Abstract

We report measurements of thermal self-locking of a Fabry–Perot cavity containing a potassium niobate (KNbO3) crystal. We develop a method to determine linear and nonlinear optical absorption coefficients in intracavity crystals by detailed analysis of the transmission line shapes. These line shapes are typical of optical bistability in thermally loaded cavities. For our crystal we determine the one-photon absorption coefficient at 846 nm to be α=(0.0034±0.0022) m-1, the two-photon absorption coefficient at 846 nm to be β=(3.2±0.5)×10-11 m/W, and the one-photon absorption coefficient at 423 nm to be (13±2) m-1. We also address the issue of blue-light-induced infrared-absorption and determine a coefficient for this excited-state absorption process. Our method is particularly well suited to bulk absorption measurements where absorption is small compared with scattering. We also report new measurements of the temperature dependence of the index of refraction at 846 nm and compare with values in the literature.

© 2001 Optical Society of America

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References

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  1. A. Arie, S. Schiller, E. K. Gustafson, and R. L. Byer, “Absolute frequency stabilization of diode-laser-pumped Nd: YAG lasers to hyperfine transitions in molecular iodine,” Opt. Lett. 17, 1204–1206 (1992).
    [CrossRef] [PubMed]
  2. E. S. Polzik and H. J. Kimble, “Frequency doubling with KNbO3 in an external cavity,” Opt. Lett. 16, 1400–1402 (1991).
    [CrossRef] [PubMed]
  3. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).
  4. P. Dube, L.-S. Ma, J. Ye, P. Jungner, and J. L. Hall, “Thermally induced self-locking of an optical cavity by overtone absorption in acetylene gas,” J. Opt. Soc. Am. B 13, 2041–2054 (1996).
    [CrossRef]
  5. K. An, B. A. Sones, C. Fang-Yen, R. R. Dasari, and M. S. Feld, “Optical bistability induced by mirror absorption: measurement of absorption coefficients at the sub-ppm level,” Opt. Lett. 22, 1433–1435 (1997).
    [CrossRef]
  6. A. Douillet, J.-J. Zondy, A. Yelisseyev, S. Lobanov, and L. Isaenko, “Stability and frequency tuning of thermally loaded continuous-wave AgGaS2 optical parametric oscillators,” J. Opt. Soc. Am. B 16, 1481–1495 (1999).
    [CrossRef]
  7. L. E. Busse, L. Goldberg, M. R. Surette, and G. Mizell, “Absorption losses in MgO-doped and undoped potassium niobate,” J. Appl. Phys. 75, 1102–1110 (1994).
    [CrossRef]
  8. Our extended cavity laser is a Vortex laser from New Focus Corp. (5215 Hellyer Ave., Suite 100 San Jose, Calif. 95138–1001). The tapered amplifier is a Model 8613 laser from SDL (80 Rose Orchard Way, San Jose, Calif. 95134–1365) with the rear cavity optics removed, configured as a single-pass amplifier.
  9. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
    [CrossRef]
  10. Our crystal is from VLOC, 7826 Photonics Drive, New Port Richey, Fla. 34655.
  11. L. Goldberg, L. E. Busse, and D. Mehuys, “High power continuous wave blue light generation in KNbO3 using semiconductor simplifier seeded by a laser diode,” Appl. Phys. Lett. 63, 2327–2329 (1993).
    [CrossRef]
  12. H. Mabuchi, E. S. Polzik, and H. J. Kimble, “Blue-light-induced infrared absorption in KNbO3,” J. Opt. Soc. Am. B 11, 2023–2029 (1994).
    [CrossRef]
  13. L. Shiv, J. L. Sorensen, and E. S. Polzik, “Inhibited light-induced absorption in KNbO3,” Opt. Lett. 20, 2270–2272 (1995).
    [CrossRef]
  14. G. Ghosh, “Dispersion of thermo-optic coefficients in a potassium niobate nonlinear crystal,” Appl. Phys. Lett. 65, 3311–3313 (1994).
    [CrossRef]
  15. R. L. Sutherland, Handbook of Nonlinear Optics (Marcel Dekker, New York, 1996), p. 502.
  16. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1970), p. 228.

