Abstract

A quality factor exceeding 5×109 is obtained in whispering-gallery mode (WGM) resonators fabricated of crystalline quartz. We observe significant electrical tunability of WGMs in x-cut resonators and demonstrate an electro-optic modulator with a submegahertz passband at 12GHz. We discuss other photonics applications of the crystal quartz WGM resonators in narrowband agile tunable filters, compact narrow linewidth lasers, and microwave and millimeter wave oscillators.

© 2008 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]

2007

2006

J. K. Poon, L. Zhu, G. A. DeRose, and A. Yariv, Opt. Lett. 31, 456 (2006).
[CrossRef] [PubMed]

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, Nature 443, 671 (2006).
[CrossRef] [PubMed]

2005

S. Gee, F. Quinlan, S. Ozharar, and P. J. Delfyett, IEEE Photon. Technol. Lett. 17, 199 (2005).
[CrossRef]

V. S. Ilchenko and A. B. Matsko, IEEE J. Sel. Top. Quantum Electron. 12, 15 (2005).

2004

V. N. Astratov, J. P. Franchak, and S. P. Ashili, Appl. Phys. Lett. 85, 5508 (2004).
[CrossRef]

2003

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, Electron. Lett. 39, 389 (2003).
[CrossRef]

K. J. Vahala, Nature (London) 424, 839 (2003).
[CrossRef]

V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, J. Opt. Soc. Am. B 20, 333 (2003).
[CrossRef]

2001

D. A. Cohen, M. Hossein-Zadeh, and A. F. J. Levi, Solid-State Electron. 45, 1577 (2001).
[CrossRef]

1997

1993

1981

G. R. Meredith, Phys. Rev. B 24, 5522 (1981).
[CrossRef]

1977

R. J. Briggs and A. K. Ramdas, Phys. Rev. B 16, 3815 (1977).
[CrossRef]

1968

H. Pursey and R. J. Newman, J. Phys. D 1, 707 (1968).
[CrossRef]

1967

1966

1965

P. D. Maker and R. W. Terhune, Phys. Rev. 137, A801 (1965).
[CrossRef]

1963

1894

F. Pockels, Abhandl. Ges. Wiss. Gottingen 39, 1 (1894).

Aoki, T.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, Nature 443, 671 (2006).
[CrossRef] [PubMed]

Arcizet, O.

P. Del Haye, A. Schliesser, O. Arcizet, T. Wilkins, R. Holzwarth, and T. J. Kippenberg, Nature 450, 1214 (2007).
[CrossRef]

Ashili, S. P.

V. N. Astratov, J. P. Franchak, and S. P. Ashili, Appl. Phys. Lett. 85, 5508 (2004).
[CrossRef]

Astratov, V. N.

V. N. Astratov, J. P. Franchak, and S. P. Ashili, Appl. Phys. Lett. 85, 5508 (2004).
[CrossRef]

Bowen, W. P.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, Nature 443, 671 (2006).
[CrossRef] [PubMed]

Briggs, R. J.

R. J. Briggs and A. K. Ramdas, Phys. Rev. B 16, 3815 (1977).
[CrossRef]

Cady, W. G.

W. G. Cady, Piezoelectricity (McGraw-Hill, 1946), p. 721.

Cohen, D. A.

D. A. Cohen, M. Hossein-Zadeh, and A. F. J. Levi, Solid-State Electron. 45, 1577 (2001).
[CrossRef]

Dayan, B.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, Nature 443, 671 (2006).
[CrossRef] [PubMed]

Del Haye, P.

P. Del Haye, A. Schliesser, O. Arcizet, T. Wilkins, R. Holzwarth, and T. J. Kippenberg, Nature 450, 1214 (2007).
[CrossRef]

Delfyett, P. J.

S. Gee, F. Quinlan, S. Ozharar, and P. J. Delfyett, IEEE Photon. Technol. Lett. 17, 199 (2005).
[CrossRef]

DeRose, G. A.

Eden, D. D.

Franchak, J. P.

V. N. Astratov, J. P. Franchak, and S. P. Ashili, Appl. Phys. Lett. 85, 5508 (2004).
[CrossRef]

Gee, S.

S. Gee, F. Quinlan, S. Ozharar, and P. J. Delfyett, IEEE Photon. Technol. Lett. 17, 199 (2005).
[CrossRef]

Harvey, G. T.

Holzwarth, R.

P. Del Haye, A. Schliesser, O. Arcizet, T. Wilkins, R. Holzwarth, and T. J. Kippenberg, Nature 450, 1214 (2007).
[CrossRef]

Hossein-Zadeh, M.

D. A. Cohen, M. Hossein-Zadeh, and A. F. J. Levi, Solid-State Electron. 45, 1577 (2001).
[CrossRef]

Ilchenko, V. S.

