Abstract

The temperature dependence of the processes which fundamentally limit optical quality factor of ideal crystalline whispering gallery mode resonators is investigated. The example of CaF2 is used to show that spontaneous Raman scattering is the main limitation of the quality factor at low temperatures. Stimulated Raman scattering is also shown to be important at any temperature. We experimentally demonstrate nonlinear absorption due to stimulated Raman scattering in a real cavity at room temperature and theoretically derive Raman gain of CaF2. We conclude that optical storage times in excess of one second could be achieved in millimeter sized cavities.

© 2007 Optical Society of America

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References

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  1. A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, "Kilohertz optical resonances in dielectric crystal cavities," Phys. Rev. A 70, 051804 (2004).
    [CrossRef]
  2. 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]
  3. I. S. Grudinin, A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, "Ultra high Q crystalline microcavities," Opt. Commun. 265, 33 (2006).
    [CrossRef]
  4. M. E. Lines, "Scattering losses in optic fiber materials. I. A new parametrization," J. Appl. Phys. 55, 4052 (1984); "II. Numerical estimates," 55, 4058 (1984).
    [CrossRef]
  5. S. Logunov and S. Kuchinsky, "Experimental and theoretical study of bulk light scattering in CaF2 monocrystals," J. Appl. Phys. 98, 053501 (2005).
    [CrossRef]
  6. I. L. Fabelinskii, Molecular scattering of light (Plenum press, New York, 1968).
  7. D. C. Wallace, Thermodynamics of crystals (Dover, New York, 1998).
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    [CrossRef]
  9. M. L. Gorodetsky, A. D. Pryamikov, V. S. Ilchenko, "Rayleigh scattering in high-Q microspheres," J. Opt. Soc. Am. B 17, 1051-1057 (2000).
    [CrossRef]
  10. M. Daimon and A. Masumara, "High-accuracy measurements of the refractive index and its temperature coefficient of calcium fluoride in a wide wavelength range from 138 to 2326 nm," Appl. Opt. 41, 5275-5281 (2002).
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    [CrossRef]
  13. A. Laufer, J. Pirog, and J. McNesby, "Effect of temperature on the vacuum ultraviolet transmittance of Lithium Fluoride, Calcium Fluoride, Barium Fluoride, and Sapphire," J. Opt. Soc. Am. 55, 64-66 (1965).
    [CrossRef]
  14. L. L. Boyer, J. A. Harrington, M. Hass, and H. B. Rosenstock, "Multiphonon absorption in ionic crystals," Phys. Rev. B 11, 1665-1680 (1975).
    [CrossRef]
  15. S. Venugopalan and A. K. Ramdas, "Effect of Uniaxial Stress on the Raman Spectra of Cubic Crystals: CaF2, BaF2, and Bi12GeO20," Phys. Rev. B 8, 717-734 (1973).
    [CrossRef]
  16. R. W. Boyd, Nonlinear Optics (Academic Press, New York, 1992).
  17. A. B. Matsko, A. A. Savchenkov, R. J. Letargad, V. S. Ilchenko and L. Maleki, "On cavity modification of stimulated Raman scattering," J. Opt. B:Quantum Semiclassical Opt.  5,272-278 (2003).
    [CrossRef]
  18. P. G. Klemens, "Anharmonic Decay of Optical Phonons," Phys. Rev. 148, 845-848 (1966).
    [CrossRef]
  19. A. B. Matsko, A. A. Savchenkov, and L. Maleki, "Ring-down spectroscopy for studying properties of CW Raman lasers," Opt. Commun. 260, 662-665 (2006).
    [CrossRef]

2006 (3)

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]

I. S. Grudinin, A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, "Ultra high Q crystalline microcavities," Opt. Commun. 265, 33 (2006).
[CrossRef]

A. B. Matsko, A. A. Savchenkov, and L. Maleki, "Ring-down spectroscopy for studying properties of CW Raman lasers," Opt. Commun. 260, 662-665 (2006).
[CrossRef]

2005 (1)

S. Logunov and S. Kuchinsky, "Experimental and theoretical study of bulk light scattering in CaF2 monocrystals," J. Appl. Phys. 98, 053501 (2005).
[CrossRef]

