Abstract

The second-order susceptibility d 36 of ammonium dihydrogen phosphate (ADP) was determined from phase-matched second-harmonic generation (SHG) at two wavelengths. A cw single-mode He–Ne laser (λ = 633 nm) and a cw single-mode Nd:YAG laser (λ = 1064 nm) were used as fundamental beam sources. The results were d 36(ADP, 633 nm) = (1.31 ± 0.05) × 10−9 esu = 0.55 ± 0.02 pm/V and d 36(ADP, 1064 nm) = (1.10 ± 0.06) × 10−9 esu = 0.46 ± 0.03 pm/V. The d 11 values of α-quartz were determined relative to d 36(ADP) to be d 11(α-quartz, 633 nm) = (7.4 ± 0.3) × 10−10 esu = 0.31 ± 0.01 pm/V and d 11(α-quartz, 1064 nm) = (7.1 ± 0.3) × 10−10 esu = 0.30 ± 0.01 pm/V by the use of the Maker fringe method. The Miller’s delta of ADP and α-quartz is in good agreement at the two wavelengths.

© 1995 Optical Society of America

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  1. W. E. Torruellas, G. Krijnen, D. Y. Kim, R. Sciek, G. I. Stegeman, P. Vidakovic, J. Zyss, “Cascading nonlinearities in an organic single crystal core fiber: the Čerenkov regime,” Opt. Commun. 112, 122–130 (1994).
    [CrossRef]
  2. G. R. Meredith, “Cascading in optical third-harmonic generation by crystalline quartz,” Phys. Rev. B 24, 5522–5532 (1981).
    [CrossRef]
  3. B. Buchalter, G. R. Meredith, “Third-order optical susceptibility of glasses determined by third harmonic generation,” Appl. Opt. 21, 3221–3224 (1982).
    [CrossRef] [PubMed]
  4. R. Hellwarth, J. Cherlow, T. T. Young, “Origin and frequency dependence of nonlinear optical susceptibilities of glasses,” Phys. Rev. 11, 964–967 (1975).
    [CrossRef]
  5. A. Owyoung, “Ellipse rotation studies in laser host materials,” IEEE J. Quantum Electron. QE-9, 1064–1069 (1973).
    [CrossRef]
  6. D. Milliam, M. J. Weber, “Measurement of nonlinear refractive-index coefficients using time-resolved interferometry: application to optical materials for high-power neodymium lasers,” J. Appl. Phys. 47, 2497–2501 (1976).
    [CrossRef]
  7. R. Adair, L. L. Chase, S. A. Payne, “Nonlinear refractive index of optical crystal,” Phys. Rev. 39, 3337–3350 (1989).
    [CrossRef]
  8. N. L. Boling, A. J. Glass, A. Owyoung, “Empirical relationships for predicting nonlinear refractive index changes in optical solids,” IEEE J. Quantum Electron. QE-14, 601–608 (1978).
    [CrossRef]
  9. J. R. Heflin, Y. M. Cai, A. F. Garito, “Dispersion measurements of electric-field-induced second-harmonic generation and third-harmonic generation in conjugated linear chains,” J. Opt. Soc. Am. B 8, 2132–2136 (1991).
    [CrossRef]
  10. M. M. Choy, R. L. Byer, “Accurate second-order susceptibility measurements of visible and infrared nonlinear crystals,” Phys. Rev. B 14, 1693–1706 (1976).
    [CrossRef]
  11. D. A. Roberts, “Simplified characterization of uniaxial and biaxial nonlinear optical crystals: a plea for standardization of nomenclature and conventions,” IEEE J. Quantum Electron. 28, 2057–2074 (1992).
    [CrossRef]
  12. R. C. Eckardt, H. Masuda, Y. X. Fan, R. L. Byer, “Absolute and relative nonlinear optical coefficients of KDP, KD*P, BaB2O4, LiIO3, MgO:LiNbO3, and KTP measured by phase-matched second-harmonic generation,” IEEE J. Quantum Electron. 26, 922–933 (1990).
    [CrossRef]
  13. A. Mito, K. Hagimoto, C. Takahashi, “Determination of the third-order optical nonlinear susceptibility of fused silica using optical harmonic generation methods,” Nonlinear Opt. (to be published).
  14. R. C. Miller, “Optical second harmonic generation in piezoelectric crystals,” Appl. Phys. Lett. 5, 17–19 (1964).
    [CrossRef]
  15. M. I. Bell, “Frequency dependence of Miller’s rule for nonlinear susceptibility,” Phys. Rev. B 6, 516–520 (1972).
    [CrossRef]
  16. I. Shoji, T. Kondo, R. Ito, “Absolute measurement of the nonlinear optical constants—verification of Miller’s rule,” in Japanese Society of Applied Physics and Related Societies, Extended Abstracts (41st Spring Meeting) (Japanese Society of Applied Physics, Kawasaki, Japan, 1994), p. 981 (in Japanese).
  17. G. E. Francois, “cw measurement of the optical nonlinearity of ammonium dihydrogen phosphate,” Phys. Rev. 143, 597–600 (1966).
    [CrossRef]
  18. J. E. Bjorkholm, A. E. Siegman, “Accurate cw measurement of optical second-harmonic generation in ammonium dihydrogen phosphate and calcite,” Phys. Rev. 154, 851–860 (1967).
    [CrossRef]
  19. J. Jerphagnon, S. K. Kurtz, “Optical nonlinear susceptibilities: accurate relative for quartz, ammonium dihydrogen phosphate, and potassium dihydrogen phosphate,” Phys. Rev. B 1, 1739–1744 (1970).
    [CrossRef]
  20. F. Zernike, “Refractive indices of ammonium dihydrogen phosphate and potassium dihydrogen phosphate between 2000 Å and 1.5 μ,” J. Opt. Soc. Am. 54, 1215–1220 (1964).
    [CrossRef]
  21. G. D. Boyd, D. A. Kleinman, “Parametric interaction of focused Gaussian light beams,” J. Appl. Phys. 39, 3597–3639 (1968).
    [CrossRef]
  22. A. Mito, C. Takahashi, “Correction of the transmittance scale of a double-beam spectrophotometer using the double-aperture method,” Jpn. J. Appl. Phys. 29, 1616–1617 (1990).
    [CrossRef]
  23. J. Jerphagnon, S. K. Kurtz, “Maker fringes: a detailed comparison of theory and experiment for isotope and uniaxial crystals,” J. Appl. Phys. 41, 1667–1681 (1970).
    [CrossRef]

