Abstract

The linear and quadratic nonlinear-optical properties of the orthorhombic P 212121 5-nitrouracil (5NU) molecular crystals are fully characterized. d14 measurements, performed by two different methods, and second-harmonic conversion efficiencies are reported. Collinear phase-matching configurations for sum-frequency generation are both calculated in the special case of third-harmonic generation and experimentally demonstrated. 5NU permits, in particular, efficient blue-light generation from a pulsed, 1.34-μm Nd3+:YAG laser source by a sequence of second-harmonic and (2ω, ω) sum-mixing processes. The good stability in air and the high damage threshold are accounted for by the presence of hydrogen bonds in the crystalline structure.

© 1993 Optical Society of America

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References

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  1. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).
  2. C. Flytzanis and J. L. Oudar, Nonlinear Optics: Materials and Devices, Vol. 7 of Proceedings in Physics (Springer, New York, 1985).
  3. D. J. Williams, Nonlinear Optical Properties of Organic and Polymer Materials, ACS Symp. Ser. 2331983.
    [Crossref]
  4. D. S. Chemla and J. Zyss, eds., Nonlinear Optical Properties of Organic Molecules and Crystals (Academic, New York, 1986).
  5. G. T. Boyd, Thin Solid Films 152, 295 (1987).
    [Crossref]
  6. K. D. Singer, M. G. Kuzyk, and J. E. Sohn, J. Opt. Soc. Am. B 4, 968 (1987).
    [Crossref]
  7. J. Zyss, D. S. Chemla, and J. F. Nicoud, J. Chem. Phys. 74, 4800 (1981).
    [Crossref]
  8. S. X. Dou, D. Josse, and J. Zyss, J. Opt. Soc. Am. B 8, 1732 (1991); S. X. Dou, D. Josse, R. Hierle, and J. Zyss, J. Opt. Soc. Am. B. 9, 687 (1992).
    [Crossref]
  9. J. Zyss, J. F. Nicoud, and M. Coquillay, J. Chem. Phys. 81, 202 (1984).
    [Crossref]
  10. R. Masse and J. Zyss, Mol. Eng. 1, 141 (1991).
    [Crossref]
  11. Z. Kotler, R. Hierle, D. Josse, J. Zyss, and R. Masse, J. Opt. Soc. Am. B 9, 534 (1992).
    [Crossref]
  12. J. G. Bergman, G. R. Crane, B. F. Levine, and C. G. Bethea, Appl. Phys. Lett. 20, 21 (1972).
    [Crossref]
  13. B. M. Pierce and R. M. Wing, in Molecular and Polymeric Optoelectronic Materials: Fundamentals and Applications, Proc. Soc. Photo-Opt. Instrum. Eng.682, 27 (1986).
    [Crossref]
  14. J. Zyss and G. Berthier, J. Chem. Phys. 77, 3635 (1982).
    [Crossref]
  15. J. Zyss and J. L. Oudar, Phys. Rev. A 26, 2028 (1982).
    [Crossref]
  16. J. L. Oudar and J. Zyss, Phys. Rev. A 26, 2016 (1982).
    [Crossref]
  17. M. M. Choy and R. L. Byer, Phys. Rev. B 14, 1693 (1976).
    [Crossref]
  18. J. Jerphagnon and S. K. Kurtz, J. Appl. Phys. 41, 1667 (1970).
    [Crossref]
  19. J. Q. Yao and T. S. Fahlen, J. Appl. Phys. 55, 65 (1984).
    [Crossref]
  20. D. Josse, R. Hierle, I. Ledoux, and J. Zyss, Appl. Phys. Lett. 53, 2251 (1988).
    [Crossref]
  21. J. L. Oudar, J. Chem. Phys. 67, 446 (1977); B. F. Levine and C. G. Bethea, Appl. Phys. Lett. 24, 445 (1974); J. Chem. Phys. 65, 2429 (1976).
    [Crossref]
  22. F. T. Arecchi and E. O. Schulz-Dubois, eds., Laser Handbook, Vol. 1 (North-Holland, Amsterdam, 1972).
  23. R. A. Laudise, The Growth of Single Crystals (Prentice Hall, Englewood Cliffs, N.J., to be published).
  24. F. C. Zumsteg, J. D. Bierlein, and T. E. Gier, J. Appl. Phys. 47, 4980 (1976).
    [Crossref]
  25. J. D. Bierlein and H. Vanherzeele, J. Opt. Soc. Am. B 6, 622 (1989).
    [Crossref]
  26. G. C. Catella, J. H. Bohn, and J. R. Luken, IEEE J. Quantum Electron. 24, 1201 (1988).
    [Crossref]
  27. C. Cassidy, J. M. Halbout, W. Donaldson, and C. L. Tang, Opt. Commun. 29, 243 (1979).
    [Crossref]
  28. S. X. Dou and D. Josse, Centre National d’Etudes des Télécommunications, 196 Avenue Henri Ravera, 92220 Bagneux, France (personal communication, 1992).

