Abstract

Comprehensive refractive-index measurements of 3-methyl-4-nitropyridine-1-oxide in the visible and near infrared are reported together with the phase-matching properties for collinear second-harmonic and sum-frequency generations in the principal dielectric planes. Noncollinear second-harmonic generation phenomena in one-beam and two-beam experiments are defined, observed, and subsequently analyzed by means of a simple geometric construction. A thorough investigation of noncollinear phase-matching configurations for second-harmonic and sum-frequency generations is performed and leads to the concept of one-beam noncritical non-collinear phase matching, which may be of great practical interest in optical parametric amplification and oscillation processes.

© 1991 Optical Society of America

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References

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  1. J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
    [CrossRef]
  2. F. T. Arecchi, E. O. Schulz-Dubois, eds., Laser Handbook (North-Holland, Amsterdam, 1972).
  3. A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975).
  4. J. Zyss, in Current Trends in Optics, F. T. Arecchi, F. R. Aussenegg, eds. (Taylor & Francis, London, 1981).
  5. J. Zyss, G. Tsoucaris, in Structure and Properties of Molecular Crystals, M. Pierrot, ed. (Elsevier, Amsterdam, 1990).
  6. J. Zyss, J. Non-cryst. Solids 47, 211 (1982).
    [CrossRef]
  7. J. Zyss, J. F. Nicoud, M. Coquillay, J. Chem. Phys. 81, 4160 (1984).
    [CrossRef]
  8. I. Ledoux, J. Zyss, A. Migus, J. Etchepare, G. Grillon, A. Antonetti, Appl. Phys. Lett. 48, 1564 (1986).
    [CrossRef]
  9. I. Ledoux, D. Josse, P. Vidakovic, J. Zyss, Opt. Eng. 25, 202 (1986).
    [CrossRef]
  10. I. Ledoux, J. Badan, J. Zyss, A. Migus, D. Hulin, J. Etchepare, G. Grillon, A. Antonetti, J. Opt. Soc. Am. B 4, 987 (1987).
    [CrossRef]
  11. I. Ledoux, C. Lepers, A. Périgaud, J. Badan, J. Zyss, Opt. Commun. 80, 149 (1990).
    [CrossRef]
  12. J. L. Oudar, R. Hierle, J. Appl. Phys. 48, 2699 (1977).
    [CrossRef]
  13. B. F. Levine, C. G. Bethea, C. D. Thurmond, R. T. Lynch, J. L. Bernstein, J. Appl. Phys. 50, 2523 (1979).
    [CrossRef]
  14. J. Zyss, D. S. Chemla, J. F. Nicoud, J. Chem. Phys. 74, 4800 (1981).
    [CrossRef]
  15. M. Sigelle, R. Hierle, J. Appl. Phys. 52, 4199 (1981).
    [CrossRef]
  16. J. Zyss, I. Ledoux, R. Hierle, R. Raj, J. Oudar, IEEE J. Quantum Electron. QE-21, 1286 (1985).
    [CrossRef]
  17. D. S. Chemla, J. Zyss, eds., Nonlinear Optical Properties of Organic Molecules and Crystals (Academic, New York, 1986).
  18. J. Zyss, in Conjugated Polymeric Materials: Opportunities in Electronics, Optoelectronics, and Molecular Electronics, J. L. Brédas, R. R. Chance, eds. (Kluwer Academic, Dordrecht, 1990).
  19. J. Warner, Opto-Electronics 1, 25 (1969).
    [CrossRef]
  20. F. Zernike, J. Midwinter, Applied Nonlinear Optics (Wiley, New York, 1973).
  21. S. A. Akhmanov, in Quantum Electronics, Vols. 1A and 1B, Nonlinear Optics, H. Rabin, C. L. Tang, eds. (Academic, New York, 1975).
  22. A. Carenco, J. Jerphagnon, A. Perigaud, J. Chem. Phys. 66, 3806 (1977).
    [CrossRef]
  23. G. C. Bhar, U. Chatterjel, Jpn. J. Appl. Phys. 29, 1103 (1990).
    [CrossRef]
  24. G. J. Zhang, T. Kinoshita, K. Sasaki, Appl. Phys. Lett. 57, 221 (1990).
    [CrossRef]
  25. R. C. Miller, G. D. Boyd, A. Savage, Appl. Phys. Lett. 6, 77 (1965).
    [CrossRef]
  26. M. V. Hobden, J. Appl. Phys. 38, 4365 (1967).
    [CrossRef]
  27. J. Q. Yao, T. S. Fahlen, J. Appl. Phys. 55, 65 (1984).
    [CrossRef]
  28. H. Ito, H. Naito, H. Inaba, J. Appl. Phys. 46, 3992 (1975).
    [CrossRef]
  29. A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).
  30. S. K. Kurtz, in Laser Handbook, F. T. Arecchi, E. O. Schulz-Dubois, eds. (North-Holland, Amsterdam, 1972).