1994 (1)

W. E. Torruellas, G. Krijnen, D. Y. Kim, R. Sciek, G. I. Stegeman, P. Vidakovic, J. Zyss, “Cascading nonlinearities in an organic single crystal core fiber: the Čerenkov regime,” Opt. Commun. 112, 122–130 (1994).
[CrossRef]

1992 (1)

D. A. Roberts, “Simplified characterization of uniaxial and biaxial nonlinear optical crystals: a plea for standardization of nomenclature and conventions,” IEEE J. Quantum Electron. 28, 2057–2074 (1992).
[CrossRef]

1991 (1)

J. R. Heflin, Y. M. Cai, A. F. Garito, “Dispersion measurements of electric-field-induced second-harmonic generation and third-harmonic generation in conjugated linear chains,” J. Opt. Soc. Am. B 8, 2132–2136 (1991).
[CrossRef]

1990 (2)

R. C. Eckardt, H. Masuda, Y. X. Fan, R. L. Byer, “Absolute and relative nonlinear optical coefficients of KDP, KD*P, BaB2O4, LiIO3, MgO:LiNbO3, and KTP measured by phase-matched second-harmonic generation,” IEEE J. Quantum Electron. 26, 922–933 (1990).
[CrossRef]

A. Mito, C. Takahashi, “Correction of the transmittance scale of a double-beam spectrophotometer using the double-aperture method,” Jpn. J. Appl. Phys. 29, 1616–1617 (1990).
[CrossRef]

1989 (1)

R. Adair, L. L. Chase, S. A. Payne, “Nonlinear refractive index of optical crystal,” Phys. Rev. 39, 3337–3350 (1989).
[CrossRef]

1982 (1)

1981 (1)

G. R. Meredith, “Cascading in optical third-harmonic generation by crystalline quartz,” Phys. Rev. B 24, 5522–5532 (1981).
[CrossRef]

1978 (1)

N. L. Boling, A. J. Glass, A. Owyoung, “Empirical relationships for predicting nonlinear refractive index changes in optical solids,” IEEE J. Quantum Electron. QE-14, 601–608 (1978).
[CrossRef]

