Abstract

A theoretical study is presented that enables the calculation of the optimal focusing parameters in a singly resonant optical parametric oscillator and difference-frequency generation with elliptical foci. The effect of diffraction, phase matching, beam walk-off, and resonator astigmatism are included in the model. The results show that an optimal focusing configuration is obtained with unequal confocal beam parameters and that an elliptical beam profile can substantially increase the conversion efficiency when beam walk-off is present in the crystal.

© 1998 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused Gaussian light beams,” J. Appl. Phys. 39, 3597 (1968).
    [CrossRef]
  2. R. Fischer, C. Tran-bá, and L. W. Wieczorek, “Optimal focusing in a singly resonant optical parametric oscillator,” Sov. J. Quantum Electron. 7, 1455 (1977).
    [CrossRef]
  3. S. Guha, F. Wu, and J. Falk, “The effects of focusing on parametric oscillation,” IEEE J. Quantum Electron. QE-18, 907 (1982).
    [CrossRef]
  4. S. Guha and J. Falk, “The effects of focusing in the three-frequency parametric upconverter,” J. Appl. Phys. 51, 50 (1980).
    [CrossRef]
  5. H. W. Kogelnik, E. P. Ippen, A. Dienes, and C. V. Shank, “Astigmatically compensated cavities for cw dye lasers,” IEEE J. Quantum Electron. QE-8, 373 (1972).
    [CrossRef]
  6. S. D. Butterworth, S. Girard, and D. C. Hanna, “High power, broadly tunable all-solid-state synchronously pumped LBO optical parametric oscillator,” J. Opt. Soc. Am. B 12, 2158 (1995).
    [CrossRef]
  7. J. D. Kafka, M. L. Watts, and J. W. Pieterse, “Synchronously pumped optical parametric oscillator with LBO,” J. Opt. Soc. Am. B 12, 2147 (1995).
    [CrossRef]
  8. P. Lorrain, D. R. Corson, and F. Lorrain, Electromagnetic Fields and Waves, 3rd ed. (Freeman, San Francisco, Calif., 1988), p. 737.
  9. E. Zauderer, Partial Differential Equations of Applied Mathematics (Wiley, New York, 1989), p. 470.
  10. W. H. Press, S. A. Teukolsky, B. P. Flannery, and W. T. Vetterling, Numerical Recipes (The Art of Scientific Computing) (Cambridge U. Press, Cambridge, UK, 1986).
  11. V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer-Verlag, Berlin, 1991).
  12. SNLO nonlinear optics code available from A. V. Smith, Sandia National Laboratories, Albuquerque, New Mexico 87185–1423.

1995

1982

S. Guha, F. Wu, and J. Falk, “The effects of focusing on parametric oscillation,” IEEE J. Quantum Electron. QE-18, 907 (1982).
[CrossRef]

1980

S. Guha and J. Falk, “The effects of focusing in the three-frequency parametric upconverter,” J. Appl. Phys. 51, 50 (1980).
[CrossRef]

1977

R. Fischer, C. Tran-bá, and L. W. Wieczorek, “Optimal focusing in a singly resonant optical parametric oscillator,” Sov. J. Quantum Electron. 7, 1455 (1977).
[CrossRef]

1972

H. W. Kogelnik, E. P. Ippen, A. Dienes, and C. V. Shank, “Astigmatically compensated cavities for cw dye lasers,” IEEE J. Quantum Electron. QE-8, 373 (1972).
[CrossRef]

1968

G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused Gaussian light beams,” J. Appl. Phys. 39, 3597 (1968).
[CrossRef]

Boyd, G. D.

G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused Gaussian light beams,” J. Appl. Phys. 39, 3597 (1968).
[CrossRef]

Butterworth, S. D.

Dienes, A.

H. W. Kogelnik, E. P. Ippen, A. Dienes, and C. V. Shank, “Astigmatically compensated cavities for cw dye lasers,” IEEE J. Quantum Electron. QE-8, 373 (1972).
[CrossRef]

Falk, J.

S. Guha, F. Wu, and J. Falk, “The effects of focusing on parametric oscillation,” IEEE J. Quantum Electron. QE-18, 907 (1982).
[CrossRef]

S. Guha and J. Falk, “The effects of focusing in the three-frequency parametric upconverter,” J. Appl. Phys. 51, 50 (1980).
[CrossRef]

Fischer, R.

R. Fischer, C. Tran-bá, and L. W. Wieczorek, “Optimal focusing in a singly resonant optical parametric oscillator,” Sov. J. Quantum Electron. 7, 1455 (1977).
[CrossRef]

Girard, S.

Guha, S.