1990 (3)

I. Ledoux, C. Lepers, A. Périgaud, J. Badan, J. Zyss, Opt. Commun. 80, 149 (1990).
[CrossRef]

G. C. Bhar, U. Chatterjel, Jpn. J. Appl. Phys. 29, 1103 (1990).
[CrossRef]

G. J. Zhang, T. Kinoshita, K. Sasaki, Appl. Phys. Lett. 57, 221 (1990).
[CrossRef]

1987 (1)

1986 (2)

I. Ledoux, J. Zyss, A. Migus, J. Etchepare, G. Grillon, A. Antonetti, Appl. Phys. Lett. 48, 1564 (1986).
[CrossRef]

I. Ledoux, D. Josse, P. Vidakovic, J. Zyss, Opt. Eng. 25, 202 (1986).
[CrossRef]

1985 (1)

J. Zyss, I. Ledoux, R. Hierle, R. Raj, J. Oudar, IEEE J. Quantum Electron. QE-21, 1286 (1985).
[CrossRef]

1984 (2)

J. Q. Yao, T. S. Fahlen, J. Appl. Phys. 55, 65 (1984).
[CrossRef]

J. Zyss, J. F. Nicoud, M. Coquillay, J. Chem. Phys. 81, 4160 (1984).
[CrossRef]

1982 (1)

J. Zyss, J. Non-cryst. Solids 47, 211 (1982).
[CrossRef]

1981 (2)

J. Zyss, D. S. Chemla, J. F. Nicoud, J. Chem. Phys. 74, 4800 (1981).
[CrossRef]

M. Sigelle, R. Hierle, J. Appl. Phys. 52, 4199 (1981).
[CrossRef]

1979 (1)

B. F. Levine, C. G. Bethea, C. D. Thurmond, R. T. Lynch, J. L. Bernstein, J. Appl. Phys. 50, 2523 (1979).
[CrossRef]

1977 (2)

A. Carenco, J. Jerphagnon, A. Perigaud, J. Chem. Phys. 66, 3806 (1977).
[CrossRef]

J. L. Oudar, R. Hierle, J. Appl. Phys. 48, 2699 (1977).
[CrossRef]

1975 (1)

H. Ito, H. Naito, H. Inaba, J. Appl. Phys. 46, 3992 (1975).
[CrossRef]

1969 (1)

J. Warner, Opto-Electronics 1, 25 (1969).
[CrossRef]

1967 (1)

M. V. Hobden, J. Appl. Phys. 38, 4365 (1967).
[CrossRef]

1965 (1)

R. C. Miller, G. D. Boyd, A. Savage, Appl. Phys. Lett. 6, 77 (1965).
[CrossRef]

1962 (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Akhmanov, S. A.

S. A. Akhmanov, in Quantum Electronics, Vols. 1A and 1B, Nonlinear Optics, H. Rabin, C. L. Tang, eds. (Academic, New York, 1975).

Antonetti, A.