1976 (2)

M. M. Choy, R. L. Byer, “Accurate second-order susceptibility measurements of visible and infrared nonlinear crystals,” Phys. Rev. B 14, 1693–1706 (1976).
[CrossRef]

D. Milliam, M. J. Weber, “Measurement of nonlinear refractive-index coefficients using time-resolved interferometry: application to optical materials for high-power neodymium lasers,” J. Appl. Phys. 47, 2497–2501 (1976).
[CrossRef]

1975 (1)

R. Hellwarth, J. Cherlow, T. T. Young, “Origin and frequency dependence of nonlinear optical susceptibilities of glasses,” Phys. Rev. 11, 964–967 (1975).
[CrossRef]

1973 (1)

A. Owyoung, “Ellipse rotation studies in laser host materials,” IEEE J. Quantum Electron. QE-9, 1064–1069 (1973).
[CrossRef]

1972 (1)

M. I. Bell, “Frequency dependence of Miller’s rule for nonlinear susceptibility,” Phys. Rev. B 6, 516–520 (1972).
[CrossRef]

1970 (2)

J. Jerphagnon, S. K. Kurtz, “Optical nonlinear susceptibilities: accurate relative for quartz, ammonium dihydrogen phosphate, and potassium dihydrogen phosphate,” Phys. Rev. B 1, 1739–1744 (1970).
[CrossRef]

J. Jerphagnon, S. K. Kurtz, “Maker fringes: a detailed comparison of theory and experiment for isotope and uniaxial crystals,” J. Appl. Phys. 41, 1667–1681 (1970).
[CrossRef]

1968 (1)

G. D. Boyd, D. A. Kleinman, “Parametric interaction of focused Gaussian light beams,” J. Appl. Phys. 39, 3597–3639 (1968).
[CrossRef]

1967 (1)

J. E. Bjorkholm, A. E. Siegman, “Accurate cw measurement of optical second-harmonic generation in ammonium dihydrogen phosphate and calcite,” Phys. Rev. 154, 851–860 (1967).
[CrossRef]

1966 (1)

G. E. Francois, “cw measurement of the optical nonlinearity of ammonium dihydrogen phosphate,” Phys. Rev. 143, 597–600 (1966).
[CrossRef]

1964 (2)

R. C. Miller, “Optical second harmonic generation in piezoelectric crystals,” Appl. Phys. Lett. 5, 17–19 (1964).
[CrossRef]

F. Zernike, “Refractive indices of ammonium dihydrogen phosphate and potassium dihydrogen phosphate between 2000 Å and 1.5 μ,” J. Opt. Soc. Am. 54, 1215–1220 (1964).
[CrossRef]

Adair, R.

R. Adair, L. L. Chase, S. A. Payne, “Nonlinear refractive index of optical crystal,” Phys. Rev. 39, 3337–3350 (1989).
[CrossRef]

Bell, M. I.

M. I. Bell, “Frequency dependence of Miller’s rule for nonlinear susceptibility,” Phys. Rev. B 6, 516–520 (1972).
[CrossRef]

Bjorkholm, J. E.

J. E. Bjorkholm, A. E. Siegman, “Accurate cw measurement of optical second-harmonic generation in ammonium dihydrogen phosphate and calcite,” Phys. Rev. 154, 851–860 (1967).
[CrossRef]

Boling, N. L.

N. L. Boling, A. J. Glass, A. Owyoung, “Empirical relationships for predicting nonlinear refractive index changes in optical solids,” IEEE J. Quantum Electron. QE-14, 601–608 (1978).
[CrossRef]

Boyd, G. D.

G. D. Boyd, D. A. Kleinman, “Parametric interaction of focused Gaussian light beams,” J. Appl. Phys. 39, 3597–3639 (1968).
[CrossRef]

Buchalter, B.

Byer, R. L.

R. C. Eckardt, H. Masuda, Y. X. Fan, R. L. Byer, “Absolute and relative nonlinear optical coefficients of KDP, KD*P, BaB2O4, LiIO3, MgO:LiNbO3, and KTP measured by phase-matched second-harmonic generation,” IEEE J. Quantum Electron. 26, 922–933 (1990).
[CrossRef]

M. M. Choy, R. L. Byer, “Accurate second-order susceptibility measurements of visible and infrared nonlinear crystals,” Phys. Rev. B 14, 1693–1706 (1976).
[CrossRef]

Cai, Y. M.

