Abstract

A theoretical model and a simplified analytic expression are developed to describe the buildup time of a pulsed confocal unstable optical parametric oscillator (OPO) with a uniform-reflectivity mirror (URM) or a Gaussian-reflectivity mirror (GRM). Two analytic expressions have been demonstrated to correspond to theoretical models with a sufficient degree of accuracy. The effects of a variety of cavity and pump parameters on the buildup time of an OPO were investigated and analyzed. It was found that a GRM unstable OPO generally exhibits a shorter buildup time than the corresponding URM unstable OPO with equally effective output coupling.

© 2005 Optical Society of America

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References

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  1. W. A. Neuman, S. P. Velsko, “Effect of cavity design on optical parametric oscillator performance,” in Advanced Solid-State Lasers, A. Payne, C. R. Pollock, eds., Vol. 1 of OSA Trends in Optics and Photonics Series (Optical Society of America, 1996), pp. 179–181.
  2. M. K. Brown, M. S. Bowers, “High energy, near diffraction limited output from optical parametric oscillators using unstable resonators,” in Solid State Lasers VI, R. Scheps, ed., Proc. SPIE2986, 113–122 (1997).
    [CrossRef]
  3. S. Pearl, Y. Ehrlich, S. Fastig, S. Rosenwaks, “Nearly diffraction-limited signal generated by a lower beam-quality pump in an optical parametric oscillator,” Appl. Opt. 42, 1048–1051 (2003).
    [CrossRef] [PubMed]
  4. G. Hansson, H. Karlsson, F. Laurell, “Unstable resonator optical parametric oscillator based on quasi-phase-matched Rb-TiOAsO4,” Appl. Opt. 40, 5446–5451 (2001).
    [CrossRef]
  5. B. C. Johnson, V. J. Newell, J. B. Clark, E. S. McPhee, “Narrow-bandwidth low-divergence optical parametric oscillator for nonlinear frequency-conversion applications,” J. Opt. Soc. Am. B 12, 2122–2127 (1995).
    [CrossRef]
  6. J. N. Farmer, M. S. Bowers, W. S. Schaprf, “High brightness eyesafe optical parametric oscillator using confocal unstable resonators,” in Advanced Solid-State Lasers, M. M. Fejer, H. Injeyan, U. Keller, eds., Vol. 26 of OSA Trends in Optics and Photonics Series (Optical Society of America, 1999), pp. 567–571.
  7. M. Morin, “Graded reflectivity mirror unstable laser resonators,” Opt. Quantum Electron. 29, 819–866 (1997).
    [CrossRef]
  8. M. Gong, S. Zou, G. Chen, P. Yan, Q. Liu, L. Huang, “Threshold studies of pulsed confocal unstable optical parametric oscillators,” Opt. Express 12, 2932–2944 (2004).
    [CrossRef] [PubMed]
  9. S. Zou, M. Gong, Q. Liu, G. Chen, “Low threshold characteristic of pulsed confocal unstable optical parametric oscillators with Gaussian reflectivity mirrors,” Opt. Express 13, 776–788 (2005).
    [CrossRef] [PubMed]

2005 (1)

2004 (1)

2003 (1)

2001 (1)

1997 (1)

M. Morin, “Graded reflectivity mirror unstable laser resonators,” Opt. Quantum Electron. 29, 819–866 (1997).
[CrossRef]

1995 (1)

Bowers, M. S.

M. K. Brown, M. S. Bowers, “High energy, near diffraction limited output from optical parametric oscillators using unstable resonators,” in Solid State Lasers VI, R. Scheps, ed., Proc. SPIE2986, 113–122 (1997).
[CrossRef]

J. N. Farmer, M. S. Bowers, W. S. Schaprf, “High brightness eyesafe optical parametric oscillator using confocal unstable resonators,” in Advanced Solid-State Lasers, M. M. Fejer, H. Injeyan, U. Keller, eds., Vol. 26 of OSA Trends in Optics and Photonics Series (Optical Society of America, 1999), pp. 567–571.

Brown, M. K.

M. K. Brown, M. S. Bowers, “High energy, near diffraction limited output from optical parametric oscillators using unstable resonators,” in Solid State Lasers VI, R. Scheps, ed., Proc. SPIE2986, 113–122 (1997).
[CrossRef]

Chen, G.

Clark, J. B.

Ehrlich, Y.

Farmer, J. N.