I. Ledoux, J. Badan, J. Zyss, A. Migus, D. Hulin, J. Etchepare, G. Grillon, A. Antonetti, J. Opt. Soc. Am. B 4, 987 (1987).
[CrossRef]

I. Ledoux, J. Zyss, A. Migus, J. Etchepare, G. Grillon, A. Antonetti, Appl. Phys. Lett. 48, 1564 (1986).
[CrossRef]

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Badan, J.

Bernstein, J. L.

B. F. Levine, C. G. Bethea, C. D. Thurmond, R. T. Lynch, J. L. Bernstein, J. Appl. Phys. 50, 2523 (1979).
[CrossRef]

Bethea, C. G.

B. F. Levine, C. G. Bethea, C. D. Thurmond, R. T. Lynch, J. L. Bernstein, J. Appl. Phys. 50, 2523 (1979).
[CrossRef]

Bhar, G. C.

G. C. Bhar, U. Chatterjel, Jpn. J. Appl. Phys. 29, 1103 (1990).
[CrossRef]

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Boyd, G. D.

R. C. Miller, G. D. Boyd, A. Savage, Appl. Phys. Lett. 6, 77 (1965).
[CrossRef]

Carenco, A.

A. Carenco, J. Jerphagnon, A. Perigaud, J. Chem. Phys. 66, 3806 (1977).
[CrossRef]

Chatterjel, U.

G. C. Bhar, U. Chatterjel, Jpn. J. Appl. Phys. 29, 1103 (1990).
[CrossRef]

Chemla, D. S.

J. Zyss, D. S. Chemla, J. F. Nicoud, J. Chem. Phys. 74, 4800 (1981).
[CrossRef]

Coquillay, M.

J. Zyss, J. F. Nicoud, M. Coquillay, J. Chem. Phys. 81, 4160 (1984).
[CrossRef]

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Etchepare, J.

I. Ledoux, J. Badan, J. Zyss, A. Migus, D. Hulin, J. Etchepare, G. Grillon, A. Antonetti, J. Opt. Soc. Am. B 4, 987 (1987).
[CrossRef]

I. Ledoux, J. Zyss, A. Migus, J. Etchepare, G. Grillon, A. Antonetti, Appl. Phys. Lett. 48, 1564 (1986).
[CrossRef]

Fahlen, T. S.

J. Q. Yao, T. S. Fahlen, J. Appl. Phys. 55, 65 (1984).
[CrossRef]

Grillon, G.

I. Ledoux, J. Badan, J. Zyss, A. Migus, D. Hulin, J. Etchepare, G. Grillon, A. Antonetti, J. Opt. Soc. Am. B 4, 987 (1987).
[CrossRef]

I. Ledoux, J. Zyss, A. Migus, J. Etchepare, G. Grillon, A. Antonetti, Appl. Phys. Lett. 48, 1564 (1986).
[CrossRef]

Hierle, R.

J. Zyss, I. Ledoux, R. Hierle, R. Raj, J. Oudar, IEEE J. Quantum Electron. QE-21, 1286 (1985).
[CrossRef]

M. Sigelle, R. Hierle, J. Appl. Phys. 52, 4199 (1981).
[CrossRef]

J. L. Oudar, R. Hierle, J. Appl. Phys. 48, 2699 (1977).
[CrossRef]

Hobden, M. V.

M. V. Hobden, J. Appl. Phys. 38, 4365 (1967).
[CrossRef]

Hulin, D.

Inaba, H.

H. Ito, H. Naito, H. Inaba, J. Appl. Phys. 46, 3992 (1975).
[CrossRef]

Ito, H.

H. Ito, H. Naito, H. Inaba, J. Appl. Phys. 46, 3992 (1975).
[CrossRef]

Jerphagnon, J.

A. Carenco, J. Jerphagnon, A. Perigaud, J. Chem. Phys. 66, 3806 (1977).
[CrossRef]

Josse, D.