1999 (1)

1997 (1)

1996 (1)

1995 (1)

1994 (3)

L. E. Busse, L. Goldberg, M. R. Surette, and G. Mizell, “Absorption losses in MgO-doped and undoped potassium niobate,” J. Appl. Phys. 75, 1102–1110 (1994).
[CrossRef]

G. Ghosh, “Dispersion of thermo-optic coefficients in a potassium niobate nonlinear crystal,” Appl. Phys. Lett. 65, 3311–3313 (1994).
[CrossRef]

H. Mabuchi, E. S. Polzik, and H. J. Kimble, “Blue-light-induced infrared absorption in KNbO3,” J. Opt. Soc. Am. B 11, 2023–2029 (1994).
[CrossRef]

1993 (1)

L. Goldberg, L. E. Busse, and D. Mehuys, “High power continuous wave blue light generation in KNbO3 using semiconductor simplifier seeded by a laser diode,” Appl. Phys. Lett. 63, 2327–2329 (1993).
[CrossRef]

1992 (1)

1991 (1)

1983 (1)

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

An, K.

Arie, A.

Busse, L. E.

L. E. Busse, L. Goldberg, M. R. Surette, and G. Mizell, “Absorption losses in MgO-doped and undoped potassium niobate,” J. Appl. Phys. 75, 1102–1110 (1994).
[CrossRef]

L. Goldberg, L. E. Busse, and D. Mehuys, “High power continuous wave blue light generation in KNbO3 using semiconductor simplifier seeded by a laser diode,” Appl. Phys. Lett. 63, 2327–2329 (1993).
[CrossRef]

Byer, R. L.

Dasari, R. R.

Douillet, A.

Drever, R. W. P.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Dube, P.

Fang-Yen, C.

Feld, M. S.

Ford, G. M.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Ghosh, G.

G. Ghosh, “Dispersion of thermo-optic coefficients in a potassium niobate nonlinear crystal,” Appl. Phys. Lett. 65, 3311–3313 (1994).
[CrossRef]

Goldberg, L.

L. E. Busse, L. Goldberg, M. R. Surette, and G. Mizell, “Absorption losses in MgO-doped and undoped potassium niobate,” J. Appl. Phys. 75, 1102–1110 (1994).
[CrossRef]

L. Goldberg, L. E. Busse, and D. Mehuys, “High power continuous wave blue light generation in KNbO3 using semiconductor simplifier seeded by a laser diode,” Appl. Phys. Lett. 63, 2327–2329 (1993).
[CrossRef]

Gustafson, E. K.

Hall, J. L.

P. Dube, L.-S. Ma, J. Ye, P. Jungner, and J. L. Hall, “Thermally induced self-locking of an optical cavity by overtone absorption in acetylene gas,” J. Opt. Soc. Am. B 13, 2041–2054 (1996).
[CrossRef]

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Hough, J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Isaenko, L.

Jungner, P.

Kimble, H. J.

Kowalski, F. V.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Lobanov, S.

Ma, L.-S.

Mabuchi, H.

Mehuys, D.

L. Goldberg, L. E. Busse, and D. Mehuys, “High power continuous wave blue light generation in KNbO3 using semiconductor simplifier seeded by a laser diode,” Appl. Phys. Lett. 63, 2327–2329 (1993).
[CrossRef]

Mizell, G.

L. E. Busse, L. Goldberg, M. R. Surette, and G. Mizell, “Absorption losses in MgO-doped and undoped potassium niobate,” J. Appl. Phys. 75, 1102–1110 (1994).
[CrossRef]

Munley, A. J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Polzik, E. S.

Schiller, S.

Shiv, L.

Sones, B. A.

Sorensen, J. L.

Surette, M. R.

L. E. Busse, L. Goldberg, M. R. Surette, and G. Mizell, “Absorption losses in MgO-doped and undoped potassium niobate,” J. Appl. Phys. 75, 1102–1110 (1994).
[CrossRef]

Ward, H.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Ye, J.

Yelisseyev, A.

Zondy, J.-J.

Appl. Phys. B (1)

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Appl. Phys. Lett. (2)

L. Goldberg, L. E. Busse, and D. Mehuys, “High power continuous wave blue light generation in KNbO3 using semiconductor simplifier seeded by a laser diode,” Appl. Phys. Lett. 63, 2327–2329 (1993).
[CrossRef]

G. Ghosh, “Dispersion of thermo-optic coefficients in a potassium niobate nonlinear crystal,” Appl. Phys. Lett. 65, 3311–3313 (1994).
[CrossRef]

J. Appl. Phys. (1)

L. E. Busse, L. Goldberg, M. R. Surette, and G. Mizell, “Absorption losses in MgO-doped and undoped potassium niobate,” J. Appl. Phys. 75, 1102–1110 (1994).
[CrossRef]

J. Opt. Soc. Am. B (3)

Opt. Lett. (4)

Other (5)

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).