2004 (1)

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, "Kilohertz optical resonances in dielectric crystal cavities," Phys. Rev. A 70, 051804 (2004).
[CrossRef]

2003 (1)

A. B. Matsko, A. A. Savchenkov, R. J. Letargad, V. S. Ilchenko and L. Maleki, "On cavity modification of stimulated Raman scattering," J. Opt. B:Quantum Semiclassical Opt.  5,272-278 (2003).
[CrossRef]

2002 (1)

2001 (1)

R. Loudon, "The Raman effect in crystals," Adv. Phys. 50, 813-864 (2001).
[CrossRef]

2000 (1)

1986 (1)

M. Lines, "Ultralow-loss glasses," Annu. Rev. Mater. Sci. 16,113-135 (1986).
[CrossRef]

1975 (1)

L. L. Boyer, J. A. Harrington, M. Hass, and H. B. Rosenstock, "Multiphonon absorption in ionic crystals," Phys. Rev. B 11, 1665-1680 (1975).
[CrossRef]

1973 (1)

S. Venugopalan and A. K. Ramdas, "Effect of Uniaxial Stress on the Raman Spectra of Cubic Crystals: CaF2, BaF2, and Bi12GeO20," Phys. Rev. B 8, 717-734 (1973).
[CrossRef]

1966 (1)

P. G. Klemens, "Anharmonic Decay of Optical Phonons," Phys. Rev. 148, 845-848 (1966).
[CrossRef]

1965 (1)

Boyer, L. L.

L. L. Boyer, J. A. Harrington, M. Hass, and H. B. Rosenstock, "Multiphonon absorption in ionic crystals," Phys. Rev. B 11, 1665-1680 (1975).
[CrossRef]

Daimon, M.

Gorodetsky, M. L.

Grudinin, I. S.

I. S. Grudinin, A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, "Ultra high Q crystalline microcavities," Opt. Commun. 265, 33 (2006).
[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]

Harrington, J. A.

L. L. Boyer, J. A. Harrington, M. Hass, and H. B. Rosenstock, "Multiphonon absorption in ionic crystals," Phys. Rev. B 11, 1665-1680 (1975).
[CrossRef]

Hass, M.

L. L. Boyer, J. A. Harrington, M. Hass, and H. B. Rosenstock, "Multiphonon absorption in ionic crystals," Phys. Rev. B 11, 1665-1680 (1975).
[CrossRef]

Ilchenko, V. S.

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]

I. S. Grudinin, A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, "Ultra high Q crystalline microcavities," Opt. Commun. 265, 33 (2006).
[CrossRef]

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, "Kilohertz optical resonances in dielectric crystal cavities," Phys. Rev. A 70, 051804 (2004).
[CrossRef]

A. B. Matsko, A. A. Savchenkov, R. J. Letargad, V. S. Ilchenko and L. Maleki, "On cavity modification of stimulated Raman scattering," J. Opt. B:Quantum Semiclassical Opt.  5,272-278 (2003).
[CrossRef]

M. L. Gorodetsky, A. D. Pryamikov, V. S. Ilchenko, "Rayleigh scattering in high-Q microspheres," J. Opt. Soc. Am. B 17, 1051-1057 (2000).
[CrossRef]

Klemens, P. G.

P. G. Klemens, "Anharmonic Decay of Optical Phonons," Phys. Rev. 148, 845-848 (1966).
[CrossRef]

Kuchinsky, S.

S. Logunov and S. Kuchinsky, "Experimental and theoretical study of bulk light scattering in CaF2 monocrystals," J. Appl. Phys. 98, 053501 (2005).
[CrossRef]

Laufer, A.

Letargad, R. J.

A. B. Matsko, A. A. Savchenkov, R. J. Letargad, V. S. Ilchenko and L. Maleki, "On cavity modification of stimulated Raman scattering," J. Opt. B:Quantum Semiclassical Opt.  5,272-278 (2003).
[CrossRef]

Lines, M.

M. Lines, "Ultralow-loss glasses," Annu. Rev. Mater. Sci. 16,113-135 (1986).
[CrossRef]

Logunov, S.