1992 (1)

1991 (2)

1989 (1)

1988 (2)

G. C. Catella, J. H. Bohn, and J. R. Luken, IEEE J. Quantum Electron. 24, 1201 (1988).
[Crossref]

D. Josse, R. Hierle, I. Ledoux, and J. Zyss, Appl. Phys. Lett. 53, 2251 (1988).
[Crossref]

1987 (2)

1984 (2)

J. Zyss, J. F. Nicoud, and M. Coquillay, J. Chem. Phys. 81, 202 (1984).
[Crossref]

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

1983 (1)

D. J. Williams, Nonlinear Optical Properties of Organic and Polymer Materials, ACS Symp. Ser. 2331983.
[Crossref]

1982 (3)

J. Zyss and G. Berthier, J. Chem. Phys. 77, 3635 (1982).
[Crossref]

J. Zyss and J. L. Oudar, Phys. Rev. A 26, 2028 (1982).
[Crossref]

J. L. Oudar and J. Zyss, Phys. Rev. A 26, 2016 (1982).
[Crossref]

1981 (1)

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

1979 (1)

C. Cassidy, J. M. Halbout, W. Donaldson, and C. L. Tang, Opt. Commun. 29, 243 (1979).
[Crossref]

1977 (1)

J. L. Oudar, J. Chem. Phys. 67, 446 (1977); B. F. Levine and C. G. Bethea, Appl. Phys. Lett. 24, 445 (1974); J. Chem. Phys. 65, 2429 (1976).
[Crossref]

1976 (2)

F. C. Zumsteg, J. D. Bierlein, and T. E. Gier, J. Appl. Phys. 47, 4980 (1976).
[Crossref]

M. M. Choy and R. L. Byer, Phys. Rev. B 14, 1693 (1976).
[Crossref]

1972 (1)

J. G. Bergman, G. R. Crane, B. F. Levine, and C. G. Bethea, Appl. Phys. Lett. 20, 21 (1972).
[Crossref]

1970 (1)

J. Jerphagnon and S. K. Kurtz, J. Appl. Phys. 41, 1667 (1970).
[Crossref]

Bergman, J. G.

J. G. Bergman, G. R. Crane, B. F. Levine, and C. G. Bethea, Appl. Phys. Lett. 20, 21 (1972).
[Crossref]

Berthier, G.

J. Zyss and G. Berthier, J. Chem. Phys. 77, 3635 (1982).
[Crossref]

Bethea, C. G.

J. G. Bergman, G. R. Crane, B. F. Levine, and C. G. Bethea, Appl. Phys. Lett. 20, 21 (1972).
[Crossref]

Bierlein, J. D.

