Abstract

We show that the signal and idler beams generated by certain types of unseeded, nanosecond optical parametric oscillators are tilted and angularly dispersed and have anomalously large bandwidths. This effect is demonstrated in both laboratory measurements and a numerical model. We show how the optical cavity design influences the tilts and how these tilts can be eliminated or minimized. We also determine the conditions necessary for injection seeding of these parametric oscillators.

© 1999 Optical Society of America

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References

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    [CrossRef]
  2. J. G. Haub, R. M. Hentschel, M. J. Johnson, and B. J. Orr, “Controlling the performance of a pulsed optical parametric oscillator: a survey of techniques and spectroscopic applications,” J. Opt. Soc. Am. B 12, 2128–2141 (1995).
    [CrossRef]
  3. J. G. Haub, M. J. Johnson, A. J. Powell, and B. J. Orr, “Bandwidth characteristics of a pulsed optical parametric oscillator: application to degenerate four-wave mixing spectroscopy,” Opt. Lett. 20, 1637–1639 (1995).
    [CrossRef] [PubMed]
  4. R. Urschel, U. Bader, A. Borsutzky, and R. Wallenstein, “Spectral properties and conversion efficiency of 355-nm-pumped pulsed optical parametric oscillators of β-barium borate with noncollinear phase matching,” J. Opt. Soc. Am. B 16, 565–579 (1999).
    [CrossRef]
  5. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).
  6. G. Arisholm, “Advanced numerical simulation models for second-order nonlinear interactions,” in Laser Optics ’98: Fundamental Problems of Laser Optics, N. N. Rozanov, ed., Proc. SPIE 3685, 86–97 (1999).
    [CrossRef]
  7. G. Arisholm, “Quantum noise initiation and macroscopic fluctuations in optical parametric oscillators,” J. Opt. Soc. Am. B 16, 117–127 (1999).
    [CrossRef]
  8. A. V. Smith, W. J. Alford, T. D. Raymond, and M. S. Bowers, “Comparison of a numerical model with measured performance of a seeded, nanosecond KTP optical parametric oscillator,” J. Opt. Soc. Am. B 12, 2253–2267 (1995).
    [CrossRef]
  9. A. V. Smith, R. J. Gehr, and M. S. Bowers, “Numerical models of broad-bandwidth nanosecond optical parametric oscillators,” J. Opt. Soc. Am. B 16, 609–619 (1999).
    [CrossRef]
  10. H. Vanherzeele, J. D. Bierlein, and F. Zumsteg, “Index of refraction measurements and parametric generation in hydrothermally grown KTiOPO4,” Appl. Opt. 27, 3314–3316 (1988).
    [CrossRef] [PubMed]
  11. R. Danielius, A. Piskarskas, P. Di Trapani, A. Andreoni, C. Solcia, and P. Foggi, “A colinearly phase-matched parametric generator/amplifier of visible femtosecond pulses,” IEEE J. Quantum Electron. 34, 459–463 (1998).
    [CrossRef]
  12. B. A. Richman, S. E. Bisson, R. Trebino, E. Sidick, and A. Jacobson, “Efficient broadband second-harmonic generation by dispersive achromatic nonlinear conversion using only prisms,” Opt. Lett. 23, 497–499 (1998).
    [CrossRef]
  13. This case was modeled with function 2Dmix-SP in the SNLO software package, which is freely distributed at http://www.sandia.gov/imrl/XWEB1128/xxtal.htm.
  14. M. J. T. Milton, T. J. McIlveen, D. C. Hanna, and P. T. Woods, “High-efficiency infrared generation by difference-frequency mixing using tangential phase matching,” Opt. Commun. 87, 273–277 (1992).
    [CrossRef]
  15. G. C. Bhar, U. Chatterjee, and S. Das, “Tunable near-infrared radiation by difference frequency mixing in beta barium borate crystal,” Appl. Phys. Lett. 58, 231–233 (1991).
    [CrossRef]
  16. T. D. Raymond, W. J. Alford, A. V. Smith, and M. S. Bowers, “Frequency shifts in injection-seeded optical parametric oscillators with phase mismatch,” Opt. Lett. 19, 1520–1522 (1994).
    [CrossRef] [PubMed]