Our extended cavity laser is a Vortex laser from New Focus Corp. (5215 Hellyer Ave., Suite 100 San Jose, Calif. 95138–1001). The tapered amplifier is a Model 8613 laser from SDL (80 Rose Orchard Way, San Jose, Calif. 95134–1365) with the rear cavity optics removed, configured as a single-pass amplifier.

Our crystal is from VLOC, 7826 Photonics Drive, New Port Richey, Fla. 34655.

R. L. Sutherland, Handbook of Nonlinear Optics (Marcel Dekker, New York, 1996), p. 502.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1970), p. 228.

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Figures (7)

Fig. 1
Fig. 1

Schematic diagram of the experimental layout: ECDL, extended-cavity diode laser; I, optical isolator; λ/2, half-wave plate; λ/4, quarter-wave plate; C1, frequency-doubling bow-tie cavity; C2, stable optical cavity; D, photodiode detectors; PBS, polarizing beam-splitter cube; BS1, uncoated quartz window; BS2, dichroic beam splitter. The short heavy lines are mirrors.

Fig. 2
Fig. 2

Infrared transmission line shape for the bow-tie cavity in the absence of blue light. The points are the measurements. The solid curve is a fit to the data [see Eq. (2)]. The infrared light is polarized along the c axis. (a) Low power, (b) high power. For high powers the fit function is not single valued above the cavity resonant frequency.

Fig. 3
Fig. 3

(a) Self-locking range, η, versus infrared detector signal. (b) The data from (a) with temperature and power calibrations. The solid curve is a weighted fit to the data, T=c1P+c2P2.

Fig. 4
Fig. 4

(a) Cavity transmission line shape in the infrared at 846 nm when generating the second harmonic at 423 nm. This signal is taken from the highest intensities in the experiment. Note that for low powers, the FWHM is 5 MHz. (b) The second-harmonic signal for the same settings as in (a). The shoulder to the left of the signal is a Maker fringe (see text). (c) Peak second-harmonic power as a function of peak infrared power. For all but the highest two power measurements, the peak blue power is given by Pblue=36.2 kW-1 Pir2.

Fig. 5
Fig. 5

(a) Self-locking range, η, in the presence of blue light versus infrared detector signal, excluding the highest-power data where the second-harmonic-generation process appears to be saturating. (b) The data from (a) with the temperature and power calibrations and with the temperature rise from the infrared light subtracted. The solid curve is a weighted fit to the data (see text).

Fig. 6
Fig. 6

Change in the index of refraction with temperature for light polarized along the b and c axes. The points are from this work. The solid curve is from Ghosh.14 The dashed curve is a second-order polynomial fit to the data.

Fig. 7
Fig. 7

Transmitted line shape as a function of cavity length for two temperatures. The upper trace has been displaced for clarity. The polarization of the light incident on the cavity is rotated a few degrees relative to the c axis. The larger feature is polarized along the c axis, and the smaller feature is polarized along the b axis, as labeled. This shows the magnitude and the direction of the change in the cavity resonance length with temperature.

Equations (14)

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P(ν)=P01+F(ν-ν0)2,
y=11+F(ν-ηy)2,
1r ddr r dudr=-GK,
G=αI+βI2,
dudy=ay[exp(-y2)-1]+By[exp(-2y2)-1],
u(y)=-A2E1(y2)-A2 ln(y2)-B2E1(2y2)-B2 ln(y2)+C,
ΔT=u(0)-Tc=A2 ln2b2a2+γ+B2 ln2b2a2+γ+ln(2)=α4πK ln2b2a2+γP+β4π2a2K ln4b2a2+γP2,
ΔP=VIbδdV=δPbL,
1r r r ur+2uz2=-z2{C exp(-4r2/a2)+D exp(-6r2/a2)}.
ΔT(z)=3δ4πK ln4b2a2+γ z2L2Pb+ξa2π2K×ln6b2a2+γ z2L2PbPir,
T=δ4πK ln4b2a2+γPb+ξ3a2π2K ln6b2a2+γPbPir.
ΔT=a1Pb+a2PbPir
dLdT=LcdnxdT+αT(nx-n0),
dnbdT=1.55809×10-9T2+4.06912×10-8T-33.76305×10-6,

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