Abstract

According to numerical models of nanosecond optical parametric oscillators, cavities with 90° image rotation can produce high-quality beams even if the Fresnel number of the cavity is large. We review the properties of such image-rotating cavities and present a method for designing them. The laboratory performance of one promising design is characterized, demonstrating its ability to produce high-quality beams with good efficiency.

© 2002 Optical Society of America

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References

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  1. G. Hansson, H. Karlson, and F. Laurell, “Unstable resonator optical parametric oscillator based on quasi-phase-matched RbTiOAsO4,” Appl. Opt. 40, 5446–5451 (2001).
    [CrossRef]
  2. J. N. Farmer, M. S. Bowers, and W. S. Scharpf, Jr., “High brightness eye safe optical parametric oscillator using confocal unstable resonators,” in Advanced Solid-State Lasers, M. M. Feyer, H. Injeyan, and U. Keller, eds., Vol. 26 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington D.C., 1999), pp. 567–571.
  3. B. C. Johnson, V. J. Newell, J. B. Clark, and 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]
  4. A. V. Smith and M. S. Bowers, “Image-rotating cavity designs for improved beam quality in nanosecond optical parametric oscillators,” J. Opt. Soc. Am. B 18, 706–713 (2001).
    [CrossRef]
  5. G. Anstett, G. Goritz, D. Kabs, R. Urschel, R. Wallenstein, and A. Borsutzky, “Reduction of the spectral width and beam divergence of a BBO-OPO by using collinear type-II phase matching and back reflection of the pump beam,” Appl. Phys. B 72, 583–589 (2001).
    [CrossRef]
  6. D. J. Armstrong and A. V. Smith, “Demonstration of improved beam quality in an image-rotating optical parametric oscillator,” Opt. Lett. 27, 40–42 (2002).
    [CrossRef]
  7. E. J. Galvez and C. D. Holmes, “Geometric phase of optical rotators,” J. Opt. Soc. Am. A 16, 1981–1985 (1999).
    [CrossRef]
  8. W. J. Alford, R. J. Gehr, R. L. Schmitt, A. V. Smith, and G. Arisholm, “Beam tilt and angular dispersion in broad-bandwidth, nanosecond optical parametric oscillators,” J. Opt. Soc. Am. B 16, 1525–1532 (1999).
    [CrossRef]
  9. Y. A. Anan’ev, Laser Resonators and the Beam Divergence Problem (Hilger, London, 1992).
  10. D. J. Armstrong, W. J. Alford, T. D. Raymond, A. V. Smith, and M. S. Bowers, “Parametric amplification and oscillation with walk-off-compensating crystals,” J. Opt. Soc. Am. B 14, 460–474 (1997).
    [CrossRef]
  11. 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]
  12. A. V. Smith and M. S. Bowers, “Phase distortions in sum- and difference-frequency mixing in crystals,” J. Opt. Soc. Am. B 12, 49–57 (1995).
    [CrossRef]
  13. A. E. Siegman, “Defining the effective radius of curvature for a non ideal optical beam,” IEEE J. Quantum Electron. 27, 1146–1148 (1991).
    [CrossRef]
  14. T. F. Johnston, “Beam propagation (M2) measurement made as easy as it gets: the four-cuts method,” Appl. Opt. 37, 4840–4850 (1998).
    [CrossRef]
  15. R. DeSalvo, A. A. Said, D. J. Hagan, E. W. Van Stryland, and M. Sheik-Bahae, “Infrared to ultraviolet measurements of two-photon absorption and n2 in wide bandgap solids,” 32, 1324–1333 (1996).
  16. M. Sheik-Bahae and M. Ebrahimzadeh, “Measurements of nonlinear refraction in the second-order χ(2) materials KTiOPO4, KNbO3, β-BaB2O4, and LiB3O5,” Opt. Commun. 142, 294–298 (1997).
    [CrossRef]
  17. H. P. Li, C. H. Kam, Y. L. Lam, and W. Ji, “Femtosecond Z-scan measurements of nonlinear refraction in nonlinear optical crystals,” Opt. Mater. 15, 237–242 (2001).
    [CrossRef]
  18. M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electronic nonlinear refraction in solids,” IEEE J. Quantum Electron. 27, 1296–1309 (1991).
    [CrossRef]