S. Logunov and S. Kuchinsky, "Experimental and theoretical study of bulk light scattering in CaF2 monocrystals," J. Appl. Phys. 98, 053501 (2005).
[CrossRef]

Loudon, R.

R. Loudon, "The Raman effect in crystals," Adv. Phys. 50, 813-864 (2001).
[CrossRef]

Maleki, L.

A. B. Matsko, A. A. Savchenkov, and L. Maleki, "Ring-down spectroscopy for studying properties of CW Raman lasers," Opt. Commun. 260, 662-665 (2006).
[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]

I. S. Grudinin, A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, "Ultra high Q crystalline microcavities," Opt. Commun. 265, 33 (2006).
[CrossRef]

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, "Kilohertz optical resonances in dielectric crystal cavities," Phys. Rev. A 70, 051804 (2004).
[CrossRef]

A. B. Matsko, A. A. Savchenkov, R. J. Letargad, V. S. Ilchenko and L. Maleki, "On cavity modification of stimulated Raman scattering," J. Opt. B:Quantum Semiclassical Opt.  5,272-278 (2003).
[CrossRef]

Masumara, A.

Matsko, A. B.

I. S. Grudinin, A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, "Ultra high Q crystalline microcavities," Opt. Commun. 265, 33 (2006).
[CrossRef]

A. B. Matsko, A. A. Savchenkov, and L. Maleki, "Ring-down spectroscopy for studying properties of CW Raman lasers," Opt. Commun. 260, 662-665 (2006).
[CrossRef]

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, "Kilohertz optical resonances in dielectric crystal cavities," Phys. Rev. A 70, 051804 (2004).
[CrossRef]

A. B. Matsko, A. A. Savchenkov, R. J. Letargad, V. S. Ilchenko and L. Maleki, "On cavity modification of stimulated Raman scattering," J. Opt. B:Quantum Semiclassical Opt.  5,272-278 (2003).
[CrossRef]

McNesby, J.

Pirog, J.

Pryamikov, A. D.

Ramdas, A. K.

S. Venugopalan and A. K. Ramdas, "Effect of Uniaxial Stress on the Raman Spectra of Cubic Crystals: CaF2, BaF2, and Bi12GeO20," Phys. Rev. B 8, 717-734 (1973).
[CrossRef]

Rosenstock, H. B.

L. L. Boyer, J. A. Harrington, M. Hass, and H. B. Rosenstock, "Multiphonon absorption in ionic crystals," Phys. Rev. B 11, 1665-1680 (1975).
[CrossRef]

Savchenkov, A. A.

I. S. Grudinin, A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, "Ultra high Q crystalline microcavities," Opt. Commun. 265, 33 (2006).
[CrossRef]

A. B. Matsko, A. A. Savchenkov, and L. Maleki, "Ring-down spectroscopy for studying properties of CW Raman lasers," Opt. Commun. 260, 662-665 (2006).
[CrossRef]

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, "Kilohertz optical resonances in dielectric crystal cavities," Phys. Rev. A 70, 051804 (2004).
[CrossRef]

A. B. Matsko, A. A. Savchenkov, R. J. Letargad, V. S. Ilchenko and L. Maleki, "On cavity modification of stimulated Raman scattering," J. Opt. B:Quantum Semiclassical Opt.  5,272-278 (2003).
[CrossRef]

Strekalov, D.

I. S. Grudinin, A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, "Ultra high Q crystalline microcavities," Opt. Commun. 265, 33 (2006).
[CrossRef]

Venugopalan, S.

S. Venugopalan and A. K. Ramdas, "Effect of Uniaxial Stress on the Raman Spectra of Cubic Crystals: CaF2, BaF2, and Bi12GeO20," Phys. Rev. B 8, 717-734 (1973).
[CrossRef]

Adv. Phys. (1)

R. Loudon, "The Raman effect in crystals," Adv. Phys. 50, 813-864 (2001).
[CrossRef]

Annu. Rev. Mater. Sci. (1)

M. Lines, "Ultralow-loss glasses," Annu. Rev. Mater. Sci. 16,113-135 (1986).
[CrossRef]

Appl. Opt. (1)

J. Appl. Phys. (1)

S. Logunov and S. Kuchinsky, "Experimental and theoretical study of bulk light scattering in CaF2 monocrystals," J. Appl. Phys. 98, 053501 (2005).
[CrossRef]