J. D. Bierlein and H. Vanherzeele, J. Opt. Soc. Am. B 6, 622 (1989).
[Crossref]

F. C. Zumsteg, J. D. Bierlein, and T. E. Gier, J. Appl. Phys. 47, 4980 (1976).
[Crossref]

Bohn, J. H.

G. C. Catella, J. H. Bohn, and J. R. Luken, IEEE J. Quantum Electron. 24, 1201 (1988).
[Crossref]

Boyd, G. T.

G. T. Boyd, Thin Solid Films 152, 295 (1987).
[Crossref]

Byer, R. L.

M. M. Choy and R. L. Byer, Phys. Rev. B 14, 1693 (1976).
[Crossref]

Cassidy, C.

C. Cassidy, J. M. Halbout, W. Donaldson, and C. L. Tang, Opt. Commun. 29, 243 (1979).
[Crossref]

Catella, G. C.

G. C. Catella, J. H. Bohn, and J. R. Luken, IEEE J. Quantum Electron. 24, 1201 (1988).
[Crossref]

Chemla, D. S.

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

Choy, M. M.

M. M. Choy and R. L. Byer, Phys. Rev. B 14, 1693 (1976).
[Crossref]

Coquillay, M.

J. Zyss, J. F. Nicoud, and M. Coquillay, J. Chem. Phys. 81, 202 (1984).
[Crossref]

Crane, G. R.

J. G. Bergman, G. R. Crane, B. F. Levine, and C. G. Bethea, Appl. Phys. Lett. 20, 21 (1972).
[Crossref]

Donaldson, W.

C. Cassidy, J. M. Halbout, W. Donaldson, and C. L. Tang, Opt. Commun. 29, 243 (1979).
[Crossref]

Dou, S. X.

S. X. Dou, D. Josse, and J. Zyss, J. Opt. Soc. Am. B 8, 1732 (1991); S. X. Dou, D. Josse, R. Hierle, and J. Zyss, J. Opt. Soc. Am. B. 9, 687 (1992).
[Crossref]

S. X. Dou and D. Josse, Centre National d’Etudes des Télécommunications, 196 Avenue Henri Ravera, 92220 Bagneux, France (personal communication, 1992).

Fahlen, T. S.

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

Flytzanis, C.

C. Flytzanis and J. L. Oudar, Nonlinear Optics: Materials and Devices, Vol. 7 of Proceedings in Physics (Springer, New York, 1985).

Gier, T. E.

F. C. Zumsteg, J. D. Bierlein, and T. E. Gier, J. Appl. Phys. 47, 4980 (1976).
[Crossref]

Halbout, J. M.

C. Cassidy, J. M. Halbout, W. Donaldson, and C. L. Tang, Opt. Commun. 29, 243 (1979).
[Crossref]

Hierle, R.

Z. Kotler, R. Hierle, D. Josse, J. Zyss, and R. Masse, J. Opt. Soc. Am. B 9, 534 (1992).
[Crossref]

D. Josse, R. Hierle, I. Ledoux, and J. Zyss, Appl. Phys. Lett. 53, 2251 (1988).
[Crossref]

Jerphagnon, J.

J. Jerphagnon and S. K. Kurtz, J. Appl. Phys. 41, 1667 (1970).
[Crossref]

Josse, D.

Z. Kotler, R. Hierle, D. Josse, J. Zyss, and R. Masse, J. Opt. Soc. Am. B 9, 534 (1992).
[Crossref]

S. X. Dou, D. Josse, and J. Zyss, J. Opt. Soc. Am. B 8, 1732 (1991); S. X. Dou, D. Josse, R. Hierle, and J. Zyss, J. Opt. Soc. Am. B. 9, 687 (1992).
[Crossref]

D. Josse, R. Hierle, I. Ledoux, and J. Zyss, Appl. Phys. Lett. 53, 2251 (1988).
[Crossref]

S. X. Dou and D. Josse, Centre National d’Etudes des Télécommunications, 196 Avenue Henri Ravera, 92220 Bagneux, France (personal communication, 1992).