2002 (1)

2001 (4)

G. Hansson, H. Karlson, and F. Laurell, “Unstable resonator optical parametric oscillator based on quasi-phase-matched RbTiOAsO4,” Appl. Opt. 40, 5446–5451 (2001).
[CrossRef]

A. V. Smith and M. S. Bowers, “Image-rotating cavity designs for improved beam quality in nanosecond optical parametric oscillators,” J. Opt. Soc. Am. B 18, 706–713 (2001).
[CrossRef]

G. Anstett, G. Goritz, D. Kabs, R. Urschel, R. Wallenstein, and A. Borsutzky, “Reduction of the spectral width and beam divergence of a BBO-OPO by using collinear type-II phase matching and back reflection of the pump beam,” Appl. Phys. B 72, 583–589 (2001).
[CrossRef]

H. P. Li, C. H. Kam, Y. L. Lam, and W. Ji, “Femtosecond Z-scan measurements of nonlinear refraction in nonlinear optical crystals,” Opt. Mater. 15, 237–242 (2001).
[CrossRef]

1999 (2)

1998 (1)

1997 (2)

M. Sheik-Bahae and M. Ebrahimzadeh, “Measurements of nonlinear refraction in the second-order χ(2) materials KTiOPO4, KNbO3, β-BaB2O4, and LiB3O5,” Opt. Commun. 142, 294–298 (1997).
[CrossRef]

D. J. Armstrong, W. J. Alford, T. D. Raymond, A. V. Smith, and M. S. Bowers, “Parametric amplification and oscillation with walk-off-compensating crystals,” J. Opt. Soc. Am. B 14, 460–474 (1997).
[CrossRef]

1995 (3)

1991 (2)

A. E. Siegman, “Defining the effective radius of curvature for a non ideal optical beam,” IEEE J. Quantum Electron. 27, 1146–1148 (1991).
[CrossRef]

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electronic nonlinear refraction in solids,” IEEE J. Quantum Electron. 27, 1296–1309 (1991).
[CrossRef]

Alford, W. J.

Anstett, G.

G. Anstett, G. Goritz, D. Kabs, R. Urschel, R. Wallenstein, and A. Borsutzky, “Reduction of the spectral width and beam divergence of a BBO-OPO by using collinear type-II phase matching and back reflection of the pump beam,” Appl. Phys. B 72, 583–589 (2001).
[CrossRef]

Arisholm, G.

Armstrong, D. J.

Borsutzky, A.

G. Anstett, G. Goritz, D. Kabs, R. Urschel, R. Wallenstein, and A. Borsutzky, “Reduction of the spectral width and beam divergence of a BBO-OPO by using collinear type-II phase matching and back reflection of the pump beam,” Appl. Phys. B 72, 583–589 (2001).
[CrossRef]

Bowers, M. S.

Clark, J. B.

Ebrahimzadeh, M.

M. Sheik-Bahae and M. Ebrahimzadeh, “Measurements of nonlinear refraction in the second-order χ(2) materials KTiOPO4, KNbO3, β-BaB2O4, and LiB3O5,” Opt. Commun. 142, 294–298 (1997).
[CrossRef]

Galvez, E. J.

Gehr, R. J.

Goritz, G.

G. Anstett, G. Goritz, D. Kabs, R. Urschel, R. Wallenstein, and A. Borsutzky, “Reduction of the spectral width and beam divergence of a BBO-OPO by using collinear type-II phase matching and back reflection of the pump beam,” Appl. Phys. B 72, 583–589 (2001).
[CrossRef]

Hagan, D. J.

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electronic nonlinear refraction in solids,” IEEE J. Quantum Electron. 27, 1296–1309 (1991).
[CrossRef]

Hansson, G.

Holmes, C. D.

Hutchings, D. C.

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electronic nonlinear refraction in solids,” IEEE J. Quantum Electron. 27, 1296–1309 (1991).
[CrossRef]

Ji, W.

H. P. Li, C. H. Kam, Y. L. Lam, and W. Ji, “Femtosecond Z-scan measurements of nonlinear refraction in nonlinear optical crystals,” Opt. Mater. 15, 237–242 (2001).
[CrossRef]

Johnson, B. C.

