Phys. Rev. 112, 1940-1949 (1958).
[CrossRef]

Schliesser, A.

P. Del Haye, A. Schliesser, O. Arcizet, T. Wilkins, R. Holzwarth, T. J. Kippenberg, "Optical frequency comb generation from a monolithic microresonator," Nature 450, 1214-1217 (2007).
[CrossRef]

Spillane, S. M.

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Kerr-Nonlinearity Optical Parametric Oscillation in an Ultrahigh-Q Toroid Microcavity," Phys. Rev. Lett. 93, 083904 (2004).
[CrossRef] [PubMed]

Strekalov, D.

A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, "Optical hyper-parametric oscillations in a whispering gallery mode resonator: threshold and phase diffusion," Phys. Rev. A 71, 033804 (2005).
[CrossRef]

A. A. Savchenkov, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, "Low Threshold Optical Oscillations in a Whispering Gallery Mode CaF2 Resonator," Phys. Rev. Lett. 93, 243905 (2004).
[CrossRef]

Townes, C. H.

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[CrossRef]

Trillo, S.

Vahala, K. J.

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Kerr-Nonlinearity Optical Parametric Oscillation in an Ultrahigh-Q Toroid Microcavity," Phys. Rev. Lett. 93, 083904 (2004).
[CrossRef] [PubMed]

Vassiliev, V. V.

V. V. Vassiliev, V. L. Velichansky, V. S. Ilchenko, M. L. Gorodetsky, L. Hollberg, and A. V. Yarovitsky, "Narrowline-width diode laser with a high-Q microsphere resonator," Opt. Commun. 158, 305312 (1998).
[CrossRef]

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V. V. Vassiliev, V. L. Velichansky, V. S. Ilchenko, M. L. Gorodetsky, L. Hollberg, and A. V. Yarovitsky, "Narrowline-width diode laser with a high-Q microsphere resonator," Opt. Commun. 158, 305312 (1998).
[CrossRef]

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Wilkins, T.

P. Del Haye, A. Schliesser, O. Arcizet, T. Wilkins, R. Holzwarth, T. J. Kippenberg, "Optical frequency comb generation from a monolithic microresonator," Nature 450, 1214-1217 (2007).
[CrossRef]

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J. J. McFerran, E. N. Ivanov, A. Bartels, G. Wilpers, C. W. Oates, S. A. Diddams, and Hollberg, "Low-noise synthesis of microwave signals from an optical source," Electron. Lett. 41, 650-651 (2005).
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Y. Ji, X. S. Yao, and L. Maleki, "Compact optoelectronic oscillator with ultralow phase noise performance," Electron. Lett. 35, 1554-1555 (1999).
[CrossRef]

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V. V. Vassiliev, V. L. Velichansky, V. S. Ilchenko, M. L. Gorodetsky, L. Hollberg, and A. V. Yarovitsky, "Narrowline-width diode laser with a high-Q microsphere resonator," Opt. Commun. 158, 305312 (1998).
[CrossRef]

Yu, N.

Zwick, T.

B. A. Floyd, S. K. Reynolds, U. R. Pfeiffer, T. Zwick, T. Beukema, and B. Gaucher, "SiGe bipolar transceiver circuits operating at 60 GHz," IEEE J. Solid-State Circuits 40, 156-167 (2005).
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Appl. Opt.

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Y. Ji, X. S. Yao, and L. Maleki, "Compact optoelectronic oscillator with ultralow phase noise performance," Electron. Lett. 35, 1554-1555 (1999).
[CrossRef]

J. J. McFerran, E. N. Ivanov, A. Bartels, G. Wilpers, C. W. Oates, S. A. Diddams, and Hollberg, "Low-noise synthesis of microwave signals from an optical source," Electron. Lett. 41, 650-651 (2005).
[CrossRef]

IEEE J. Solid-State Circuits

B. A. Floyd, S. K. Reynolds, U. R. Pfeiffer, T. Zwick, T. Beukema, and B. Gaucher, "SiGe bipolar transceiver circuits operating at 60 GHz," IEEE J. Solid-State Circuits 40, 156-167 (2005).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

E. N. Ivanov and M. E. Tobar, "Low phase-noise microwave oscillators with interferometric signal processing," IEEE Trans. Microwave Theory Tech. 54, 3284-3294 (2006).
[CrossRef]

J. F. Gravel and J. S. Wight, "On the conception and analysis of a 12-GHz push-push phase-locked DRO," IEEE Trans. Microwave Theory Tech. 54, 153-159 (2006).
[CrossRef]

K. Hosoya, K. Ohata, M. Funabashi, T. Inoue, and M. Kuzuhara, "V-band HJFET MMIC DROs with low phase noise, high power, and excellent temperature stability," IEEE Trans. Microwave Theory Tech. 51, 2250-2258 (2003).
[CrossRef]

J. Opt. Soc. Am. B

Nature

P. Del Haye, A. Schliesser, O. Arcizet, T. Wilkins, R. Holzwarth, T. J. Kippenberg, "Optical frequency comb generation from a monolithic microresonator," Nature 450, 1214-1217 (2007).
[CrossRef]

Opt. Commun.