I. Ledoux, D. Josse, P. Vidakovic, J. Zyss, Opt. Eng. 25, 202 (1986).
[CrossRef]

Kinoshita, T.

G. J. Zhang, T. Kinoshita, K. Sasaki, Appl. Phys. Lett. 57, 221 (1990).
[CrossRef]

Kurtz, S. K.

S. K. Kurtz, in Laser Handbook, F. T. Arecchi, E. O. Schulz-Dubois, eds. (North-Holland, Amsterdam, 1972).

Ledoux, I.

I. Ledoux, C. Lepers, A. Périgaud, J. Badan, J. Zyss, Opt. Commun. 80, 149 (1990).
[CrossRef]

I. Ledoux, J. Badan, J. Zyss, A. Migus, D. Hulin, J. Etchepare, G. Grillon, A. Antonetti, J. Opt. Soc. Am. B 4, 987 (1987).
[CrossRef]

I. Ledoux, J. Zyss, A. Migus, J. Etchepare, G. Grillon, A. Antonetti, Appl. Phys. Lett. 48, 1564 (1986).
[CrossRef]

I. Ledoux, D. Josse, P. Vidakovic, J. Zyss, Opt. Eng. 25, 202 (1986).
[CrossRef]

J. Zyss, I. Ledoux, R. Hierle, R. Raj, J. Oudar, IEEE J. Quantum Electron. QE-21, 1286 (1985).
[CrossRef]

Lepers, C.

I. Ledoux, C. Lepers, A. Périgaud, J. Badan, J. Zyss, Opt. Commun. 80, 149 (1990).
[CrossRef]

Levine, B. F.

B. F. Levine, C. G. Bethea, C. D. Thurmond, R. T. Lynch, J. L. Bernstein, J. Appl. Phys. 50, 2523 (1979).
[CrossRef]

Lynch, R. T.

B. F. Levine, C. G. Bethea, C. D. Thurmond, R. T. Lynch, J. L. Bernstein, J. Appl. Phys. 50, 2523 (1979).
[CrossRef]

Midwinter, J.

F. Zernike, J. Midwinter, Applied Nonlinear Optics (Wiley, New York, 1973).

Migus, A.

I. Ledoux, J. Badan, J. Zyss, A. Migus, D. Hulin, J. Etchepare, G. Grillon, A. Antonetti, J. Opt. Soc. Am. B 4, 987 (1987).
[CrossRef]

I. Ledoux, J. Zyss, A. Migus, J. Etchepare, G. Grillon, A. Antonetti, Appl. Phys. Lett. 48, 1564 (1986).
[CrossRef]

Miller, R. C.

R. C. Miller, G. D. Boyd, A. Savage, Appl. Phys. Lett. 6, 77 (1965).
[CrossRef]

Naito, H.

H. Ito, H. Naito, H. Inaba, J. Appl. Phys. 46, 3992 (1975).
[CrossRef]

Nicoud, J. F.

J. Zyss, J. F. Nicoud, M. Coquillay, J. Chem. Phys. 81, 4160 (1984).
[CrossRef]

J. Zyss, D. S. Chemla, J. F. Nicoud, J. Chem. Phys. 74, 4800 (1981).
[CrossRef]

Oudar, J.

J. Zyss, I. Ledoux, R. Hierle, R. Raj, J. Oudar, IEEE J. Quantum Electron. QE-21, 1286 (1985).
[CrossRef]

Oudar, J. L.

J. L. Oudar, R. Hierle, J. Appl. Phys. 48, 2699 (1977).
[CrossRef]

Perigaud, A.

A. Carenco, J. Jerphagnon, A. Perigaud, J. Chem. Phys. 66, 3806 (1977).
[CrossRef]

Périgaud, A.

I. Ledoux, C. Lepers, A. Périgaud, J. Badan, J. Zyss, Opt. Commun. 80, 149 (1990).
[CrossRef]

Pershan, P. S.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Raj, R.