J. R. Heflin, Y. M. Cai, A. F. Garito, “Dispersion measurements of electric-field-induced second-harmonic generation and third-harmonic generation in conjugated linear chains,” J. Opt. Soc. Am. B 8, 2132–2136 (1991).
[CrossRef]

Chase, L. L.

R. Adair, L. L. Chase, S. A. Payne, “Nonlinear refractive index of optical crystal,” Phys. Rev. 39, 3337–3350 (1989).
[CrossRef]

Cherlow, J.

R. Hellwarth, J. Cherlow, T. T. Young, “Origin and frequency dependence of nonlinear optical susceptibilities of glasses,” Phys. Rev. 11, 964–967 (1975).
[CrossRef]

Choy, M. M.

M. M. Choy, R. L. Byer, “Accurate second-order susceptibility measurements of visible and infrared nonlinear crystals,” Phys. Rev. B 14, 1693–1706 (1976).
[CrossRef]

Eckardt, R. C.

R. C. Eckardt, H. Masuda, Y. X. Fan, R. L. Byer, “Absolute and relative nonlinear optical coefficients of KDP, KD*P, BaB2O4, LiIO3, MgO:LiNbO3, and KTP measured by phase-matched second-harmonic generation,” IEEE J. Quantum Electron. 26, 922–933 (1990).
[CrossRef]

Fan, Y. X.

R. C. Eckardt, H. Masuda, Y. X. Fan, R. L. Byer, “Absolute and relative nonlinear optical coefficients of KDP, KD*P, BaB2O4, LiIO3, MgO:LiNbO3, and KTP measured by phase-matched second-harmonic generation,” IEEE J. Quantum Electron. 26, 922–933 (1990).
[CrossRef]

Francois, G. E.

G. E. Francois, “cw measurement of the optical nonlinearity of ammonium dihydrogen phosphate,” Phys. Rev. 143, 597–600 (1966).
[CrossRef]

Garito, A. F.

J. R. Heflin, Y. M. Cai, A. F. Garito, “Dispersion measurements of electric-field-induced second-harmonic generation and third-harmonic generation in conjugated linear chains,” J. Opt. Soc. Am. B 8, 2132–2136 (1991).
[CrossRef]

Glass, A. J.

N. L. Boling, A. J. Glass, A. Owyoung, “Empirical relationships for predicting nonlinear refractive index changes in optical solids,” IEEE J. Quantum Electron. QE-14, 601–608 (1978).
[CrossRef]

Hagimoto, K.

A. Mito, K. Hagimoto, C. Takahashi, “Determination of the third-order optical nonlinear susceptibility of fused silica using optical harmonic generation methods,” Nonlinear Opt. (to be published).

Heflin, J. R.

J. R. Heflin, Y. M. Cai, A. F. Garito, “Dispersion measurements of electric-field-induced second-harmonic generation and third-harmonic generation in conjugated linear chains,” J. Opt. Soc. Am. B 8, 2132–2136 (1991).
[CrossRef]

Hellwarth, R.

R. Hellwarth, J. Cherlow, T. T. Young, “Origin and frequency dependence of nonlinear optical susceptibilities of glasses,” Phys. Rev. 11, 964–967 (1975).
[CrossRef]

Ito, R.

I. Shoji, T. Kondo, R. Ito, “Absolute measurement of the nonlinear optical constants—verification of Miller’s rule,” in Japanese Society of Applied Physics and Related Societies, Extended Abstracts (41st Spring Meeting) (Japanese Society of Applied Physics, Kawasaki, Japan, 1994), p. 981 (in Japanese).

Jerphagnon, J.

J. Jerphagnon, S. K. Kurtz, “Optical nonlinear susceptibilities: accurate relative for quartz, ammonium dihydrogen phosphate, and potassium dihydrogen phosphate,” Phys. Rev. B 1, 1739–1744 (1970).
[CrossRef]

J. Jerphagnon, S. K. Kurtz, “Maker fringes: a detailed comparison of theory and experiment for isotope and uniaxial crystals,” J. Appl. Phys. 41, 1667–1681 (1970).
[CrossRef]

Kim, D. Y.