1999 (4)

1998 (2)

R. Danielius, A. Piskarskas, P. Di Trapani, A. Andreoni, C. Solcia, and P. Foggi, “A colinearly phase-matched parametric generator/amplifier of visible femtosecond pulses,” IEEE J. Quantum Electron. 34, 459–463 (1998).
[CrossRef]

B. A. Richman, S. E. Bisson, R. Trebino, E. Sidick, and A. Jacobson, “Efficient broadband second-harmonic generation by dispersive achromatic nonlinear conversion using only prisms,” Opt. Lett. 23, 497–499 (1998).
[CrossRef]

1995 (4)

1994 (1)

1992 (1)

M. J. T. Milton, T. J. McIlveen, D. C. Hanna, and P. T. Woods, “High-efficiency infrared generation by difference-frequency mixing using tangential phase matching,” Opt. Commun. 87, 273–277 (1992).
[CrossRef]

1991 (1)

G. C. Bhar, U. Chatterjee, and S. Das, “Tunable near-infrared radiation by difference frequency mixing in beta barium borate crystal,” Appl. Phys. Lett. 58, 231–233 (1991).
[CrossRef]

1988 (1)

Alford, W. J.

Andreoni, A.

R. Danielius, A. Piskarskas, P. Di Trapani, A. Andreoni, C. Solcia, and P. Foggi, “A colinearly phase-matched parametric generator/amplifier of visible femtosecond pulses,” IEEE J. Quantum Electron. 34, 459–463 (1998).
[CrossRef]

Arisholm, G.

G. Arisholm, “Advanced numerical simulation models for second-order nonlinear interactions,” in Laser Optics ’98: Fundamental Problems of Laser Optics, N. N. Rozanov, ed., Proc. SPIE 3685, 86–97 (1999).
[CrossRef]

G. Arisholm, “Quantum noise initiation and macroscopic fluctuations in optical parametric oscillators,” J. Opt. Soc. Am. B 16, 117–127 (1999).
[CrossRef]

Bader, U.

Bhar, G. C.

G. C. Bhar, U. Chatterjee, and S. Das, “Tunable near-infrared radiation by difference frequency mixing in beta barium borate crystal,” Appl. Phys. Lett. 58, 231–233 (1991).
[CrossRef]

Bierlein, J. D.

Bisson, S. E.

Borsutzky, A.

Bowers, M. S.

Chatterjee, U.

G. C. Bhar, U. Chatterjee, and S. Das, “Tunable near-infrared radiation by difference frequency mixing in beta barium borate crystal,” Appl. Phys. Lett. 58, 231–233 (1991).
[CrossRef]

Danielius, R.

R. Danielius, A. Piskarskas, P. Di Trapani, A. Andreoni, C. Solcia, and P. Foggi, “A colinearly phase-matched parametric generator/amplifier of visible femtosecond pulses,” IEEE J. Quantum Electron. 34, 459–463 (1998).
[CrossRef]

Das, S.

G. C. Bhar, U. Chatterjee, and S. Das, “Tunable near-infrared radiation by difference frequency mixing in beta barium borate crystal,” Appl. Phys. Lett. 58, 231–233 (1991).
[CrossRef]

Di Trapani, P.

R. Danielius, A. Piskarskas, P. Di Trapani, A. Andreoni, C. Solcia, and P. Foggi, “A colinearly phase-matched parametric generator/amplifier of visible femtosecond pulses,” IEEE J. Quantum Electron. 34, 459–463 (1998).
[CrossRef]

Foggi, P.

R. Danielius, A. Piskarskas, P. Di Trapani, A. Andreoni, C. Solcia, and P. Foggi, “A colinearly phase-matched parametric generator/amplifier of visible femtosecond pulses,” IEEE J. Quantum Electron. 34, 459–463 (1998).
[CrossRef]

Gehr, R. J.

