Abstract

Results of a linear- and nonlinear-optical investigation of GaN thin films epitaxially deposited onto (0001)-oriented sapphire are reported. Wavelength- and angle-dependent linear transmission measurements were used to determine the thickness and the refractive index in the 500–1200-nm spectral region for a series of six GaN films. Analysis of angle-dependent, second-harmonic (SH) transmission profiles at 532 nm provided a quantitative evaluation of χxzx(2),χzxx(2), and χzzz(2) and a determination of the GaN lattice structure and tilt angle between the optical axis of the film and the surface normal of the sample. Dispersion effects between 500 nm and 1.064 μm prevented efficient SH production in individual GaN films that were greater than 2.5 μm in thickness. However, field calculations on a proposed multilayer GaN–sapphire structure observed a ninefold increase in the transmitted SH power as compared with a single GaN film.

© 1993 Optical Society of America

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  1. D. K. Wickenden, T. J. Kistenmacher, W. A. Bryden, J. S. Morgan, A. Estes-Wickenden, “The effect of self-nucleation layers on the MOCVD growth of GaN on sapphire,” Mater. Res. Soc. Symp. Proc. 221, 167 (1991).
    [CrossRef]
  2. M. A. Khan, J. M. Van Hove, J. N. Kuznia, D. T. Olsen, “Reflective filters based on single crystal GaN/Alx GaN1−x N multilayers deposited using low pressure MOCVD,” Appl. Phys. Lett. 59, 2408 (1991).
    [CrossRef]
  3. J. S. Morgan, W. A. Bryden, T. J. Kistenmacher, S. A. Ecelberger, T. O. Poehler, “Single-phase aluminum nitride films by dc-magnetron sputtering,” J. Mater. Res. 5, 2677 (1990).
    [CrossRef]
  4. T. J. Kistenmacher, W. A. Bryden, J. S. Morgan, T. O. Poehler, “Characterization of rf-sputtered InN films and AlN/InN bilayers on (0001) sapphire by the x-ray precession method,” J. Appl. Phys. 68, 1541 (1990).
    [CrossRef]
  5. S. Strite, H. Morkoc, “GaN, AlN, and InN: a review,” J. Vac. Sci. Tech. B 10, 1238 (1992).
    [CrossRef]
  6. S. Nakamura, N. Iwasa, M. Senoh, T. Mukai, “Hole compensation of p-type GaN films,” Jpn. J. Appl. Phys. 31, 107 (1992).
    [CrossRef]
  7. Y. Li, G. Eichmann, X. Luo, P. P. Ho, R. R. Alfano, “Noncollinear SHG-based ultrafast optical signal processing for optical digital computing,” Opt. Commun. 64, 322 (1987).
    [CrossRef]
  8. D. R. Ulrich, “Overview: nonlinear optical organics and devices,” in Organic Materials for Nonlinear Materials, R. A. Hann, D. Bloor, eds. (Royal Society of Chemistry, London, 1989), p. 241.
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    [CrossRef]
  10. N. Bloembergen, P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev. 128, 606 (1962).
    [CrossRef]
  11. J. Jerphagnon, S. K. Durtz, “Maker fringes: a detailed comparison of theory and experiment for isotropic and uniaxial crystals,” J. Appl. Phys. 41, 1667 (1970).
    [CrossRef]
  12. Y. Hase, K. Kumata, S. S. Kano, M. Ohashi, T. Kondo, R. Ito, Y. Shiraki, “New method for determining the nonlinear optical coefficients of thin films,” Appl. Phys. Lett. 61, 145 (1992).
    [CrossRef]
  13. Y. R. Shen, Principles of Nonlinear Optics, 1st ed. (Wiley, New York, 1984), Chap. 2.
  14. N. Bloembergen, Nonlinear Optics (Benjamin-Cummings, New York, 1965), Chap. 4.
  15. G. D. Boyd, H. Kasper, J. H. McFee, “Linear and nonlinear optical properties of AgGaS2, CuGaS2, and CuInS2, and theory of the wedge technique for the measurement of nonlinear coefficients,” IEEE J. Quantum Electron. QE-7, 563 (1971).
    [CrossRef]
  16. R. Boyd, Nonlinear Optics (Academic, San Diego, Calif., 1992), Chap. 1.
  17. B. F. Levine, “Bond-charge calculation of nonlinear optical susceptibilities for various crystal structures,” Phys. Rev. B 7, 2600 (1973).
    [CrossRef]
  18. H. Goldstein, Classical Mechanics, 2nd ed. (Addison-Wesley, Reading, Mass., 1981), Chap. 4.
  19. P. D. Maker, R. W. Terhune, M. Nisenoff, C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8, 21 (1962).
    [CrossRef]
  20. M. Choy, R. L. Byer, “Accurate second-order measurements of visible and infrared nonlinear of crystals,” Phys. Rev. B 14, 1693 (1976).
    [CrossRef]
  21. E. Ejder, Phys. Status Solidi A 6, 442 (1971).
    [CrossRef]
  22. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980).
  23. I. H. Malitson, “Refraction and dispersion of synthetic sapphire,” J. Opt. Soc. Am. 52, 1377 (1962).
    [CrossRef]
  24. B. F. Levine, “A new contribution to the nonlinear optical susceptibility arising from unequal atomic radii,” Phys. Rev. Lett. 25, 440 (1970).
    [CrossRef]
  25. B. F. Levine, “d-Electron effects on bond susceptibilities and ionicities,” Phys. Rev. B 7, 2591 (1973).
    [CrossRef]
  26. I. M. Catalano, A. Cingolani, M. Lugara, A. Minafra, “Nonlinear optical properties of GaN,” Opt. Commun. 23, 419 (1977).
    [CrossRef]
  27. T. Ishidate, K. Inoue, M. Aoki, “SHG of epitaxially-grown GaN crystal,” Jpn. J. Appl. Phys. 19, 1641 (1980).
    [CrossRef]
  28. D. S. Bethune, “Optical harmonic generation and mixing in multilayer media: analysis using optical matrix techniques,” J. Opt. Soc. Am. B 6, 910 (1989).
    [CrossRef]
  29. D. S. Bethune, “Optical harmonic generation and mixing in multilayer media: extension of optical transfer matrix approach to include anisotropic materials,” J. Opt. Soc. Am. B 8, 367 (1991).
    [CrossRef]