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, and L. Maleki, Opt. Express 15, 6768 (2007).
[CrossRef] [PubMed]

V. S. Ilchenko and A. B. Matsko, IEEE J. Sel. Top. Quantum Electron. 12, 15 (2005).

V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, J. Opt. Soc. Am. B 20, 333 (2003).
[CrossRef]

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, Electron. Lett. 39, 389 (2003).
[CrossRef]

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, arXiv:0804.0263v1 [physics.optics].

Kaminow, I. P.

Kimble, H. J.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, Nature 443, 671 (2006).
[CrossRef] [PubMed]

Kippenberg, T. J.

P. Del Haye, A. Schliesser, O. Arcizet, T. Wilkins, R. Holzwarth, and T. J. Kippenberg, Nature 450, 1214 (2007).
[CrossRef]

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, Nature 443, 671 (2006).
[CrossRef] [PubMed]

Levi, A. F. J.

D. A. Cohen, M. Hossein-Zadeh, and A. F. J. Levi, Solid-State Electron. 45, 1577 (2001).
[CrossRef]

Maker, P. D.

P. D. Maker and R. W. Terhune, Phys. Rev. 137, A801 (1965).
[CrossRef]

Maleki, L.

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, and L. Maleki, Opt. Express 15, 6768 (2007).
[CrossRef] [PubMed]

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, Electron. Lett. 39, 389 (2003).
[CrossRef]

V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, J. Opt. Soc. Am. B 20, 333 (2003).
[CrossRef]

X. S. Yao and L. Maleki, Opt. Lett. 22, 1867 (1997).
[CrossRef]

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, arXiv:0804.0263v1 [physics.optics].

Matsko, A. B.

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, and L. Maleki, Opt. Express 15, 6768 (2007).
[CrossRef] [PubMed]

V. S. Ilchenko and A. B. Matsko, IEEE J. Sel. Top. Quantum Electron. 12, 15 (2005).

V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, J. Opt. Soc. Am. B 20, 333 (2003).
[CrossRef]

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, Electron. Lett. 39, 389 (2003).
[CrossRef]

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, arXiv:0804.0263v1 [physics.optics].

Meredith, G. R.

G. R. Meredith, Phys. Rev. B 24, 5522 (1981).
[CrossRef]

Mollenauer, L. F.

Mookherjea, S.

Newman, R. J.

H. Pursey and R. J. Newman, J. Phys. D 1, 707 (1968).
[CrossRef]

Oh, A.

Ozharar, S.

S. Gee, F. Quinlan, S. Ozharar, and P. J. Delfyett, IEEE Photon. Technol. Lett. 17, 199 (2005).
[CrossRef]

Parkins, A. S.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, Nature 443, 671 (2006).
[CrossRef] [PubMed]

Pockels, F.

F. Pockels, Abhandl. Ges. Wiss. Gottingen 39, 1 (1894).

Poon, J. K.

Porto, S. P. S.

J. F. Scott and S. P. S. Porto, Phys. Rev. 161, 903 (1967).
[CrossRef]

Pursey, H.

H. Pursey and R. J. Newman, J. Phys. D 1, 707 (1968).
[CrossRef]

Quinlan, F.

S. Gee, F. Quinlan, S. Ozharar, and P. J. Delfyett, IEEE Photon. Technol. Lett. 17, 199 (2005).
[CrossRef]

Ramdas, A. K.

R. J. Briggs and A. K. Ramdas, Phys. Rev. B 16, 3815 (1977).
[CrossRef]

Rosner, R. D.

Savchenkov, A. A.

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, and L. Maleki, Opt. Express 15, 6768 (2007).
[CrossRef] [PubMed]

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, Electron. Lett. 39, 389 (2003).
[CrossRef]

V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, J. Opt. Soc. Am. B 20, 333 (2003).
[CrossRef]

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, arXiv:0804.0263v1 [physics.optics].

Schliesser, A.

P. Del Haye, A. Schliesser, O. Arcizet, T. Wilkins, R. Holzwarth, and T. J. Kippenberg, Nature 450, 1214 (2007).
[CrossRef]

Scott, J. F.

J. F. Scott and S. P. S. Porto, Phys. Rev. 161, 903 (1967).
[CrossRef]

Seidel, D.

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, arXiv:0804.0263v1 [physics.optics].

Solomatine, I.

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, arXiv:0804.0263v1 [physics.optics].

Tannenwald, P. E.

P. E. Tannenwald and J. B. Thaxter, Science 154, 1319 (1966).
[CrossRef] [PubMed]

Terhune, R. W.

P. D. Maker and R. W. Terhune, Phys. Rev. 137, A801 (1965).
[CrossRef]

Thaxter, J. B.

P. E. Tannenwald and J. B. Thaxter, Science 154, 1319 (1966).
[CrossRef] [PubMed]

Thiess, G. H.

Turner, E. H.