Kotler, Z.

Kurtz, S. K.

J. Jerphagnon and S. K. Kurtz, J. Appl. Phys. 41, 1667 (1970).
[Crossref]

Kuzyk, M. G.

Laudise, R. A.

R. A. Laudise, The Growth of Single Crystals (Prentice Hall, Englewood Cliffs, N.J., to be published).

Ledoux, I.

D. Josse, R. Hierle, I. Ledoux, and J. Zyss, Appl. Phys. Lett. 53, 2251 (1988).
[Crossref]

Levine, B. F.

J. G. Bergman, G. R. Crane, B. F. Levine, and C. G. Bethea, Appl. Phys. Lett. 20, 21 (1972).
[Crossref]

Luken, J. R.

G. C. Catella, J. H. Bohn, and J. R. Luken, IEEE J. Quantum Electron. 24, 1201 (1988).
[Crossref]

Masse, R.

Nicoud, J. F.

J. Zyss, J. F. Nicoud, and M. Coquillay, J. Chem. Phys. 81, 202 (1984).
[Crossref]

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

Oudar, J. L.

J. Zyss and J. L. Oudar, Phys. Rev. A 26, 2028 (1982).
[Crossref]

J. L. Oudar and J. Zyss, Phys. Rev. A 26, 2016 (1982).
[Crossref]

J. L. Oudar, J. Chem. Phys. 67, 446 (1977); B. F. Levine and C. G. Bethea, Appl. Phys. Lett. 24, 445 (1974); J. Chem. Phys. 65, 2429 (1976).
[Crossref]

C. Flytzanis and J. L. Oudar, Nonlinear Optics: Materials and Devices, Vol. 7 of Proceedings in Physics (Springer, New York, 1985).

Pierce, B. M.

B. M. Pierce and R. M. Wing, in Molecular and Polymeric Optoelectronic Materials: Fundamentals and Applications, Proc. Soc. Photo-Opt. Instrum. Eng.682, 27 (1986).
[Crossref]

Shen, Y. R.

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).

Singer, K. D.

Sohn, J. E.

Tang, C. L.

C. Cassidy, J. M. Halbout, W. Donaldson, and C. L. Tang, Opt. Commun. 29, 243 (1979).
[Crossref]

Vanherzeele, H.

Williams, D. J.

D. J. Williams, Nonlinear Optical Properties of Organic and Polymer Materials, ACS Symp. Ser. 2331983.
[Crossref]

Wing, R. M.

B. M. Pierce and R. M. Wing, in Molecular and Polymeric Optoelectronic Materials: Fundamentals and Applications, Proc. Soc. Photo-Opt. Instrum. Eng.682, 27 (1986).
[Crossref]

Yao, J. Q.

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

Zumsteg, F. C.

F. C. Zumsteg, J. D. Bierlein, and T. E. Gier, J. Appl. Phys. 47, 4980 (1976).
[Crossref]

Zyss, J.

Z. Kotler, R. Hierle, D. Josse, J. Zyss, and R. Masse, J. Opt. Soc. Am. B 9, 534 (1992).
[Crossref]

S. X. Dou, D. Josse, and J. Zyss, J. Opt. Soc. Am. B 8, 1732 (1991); S. X. Dou, D. Josse, R. Hierle, and J. Zyss, J. Opt. Soc. Am. B. 9, 687 (1992).
[Crossref]

R. Masse and J. Zyss, Mol. Eng. 1, 141 (1991).
[Crossref]

D. Josse, R. Hierle, I. Ledoux, and J. Zyss, Appl. Phys. Lett. 53, 2251 (1988).
[Crossref]

J. Zyss, J. F. Nicoud, and M. Coquillay, J. Chem. Phys. 81, 202 (1984).
[Crossref]

J. Zyss and G. Berthier, J. Chem. Phys. 77, 3635 (1982).
[Crossref]

J. Zyss and J. L. Oudar, Phys. Rev. A 26, 2028 (1982).
[Crossref]

J. L. Oudar and J. Zyss, Phys. Rev. A 26, 2016 (1982).
[Crossref]

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

Appl. Phys. Lett. (2)