J. Opt. B:Quantum (1)

A. B. Matsko, A. A. Savchenkov, R. J. Letargad, V. S. Ilchenko and L. Maleki, "On cavity modification of stimulated Raman scattering," J. Opt. B:Quantum Semiclassical Opt.  5,272-278 (2003).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Opt. Commun. (2)

A. B. Matsko, A. A. Savchenkov, and L. Maleki, "Ring-down spectroscopy for studying properties of CW Raman lasers," Opt. Commun. 260, 662-665 (2006).
[CrossRef]

I. S. Grudinin, A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, "Ultra high Q crystalline microcavities," Opt. Commun. 265, 33 (2006).
[CrossRef]

Phys. Rev. (1)

P. G. Klemens, "Anharmonic Decay of Optical Phonons," Phys. Rev. 148, 845-848 (1966).
[CrossRef]

Phys. Rev. A (2)

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, "Kilohertz optical resonances in dielectric crystal cavities," Phys. Rev. A 70, 051804 (2004).
[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. B (2)

L. L. Boyer, J. A. Harrington, M. Hass, and H. B. Rosenstock, "Multiphonon absorption in ionic crystals," Phys. Rev. B 11, 1665-1680 (1975).
[CrossRef]

S. Venugopalan and A. K. Ramdas, "Effect of Uniaxial Stress on the Raman Spectra of Cubic Crystals: CaF2, BaF2, and Bi12GeO20," Phys. Rev. B 8, 717-734 (1973).
[CrossRef]

Other (5)

R. W. Boyd, Nonlinear Optics (Academic Press, New York, 1992).

M. E. Lines, "Scattering losses in optic fiber materials. I. A new parametrization," J. Appl. Phys. 55, 4052 (1984); "II. Numerical estimates," 55, 4058 (1984).
[CrossRef]

I. L. Fabelinskii, Molecular scattering of light (Plenum press, New York, 1968).

D. C. Wallace, Thermodynamics of crystals (Dover, New York, 1998).

E. Palik, Handbook of optical constants of solids (Academic, New York, 1998).

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Figures (3)

Fig. 1.
Fig. 1.

Attenuation in ideal CaF2 (left) and Q factor (right) of an ideal fluorite WGM resonators at room and nearly absolute zero temperature. Contributions from spontaneous Brillouin, Rayleigh and Raman scattering as well as blue and red wing absorption are added.

Fig. 2.
Fig. 2.

A) SRS threshold for a 1 mm ideal-surface cavity made with an ideal CaF2. B) Low temperature SRS threshold for a 1 mm ideal cavity made with CaF2 in terms of photon number. C) Theoretically evaluated wavelength dependence of the Raman gain in CaF2.

Fig. 3.
Fig. 3.

Experimental observation of the ringdown signal of a calcium fluoride resonator and setup scheme. The observations were performed at 780 nm. The threshold power of the SRS process was on the order of a few microwatt. Linear fits of the amplitude decay are presented by red lines, emphasizing two different ringdown constants at the beginning and at the end of the process. Inset shows the actual signal recorded on the photodetector. Blue points in the graph represent the amplitude of the signal shown in the inset.

Equations (10)

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α Ri α B β T β S 1
β T β S 1 = C P C V 1 ~ T 4 T→ 0 ,
α B , R α B 0 , R 0 ( λ 0 λ ) 4 [ ( exp h ̄ Ω B , R k B T 1 ) 1 + 1 2 ]
n ˙ S = 2 γ S n S + h ¯ ω p c 2 n 2 g b V n p n S ,
n ˙ p = 2 γ p n p h ̅ ω p c 2 n 2 g b V S n p n S ,
g b ( λ p ) = α R ( λ p ) λ p 4 8 π 2 c 2 n 2 ω p h ̅ Γ ,
Γ = Γ 0 [ 1 + 2 exp ( h ¯ Ω R 2 kT ) 1 ]
2 γ SRS = h ¯ ω p c 2 n 2 g b v N S n S ,
Q QSRS = P P th ,
P th = π 2 n 2 g b Q p Q S V λ p λ S ,

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