Vahala, K. J.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, Nature 443, 671 (2006).
[CrossRef] [PubMed]

K. J. Vahala, Nature (London) 424, 839 (2003).
[CrossRef]

Wilcut, E.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, Nature 443, 671 (2006).
[CrossRef] [PubMed]

Wilkins, T.

P. Del Haye, A. Schliesser, O. Arcizet, T. Wilkins, R. Holzwarth, and T. J. Kippenberg, Nature 450, 1214 (2007).
[CrossRef]

Yao, X. S.

Yariv, A.

Zhu, L.

Abhandl. Ges. Wiss. Gottingen

F. Pockels, Abhandl. Ges. Wiss. Gottingen 39, 1 (1894).

Appl. Opt.

Appl. Phys. Lett.

V. N. Astratov, J. P. Franchak, and S. P. Ashili, Appl. Phys. Lett. 85, 5508 (2004).
[CrossRef]

Electron. Lett.

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, Electron. Lett. 39, 389 (2003).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

V. S. Ilchenko and A. B. Matsko, IEEE J. Sel. Top. Quantum Electron. 12, 15 (2005).

IEEE Photon. Technol. Lett.

S. Gee, F. Quinlan, S. Ozharar, and P. J. Delfyett, IEEE Photon. Technol. Lett. 17, 199 (2005).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. D

H. Pursey and R. J. Newman, J. Phys. D 1, 707 (1968).
[CrossRef]

Nature

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, Nature 443, 671 (2006).
[CrossRef] [PubMed]

P. Del Haye, A. Schliesser, O. Arcizet, T. Wilkins, R. Holzwarth, and T. J. Kippenberg, Nature 450, 1214 (2007).
[CrossRef]

Nature (London)

K. J. Vahala, Nature (London) 424, 839 (2003).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev.

J. F. Scott and S. P. S. Porto, Phys. Rev. 161, 903 (1967).
[CrossRef]

P. D. Maker and R. W. Terhune, Phys. Rev. 137, A801 (1965).
[CrossRef]

Phys. Rev. B

G. R. Meredith, Phys. Rev. B 24, 5522 (1981).
[CrossRef]

R. J. Briggs and A. K. Ramdas, Phys. Rev. B 16, 3815 (1977).
[CrossRef]

Science

P. E. Tannenwald and J. B. Thaxter, Science 154, 1319 (1966).
[CrossRef] [PubMed]

Solid-State Electron.

D. A. Cohen, M. Hossein-Zadeh, and A. F. J. Levi, Solid-State Electron. 45, 1577 (2001).
[CrossRef]

Other

W. G. Cady, Piezoelectricity (McGraw-Hill, 1946), p. 721.

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, arXiv:0804.0263v1 [physics.optics].

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Figures (4)

Fig. 1
Fig. 1

(a) Schematic of the setup for measuring the spectrum of the WGM resonator. (b) Schematic of the electro-optical modulator made with the x-cut quartz WGM resonator.

Fig. 2
Fig. 2

A WGM resonance belonging to a z-cut quartz WGM resonator. The solid curve is a Lorentzian fit to the experimental data. The optical power sent to the mode is small enough ( P in = 3 μ W ) to avoid nonlinear processes. The linewidth corresponds to Q = 5 × 10 9 .

Fig. 3
Fig. 3

RF return for the modulator based on the x-cut quartz resonator versus RF modulation frequency (the ratio of the powers of the demodulated signal and the input signal). The input microwave as well as the optical power at the high-speed photodetector is equal to 1 mW . The RF return frequency bandwidth is 0.8 MHz at 3 dB . The loaded quality factor of the optically pumped WGM is Q = 2 × 10 8 (optical bandwidth is 1 MHz ). The optical mode contrast is 50%. The laser is manually tuned to the mode. The maximum RF return (the ratio of the output and input RF powers, see Fig. 1) corresponds to S 21 2 × 10 5 .

Fig. 4
Fig. 4

Stimulated Raman scattering detected in the WGM resonators fabricated from x-cut (radius R = 2.7 mm , thickness h = 0.22 mm , circumference shape given mode volume V 6 × 10 5 cm 3 , quality factor Q 2 × 10 8 , optical power entering the mode P in = 40 mW ) and z-cut ( R = 3.25 mm , h = 0.1 mm , V 7 × 10 5 cm 3 , Q 5 × 10 9 , P in = 8 mW ) quartz. The hump in the vicinity of the laser line results from the spontaneous emission noise of our optical amplifier. Raman detuning is equal to 13.95 THz in both cases. The threshold for the Raman scattering exceeds 10 mW in the x-cut resonator, and 1 mW in the z-cut resonator.

Equations (2)

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S 21 = ξ ρ pd R 2 P in 2 P sat ,
P sat = n RF 2 ω RF V RF 8 π Q 2 Q RF r 11 2 n 4 η 2 ,

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