Hanna, D. C.

M. J. T. Milton, T. J. McIlveen, D. C. Hanna, and P. T. Woods, “High-efficiency infrared generation by difference-frequency mixing using tangential phase matching,” Opt. Commun. 87, 273–277 (1992).
[CrossRef]

Haub, J. G.

Hentschel, R. M.

Jacobson, A.

Johnson, M. J.

McIlveen, T. J.

M. J. T. Milton, T. J. McIlveen, D. C. Hanna, and P. T. Woods, “High-efficiency infrared generation by difference-frequency mixing using tangential phase matching,” Opt. Commun. 87, 273–277 (1992).
[CrossRef]

Milton, M. J. T.

M. J. T. Milton, T. J. McIlveen, D. C. Hanna, and P. T. Woods, “High-efficiency infrared generation by difference-frequency mixing using tangential phase matching,” Opt. Commun. 87, 273–277 (1992).
[CrossRef]

Orr, B. J.

Piskarskas, A.

R. Danielius, A. Piskarskas, P. Di Trapani, A. Andreoni, C. Solcia, and P. Foggi, “A colinearly phase-matched parametric generator/amplifier of visible femtosecond pulses,” IEEE J. Quantum Electron. 34, 459–463 (1998).
[CrossRef]

Powell, A. J.

Raymond, T. D.

Richman, B. A.

Sidick, E.

Smith, A. V.

Solcia, C.

R. Danielius, A. Piskarskas, P. Di Trapani, A. Andreoni, C. Solcia, and P. Foggi, “A colinearly phase-matched parametric generator/amplifier of visible femtosecond pulses,” IEEE J. Quantum Electron. 34, 459–463 (1998).
[CrossRef]

Trebino, R.

Urschel, R.

Vanherzeele, H.

Wallenstein, R.

Woods, P. T.

M. J. T. Milton, T. J. McIlveen, D. C. Hanna, and P. T. Woods, “High-efficiency infrared generation by difference-frequency mixing using tangential phase matching,” Opt. Commun. 87, 273–277 (1992).
[CrossRef]

Zumsteg, F.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

G. C. Bhar, U. Chatterjee, and S. Das, “Tunable near-infrared radiation by difference frequency mixing in beta barium borate crystal,” Appl. Phys. Lett. 58, 231–233 (1991).
[CrossRef]

IEEE J. Quantum Electron. (1)

R. Danielius, A. Piskarskas, P. Di Trapani, A. Andreoni, C. Solcia, and P. Foggi, “A colinearly phase-matched parametric generator/amplifier of visible femtosecond pulses,” IEEE J. Quantum Electron. 34, 459–463 (1998).
[CrossRef]

J. Opt. Soc. Am. B (6)

Opt. Commun. (1)

M. J. T. Milton, T. J. McIlveen, D. C. Hanna, and P. T. Woods, “High-efficiency infrared generation by difference-frequency mixing using tangential phase matching,” Opt. Commun. 87, 273–277 (1992).
[CrossRef]

Opt. Lett. (3)

Proc. SPIE (1)

G. Arisholm, “Advanced numerical simulation models for second-order nonlinear interactions,” in Laser Optics ’98: Fundamental Problems of Laser Optics, N. N. Rozanov, ed., Proc. SPIE 3685, 86–97 (1999).
[CrossRef]

Other (2)

This case was modeled with function 2Dmix-SP in the SNLO software package, which is freely distributed at http://www.sandia.gov/imrl/XWEB1128/xxtal.htm.

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).