V. V. Vassiliev, V. L. Velichansky, V. S. Ilchenko, M. L. Gorodetsky, L. Hollberg, and A. V. Yarovitsky, "Narrowline-width diode laser with a high-Q microsphere resonator," Opt. Commun. 158, 305312 (1998).
[CrossRef]

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Phys. Rev.

A. L. Schawlow and C. H. Townes, "Infrared and optical masers," Phys. Rev. 112, 1940-1949 (1958).
[CrossRef]

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A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, "Optical hyper-parametric oscillations in a whispering gallery mode resonator: threshold and phase diffusion," Phys. Rev. A 71, 033804 (2005).
[CrossRef]

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A. A. Savchenkov, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, "Low Threshold Optical Oscillations in a Whispering Gallery Mode CaF2 Resonator," Phys. Rev. Lett. 93, 243905 (2004).
[CrossRef]

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Kerr-Nonlinearity Optical Parametric Oscillation in an Ultrahigh-Q Toroid Microcavity," Phys. Rev. Lett. 93, 083904 (2004).
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[CrossRef]

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A. B. Matsko, A. A. Savchenkov, D. Strekalov, and L Maleki, "High frequency photonic microwave oscillators based on WGM resonators," 2005 Digest of the LEOS Summer Topical Meetings, 113-114 (2005).
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A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, and L. Maleki, "Nonlinear optics with WGM crystalline resonators: advances and puzzles," 2004 Digest of the LEOS Summer Topical Meeting "WGM Microcavities" (2004).

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[CrossRef]

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Figures (8)

Fig. 1.
Fig. 1.

A model of a WGM based hyperparametric oscillator. The ring resonator contains a lossless Kerr nonlinear medium and a linear absorber. The nonlinear medium is characterized with nonlinearity coefficient n 2, and the absorber is characterized with absorption coefficient α. Pump light is sent into the ring resonator through a coupling mirror. We assume that the light field inside the resonator includes carrier A and idler and signal sidebands B + and B - respectively(E=Aexp[-i(ωt-kz)]+B +exp[-i(ω + t-k + z)]+B -exp[-i(ω - t-k - z)]), k=ωn/c, k ±=ω ± n/c; and that only the optical carrier is pumped from outside Ein =Ain exp(-iωt).

Fig. 2.
Fig. 2.

Experimental setup. Light from a YAG laser is split at a 50/50 splitter Sp1. One part is sent into a CaF2 WGM resonator (WGMR) through coupler Cp1. The other part is sent to a fiber delay line. The light is retrieved out of the resonator using the coupler Cp2, is combined with the light propagated through the delay line using splitter Sp2, and sent to the fast photodiode (PD). About 90% of light from the resonator goes to the photodiode. Microwave signal at the output of the photodiode is preamplified with an amplifier (g) and forwarded to a microwave spectrum analyzer (SA).

Fig. 3.
Fig. 3.

Typical phase noise of the oscillator. The loaded quality factor of the resonator is Q≃109, so that half width at the half maximum of the resonance is γ≃115 kHz. The length of the delay line is ~115 m. This is shorter length compared with the length of the delay line that corresponds to Q=109 (~300 m), however the delay line gave us the best overall oscillator performance. The total optical power on the detector PD is 6 mW. The power of the microwave signal leaving the detector is -46.1 dBm. The output microwave amplifier has an estimated 7 dB noise figure and 43.1 dB of gain. The power of the output microwave signal at the spectrum analyzer is -3 dBm.

Fig. 4.
Fig. 4.

Phase noise of the oscillators with different lengths of the delay line. The quality factor of the resonator is Q≃109. The optical power at the detector is 6 mW. The power of the output microwave signal at the spectrum analyzer is -12 dBm. The output microwave amplifier has an estimated 15 dB noise figure and 35 dB of gain. The noise decreases when the group delay of the resonator approaches the delay of the fiber link.

Fig. 5.
Fig. 5.

Phase noise of the microwave signal as a function of the Q. The Q was changed by controlling the loaded coupling to the resonator. The higher Q value was achieved with a smaller loading. It results in a smaller corner frequency, but also in a larger noise floor. Noise floor rises because the higher Q corresponds to the bigger insertion loss in the resonator. On the other hand, the higher Q results in more efficient nonlinear process and increase of the generated sideband that reduces the phase diffusion of the oscillator.

Fig. 6.
Fig. 6.

Dispersion of CaF2 resonator shown as the dependence of difference between frequencies of two adjacent FSRs vs. the wavelength. The resonator has an average FSR≃9.44 GHz. Solid lines correspond to the dependencies derived from the corresponding Sellmeier’s equation. Blue line stands for the bulk material dispersion, red line - for the resonator dispersion (geometrical and material). The red line shifts to the right for smaller resonators.