S. Guha, F. Wu, and J. Falk, “The effects of focusing on parametric oscillation,” IEEE J. Quantum Electron. QE-18, 907 (1982).
[CrossRef]

S. Guha and J. Falk, “The effects of focusing in the three-frequency parametric upconverter,” J. Appl. Phys. 51, 50 (1980).
[CrossRef]

Hanna, D. C.

Ippen, E. P.

H. W. Kogelnik, E. P. Ippen, A. Dienes, and C. V. Shank, “Astigmatically compensated cavities for cw dye lasers,” IEEE J. Quantum Electron. QE-8, 373 (1972).
[CrossRef]

Kafka, J. D.

Kleinman, D. A.

G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused Gaussian light beams,” J. Appl. Phys. 39, 3597 (1968).
[CrossRef]

Kogelnik, H. W.

H. W. Kogelnik, E. P. Ippen, A. Dienes, and C. V. Shank, “Astigmatically compensated cavities for cw dye lasers,” IEEE J. Quantum Electron. QE-8, 373 (1972).
[CrossRef]

Pieterse, J. W.

Shank, C. V.

H. W. Kogelnik, E. P. Ippen, A. Dienes, and C. V. Shank, “Astigmatically compensated cavities for cw dye lasers,” IEEE J. Quantum Electron. QE-8, 373 (1972).
[CrossRef]

Tran-bá, C.

R. Fischer, C. Tran-bá, and L. W. Wieczorek, “Optimal focusing in a singly resonant optical parametric oscillator,” Sov. J. Quantum Electron. 7, 1455 (1977).
[CrossRef]

Watts, M. L.

Wieczorek, L. W.

R. Fischer, C. Tran-bá, and L. W. Wieczorek, “Optimal focusing in a singly resonant optical parametric oscillator,” Sov. J. Quantum Electron. 7, 1455 (1977).
[CrossRef]

Wu, F.

S. Guha, F. Wu, and J. Falk, “The effects of focusing on parametric oscillation,” IEEE J. Quantum Electron. QE-18, 907 (1982).
[CrossRef]

IEEE J. Quantum Electron.

H. W. Kogelnik, E. P. Ippen, A. Dienes, and C. V. Shank, “Astigmatically compensated cavities for cw dye lasers,” IEEE J. Quantum Electron. QE-8, 373 (1972).
[CrossRef]

S. Guha, F. Wu, and J. Falk, “The effects of focusing on parametric oscillation,” IEEE J. Quantum Electron. QE-18, 907 (1982).
[CrossRef]

J. Appl. Phys.

S. Guha and J. Falk, “The effects of focusing in the three-frequency parametric upconverter,” J. Appl. Phys. 51, 50 (1980).
[CrossRef]

G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused Gaussian light beams,” J. Appl. Phys. 39, 3597 (1968).
[CrossRef]

J. Opt. Soc. Am. B

Sov. J. Quantum Electron.

R. Fischer, C. Tran-bá, and L. W. Wieczorek, “Optimal focusing in a singly resonant optical parametric oscillator,” Sov. J. Quantum Electron. 7, 1455 (1977).
[CrossRef]

Other

P. Lorrain, D. R. Corson, and F. Lorrain, Electromagnetic Fields and Waves, 3rd ed. (Freeman, San Francisco, Calif., 1988), p. 737.

E. Zauderer, Partial Differential Equations of Applied Mathematics (Wiley, New York, 1989), p. 470.

W. H. Press, S. A. Teukolsky, B. P. Flannery, and W. T. Vetterling, Numerical Recipes (The Art of Scientific Computing) (Cambridge U. Press, Cambridge, UK, 1986).

V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer-Verlag, Berlin, 1991).

SNLO nonlinear optics code available from A. V. Smith, Sandia National Laboratories, Albuquerque, New Mexico 87185–1423.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Experimental layout of a synchronously pumped OPO based on a Brewster-angled nonlinear crystal: M1, 100-mm radius of curvature; M2, 250-mm radius of curvature; OC, 9% output coupler; FL, focusing lens, 200 mm.

Fig. 2
Fig. 2

Signal-beam area in a Brewster-angled nonlinear for an astigmatism-compensated cavity. The dashed and dotted lines indicate the focus locations in the x and y planes, respectively. The minimum beam area is located at 12 mm, and the mean focus location is at the crystal center.

Fig. 3
Fig. 3

Variation of the spatial-overlap coefficient hsm as a function of the pump-focusing parameter ξp=lc/bpx with the signal-focusing parameter ξs=0.2, 1, 5 for a Brewster-angled LBO OPO.

Fig. 4
Fig. 4

Variation of the spatial-overlap coefficient hsm as a function of the mean focus position z0 with the signal-focusing parameter ξs=2.1g for a Brewster-angled LBO OPO. The solid curve at 15 mm is the crystal center.