J. G. Bergman, G. R. Crane, B. F. Levine, and C. G. Bethea, Appl. Phys. Lett. 20, 21 (1972).
[Crossref]

D. Josse, R. Hierle, I. Ledoux, and J. Zyss, Appl. Phys. Lett. 53, 2251 (1988).
[Crossref]

IEEE J. Quantum Electron. (1)

G. C. Catella, J. H. Bohn, and J. R. Luken, IEEE J. Quantum Electron. 24, 1201 (1988).
[Crossref]

J. Appl. Phys. (3)

J. Jerphagnon and S. K. Kurtz, J. Appl. Phys. 41, 1667 (1970).
[Crossref]

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

F. C. Zumsteg, J. D. Bierlein, and T. E. Gier, J. Appl. Phys. 47, 4980 (1976).
[Crossref]

J. Chem. Phys. (4)

J. L. Oudar, J. Chem. Phys. 67, 446 (1977); B. F. Levine and C. G. Bethea, Appl. Phys. Lett. 24, 445 (1974); J. Chem. Phys. 65, 2429 (1976).
[Crossref]

J. Zyss, J. F. Nicoud, and M. Coquillay, J. Chem. Phys. 81, 202 (1984).
[Crossref]

J. Zyss and G. Berthier, J. Chem. Phys. 77, 3635 (1982).
[Crossref]

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

J. Opt. Soc. Am. B (4)

Mol. Eng. (1)

R. Masse and J. Zyss, Mol. Eng. 1, 141 (1991).
[Crossref]

Nonlinear Optical Properties of Organic and Polymer Materials (1)

D. J. Williams, Nonlinear Optical Properties of Organic and Polymer Materials, ACS Symp. Ser. 2331983.
[Crossref]

Opt. Commun. (1)

C. Cassidy, J. M. Halbout, W. Donaldson, and C. L. Tang, Opt. Commun. 29, 243 (1979).
[Crossref]

Phys. Rev. A (2)

J. Zyss and J. L. Oudar, Phys. Rev. A 26, 2028 (1982).
[Crossref]

J. L. Oudar and J. Zyss, Phys. Rev. A 26, 2016 (1982).
[Crossref]

Phys. Rev. B (1)

M. M. Choy and R. L. Byer, Phys. Rev. B 14, 1693 (1976).
[Crossref]

Thin Solid Films (1)

G. T. Boyd, Thin Solid Films 152, 295 (1987).
[Crossref]

Other (7)

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

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).

C. Flytzanis and J. L. Oudar, Nonlinear Optics: Materials and Devices, Vol. 7 of Proceedings in Physics (Springer, New York, 1985).

B. M. Pierce and R. M. Wing, in Molecular and Polymeric Optoelectronic Materials: Fundamentals and Applications, Proc. Soc. Photo-Opt. Instrum. Eng.682, 27 (1986).
[Crossref]

S. X. Dou and D. Josse, Centre National d’Etudes des Télécommunications, 196 Avenue Henri Ravera, 92220 Bagneux, France (personal communication, 1992).

F. T. Arecchi and E. O. Schulz-Dubois, eds., Laser Handbook, Vol. 1 (North-Holland, Amsterdam, 1972).

R. A. Laudise, The Growth of Single Crystals (Prentice Hall, Englewood Cliffs, N.J., to be published).

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Figures (18)

Fig. 1
Fig. 1

Molecular structure of 5-nitrouracil (5NU).

Fig. 2
Fig. 2

Mesomeric forms of the 5NU molecule.

Fig. 3
Fig. 3

Absorption spectra of 5NU in various solvents: alcohols (methanol for the long-dashed curve, ethanol for the solid curve, and propanol for the dashed–dotted curve) or, the best solvent, water (short-dashed curve).