1992 (3)

S. Strite, H. Morkoc, “GaN, AlN, and InN: a review,” J. Vac. Sci. Tech. B 10, 1238 (1992).
[CrossRef]

S. Nakamura, N. Iwasa, M. Senoh, T. Mukai, “Hole compensation of p-type GaN films,” Jpn. J. Appl. Phys. 31, 107 (1992).
[CrossRef]

Y. Hase, K. Kumata, S. S. Kano, M. Ohashi, T. Kondo, R. Ito, Y. Shiraki, “New method for determining the nonlinear optical coefficients of thin films,” Appl. Phys. Lett. 61, 145 (1992).
[CrossRef]

1991 (3)

D. K. Wickenden, T. J. Kistenmacher, W. A. Bryden, J. S. Morgan, A. Estes-Wickenden, “The effect of self-nucleation layers on the MOCVD growth of GaN on sapphire,” Mater. Res. Soc. Symp. Proc. 221, 167 (1991).
[CrossRef]

M. A. Khan, J. M. Van Hove, J. N. Kuznia, D. T. Olsen, “Reflective filters based on single crystal GaN/Alx GaN1−x N multilayers deposited using low pressure MOCVD,” Appl. Phys. Lett. 59, 2408 (1991).
[CrossRef]

D. S. Bethune, “Optical harmonic generation and mixing in multilayer media: extension of optical transfer matrix approach to include anisotropic materials,” J. Opt. Soc. Am. B 8, 367 (1991).
[CrossRef]

1990 (2)

J. S. Morgan, W. A. Bryden, T. J. Kistenmacher, S. A. Ecelberger, T. O. Poehler, “Single-phase aluminum nitride films by dc-magnetron sputtering,” J. Mater. Res. 5, 2677 (1990).
[CrossRef]

T. J. Kistenmacher, W. A. Bryden, J. S. Morgan, T. O. Poehler, “Characterization of rf-sputtered InN films and AlN/InN bilayers on (0001) sapphire by the x-ray precession method,” J. Appl. Phys. 68, 1541 (1990).
[CrossRef]

1989 (1)

1987 (1)

Y. Li, G. Eichmann, X. Luo, P. P. Ho, R. R. Alfano, “Noncollinear SHG-based ultrafast optical signal processing for optical digital computing,” Opt. Commun. 64, 322 (1987).
[CrossRef]

1980 (1)

T. Ishidate, K. Inoue, M. Aoki, “SHG of epitaxially-grown GaN crystal,” Jpn. J. Appl. Phys. 19, 1641 (1980).
[CrossRef]

1977 (1)

I. M. Catalano, A. Cingolani, M. Lugara, A. Minafra, “Nonlinear optical properties of GaN,” Opt. Commun. 23, 419 (1977).
[CrossRef]

1976 (1)

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

1973 (2)

B. F. Levine, “Bond-charge calculation of nonlinear optical susceptibilities for various crystal structures,” Phys. Rev. B 7, 2600 (1973).
[CrossRef]

B. F. Levine, “d-Electron effects on bond susceptibilities and ionicities,” Phys. Rev. B 7, 2591 (1973).
[CrossRef]

1971 (2)

G. D. Boyd, H. Kasper, J. H. McFee, “Linear and nonlinear optical properties of AgGaS2, CuGaS2, and CuInS2, and theory of the wedge technique for the measurement of nonlinear coefficients,” IEEE J. Quantum Electron. QE-7, 563 (1971).
[CrossRef]

E. Ejder, Phys. Status Solidi A 6, 442 (1971).
[CrossRef]

1970 (2)

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

B. F. Levine, “A new contribution to the nonlinear optical susceptibility arising from unequal atomic radii,” Phys. Rev. Lett. 25, 440 (1970).
[CrossRef]

1962 (3)

I. H. Malitson, “Refraction and dispersion of synthetic sapphire,” J. Opt. Soc. Am. 52, 1377 (1962).
[CrossRef]

P. D. Maker, R. W. Terhune, M. Nisenoff, C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8, 21 (1962).
[CrossRef]

N. Bloembergen, P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev. 128, 606 (1962).
[CrossRef]

Alfano, R. R.