W. E. Torruellas, G. Krijnen, D. Y. Kim, R. Sciek, G. I. Stegeman, P. Vidakovic, J. Zyss, “Cascading nonlinearities in an organic single crystal core fiber: the Čerenkov regime,” Opt. Commun. 112, 122–130 (1994).
[CrossRef]

Kleinman, D. A.

G. D. Boyd, D. A. Kleinman, “Parametric interaction of focused Gaussian light beams,” J. Appl. Phys. 39, 3597–3639 (1968).
[CrossRef]

Kondo, T.

I. Shoji, T. Kondo, R. Ito, “Absolute measurement of the nonlinear optical constants—verification of Miller’s rule,” in Japanese Society of Applied Physics and Related Societies, Extended Abstracts (41st Spring Meeting) (Japanese Society of Applied Physics, Kawasaki, Japan, 1994), p. 981 (in Japanese).

Krijnen, G.

W. E. Torruellas, G. Krijnen, D. Y. Kim, R. Sciek, G. I. Stegeman, P. Vidakovic, J. Zyss, “Cascading nonlinearities in an organic single crystal core fiber: the Čerenkov regime,” Opt. Commun. 112, 122–130 (1994).
[CrossRef]

Kurtz, S. K.

J. Jerphagnon, S. K. Kurtz, “Maker fringes: a detailed comparison of theory and experiment for isotope and uniaxial crystals,” J. Appl. Phys. 41, 1667–1681 (1970).
[CrossRef]

J. Jerphagnon, S. K. Kurtz, “Optical nonlinear susceptibilities: accurate relative for quartz, ammonium dihydrogen phosphate, and potassium dihydrogen phosphate,” Phys. Rev. B 1, 1739–1744 (1970).
[CrossRef]

Masuda, H.

R. C. Eckardt, H. Masuda, Y. X. Fan, R. L. Byer, “Absolute and relative nonlinear optical coefficients of KDP, KD*P, BaB2O4, LiIO3, MgO:LiNbO3, and KTP measured by phase-matched second-harmonic generation,” IEEE J. Quantum Electron. 26, 922–933 (1990).
[CrossRef]

Meredith, G. R.

B. Buchalter, G. R. Meredith, “Third-order optical susceptibility of glasses determined by third harmonic generation,” Appl. Opt. 21, 3221–3224 (1982).
[CrossRef] [PubMed]

G. R. Meredith, “Cascading in optical third-harmonic generation by crystalline quartz,” Phys. Rev. B 24, 5522–5532 (1981).
[CrossRef]

Miller, R. C.

R. C. Miller, “Optical second harmonic generation in piezoelectric crystals,” Appl. Phys. Lett. 5, 17–19 (1964).
[CrossRef]

Milliam, D.

D. Milliam, M. J. Weber, “Measurement of nonlinear refractive-index coefficients using time-resolved interferometry: application to optical materials for high-power neodymium lasers,” J. Appl. Phys. 47, 2497–2501 (1976).
[CrossRef]

Mito, A.

A. Mito, C. Takahashi, “Correction of the transmittance scale of a double-beam spectrophotometer using the double-aperture method,” Jpn. J. Appl. Phys. 29, 1616–1617 (1990).
[CrossRef]

A. Mito, K. Hagimoto, C. Takahashi, “Determination of the third-order optical nonlinear susceptibility of fused silica using optical harmonic generation methods,” Nonlinear Opt. (to be published).

Owyoung, A.

N. L. Boling, A. J. Glass, A. Owyoung, “Empirical relationships for predicting nonlinear refractive index changes in optical solids,” IEEE J. Quantum Electron. QE-14, 601–608 (1978).
[CrossRef]

A. Owyoung, “Ellipse rotation studies in laser host materials,” IEEE J. Quantum Electron. QE-9, 1064–1069 (1973).
[CrossRef]

Payne, S. A.

R. Adair, L. L. Chase, S. A. Payne, “Nonlinear refractive index of optical crystal,” Phys. Rev. 39, 3337–3350 (1989).
[CrossRef]

Roberts, D. A.

D. A. Roberts, “Simplified characterization of uniaxial and biaxial nonlinear optical crystals: a plea for standardization of nomenclature and conventions,” IEEE J. Quantum Electron. 28, 2057–2074 (1992).
[CrossRef]

Sciek, R.

