Abstract

The azimuthal dependence of third-order and cascaded second-order nonlinear coupling was used to measure the relative contributions of each to direct third-harmonic generation in β-barium borate. This permitted the measurement of the values of tensor elements χ103, χ113, and χ163 relative to the known χij2. Finally, conversion efficiencies to 3ω of up to 6% were achieved with a femtosecond chirped-pulse amplification laser with 200 GW/cm2 in collimated beams.

© 1999 Optical Society of America

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  1. R. W. Terhune, P. D. Maker, and C. M. Savage, Appl. Phys. Lett. 2, 54 (1963).
    [CrossRef]
  2. P. D. Maker and R. W. Terhune, Phys. Rev. A 137, 801 (1965).
    [CrossRef]
  3. R. C. Eckardt and C. H. Lee, Appl. Phys. Lett. 15, 425 (1969).
    [CrossRef]
  4. B. C. Stuart, M. D. Feit, A. M. Rubenchik, B. W. Shore, and M. D. Perry, Phys. Rev. Lett. 74, 2248 (1995).
    [CrossRef] [PubMed]
  5. A. Penzkofer, F. Ossig, and P. Qiu, Appl. Phys. B 47, 71 (1988).
    [CrossRef]
  6. P. Qiu and A. Penzkofer, Appl. Phys. B 45, 225 (1988).
    [CrossRef]
  7. I. V. Tomov, B. Van Wonterghem, and P. M. Rentzepis, Appl. Opt. 31, 4172 (1992).
    [CrossRef] [PubMed]
  8. C. Flytzanis and N. Bloembergen, Prog. Quantum Electron. 4, 271 (1976).
    [CrossRef]
  9. G. R. Meredith, J. Chem. Phys. 77, 5863 (1982).
    [CrossRef]
  10. For an excellent explanation of the use of degeneracy factors in nonlinear optics, see P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge U. Press, Cambridge, 1990), Chaps. 2 and 7.
  11. B. C. Stuart, S. Herman, and M. D. Perry, IEEE J. Quantum Electron. 31, 528 (1995).
    [CrossRef]
  12. K. Kato, IEEE J. Quantum Electron. QE-22, 1013 (1986).
    [CrossRef]
  13. Y. X. Fan, R. C. Eckardt, R. L. Byer, C. Chen, and A. D. Jiang, IEEE J. Quantum Electron. 25, 1196 (1989).
    [CrossRef]

1995 (2)

B. C. Stuart, M. D. Feit, A. M. Rubenchik, B. W. Shore, and M. D. Perry, Phys. Rev. Lett. 74, 2248 (1995).
[CrossRef] [PubMed]

B. C. Stuart, S. Herman, and M. D. Perry, IEEE J. Quantum Electron. 31, 528 (1995).
[CrossRef]

1992 (1)

1989 (1)

Y. X. Fan, R. C. Eckardt, R. L. Byer, C. Chen, and A. D. Jiang, IEEE J. Quantum Electron. 25, 1196 (1989).
[CrossRef]

1988 (2)

A. Penzkofer, F. Ossig, and P. Qiu, Appl. Phys. B 47, 71 (1988).
[CrossRef]

P. Qiu and A. Penzkofer, Appl. Phys. B 45, 225 (1988).
[CrossRef]

1986 (1)

K. Kato, IEEE J. Quantum Electron. QE-22, 1013 (1986).
[CrossRef]

1982 (1)

G. R. Meredith, J. Chem. Phys. 77, 5863 (1982).
[CrossRef]

1976 (1)

C. Flytzanis and N. Bloembergen, Prog. Quantum Electron. 4, 271 (1976).
[CrossRef]

1969 (1)

R. C. Eckardt and C. H. Lee, Appl. Phys. Lett. 15, 425 (1969).
[CrossRef]

1965 (1)

P. D. Maker and R. W. Terhune, Phys. Rev. A 137, 801 (1965).
[CrossRef]

1963 (1)

R. W. Terhune, P. D. Maker, and C. M. Savage, Appl. Phys. Lett. 2, 54 (1963).
[CrossRef]

Bloembergen, N.

C. Flytzanis and N. Bloembergen, Prog. Quantum Electron. 4, 271 (1976).
[CrossRef]

Butcher, P. N.

For an excellent explanation of the use of degeneracy factors in nonlinear optics, see P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge U. Press, Cambridge, 1990), Chaps. 2 and 7.

Byer, R. L.

Y. X. Fan, R. C. Eckardt, R. L. Byer, C. Chen, and A. D. Jiang, IEEE J. Quantum Electron. 25, 1196 (1989).
[CrossRef]

Chen, C.