J. Zyss, I. Ledoux, R. Hierle, R. Raj, J. Oudar, IEEE J. Quantum Electron. QE-21, 1286 (1985).
[CrossRef]

Sasaki, K.

G. J. Zhang, T. Kinoshita, K. Sasaki, Appl. Phys. Lett. 57, 221 (1990).
[CrossRef]

Savage, A.

R. C. Miller, G. D. Boyd, A. Savage, Appl. Phys. Lett. 6, 77 (1965).
[CrossRef]

Sigelle, M.

M. Sigelle, R. Hierle, J. Appl. Phys. 52, 4199 (1981).
[CrossRef]

Thurmond, C. D.

B. F. Levine, C. G. Bethea, C. D. Thurmond, R. T. Lynch, J. L. Bernstein, J. Appl. Phys. 50, 2523 (1979).
[CrossRef]

Tsoucaris, G.

J. Zyss, G. Tsoucaris, in Structure and Properties of Molecular Crystals, M. Pierrot, ed. (Elsevier, Amsterdam, 1990).

Vidakovic, P.

I. Ledoux, D. Josse, P. Vidakovic, J. Zyss, Opt. Eng. 25, 202 (1986).
[CrossRef]

Warner, J.

J. Warner, Opto-Electronics 1, 25 (1969).
[CrossRef]

Yao, J. Q.

J. Q. Yao, T. S. Fahlen, J. Appl. Phys. 55, 65 (1984).
[CrossRef]

Yariv, A.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975).

Yeh, P.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

Zernike, F.

F. Zernike, J. Midwinter, Applied Nonlinear Optics (Wiley, New York, 1973).

Zhang, G. J.

G. J. Zhang, T. Kinoshita, K. Sasaki, Appl. Phys. Lett. 57, 221 (1990).
[CrossRef]

Zyss, J.

I. Ledoux, C. Lepers, A. Périgaud, J. Badan, J. Zyss, Opt. Commun. 80, 149 (1990).
[CrossRef]

I. Ledoux, J. Badan, J. Zyss, A. Migus, D. Hulin, J. Etchepare, G. Grillon, A. Antonetti, J. Opt. Soc. Am. B 4, 987 (1987).
[CrossRef]

I. Ledoux, J. Zyss, A. Migus, J. Etchepare, G. Grillon, A. Antonetti, Appl. Phys. Lett. 48, 1564 (1986).
[CrossRef]

I. Ledoux, D. Josse, P. Vidakovic, J. Zyss, Opt. Eng. 25, 202 (1986).
[CrossRef]

J. Zyss, I. Ledoux, R. Hierle, R. Raj, J. Oudar, IEEE J. Quantum Electron. QE-21, 1286 (1985).
[CrossRef]

J. Zyss, J. F. Nicoud, M. Coquillay, J. Chem. Phys. 81, 4160 (1984).
[CrossRef]

J. Zyss, J. Non-cryst. Solids 47, 211 (1982).
[CrossRef]

J. Zyss, D. S. Chemla, J. F. Nicoud, J. Chem. Phys. 74, 4800 (1981).
[CrossRef]

J. Zyss, in Current Trends in Optics, F. T. Arecchi, F. R. Aussenegg, eds. (Taylor & Francis, London, 1981).

J. Zyss, in Conjugated Polymeric Materials: Opportunities in Electronics, Optoelectronics, and Molecular Electronics, J. L. Brédas, R. R. Chance, eds. (Kluwer Academic, Dordrecht, 1990).