W. E. Torruellas, G. Krijnen, D. Y. Kim, R. Sciek, G. I. Stegeman, P. Vidakovic, J. Zyss, “Cascading nonlinearities in an organic single crystal core fiber: the Čerenkov regime,” Opt. Commun. 112, 122–130 (1994).
[CrossRef]

Shoji, I.

I. Shoji, T. Kondo, R. Ito, “Absolute measurement of the nonlinear optical constants—verification of Miller’s rule,” in Japanese Society of Applied Physics and Related Societies, Extended Abstracts (41st Spring Meeting) (Japanese Society of Applied Physics, Kawasaki, Japan, 1994), p. 981 (in Japanese).

Siegman, A. E.

J. E. Bjorkholm, A. E. Siegman, “Accurate cw measurement of optical second-harmonic generation in ammonium dihydrogen phosphate and calcite,” Phys. Rev. 154, 851–860 (1967).
[CrossRef]

Stegeman, G. I.

W. E. Torruellas, G. Krijnen, D. Y. Kim, R. Sciek, G. I. Stegeman, P. Vidakovic, J. Zyss, “Cascading nonlinearities in an organic single crystal core fiber: the Čerenkov regime,” Opt. Commun. 112, 122–130 (1994).
[CrossRef]

Takahashi, C.

A. Mito, C. Takahashi, “Correction of the transmittance scale of a double-beam spectrophotometer using the double-aperture method,” Jpn. J. Appl. Phys. 29, 1616–1617 (1990).
[CrossRef]

A. Mito, K. Hagimoto, C. Takahashi, “Determination of the third-order optical nonlinear susceptibility of fused silica using optical harmonic generation methods,” Nonlinear Opt. (to be published).

Torruellas, W. E.

W. E. Torruellas, G. Krijnen, D. Y. Kim, R. Sciek, G. I. Stegeman, P. Vidakovic, J. Zyss, “Cascading nonlinearities in an organic single crystal core fiber: the Čerenkov regime,” Opt. Commun. 112, 122–130 (1994).
[CrossRef]

Vidakovic, P.

W. E. Torruellas, G. Krijnen, D. Y. Kim, R. Sciek, G. I. Stegeman, P. Vidakovic, J. Zyss, “Cascading nonlinearities in an organic single crystal core fiber: the Čerenkov regime,” Opt. Commun. 112, 122–130 (1994).
[CrossRef]

Weber, M. J.

D. Milliam, M. J. Weber, “Measurement of nonlinear refractive-index coefficients using time-resolved interferometry: application to optical materials for high-power neodymium lasers,” J. Appl. Phys. 47, 2497–2501 (1976).
[CrossRef]

Young, T. T.

R. Hellwarth, J. Cherlow, T. T. Young, “Origin and frequency dependence of nonlinear optical susceptibilities of glasses,” Phys. Rev. 11, 964–967 (1975).
[CrossRef]

Zernike, F.

F. Zernike, “Refractive indices of ammonium dihydrogen phosphate and potassium dihydrogen phosphate between 2000 Å and 1.5 μ,” J. Opt. Soc. Am. 54, 1215–1220 (1964).
[CrossRef]

Zyss, J.

W. E. Torruellas, G. Krijnen, D. Y. Kim, R. Sciek, G. I. Stegeman, P. Vidakovic, J. Zyss, “Cascading nonlinearities in an organic single crystal core fiber: the Čerenkov regime,” Opt. Commun. 112, 122–130 (1994).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

R. C. Miller, “Optical second harmonic generation in piezoelectric crystals,” Appl. Phys. Lett. 5, 17–19 (1964).
[CrossRef]

IEEE J. Quantum Electron. (1)

D. A. Roberts, “Simplified characterization of uniaxial and biaxial nonlinear optical crystals: a plea for standardization of nomenclature and conventions,” IEEE J. Quantum Electron. 28, 2057–2074 (1992).
[CrossRef]

IEEE J. Quantum Electron. (1)

A. Owyoung, “Ellipse rotation studies in laser host materials,” IEEE J. Quantum Electron. QE-9, 1064–1069 (1973).
[CrossRef]

IEEE J. Quantum Electron. (2)

N. L. Boling, A. J. Glass, A. Owyoung, “Empirical relationships for predicting nonlinear refractive index changes in optical solids,” IEEE J. Quantum Electron. QE-14, 601–608 (1978).
[CrossRef]