J. N. Farmer, M. S. Bowers, W. S. Schaprf, “High brightness eyesafe optical parametric oscillator using confocal unstable resonators,” in Advanced Solid-State Lasers, M. M. Fejer, H. Injeyan, U. Keller, eds., Vol. 26 of OSA Trends in Optics and Photonics Series (Optical Society of America, 1999), pp. 567–571.

Fastig, S.

Gong, M.

Hansson, G.

Huang, L.

Johnson, B. C.

Karlsson, H.

Laurell, F.

Liu, Q.

McPhee, E. S.

Morin, M.

M. Morin, “Graded reflectivity mirror unstable laser resonators,” Opt. Quantum Electron. 29, 819–866 (1997).
[CrossRef]

Neuman, W. A.

W. A. Neuman, S. P. Velsko, “Effect of cavity design on optical parametric oscillator performance,” in Advanced Solid-State Lasers, A. Payne, C. R. Pollock, eds., Vol. 1 of OSA Trends in Optics and Photonics Series (Optical Society of America, 1996), pp. 179–181.

Newell, V. J.

Pearl, S.

Rosenwaks, S.

Schaprf, W. S.

J. N. Farmer, M. S. Bowers, W. S. Schaprf, “High brightness eyesafe optical parametric oscillator using confocal unstable resonators,” in Advanced Solid-State Lasers, M. M. Fejer, H. Injeyan, U. Keller, eds., Vol. 26 of OSA Trends in Optics and Photonics Series (Optical Society of America, 1999), pp. 567–571.

Velsko, S. P.

W. A. Neuman, S. P. Velsko, “Effect of cavity design on optical parametric oscillator performance,” in Advanced Solid-State Lasers, A. Payne, C. R. Pollock, eds., Vol. 1 of OSA Trends in Optics and Photonics Series (Optical Society of America, 1996), pp. 179–181.

Yan, P.

Zou, S.

Appl. Opt. (2)

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

Opt. Express (2)

Opt. Quantum Electron. (1)

M. Morin, “Graded reflectivity mirror unstable laser resonators,” Opt. Quantum Electron. 29, 819–866 (1997).
[CrossRef]

Other (3)

W. A. Neuman, S. P. Velsko, “Effect of cavity design on optical parametric oscillator performance,” in Advanced Solid-State Lasers, A. Payne, C. R. Pollock, eds., Vol. 1 of OSA Trends in Optics and Photonics Series (Optical Society of America, 1996), pp. 179–181.

M. K. Brown, M. S. Bowers, “High energy, near diffraction limited output from optical parametric oscillators using unstable resonators,” in Solid State Lasers VI, R. Scheps, ed., Proc. SPIE2986, 113–122 (1997).
[CrossRef]

J. N. Farmer, M. S. Bowers, W. S. Schaprf, “High brightness eyesafe optical parametric oscillator using confocal unstable resonators,” in Advanced Solid-State Lasers, M. M. Fejer, H. Injeyan, U. Keller, eds., Vol. 26 of OSA Trends in Optics and Photonics Series (Optical Society of America, 1999), pp. 567–571.

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Figures (5)

Fig. 1
Fig. 1

Confocal unstable singly resonant OPO. Input mirror M1 is a concave mirror, which is highly reflecting at the signal wavelength and highly transmitting at the pump and idler wavelengths. Output coupler M2 is a convex mirror, which is highly reflective at the pump wavelength, highly transmitting at the idler wavelength, and has a uniform signal reflectivity or a radial Gaussian signal reflectance profile. Other variables are defined in text.

Fig. 2
Fig. 2

Ratio of buildup time to pump FWHM pulse width versus cavity physical length. M = 1.06, R = 0.82, Rmax = 0.92, Ic = 20 mm, T = 13.5 ns, w = 1.45, and 2rp = 2.8 mm. Solid curves, results of the theoretical model for several normalized pump intensities of URM or GRM unstable OPOs. Dashed curves, theoretical results of URM or GRM unstable OPOs with a pump-peak intensity of 40 MW/cm2. Dotted lines, analytic expression results of URM and GRM unstable OPOs for N = 1.2.

Fig. 3
Fig. 3

Ratio of buildup time to pump FWHM pulse width versus cavity magnification factor. L = 60 mm, lc = 20 mm, T = 13.5 ns, w = 1.45, and 2rp = 2.8 mm. The output coupler signal reflectivity of the URM unstable OPO is R = 0.5. The output coupler central signal reflectance of the GRM unstable OPO is taken as Rmax = RM2. Solid curves, results of the theoretical model for several normalized pump intensities of URM or GRM unstable OPOs. Dashed curves, theoretical results with a pump peak intensity of 65 MW/cm2.