Y. X. Fan, R. C. Eckardt, R. L. Byer, C. Chen, and A. D. Jiang, IEEE J. Quantum Electron. 25, 1196 (1989).
[CrossRef]

Cotter, D.

For an excellent explanation of the use of degeneracy factors in nonlinear optics, see P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge U. Press, Cambridge, 1990), Chaps. 2 and 7.

Eckardt, R. C.

Y. X. Fan, R. C. Eckardt, R. L. Byer, C. Chen, and A. D. Jiang, IEEE J. Quantum Electron. 25, 1196 (1989).
[CrossRef]

R. C. Eckardt and C. H. Lee, Appl. Phys. Lett. 15, 425 (1969).
[CrossRef]

Fan, Y. X.

Y. X. Fan, R. C. Eckardt, R. L. Byer, C. Chen, and A. D. Jiang, IEEE J. Quantum Electron. 25, 1196 (1989).
[CrossRef]

Feit, M. D.

B. C. Stuart, M. D. Feit, A. M. Rubenchik, B. W. Shore, and M. D. Perry, Phys. Rev. Lett. 74, 2248 (1995).
[CrossRef] [PubMed]

Flytzanis, C.

C. Flytzanis and N. Bloembergen, Prog. Quantum Electron. 4, 271 (1976).
[CrossRef]

Herman, S.

B. C. Stuart, S. Herman, and M. D. Perry, IEEE J. Quantum Electron. 31, 528 (1995).
[CrossRef]

Jiang, A. D.

Y. X. Fan, R. C. Eckardt, R. L. Byer, C. Chen, and A. D. Jiang, IEEE J. Quantum Electron. 25, 1196 (1989).
[CrossRef]

Kato, K.

K. Kato, IEEE J. Quantum Electron. QE-22, 1013 (1986).
[CrossRef]

Lee, C. H.

R. C. Eckardt and C. H. Lee, Appl. Phys. Lett. 15, 425 (1969).
[CrossRef]

Maker, P. D.

P. D. Maker and R. W. Terhune, Phys. Rev. A 137, 801 (1965).
[CrossRef]

R. W. Terhune, P. D. Maker, and C. M. Savage, Appl. Phys. Lett. 2, 54 (1963).
[CrossRef]

Meredith, G. R.

G. R. Meredith, J. Chem. Phys. 77, 5863 (1982).
[CrossRef]

Ossig, F.

A. Penzkofer, F. Ossig, and P. Qiu, Appl. Phys. B 47, 71 (1988).
[CrossRef]

Penzkofer, A.

A. Penzkofer, F. Ossig, and P. Qiu, Appl. Phys. B 47, 71 (1988).
[CrossRef]

P. Qiu and A. Penzkofer, Appl. Phys. B 45, 225 (1988).
[CrossRef]

Perry, M. D.

B. C. Stuart, S. Herman, and M. D. Perry, IEEE J. Quantum Electron. 31, 528 (1995).
[CrossRef]

B. C. Stuart, M. D. Feit, A. M. Rubenchik, B. W. Shore, and M. D. Perry, Phys. Rev. Lett. 74, 2248 (1995).
[CrossRef] [PubMed]

Qiu, P.

A. Penzkofer, F. Ossig, and P. Qiu, Appl. Phys. B 47, 71 (1988).
[CrossRef]

P. Qiu and A. Penzkofer, Appl. Phys. B 45, 225 (1988).
[CrossRef]

Rentzepis, P. M.

Rubenchik, A. M.

B. C. Stuart, M. D. Feit, A. M. Rubenchik, B. W. Shore, and M. D. Perry, Phys. Rev. Lett. 74, 2248 (1995).
[CrossRef] [PubMed]

Savage, C. M.

R. W. Terhune, P. D. Maker, and C. M. Savage, Appl. Phys. Lett. 2, 54 (1963).
[CrossRef]

Shore, B. W.

B. C. Stuart, M. D. Feit, A. M. Rubenchik, B. W. Shore, and M. D. Perry, Phys. Rev. Lett. 74, 2248 (1995).
[CrossRef] [PubMed]

Stuart, B. C.

B. C. Stuart, M. D. Feit, A. M. Rubenchik, B. W. Shore, and M. D. Perry, Phys. Rev. Lett. 74, 2248 (1995).
[CrossRef] [PubMed]

B. C. Stuart, S. Herman, and M. D. Perry, IEEE J. Quantum Electron. 31, 528 (1995).
[CrossRef]

Terhune, R. W.