Johnston, T. F.

Kabs, D.

G. Anstett, G. Goritz, D. Kabs, R. Urschel, R. Wallenstein, and A. Borsutzky, “Reduction of the spectral width and beam divergence of a BBO-OPO by using collinear type-II phase matching and back reflection of the pump beam,” Appl. Phys. B 72, 583–589 (2001).
[CrossRef]

Kam, C. H.

H. P. Li, C. H. Kam, Y. L. Lam, and W. Ji, “Femtosecond Z-scan measurements of nonlinear refraction in nonlinear optical crystals,” Opt. Mater. 15, 237–242 (2001).
[CrossRef]

Karlson, H.

Lam, Y. L.

H. P. Li, C. H. Kam, Y. L. Lam, and W. Ji, “Femtosecond Z-scan measurements of nonlinear refraction in nonlinear optical crystals,” Opt. Mater. 15, 237–242 (2001).
[CrossRef]

Laurell, F.

Li, H. P.

H. P. Li, C. H. Kam, Y. L. Lam, and W. Ji, “Femtosecond Z-scan measurements of nonlinear refraction in nonlinear optical crystals,” Opt. Mater. 15, 237–242 (2001).
[CrossRef]

McPhee, E. S.

Newell, V. J.

Raymond, T. D.

Schmitt, R. L.

Sheik-Bahae, M.

M. Sheik-Bahae and M. Ebrahimzadeh, “Measurements of nonlinear refraction in the second-order χ(2) materials KTiOPO4, KNbO3, β-BaB2O4, and LiB3O5,” Opt. Commun. 142, 294–298 (1997).
[CrossRef]

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electronic nonlinear refraction in solids,” IEEE J. Quantum Electron. 27, 1296–1309 (1991).
[CrossRef]

Siegman, A. E.

A. E. Siegman, “Defining the effective radius of curvature for a non ideal optical beam,” IEEE J. Quantum Electron. 27, 1146–1148 (1991).
[CrossRef]

Smith, A. V.

Urschel, R.

G. Anstett, G. Goritz, D. Kabs, R. Urschel, R. Wallenstein, and A. Borsutzky, “Reduction of the spectral width and beam divergence of a BBO-OPO by using collinear type-II phase matching and back reflection of the pump beam,” Appl. Phys. B 72, 583–589 (2001).
[CrossRef]

Van Stryland, E. W.

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electronic nonlinear refraction in solids,” IEEE J. Quantum Electron. 27, 1296–1309 (1991).
[CrossRef]

Wallenstein, R.

G. Anstett, G. Goritz, D. Kabs, R. Urschel, R. Wallenstein, and A. Borsutzky, “Reduction of the spectral width and beam divergence of a BBO-OPO by using collinear type-II phase matching and back reflection of the pump beam,” Appl. Phys. B 72, 583–589 (2001).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. B (1)

G. Anstett, G. Goritz, D. Kabs, R. Urschel, R. Wallenstein, and A. Borsutzky, “Reduction of the spectral width and beam divergence of a BBO-OPO by using collinear type-II phase matching and back reflection of the pump beam,” Appl. Phys. B 72, 583–589 (2001).
[CrossRef]

IEEE J. Quantum Electron. (2)

A. E. Siegman, “Defining the effective radius of curvature for a non ideal optical beam,” IEEE J. Quantum Electron. 27, 1146–1148 (1991).
[CrossRef]

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electronic nonlinear refraction in solids,” IEEE J. Quantum Electron. 27, 1296–1309 (1991).
[CrossRef]

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

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

Opt. Commun. (1)

M. Sheik-Bahae and M. Ebrahimzadeh, “Measurements of nonlinear refraction in the second-order χ(2) materials KTiOPO4, KNbO3, β-BaB2O4, and LiB3O5,” Opt. Commun. 142, 294–298 (1997).
[CrossRef]

Opt. Lett. (1)

Opt. Mater. (1)

H. P. Li, C. H. Kam, Y. L. Lam, and W. Ji, “Femtosecond Z-scan measurements of nonlinear refraction in nonlinear optical crystals,” Opt. Mater. 15, 237–242 (2001).
[CrossRef]

Other (3)

R. DeSalvo, A. A. Said, D. J. Hagan, E. W. Van Stryland, and M. Sheik-Bahae, “Infrared to ultraviolet measurements of two-photon absorption and n2 in wide bandgap solids,” 32, 1324–1333 (1996).