J. Zyss, G. Tsoucaris, in Structure and Properties of Molecular Crystals, M. Pierrot, ed. (Elsevier, Amsterdam, 1990).

Appl. Phys. Lett. (3)

G. J. Zhang, T. Kinoshita, K. Sasaki, Appl. Phys. Lett. 57, 221 (1990).
[CrossRef]

R. C. Miller, G. D. Boyd, A. Savage, Appl. Phys. Lett. 6, 77 (1965).
[CrossRef]

I. Ledoux, J. Zyss, A. Migus, J. Etchepare, G. Grillon, A. Antonetti, Appl. Phys. Lett. 48, 1564 (1986).
[CrossRef]

IEEE J. Quantum Electron (1)

J. Zyss, I. Ledoux, R. Hierle, R. Raj, J. Oudar, IEEE J. Quantum Electron. QE-21, 1286 (1985).
[CrossRef]

J. Appl. Phys. (6)

J. L. Oudar, R. Hierle, J. Appl. Phys. 48, 2699 (1977).
[CrossRef]

B. F. Levine, C. G. Bethea, C. D. Thurmond, R. T. Lynch, J. L. Bernstein, J. Appl. Phys. 50, 2523 (1979).
[CrossRef]

M. Sigelle, R. Hierle, J. Appl. Phys. 52, 4199 (1981).
[CrossRef]

M. V. Hobden, J. Appl. Phys. 38, 4365 (1967).
[CrossRef]

J. Q. Yao, T. S. Fahlen, J. Appl. Phys. 55, 65 (1984).
[CrossRef]

H. Ito, H. Naito, H. Inaba, J. Appl. Phys. 46, 3992 (1975).
[CrossRef]

J. Chem. Phys. (3)

J. Zyss, D. S. Chemla, J. F. Nicoud, J. Chem. Phys. 74, 4800 (1981).
[CrossRef]

A. Carenco, J. Jerphagnon, A. Perigaud, J. Chem. Phys. 66, 3806 (1977).
[CrossRef]

J. Zyss, J. F. Nicoud, M. Coquillay, J. Chem. Phys. 81, 4160 (1984).
[CrossRef]

J. Non-cryst. Solids (1)

J. Zyss, J. Non-cryst. Solids 47, 211 (1982).
[CrossRef]

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

Jpn. J. Appl. Phys. (1)

G. C. Bhar, U. Chatterjel, Jpn. J. Appl. Phys. 29, 1103 (1990).
[CrossRef]

Opt. Commun. (1)

I. Ledoux, C. Lepers, A. Périgaud, J. Badan, J. Zyss, Opt. Commun. 80, 149 (1990).
[CrossRef]

Opt. Eng. (1)

I. Ledoux, D. Josse, P. Vidakovic, J. Zyss, Opt. Eng. 25, 202 (1986).
[CrossRef]

Opto-Electronics (1)

J. Warner, Opto-Electronics 1, 25 (1969).
[CrossRef]

Phys. Rev. (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Other (10)

F. T. Arecchi, E. O. Schulz-Dubois, eds., Laser Handbook (North-Holland, Amsterdam, 1972).

A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975).

J. Zyss, in Current Trends in Optics, F. T. Arecchi, F. R. Aussenegg, eds. (Taylor & Francis, London, 1981).

J. Zyss, G. Tsoucaris, in Structure and Properties of Molecular Crystals, M. Pierrot, ed. (Elsevier, Amsterdam, 1990).

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

S. K. Kurtz, in Laser Handbook, F. T. Arecchi, E. O. Schulz-Dubois, eds. (North-Holland, Amsterdam, 1972).

F. Zernike, J. Midwinter, Applied Nonlinear Optics (Wiley, New York, 1973).

S. A. Akhmanov, in Quantum Electronics, Vols. 1A and 1B, Nonlinear Optics, H. Rabin, C. L. Tang, eds. (Academic, New York, 1975).

D. S. Chemla, J. Zyss, eds., Nonlinear Optical Properties of Organic Molecules and Crystals (Academic, New York, 1986).

J. Zyss, in Conjugated Polymeric Materials: Opportunities in Electronics, Optoelectronics, and Molecular Electronics, J. L. Brédas, R. R. Chance, eds. (Kluwer Academic, Dordrecht, 1990).