Fig. 4
Fig. 4

Typical as-grown 5NU crystal with orientation of the crystallographic and dielectric framework.

Fig. 5
Fig. 5

Representations of the 5NU molecules unit cell projected along c and a.

Fig. 6
Fig. 6

Intermediate frameworks introduced in the oriented-gas description: (X0, Y0, Z0) is a molecular framework, (X′, Y′, Z′) is a dielectric framework rotated around Z, and (X, Y, Z) is the dielectric framework.

Fig. 7
Fig. 7

Transmission spectra of a 5NU crystal cut and polished with its faces parallel to the (ab) plane. Recordings are shown for the two dielectric axis polarization directions a and b (solid and dashed curves, respectively).

Fig. 8
Fig. 8

Index dispersion along the three principal dielectric axes calculated from the Sellmeier coefficients with experimental data as points.

Fig. 9
Fig. 9

Calculated second-harmonic phase-matching curves in the three principal dielectric planes. The solid curve holds for type-I phase-matching, while the dashed lined holds for type II.

Fig. 10
Fig. 10

Experimental Maker-fringe pattern of a 5NU crystalline slab (solid curve). The polarization configuration of both fundamental and harmonic waves with respect to the crystal orientation are shown in the inset. The dashed curve corresponds to the theoretical fit of the fringes.

Fig. 11
Fig. 11

Type-I phase-matched SHG versus angle for 5NU and POM crystals at a 1.06-μm fundamental wavelength.

Fig. 12
Fig. 12

Out-of-plane second-harmonic phase-matching curves calculated at a fundamental wavelength of 1.06 μm. The lower solid curve holds for type-I phase matching and the lower dashed curve for type II. Corresponding calculated nonlinear effective coefficients are shown for the out-of-plane type-I (upper solid curve) and type-II (upper dashed curve) phase-matching configurations.

Fig. 13
Fig. 13

Out-of-plane second-harmonic phase-matching curves calculated at a fundamental wavelength of 0.83 μm. The lower solid curve holds for type-I phase matching and the upper dashed curve for type II. For type I (type II), Φ = 0° corresponds to the XY (ZX) plane. Corresponding calculated nonlinear effective coefficients are shown for the out-of-plane type-I (upper solid curve) and type-II (lower dashed curve) phase-matching configurations.

Fig. 14
Fig. 14

Calculated sum-frequency (third-harmonic) phase matching curves in the XY plane. Curve (1′) holds for type I (e + eo) and Curves (2′) and (3′) for type II (e + oe, o + ee). The two SHG curves are also represented (solid and long-dashed curves).

Fig. 15
Fig. 15

Configurations of the optical wave polarizations in the case of two-stage third-harmonic generation. The input fundamental electric field is polarized in the XY plane for the type-I interaction; the second-harmonic field E2ω is polarized in the XY plane in the type-II interaction.

Fig. 16
Fig. 16

Out-of-plane XY calculated SFG third-harmonic-generation phase-matching curves for a fundamental wavelength of 1.34 μm. The short-and-long-dashed curve holds for type-I phase matching, while the dashed curves hold for type II.

Fig. 17
Fig. 17

Effective nonlinear coefficients, corresponding to the three SFG curves shown in Fig. 16. The short-and-long-dashed curve holds for type-I phase matching, while the short-dashed curves hold for type II

Fig. 18
Fig. 18

Extended view of the out-of-plane SHG (type I, solid curve; type II, long-dashed curve) and SFG (type I, short-and-long-dashed curve; type II, short-dashed curve) phase-matching curves.