P. D. Maker and R. W. Terhune, Phys. Rev. A 137, 801 (1965).
[CrossRef]

R. W. Terhune, P. D. Maker, and C. M. Savage, Appl. Phys. Lett. 2, 54 (1963).
[CrossRef]

Tomov, I. V.

Van Wonterghem, B.

Appl. Opt. (1)

Appl. Phys. B (2)

A. Penzkofer, F. Ossig, and P. Qiu, Appl. Phys. B 47, 71 (1988).
[CrossRef]

P. Qiu and A. Penzkofer, Appl. Phys. B 45, 225 (1988).
[CrossRef]

Appl. Phys. Lett. (2)

R. W. Terhune, P. D. Maker, and C. M. Savage, Appl. Phys. Lett. 2, 54 (1963).
[CrossRef]

R. C. Eckardt and C. H. Lee, Appl. Phys. Lett. 15, 425 (1969).
[CrossRef]

IEEE J. Quantum Electron. (3)

B. C. Stuart, S. Herman, and M. D. Perry, IEEE J. Quantum Electron. 31, 528 (1995).
[CrossRef]

K. Kato, IEEE J. Quantum Electron. QE-22, 1013 (1986).
[CrossRef]

Y. X. Fan, R. C. Eckardt, R. L. Byer, C. Chen, and A. D. Jiang, IEEE J. Quantum Electron. 25, 1196 (1989).
[CrossRef]

J. Chem. Phys. (1)

G. R. Meredith, J. Chem. Phys. 77, 5863 (1982).
[CrossRef]

Phys. Rev. A (1)

P. D. Maker and R. W. Terhune, Phys. Rev. A 137, 801 (1965).
[CrossRef]

Phys. Rev. Lett. (1)

B. C. Stuart, M. D. Feit, A. M. Rubenchik, B. W. Shore, and M. D. Perry, Phys. Rev. Lett. 74, 2248 (1995).
[CrossRef] [PubMed]

Prog. Quantum Electron. (1)

C. Flytzanis and N. Bloembergen, Prog. Quantum Electron. 4, 271 (1976).
[CrossRef]

Other (1)

For an excellent explanation of the use of degeneracy factors in nonlinear optics, see P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge U. Press, Cambridge, 1990), Chaps. 2 and 7.

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Figures (2)

Fig. 1
Fig. 1

Measured effective nonlinear coupling for internal azimuthal angle ϕint for (a) type  I and (b) type  II phase matching. The curves in (a) and (b) are the fits to the data by use of Eqs.  (6) and (8), respectively.

Fig. 2
Fig. 2

Conversion efficiency E3ω/Eω from a single BBO crystal at 351  nm, along with a quadratic fit to low drive points. (a) Type  I phase matching with ϕint=-15°. (b) Type  II phase matching with ϕint=0°.

Equations (8)

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Ceff=2ωdSHGdSFGn2ωcΔkSFG,
Ceff=Ceff3+Ki=1nkiCi,eff2,
CeffI=Ceff3+ωcdSHGooodSFGooen2ωoΔkSFGooe+dSHGooedSFGoeen2ωeΔkSFGoee.
CeffII=Ceff3+ω3cdSHGooodSFGeoen2ωoΔkSFGeoe+dSHGooedSFGeeen2ωeΔkSFGeee+2dSHGoeodSFGooen2ωoΔkSFGooe+2dSHGoeedSFGoeen2ωeΔkSFGoee.
Ceff=C10cos3ϕsinθm+ωc×d222sin6ϕ2cosθmn2ωoΔkSFGooe-cos3θmn2ωeΔkSFGoee+d22d15cos3ϕcos2θmsinθmn2ωeΔkSFGoee-sinθmn2ωoΔkSFGooe.
Ceff=Asin6ϕ+sinθmC10-Bcos3ϕ,
Ceff=ω3cd222cos23ϕ2cos4θmn2ωeΔkSFGoee-cos2θmn2ωoΔkSFGeoe+sin23ϕ2cos2θmn2ωoΔkSFGooe-cos4θmn2ωeΔkSFGeee-2d22d15×sin3ϕsinθmcos3θmn2ωeΔkSFGeee+sin2θmn2ωoΔkSFGooe+d152× sin2θm3cos2θmn2ωeΔkSFGeee+2n2ωoΔkSFGooe+d33n2ωeΔkSFGeee×(-d22sin3ϕcosθm sin3θm+d15 sin4θm)+C113cos2θm+C16 sin2θm+C10sin2θmsin3ϕ.
Ceff=A cos23ϕ+B sin23ϕ+sin3ϕD+Ed33+3C10sin2θm+Fd33+3C113cos2θm+C16 sin2θm,

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