Fig. 4
Fig. 4

Ratio of buildup time to pump FWHM pulse width versus signal reflectance, M = 1.06, L = 60 mm, lc = 20 mm, T = 13.5 ns, w = 1.45, 2rp = 2.8 mm. Output coupler signal reflectivity R of a URM unstable OPO is taken to correspond to the coordinate values of central signal reflectance Rmax with R = Rmax/M2. Solid curves, results of the theoretical model for several normalized pump intensities of URM or GRM unstable OPOs. Dashed curves, theoretical results with a pump peak intensity of 75 MW/cm2.

Fig. 5
Fig. 5

Buildup time versus pump FWHM pulse width M = 1.06, L = 60 mm, lc = 20 mm, R = 0.82, Rmax = 0.92, w = 1.45, and 2rp = 2.8 mm. Solid curves, results of the theoretical model for several normalized pump intensities of URM or GRM unstable OPOs. Dashed curves, theoretical results with a pump peak intensity of 50 MW/cm2.

Equations (13)

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g m = R exp [ - 2 ( α f + α b ) l c ] { 1 16 ( r s 1 r s ) 2 × exp [ 2 β f l c ( 1 + γ ) ] + 1 8 ( r s 2 r s ) 2 × exp ( 2 β f l c γ ) + 1 8 ( r s 3 r s ) 2 exp ( 2 β f l c ) + 1 4 } ,
1 r s 1 2 = 1 r s 2 + β f l c ( 1 + γ ) r p 2 + 4 β f l c γ ( R 2 n s ) 2 , 1 r s 2 2 = 1 r s 2 + β f l c γ r p 2 + 4 β f l c γ ( R 2 n s ) 2 , 1 r s 3 2 = 1 r s 2 + β f l c r p 2 .
β f = { 2 N s f N i f n p c ɛ 0 I p 0 exp [ - ( t / τ p ) 2 ] } 1 / 2 ,
g m = R exp [ - 2 ( α f + α b ) l c ] { 1 16 ( r s 1 r s ) 2 × exp [ 2 β f l c ( 1 + γ ) ] + 1 4 } ,
1 r s 1 2 = 1 r s 2 + β f l c ( 1 + γ ) r p 2 .
t on = - τ p [ ln ( 8 N s f N i f n p c ɛ 0 × I p 0 l c 2 ( 1 + γ ) 2 ln 2 { 16 exp [ 2 ( α f + α b ) l c ] R - 4 } ) ] 1 / 2 .
T b = t on - t p = τ p { 6 - [ ln ( 8 N s f N i f n p c ɛ 0 × I p 0 l c 2 ( 1 + γ ) 2 ln 2 { 16 exp [ 2 ( α f + α b ) l c ] R - 4 } ) ] 1 / 2 } .
R ( r ) = R max exp [ - ( r / w ) 2 ] ,
g m = R max exp [ - 2 ( α f + α b ) l c ] { 1 16 ( r s 1 r s ) 2 × exp [ 2 β f l c ( 1 + γ ) ] + 1 8 ( r s 2 r s ) 2 × exp ( 2 β f l c γ ) + 1 8 ( r s 3 r s ) 2 exp ( 2 β f l c ) + 1 4 ( r s 4 r l s ) 2 } .
1 r s 1 2 = 1 r s 2 + 1 w 2 + β f l c ( 1 + γ ) r p 2 + 4 β f l c γ ( R 2 n s ) 2 , 1 r s 2 2 = 1 r s 2 + 1 w 2 + β f l c γ r p 2 + 4 β f l c γ ( R 2 n s ) 2 , 1 r s 3 2 = 1 r s 2 + 1 w 2 + β f l c r p 2 , 1 r s 4 2 = 1 r s 2 + 1 w 2 ,
g m = R max exp [ - 2 ( α f + α b ) l c ] { 1 16 ( r s 1 r s ) 2 × exp [ 2 β f l c ( 1 + γ ) ] + 3 4 ( r s 4 r s ) 2 } .
t on = - τ p [ ln ( 8 N s f N i f n p c ɛ 0 × I p 0 l c 2 ( 1 + γ ) 2 ln 2 { 16 M 2 exp [ 2 ( α f + α b ) l c ] R max - 12 } ) ] 1 / 2 .
T b = t on - t p = τ p { 6 - [ ln ( 8 N s f N i f n p c ɛ 0 × I p 0 l c 2 ( 1 + γ ) 2 ln 2 { 16 M 2 exp [ 2 ( α f + α b ) l c ] R max - 12 } ) ] 1 / 2 } .

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