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Figures (8)

Fig. 1
Fig. 1

Collinear type I and type II SHG PM angles (angles between the collinear PM direction and the related principal dielectric axis) of POM in the principal planes (i.e., YZ, ZX, and XY planes) as a function of the fundamental wavelength. Solid curves represent nonzero-coefficient type I PM and long-dashed curves nonzero-coefficient type II. Short-dashed lines represent zero-coefficient type I and type II configurations. Filled circles represent the PM angles experimentally observed with 1.064- and 1.338-μm Nd3+:YAG lasers. For the nonzero-coefficient type I configuration in the XZ plane, the measured and calculated PM angles at 1.338 μm are 44.8° and 44.9°, respectively (position A), and those at 1.064 μm are 53.8° and 54.3°, respectively (position B).

Fig. 2
Fig. 2

Collinear PM angles and the corresponding generated wavelengths for SFG at 1.064 or 1.338 μm for one beam and a variable wavelength for the other beam. The PM scheme corresponds to the nonzero-coefficient type I configuration in the XZ plane. The curve for SHG is the same as that in Fig. 1, which is drawn here for comparison. The dashed curves represent the wavelength generated from the SFG process. Filled circles represent experimental results.

Fig. 3
Fig. 3

Scheme representing the wave vector’s geometry in the noncollinear SHG experiment. Here curves f1, f2, f2′, and f3 represent the intersections of the normal surface of the crystal at ω and 2ω with the XZ principal plane. Here we have plotted only curves that correspond to the extraordinary wave at ω and ordinary wave at 2ω. A and B are the intersections of f2 with f3, while C is that of f2′ with f3. Here the angle between vectors K1 and K1S is near zero, so the beam with K1 is near the collinear PM direction. In labeling the intersections of the curves with the X and Z axes, the factor ω/c is eliminated from /c for simplicity, where c is the velocity of light in air. This is also the case in Fig. 5.

Fig. 4
Fig. 4

Phenomena observed in noncollinear PM SHG experiment. For both (a) and (b) the photos are taken as Θ1 and Θ2 are decreased by rotating the crystal sample along the Y axis while the before-incidence angle of intersection of the two incident beams remains fixed. When the two beams are off their noncollinear PM angles, the closed circle and the curved line are generated by the two beams separately by recombination with scattered light that propagates in noncollinear PM directions. In (a) the first picture on the left corresponds to the situation depicted in Fig. 3, and the second one is the usual noncollinear PM of the two beams, corresponding to coincident B1 and C1 in Fig. 3. When the circle disappears (the fourth picture), it means that there is no PM with scattered light for the first beam. In (b) the first two pictures on the left correspond to the situation in Fig. 3, and the third gives the one-beam noncritical noncollinear PM, corresponding to coincident A1, B1 and C1. The bright spots on the left-hand side of the first photos in (a) and (b) are generated from collinear SHG because the beam with K1 is near the collinear PM direction (see Fig. 3).

Fig. 5
Fig. 5

Geometric representation of the noncollinear PM condition. (a) For a given Θ1 of the first beam, the PM condition for the second beam is satisfied by two Θ2 values (Θ2′ and Θ2″). Correspondingly, there are two directions for K2 as well as for K3. (b) The noncollinear PM is one-beam noncritical for the second beam. The Poynting vector of the noncritical beam S2 is then parallel to that of the ordinary second-harmonic wave S3, which is in the same direction as K3.

Fig. 6
Fig. 6

Noncollinear PM angles for SHG at different fundamental wavelengths and the angular derivative of the phase-mismatch factor ΔK with respect to the rotation of the crystal or to the second beam for noncollinear SHG PM at 1.338 μm. Generally, for each PM angle Θ1 of the first beam, two values for Θ2 are found, which are defined as Θ2″, Θ2′ (Θ2″ ≥ Θ2′). Θ2″ is presented as dashed curves and Θ2′ as solid curves. Curve 11 (l2) gives the spectral dispersion of the one-beam noncritical noncollinear PM angles when it is noncritical for the vector K1 (K2) beam. Correspondingly, for |d(ΔK)/dΘ)| and |d(ΔK)/dΘ2|, dashed curves are related to noncollinear PM with Θ2 = Θ2″ and solid curves to noncollinear PM with Θ2 = Θ2′. Filled circles represent the experimentally observed PM angles of collinear and the one-beam noncritical noncollinear SHG interactions.