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Figures (8)

Fig. 1
Fig. 1

The test OPO uses a 10-mm-long, type II phase-matched KTP crystal pumped by a 10-ns (FWHM), 532-nm, 0.65-mm-diameter (FWHM irradiance), single-longitudinal-mode pulse. The physical cavity length is 12 mm. The signal walk-off angle is 48.7 mrad; deff is 3.0 pm/V; signal, idler, and pump refractive indices are 1.816, 1.735, and 1.790, respectively; signal, idler, and pump group-velocity indices are 1.876, 1.765, and 1.911, respectively; the phase-matching angle is θ=57°, ϕ=0°.

Fig. 2
Fig. 2

(a) Beam path assumed by the signal wave in the monochromatic, phase-matched OPO, (b) signal beam path for the highest gain mode of operation. Dotted lines, the walk-off path for an e-polarized beam with its propagation vector along the cavity axis. Δk, collinear phase mismatch. Note that the tilt angles are greatly exaggerated; the actual beam tilts of ∼5 mrad are much smaller than the walk-off angle of ∼50 mrad.

Fig. 3
Fig. 3

(a) Model-generated contour plots of signal fluence for the test OPO versus angle relative to the cavity axis on the horizontal axis and detuning from the phase-matched wavelength on the vertical axis. Dotted line, the calculated phase-matching frequency versus crystal angle. (b) Far-field signal fluence contours.

Fig. 4
Fig. 4

Laboratory apparatus for characterizing KTP OPO’s. Details are given in the text. PBS, polarizing beam splitter; PZT, piezoelectric transducer.

Fig. 5
Fig. 5

(a) Measured contour plots of signal fluence for the test OPO versus angle relative to the cavity axis on the horizontal axis and detuning from the phase-matched wavelength on the vertical axis. (b) Far-field signal fluence contours.

Fig. 6
Fig. 6

Noncollinear phase matching for a pump beam propagating at angle θp relative to the crystal optic axis z. Ss is the signal Poynting vector tilted by angle ρs relative to the signal propagation vector ks. The Poynting vector makes an angle of αs with respect to the optic axis.

Fig. 7
Fig. 7

(a) Parametric amplification of a small-diameter, short-duration signal–idler pulse by a larger, longer pump pulse, illustrating the origin of tilted structure in the amplified signal and idler waves. The ellipses represent half-height contours of irradiance for the input pump, signal, and idler at the left. At the right, the dotted lines show the paths (in the reference frame moving with the pump pulse) that would be followed by the input signal and idler pulses during linear propagation through the crystal. Owing to the combination of group velocity and birefringent walk-off relative to the pump, the input signal and idler pulses trace the lower and upper dotted lines, respectively. The signal and idler light generated in the crystal fills in the slanted ellipse that connects the signal and idler end points. (b) Equivalent slanted pulses can be created by reflection of a short, unslanted signal pulse off a diffraction grating.

Fig. 8
Fig. 8

(a) Measured signal dispersion diagrams showing partial seeding for a crystal tilted to a shift-free running wavelength toward the seed wavelength and (b) the corresponding far-field signal fluence profile.

Tables (2)

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Table 1 Model Results for a 12-mm-Long Cavity with a 10-mm Crystal and a 6-mJ Pump

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Table 2 Signal Tilt for Several Cavity Lengths with a 10-mm Crystal

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

z-i2kjt2+tan ρjx+1vjt+iαj2t2j(x, y, z, t)
=Pj(x, y, z, t)exp(±iΔkz),
Δktilt=2πnsνsc(ρs+ϕs-ρi+ϕi)δϕs,
ρj=-1njdnjdϕ
δϕi=nsνsniνiδϕs.
Δktilt=2πnsνsc(αs-αi)δϕs.
Δktune=2πcni+dnidνi-ns-dnsdνsδνs,
1vj=12πdkjdνj=1cnj+νj dnjdνj
Δktune=2πc(gi-gs)δνs,
dνsdϕs=nsνs(αs-αi)gs-gi.
dνsdϕs=νs(αs-αi)gs-gi,
ϕ=arctangs-giαs-αi.
ϕ=arctanν dϕdν,
dνsdϕs=νs(αs-αi)gs-gi.
ϕp=ρs niωinpωp=15mrad.

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