Fig. 5
Fig. 5

Variation of the spatial-overlap coefficient hsm as a function of the focusing parameter ξ=ξs=ξp=lc/bpx with the parameter ϑellips=1, 2.5, 5, 10 for downconversion in LiNbO3.

Fig. 6
Fig. 6

Variation of the spatial-overlap coefficient hsm as a function of the focusing parameter ξ=ξs=ξp=lc/bpx with the parameter ϑellips=1, 2.5, 5, 10 for downconversion in AgGaS2.

Fig. 7
Fig. 7

Variation of the spatial-overlap coefficient hsm as a function of the parameter ϑellips for downconversion in LiNbO3 and AgGaS2.

Equations (46)

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

ΔPs=-12 ωs Im Es*Psnldxdydz,
Psnl=20deffEpEi*,
ΔPs=-ωs0deff Im Es*EpEi*dxdydz.
Pinl=20deffEpEs*
2Ei(r, t)-μ0 2t2 Ei(r, t)=μ0 2t2 Pinl(r, t).
Ei(r, t)=μ0ωi24π d3r Pinl(r)exp(-iωit)|r-r|,
t=t-|r-r|vi.
ki=kp-ks.
|r-r|=z-z+12 (x-x)2+(y-y)2(z-z).
Ep(x, y, z, t)=E0p(1+iζpx)(1+iζpy) exp(ikpz)×exp(-iωpt)exp-x2w0p2(1+iζpx)×exp-[y-ρ(z-zc)]2ϑellips2w0p2(1+iζpy).
Es(x, y, z, t)=E0s(1+iζsx)(1+iζsy)× exp(iksz)exp(-iωst)×exp-x2w0s2(1+iζsx)×exp-y2ϑellips2w0s2(1+iζsy).
|E0j|2=4Pjπϑellipsw0j20njc,
ζjx=2bjx (z-z0x),ζjy=2bjy (z-z0y),
ϑellips=w0yw0x,bjx=w0j2kj,bjy=ϑellips2w0j2kj,
Ei(x, y, z)=0zK1 exp(iΔkz)exp(ikiz)π2ibxiby×exp(a1xx2+a1yy2+2a2ρy-a3ρ2)dz,
Δk=kp-(ks+ki),
K1=ωi2deff2πc2 E0pE0s*(1+iζpx)(1+iζpy)(1-iζsx)(1-iζsy)×1(z-z),
ibj=1cpj+1csj*-iki2(z-z),
cpx=w0p2(1+iζpx)=w0p21+i 2bpx (z-z0x),
csx=w0s2(1+iζsx)=w0s21+i 2bsx (z-z0x),
cpy=ϑellips2w0p2(1+iζpy)=ϑellips2w0p21+i 2bpy (z-z0y),
csy=ϑellips2w0s2(1+iζsy)=ϑellips2w0s21+i 2bsy (z-z0y),
a1j=iki2(z-z)-ki2(z-z)24ibj,
a2=-2iki(z-zc)4iby(z-z)cpy,
a3=(z-zc)21cpy-1cpy2iby,
ΔPs=32πdeff2PpPslcnpnsnic0λsλi kskpks+kp hs,
hs=14 k+1kξs+ξp×Re 010z2 ϑellips exp[iΔklc(z2-z1)]exp(-fwρ2)dz1dz2[(z1+Asx)(z2+Asx*)+Csx][(z1+Asy)(z2+Asy*)+Csy],
Asx=-z0xlc-i4 1d1+1d2,
Csx=-116 1d1-1d22,
Asy=-z0ylc-iϑellips24 1d1+1d2,
Csy=-ϑellips416 1d1-1d22,
d1=ξsξp(k-1)kξp+ξs,ξp=lcbpx,ξs=lcbsx,
d2=kξs+ξpk-1,k=kpks,z1=zlc,
z2=zlc,z3=zclc,
fw=a3*+lc2(z2-z3)2cpy-1ib1y lc(z2-z3)cpy+a2*2,
ib1y=1cpy+1csy*-a1y*,
cpy=ϑellips2w0p2(1+iζpy)=ϑellips2w0p21+i 2bpy (z-z0y),
csy*=ϑellips2w0s2(1-iζsy)=ϑellips2w0s21-i 2bsy (z-z0y).
ΔPs=lossPs,
lossPs=K2PsPpths,
K2=32πdeff2lcnpnsnic0λsλi kskpks+kp.
Ppt=lossK2hs.
ΔPi=-12 ωi Im Ei*Pinldxdydz.
ΔPi=-ωi0deff Im Ei*EpEs*dxdydz.
ΔPi=32πdeff2PpPslcnpnsnic0λi2 kskpks+kp hs,
z0=z0x+z0y2.

Metrics