Y. A. Anan’ev, Laser Resonators and the Beam Divergence Problem (Hilger, London, 1992).

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

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Figures (19)

Fig. 1
Fig. 1

(a) Diagram of reference frame and image rotation for successive reflections with nonparallel planes of incidence, and (b) the same diagram showing the reversed propagation vector for the second leg. The sense of rotation as measured in the lower diagram is opposite that measured in the upper diagram. A counterclockwise rotation of the reference frame in the lower diagram corresponds to a clockwise image rotation in going from the initial to the final reference plane.

Fig. 2
Fig. 2

Example of a four-mirror nonplanar ring resonator. The even-numbered propagation vectors are drawn reversed, as discussed in the text.

Fig. 3
Fig. 3

Unit-sphere diagrams of the propagation vectors (kˆ1,-kˆ2, kˆ3,-kˆ4) for the cavity shown in Fig. 2. The upper figure (a) is drawn on a transparent sphere and shows great arcs connecting the tips of pairs of kˆ vectors. These arcs lie in the plane of incidence for the corresponding reflection and have an are length equal to the reflection angle. The image-rotation angle for one pass of the resonator is given by -(γ1+γ2+γ3+γ4). The lower figure (b) is drawn on an opaque sphere and shows auxiliary arcs connecting the tip of each kˆ vector with an auxiliary point O along with the labeling convention used in the text.

Fig. 4
Fig. 4

Diagram of the RISTRA resonator viewed from the top, side, and end, showing how α and β are defined.

Fig. 5
Fig. 5

Unit-sphere diagram of the RISTRA resonator. The spherical quadrilateral is symmetric to reflection in the XZ and XY planes. All sides are equal to 65.53°, so all mirrors have 32.8° angles of incidence. The image-rotation angle is 90°.

Fig. 6
Fig. 6

Diagram of the RISTRA OPO incorporating walk-off-compensating nonlinear crystals. Legs L1 and L2 lie in the horizontal plane; legs L1 and L4 lie in the vertical plane. The eigenpolarizations of the crystal and the cavity lie in the horizontal and vertical planes.

Fig. 7
Fig. 7

Model predictions of (a) signal energy and (b) signal-beam quality factor M2 for a 15-mJ pump pulse as a function of output-coupler reflectivity for various pump-pulse durations. The RISTRA cavity is 110 mm long with one 15-mm KTP crystal, and the pump-beam diameter is 2.1 mm 1/e2.

Fig. 8
Fig. 8

Measured far-field signal fluence profile shown in (a) wire grid and (b) contour for the RISTRA OPO pumped at 4× threshold by a small-diameter (∼2 mm 1/e2), spatially filtered pump beam. The fluence contours in the lower figure (b) are exponentially spaced to emphasize the low-level structure. The lowest contour is at 0.01 of the maximum fluence, and each contour is at 1.31 times the previous. The highest contour corresponds to 0.88 of the maximum fluence.

Fig. 9
Fig. 9

(a) Large-diameter, unfiltered pump-beam fluence profile at the input to the OPO and (b) corresponding signal fluence profile at the output coupler of the OPO.

Fig. 10
Fig. 10

Far-field pump fluence profile shown in (a) wire grid and (b) contour. The contours are exponentially spaced as in Fig. 8.

Fig. 11
Fig. 11

Signal energy versus pump energy for the seeded and unseeded RISTRA OPO pumped by the large-diameter pump beam.

Fig. 12
Fig. 12

OPO is injection seeded with parallel idler and pump Poynting vectors. The far-field signal fluence profile in (a) wire grid and (b) contour for the RISTRA OPO pumped at 3× threshold by the large-diameter pump. The contours are exponentially spaced as in Fig. 8.

Fig. 13
Fig. 13

Second-moment data (squares) and least-squares fit (solid curve), plus knife-edge data (diamonds) and least-squares fit (dashed curve) for the experimental conditions of Fig. 12.