Fig. 7
Fig. 7

One-beam noncritical noncollinear PM angles (solid curves) and the corresponding effective nonlinear coefficient (dashed curve) for SHG at various wavelengths. Θ2 is the PM angle for the noncritical beam, Θ1 is that for the other fundamental beam, and Θ3 is the PM angle for the second-harmonic wave. Filled circles represent experimental results.

Fig. 8
Fig. 8

Noncollinear PM angles and corresponding effective nonlinear coefficient for SFG with 1.064- and 1.338-μm Nd3+:YAG lasers. Θ12) is for the PM angles of 1.064-μm (1.338-μm) light, and (Θ3 is for that of the generated wave (0.5927 μm). The two straight lines correspond to the two symmetry axes of the (Θ2, Θ1) curve. Filled circles represent experimentally observed results.

Tables (1)

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Table 1 Sellmeir Coefficients of POM and Refractive Indices at Selected Wavelengths of Light in Vacuum

Equations (14)

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n c < n a < n b .
n 2 = A + B 1 - C / λ 2 - D λ 2 ,
K 3 - ( K 1 + K 1 S ) = 0.
n 1 2 ( ω ) + n 2 2 ( ω ) + 2 n 1 ( ω ) n 2 ( ω ) cos ( Θ 1 - Θ 2 ) = [ 2 n Y ( 2 ω ) ] 2 ,
d eff ( Θ 1 , Θ 2 ) = sin ( Θ 1 + Θ 2 + ρ 1 + ρ 2 ) d 14 ,
n 1 2 ( ω ) [ n x - 2 ( ω ) - n z - 2 ( ω ) ] sin ( 2 Θ 1 ) [ n 1 ( ω ) + n 2 ( ω ) × cos ( Θ 1 - Θ 2 ) ] - 2 n 2 ( ω ) sin ( Θ 1 - Θ 2 ) = 0.
Δ K = K 3 - ( K 1 + K 2 ) .
| d ( Δ K ) d Θ | = 2 π λ { [ n 1 ( ω ) ] 2 + [ n 2 ( ω ) ] 2 + 2 n 1 ( ω ) n 2 ( ω ) cos ( Θ 1 - Θ 2 ) - [ n 1 ( ω ) n 2 ( ω ) - n 2 ( ω ) n 1 ( ω ) ] 2 sin 2 ( Θ 1 - Θ 2 ) [ 2 n Y ( 2 ω ) ] 2 } 1 / 2 .
| d ( Δ K ) d Θ 2 | = 2 π λ 1 2 n Y ( 2 ω ) [ n 2 ( ω ) n 2 ( ω ) + n 1 ( ω ) n 2 ( ω ) × cos ( Θ 2 - Θ 1 ) - n 1 ( ω ) n 2 ( ω ) sin ( Θ 2 - Θ 1 ) ] .
n 1 ( ω ) = d n 1 ( ω ) d Θ 1 = d n ( ω ) d Θ | Θ = Θ 1 ,
n 2 ( ω ) = d n 2 ( ω ) d Θ 2 = d n ( ω ) d Θ | Θ = Θ 2 .
d K 3 d Θ 2 = d K 2 d Θ 2 .
d K 3 d Θ 3 d Θ 3 d Θ 2 = d K 2 d Θ 2 .
ω 1 2 n 1 2 ( ω 1 ) + ω 2 2 n 2 2 ( ω 2 ) + 2 ω 1 ω 2 n 1 ( ω 1 ) n 2 ( ω 2 ) cos ( Θ 1 - Θ 2 ) = ω 3 2 n Y 2 ( ω 3 ) ,

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