R. C. Eckardt, H. Masuda, Y. X. Fan, R. L. Byer, “Absolute and relative nonlinear optical coefficients of KDP, KD*P, BaB2O4, LiIO3, MgO:LiNbO3, and KTP measured by phase-matched second-harmonic generation,” IEEE J. Quantum Electron. 26, 922–933 (1990).
[CrossRef]

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

J. R. Heflin, Y. M. Cai, A. F. Garito, “Dispersion measurements of electric-field-induced second-harmonic generation and third-harmonic generation in conjugated linear chains,” J. Opt. Soc. Am. B 8, 2132–2136 (1991).
[CrossRef]

J. Appl. Phys. (1)

G. D. Boyd, D. A. Kleinman, “Parametric interaction of focused Gaussian light beams,” J. Appl. Phys. 39, 3597–3639 (1968).
[CrossRef]

J. Appl. Phys. (2)

D. Milliam, M. J. Weber, “Measurement of nonlinear refractive-index coefficients using time-resolved interferometry: application to optical materials for high-power neodymium lasers,” J. Appl. Phys. 47, 2497–2501 (1976).
[CrossRef]

J. Jerphagnon, S. K. Kurtz, “Maker fringes: a detailed comparison of theory and experiment for isotope and uniaxial crystals,” J. Appl. Phys. 41, 1667–1681 (1970).
[CrossRef]

J. Opt. Soc. Am. (1)

F. Zernike, “Refractive indices of ammonium dihydrogen phosphate and potassium dihydrogen phosphate between 2000 Å and 1.5 μ,” J. Opt. Soc. Am. 54, 1215–1220 (1964).
[CrossRef]

Jpn. J. Appl. Phys. (1)

A. Mito, C. Takahashi, “Correction of the transmittance scale of a double-beam spectrophotometer using the double-aperture method,” Jpn. J. Appl. Phys. 29, 1616–1617 (1990).
[CrossRef]

Opt. Commun. (1)

W. E. Torruellas, G. Krijnen, D. Y. Kim, R. Sciek, G. I. Stegeman, P. Vidakovic, J. Zyss, “Cascading nonlinearities in an organic single crystal core fiber: the Čerenkov regime,” Opt. Commun. 112, 122–130 (1994).
[CrossRef]

Phys. Rev. B (1)

G. R. Meredith, “Cascading in optical third-harmonic generation by crystalline quartz,” Phys. Rev. B 24, 5522–5532 (1981).
[CrossRef]

Phys. Rev. (4)

R. Hellwarth, J. Cherlow, T. T. Young, “Origin and frequency dependence of nonlinear optical susceptibilities of glasses,” Phys. Rev. 11, 964–967 (1975).
[CrossRef]

R. Adair, L. L. Chase, S. A. Payne, “Nonlinear refractive index of optical crystal,” Phys. Rev. 39, 3337–3350 (1989).
[CrossRef]

G. E. Francois, “cw measurement of the optical nonlinearity of ammonium dihydrogen phosphate,” Phys. Rev. 143, 597–600 (1966).
[CrossRef]

J. E. Bjorkholm, A. E. Siegman, “Accurate cw measurement of optical second-harmonic generation in ammonium dihydrogen phosphate and calcite,” Phys. Rev. 154, 851–860 (1967).
[CrossRef]

Phys. Rev. B (3)

J. Jerphagnon, S. K. Kurtz, “Optical nonlinear susceptibilities: accurate relative for quartz, ammonium dihydrogen phosphate, and potassium dihydrogen phosphate,” Phys. Rev. B 1, 1739–1744 (1970).
[CrossRef]

M. I. Bell, “Frequency dependence of Miller’s rule for nonlinear susceptibility,” Phys. Rev. B 6, 516–520 (1972).
[CrossRef]

M. M. Choy, R. L. Byer, “Accurate second-order susceptibility measurements of visible and infrared nonlinear crystals,” Phys. Rev. B 14, 1693–1706 (1976).
[CrossRef]

Other (2)

I. Shoji, T. Kondo, R. Ito, “Absolute measurement of the nonlinear optical constants—verification of Miller’s rule,” in Japanese Society of Applied Physics and Related Societies, Extended Abstracts (41st Spring Meeting) (Japanese Society of Applied Physics, Kawasaki, Japan, 1994), p. 981 (in Japanese).