Fig. 14
Fig. 14

OPO is unseeded with parallel idler and pump Poynting vectors. The far-field signal-fluence profile in (a) wire grid and (b) contour for the RISTRA OPO pumped at 3× the seeded threshold by the large-diameter pump. The contours are exponentially spaced as in Fig. 8.

Fig. 15
Fig. 15

Comparison of far-field signal fluence profiles for (a) three-mirror-ring image-inverting OPO and (b) the RISTRA OPO, both pumped 4× threshold with the large-diameter pump beam. Both OPOs are injection seeded, with parallel idler and pump Poynting vectors. The contours are exponentially spaced as in Fig. 8.

Fig. 16
Fig. 16

OPO is injection seeded with parallel idler and signal Poynting vectors. The far-field signal fluence profile in (a) wire grid and (b) contour for the RISTRA OPO pumped 4× threshold with the large-diameter pump beam. The contours are exponentially spaced as in Fig. 8.

Fig. 17
Fig. 17

OPO is unseeded and with parallel idler and signal Poynting vectors. The far-field signal fluence profile in (a) wire grid and (b) contour for the RISTRA OPO pumped 4× the seeded threshold with the large-diameter pump beam. Contours are exponentially spaced as in Fig. 8.

Fig. 18
Fig. 18

OPO is injection seeded with parallel signal and pump Poynting vectors. The far-field signal fluence profile in (a) wire grid and (b) contour for the RISTRA OPO pumped 3× threshold with the large-diameter pump beam. The contours are exponentially spaced as in Fig. 8.

Fig. 19
Fig. 19

OPO is injection seeded with parallel signal and pump Poynting vectors. A phase-distorting microscope slide was inserted in the pump beam 50 mm in front of the OPO input coupler. The far-field signal fluence profile in (a) wire grid and (b) contour for the RISTRA OPO pumped 3× threshold with the large-diameter pump beam. The contours are exponentially spaced as in Fig. 8.

Tables (1)

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Table 1 Specifications for the Twisted-Rectangle OPO

Equations (41)

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xy=x-y=Mxy
M=100-1.
xy=Rxy,
R=cos γsin γ-sin γcos γ.
xy=Mxy,
xy=MRMxy.
x1y1=MR41MR34MR23MR12x0y0,
x1y1=(MR41M)R34(MR23M)R12x0y0.
(MRM)=100-1cos γsin γ-sin γcos γ100-1=cos γ-sin γsin γcos γ=R-1,
x1y1=R41-1R34R23-1R12x0y0.
x1y1=R¯41R34R¯23R12x0y0,
Θ=-(γ1+γ2+γ3+γ4).
Θ=A+B+C+D+E+F+G+H-4π
=(A+B+I)+(C+D+J)+(E+F+K)+(G+H+L)-6π.
Θ=(AreaΔQRO+AreaΔRSO+AreaΔSTO+AreaΔTQO)-2π=AreaQuadrilateral-2π,
L1 sin θ1 cos ϕ1+L2 sin θ2 cos ϕ2+L3 sin θ3 cos ϕ3
+L4 sin θ4 cos ϕ4=0,
L1 sin θ1 sin ϕ1+L2 sin θ2 sin ϕ2+L3 sin θ3 sin ϕ3
+L4 sin θ4 sin ϕ4=0,
L1 cos θ1+L2 cos θ2+L3 cos θ3+L4 cos θ4=0.
4(A+B+C-π)=π/2,
A+B=5π/8.
cos A=-cos B cos C+sin B sin C cos a,
a=arccos12 sin 38π.
L1 sin α=L2 sin β,
xyαxαy=0-1001000000-1001010L0010L00100001xyαxαy,
x+y+αyL=0,
x-y+αxL=0,
αx+αy=0,
αx-αy=0,
x=y=αx=αy=0
xyαx+2ϕxαy+2ϕy,
x+y+(αy+2ϕy)L=0,
x-y+(αx+2ϕx)L=0,
αx+αy+2ϕy=0,
αx+2ϕx-αy=0,
x=-Lϕx,
y=-Lϕy,
αx=-ϕx-ϕy,
αy=ϕx-ϕy,
θp=ρs ωiωp=16mrad,

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