Fig. 7.
Fig. 7.

Setup for measurement of the dispersion of CaF2 resonator.

Fig. 8.
Fig. 8.

Preamplified microwave signal measured using an RF spectrum analyzer.

Equations (42)

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G = L ω 0 n 2 h ¯ ω 𝒱 n A 2 ,
A Gout = A Gin e iG ,
B Gout + = [ B Gin + + i G ( B Gin + + B Gin * e 2 i ϕ A ) ] e iG ,
B Gout * = [ B Gin * i G ( B Gin + e 2 i ϕ A + B Gin * ) ] e iG ,
2 ω = ω + + ω ,
A Gin = A Gout e i ω L n c e α 1 T c + T c A in ,
B Gin ± = B Gout ± e ± Ln c e α 1 T c ,
A Gin e i ϕ A { 1 e i ( G + ω L n c ) e α 1 T c } = T c A in ;
B Gin + [ e + L n c + α ( 1 T c ) 1 2 ( 1 + iG ) e iG ] = i G e i ( 2 ϕ A + G ) B Gin * ,
B Gin * [ e i ω L n c + α ( 1 T c ) 1 2 ( 1 i G ) e i G ] = i G e i ( 2 ϕ A + G ) B Gin + ,
[ e i ω + ω 2 Ln c + α 1 T c ] 2 = e i ω + ω 2 Ln c + α 1 T c [ e i ( ω L n c + G ) ( 1 i G ) + c . c . 2 ] .
exp [ i ω + ω 2 L n c ] = 1 ,
[ e α 1 T c ] 2 = e α 1 T c [ e i ( ω L n c + G ) ( 1 i G ) + c . c . 2 ] ,
A out = A Gin e i ( G + ω L n c ) e α T c + A in 1 T c :
A out = 1 T c exp [ i ( G + ω L n c ) ] exp [ α ] 1 exp [ i ( G + ω L n c ) ] exp [ α ] 1 T c A in
i ( e i ω L n c 1 ) 2 ( α + T c 2 ) ,
G α + T c 2 .
ω + ω = 2 c Rn = 2 Ω FSR .
ω + ω = ω ω = Ω FSR .
e i ω L n c = e i ω ± L n c .
B Gin + = B Gin ,
e i ( 2 ϕ A ϕ ϕ + ) G 2 ( α + T c 2 ) 2 + i ( α + T c 2 ) G 1 ,
A out α T c 2 i ( G 2 ( α + T c 2 ) 2 G ) α + T c 2 i ( G 2 ( α + T c 2 ) 2 G ) A in ,
B + A out * + A out B * 2 0 , if G T c 2 + α .
E out = A + 2 i B sin [ ω M t + ϕ ( t ) ] ,
E PD = E out e α c 2 r + E LO e LO 1 r 2 ,
P PD = P A e 2 α c 2 r 2 + P LO ( 1 r 2 ) ,
j = 4 𝓡 E LO B e α c 2 1 r 2 sin [ ω M t + ϕ ( t ) ] ,
P mw = 8 ρ 𝓡 2 P LO P B e 2 α c 2 ( 1 r 2 ) ,
S ϕ [ 1 + η P mw 2 ρ 𝓡 2 P PD 2 P PD P B γ 2 f 2 ] 2 h ν 0 η P PD [ 1 + 4 η e 2 α c 2 γ 2 f 2 ] 2 h ν 0 η P LO ( 1 r 2 ) ,
D ϕ ( 2 π γ ) 2 4 h ν 0 P B ,
S ( f ) = 4 D ϕ ( 2 π f ) 2 .
S s h o t = 2 q R P ¯ D ρ = 7.7 × 10 20 W / Hz ( 161 dBm / Hz ) ,
S thermal = k T = 4 × 10 21 W / Hz ( 174 dBm / Hz ) .
n ( ω l ) c ω l l R [ 1 + 1.86 l 2 3 ] ,
ω l c n ( ω l ) ω l 0 c n ( ω l 0 ) + β ( ω l 0 ) [ ω l ω l 0 ] + 1 2 β ( ω l 0 ) [ ω l ω l 0 ] 2 + 1 6 β ( ω l 0 ) [ ω l ω l 0 ] 3 ,
β ( ω l 0 ) R [ β ( ω l 0 ) ] 2 l 5 3 ,
[ ω l 0 + μ + 1 ω l 0 + μ ] = [ ω l 0 + 1 ω l 0 ] + μ 2 2 [ β ( ω l 0 ) ] 2 β ( ω l 0 ) β ( ω l 0 ) 2 R 3 [ β ( ω l 0 ) ] 5 ,
Δ ω comb = β ( ω l 0 ) 𝓕 1 2 { 2 [ β ( ω l 0 ) ] 2 β ( ω l 0 ) β ( ω l 0 ) } 1 2 ,
E = e i ω 0 t k = 1 N E k e i ( k 1 ) ω M t ,
P mw k = 1 N E k * E k + 1 2 .
P mw P 0 2 ,

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