A. Mito, K. Hagimoto, C. Takahashi, “Determination of the third-order optical nonlinear susceptibility of fused silica using optical harmonic generation methods,” Nonlinear Opt. (to be published).

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Figures (8)

Fig. 1
Fig. 1

Schematic of phase-matched SHG by a He–Ne laser. PMT, photomultiplier tube.

Fig. 2
Fig. 2

Spot size w(z′) of the He–Ne laser beam as a function of distance z′. The open circles and solid curve show measured values and the results of a least-squares fit, respectively.

Fig. 3
Fig. 3

Phase matching of the tuning curve (open circles) of ADP at 633 nm with the calculated curve (solid curve).

Fig. 4
Fig. 4

Second-harmonic power as a function of fundamental power at 633 nm. The solid curve shows the result of a least-squares fit, with the assumption that SHG power is proportional to the square of the fundamental power.

Fig. 5
Fig. 5

Spot size w(z′) of a YAG laser beam with an elliptical cross section as a function of distance z′. The open squares and circles are the measured values of the horizontal and the vertical components, respectively. The solid and dotted curves are the results of a least-squares fit.

Fig. 6
Fig. 6

Arrangement of prisms used to transform an elliptical-cross-section beam into a circular one.

Fig. 7
Fig. 7

Spot size w(z′) of the transformed YAG laser beam with a circular cross section as a function of distance z′. The open squares and circles are the measured values of the horizontal and the vertical components, respectively. The solid and dotted lines are the results of a least-squares fit.

Fig. 8
Fig. 8

Phase matching of the tuning curves of ADP at 1064 nm for circular- (open squares) and elliptical-cross-section (open circles) YAG laser beams with the calculated curves (solid curves).

Tables (1)

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Table 1 Experimental Error (in Percent)

Equations (18)

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P 2 = ( T ND / T U ) P He - Ne ( V 2 / V He - Ne ) ( R / T ) ,
w ( z ) 2 = w 0 2 + ( λ z / π w 0 ) 2 .
d 36 ( ADP , 633 nm ) = ( 1.31 ± 0.05 ) × 10 - 9 esu = 0.55 ± 0.02 pm / V .
d 36 ( ADP , 1064 nm ) = ( 1.10 ± 0.06 ) × 10 - 9 esu = 0.46 ± 0.03 pm / V .
d 36 ( ADP , 1064 nm ) = 1.08 × 10 - 9 esu = 0.45 pm / V .
d 36 ( ADP ) / d 11 ( α - quartz ) = 1.77 ± 0.03.
d 36 ( ADP ) / d 11 ( α - quartz ) = 1.56 ± 0.03.
d 11 ( α - quartz , 633 nm ) = ( 7.4 ± 0.3 ) × 10 - 10 esu = 0.31 ± 0.01 pm / V ,
d 11 ( α - quartz , 1064 nm ) = ( 7.1 ± 0.4 ) × 10 - 10 esu = 0.30 ± 0.02 pm / V .
d ( P 2 / P 1 2 ) 1 / 2 [ ( P He - Ne R ) / P 1 2 ] 1 / 2 .
d 1 / [ sin ( θ + ρ ) sin ( 2 ϕ ) ] .
sin 2 θ = n o , λ / 2 - 2 - n o , λ - 2 n e , λ - 2 - n o , λ - 2 ,
δ i j k = d i j k ( ω ) χ i i ( 2 ω ) χ j j ( ω ) χ k k ( ω ) ,
δ 36 = d 36 ( λ ) / ( n e , λ / 2 2 - 1 ) ( n o , λ 2 - 1 ) 2
= ( 5.9 ± 0.2 ) × 10 - 10 esu = 0.248 ± 0.009 pm / V ( at 633 nm )
= ( 5.7 ± 0.3 ) × 10 - 10 esu = 0.240 ± 0.013 pm / V ( at 1064 nm ) ,
δ 11 = d 11 ( λ ) / ( n o , λ / 2 2 - 1 ) ( n o , λ 2 - 1 ) 2 = ( 2.6 ± 0.1 ) × 10 - 10 esu = 0.110 ± 0.004 pm / V ( at 633 nm )
= ( 2.8 ± 0.2 ) × 10 - 10 esu = 0.117 ± 0.007 pm / V ( at 1064 nm ) ,

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