Tables (10)

Tables Icon

Table 1 Experimental Refractive Indices of 5NU Measured at Various Wavelengths with Spectral Lamps and Laser Sources

Tables Icon

Table 2 Sellmeier Coefficients of 5NU in the Three Main Polarization Directions and Optical Indexes at Selected Wavelengths

Tables Icon

Table 3 SHG Phase-Matching Conditions, Polarization Geometries, and deff Corresponding to the Curves

Tables Icon

Table 4 Experimental and Calculated SHG Phase-Matching Angles for Type I and Type II at 0.83, 1.06, and 1.34 μm

Tables Icon

Table 5 Calculated Angular Aperture Coefficient Cθ for Type-I Phase-Matched SHG at Selected Wavelengths

Tables Icon

Table 6 Calculated Angular Aperture Coefficients for Type-II Phase-Matching Peaks at Selected Wavelengths

Tables Icon

Table 7 Optical Damage Thresholds for a 5NU Crystala

Tables Icon

Table 8 SFG Third-Harmonic-Generation Phase-Matching Configuration Polarizations and deff Corresponding to Curves in Fig. 14

Tables Icon

Table 9 Angular Aperture Coefficients of SFG Third-Harmonic-Generation Type-I and -II Phase-Matching Peaks at a Fundamental Wavelength of 1.34 μm

Tables Icon

Table 10 Comparison of 5NU with Some Well-Known Mineral and Organic Crystals

Equations (14)

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

a = 0.994 nm , b = 1.030 nm , c = 0.547 nm ,             Z = 4 ,
d I J K ω 1 ω 2 ω 3 = N f I ω 1 f J ω 2 f K ω 3 C I i ( s ) C J j ( s ) C K k ( s ) β i j k ( ω 1 , ω 2 , ω 3 ) ,
d 14 = d a b c = N f 2 ω f ω f ω 12 β Z X X ( sin θ ) ( cos θ ) ,
β z x x = 2 β Z 0 Z 0 Z 0 ( cos ϕ ) ( sin 2 ϕ ) + 2 β Z 0 X 0 X 0 ( cos ϕ ) × [ ( cos 2 ϕ ) - 2 ( sin 2 ϕ ) ] - 2 β X 0 X 0 X 0 ( sin ϕ ) ( cos 2 ϕ ) - 2 β X 0 Z 0 Z 0 ( sin ϕ ) [ ( sin 2 ϕ ) - 2 ( cos 2 ϕ ) ] .
n 2 = A + B 1 - ( C / λ 2 ) - D λ 2 ,
I 2 ω = 8 π c ( n ω 2 - n 2 ω 2 ) 2 t ω 4 d 2 p 1 2 ( θ ) p 2 2 ( θ ) E ω 4 T 2 ω ( sin 2 ψ ) ,
d eff = i j p i ω 1 ( θ ω 1 , ϕ ω 1 ) p j ω 2 ( θ ω 2 , ϕ ω 2 ) p k ω 3 ( θ ω 3 , ϕ ω 3 ) d i j k .
ψ = π 2 l l c             with l c = λ 4 ( n 2 ω - n ω ) .
d eff = P 2 ω ¯ · E 2 ω ¯ E ω 2 E 2 ω ,
E ω i = { ( sin θ i ) ( cos ϕ i ) ( n x i ) 2 - n 2 ( sin θ i ) ( sin ϕ i ) ( n y i ) 2 - n 2 . cos θ i ( n z i ) 2 - n 2
I 2 ω = 2 π c P 2 ω 2 16 ( cos 4 θ ) [ ( cos θ ) + n ( cos θ ) ] 2 ( π l λ ) 2 T 2 ω ( t ω ) 4 ,
C θ = 1 1 λ s d n s d θ - 1 λ 1 d n 1 d θ - 1 λ 2 d n 2 d θ ,
C θ = λ / 2 1 2 ( d n 1 ω d θ + d n 2 ω d θ ) - d n 2 ω d θ .
Δ θ I = λ / 2 l ( n e ω ) 3 sin ( 2 θ 0 ) { [ 1 / ( n a ω ) 2 ] - [ 1 / ( n b ω ) 2 ] } .

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