Y. Li, G. Eichmann, X. Luo, P. P. Ho, R. R. Alfano, “Noncollinear SHG-based ultrafast optical signal processing for optical digital computing,” Opt. Commun. 64, 322 (1987).
[CrossRef]

Aoki, M.

T. Ishidate, K. Inoue, M. Aoki, “SHG of epitaxially-grown GaN crystal,” Jpn. J. Appl. Phys. 19, 1641 (1980).
[CrossRef]

Bethune, D. S.

Bloembergen, N.

N. Bloembergen, P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev. 128, 606 (1962).
[CrossRef]

N. Bloembergen, Nonlinear Optics (Benjamin-Cummings, New York, 1965), Chap. 4.

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980).

Boyd, G. D.

G. D. Boyd, H. Kasper, J. H. McFee, “Linear and nonlinear optical properties of AgGaS2, CuGaS2, and CuInS2, and theory of the wedge technique for the measurement of nonlinear coefficients,” IEEE J. Quantum Electron. QE-7, 563 (1971).
[CrossRef]

Boyd, R.

R. Boyd, Nonlinear Optics (Academic, San Diego, Calif., 1992), Chap. 1.

Bryden, W. A.

D. K. Wickenden, T. J. Kistenmacher, W. A. Bryden, J. S. Morgan, A. Estes-Wickenden, “The effect of self-nucleation layers on the MOCVD growth of GaN on sapphire,” Mater. Res. Soc. Symp. Proc. 221, 167 (1991).
[CrossRef]

J. S. Morgan, W. A. Bryden, T. J. Kistenmacher, S. A. Ecelberger, T. O. Poehler, “Single-phase aluminum nitride films by dc-magnetron sputtering,” J. Mater. Res. 5, 2677 (1990).
[CrossRef]

T. J. Kistenmacher, W. A. Bryden, J. S. Morgan, T. O. Poehler, “Characterization of rf-sputtered InN films and AlN/InN bilayers on (0001) sapphire by the x-ray precession method,” J. Appl. Phys. 68, 1541 (1990).
[CrossRef]

Byer, R. L.

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

Catalano, I. M.

I. M. Catalano, A. Cingolani, M. Lugara, A. Minafra, “Nonlinear optical properties of GaN,” Opt. Commun. 23, 419 (1977).
[CrossRef]

Choy, M.

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

Cingolani, A.

I. M. Catalano, A. Cingolani, M. Lugara, A. Minafra, “Nonlinear optical properties of GaN,” Opt. Commun. 23, 419 (1977).
[CrossRef]

Durtz, S. K.

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

Ecelberger, S. A.

J. S. Morgan, W. A. Bryden, T. J. Kistenmacher, S. A. Ecelberger, T. O. Poehler, “Single-phase aluminum nitride films by dc-magnetron sputtering,” J. Mater. Res. 5, 2677 (1990).
[CrossRef]

Eichmann, G.

Y. Li, G. Eichmann, X. Luo, P. P. Ho, R. R. Alfano, “Noncollinear SHG-based ultrafast optical signal processing for optical digital computing,” Opt. Commun. 64, 322 (1987).
[CrossRef]

Ejder, E.

E. Ejder, Phys. Status Solidi A 6, 442 (1971).
[CrossRef]

Estes-Wickenden, A.

D. K. Wickenden, T. J. Kistenmacher, W. A. Bryden, J. S. Morgan, A. Estes-Wickenden, “The effect of self-nucleation layers on the MOCVD growth of GaN on sapphire,” Mater. Res. Soc. Symp. Proc. 221, 167 (1991).
[CrossRef]

Goldstein, H.

H. Goldstein, Classical Mechanics, 2nd ed. (Addison-Wesley, Reading, Mass., 1981), Chap. 4.

Hase, Y.

Y. Hase, K. Kumata, S. S. Kano, M. Ohashi, T. Kondo, R. Ito, Y. Shiraki, “New method for determining the nonlinear optical coefficients of thin films,” Appl. Phys. Lett. 61, 145 (1992).
[CrossRef]

Ho, P. P.

Y. Li, G. Eichmann, X. Luo, P. P. Ho, R. R. Alfano, “Noncollinear SHG-based ultrafast optical signal processing for optical digital computing,” Opt. Commun. 64, 322 (1987).
[CrossRef]

Inoue, K.

T. Ishidate, K. Inoue, M. Aoki, “SHG of epitaxially-grown GaN crystal,” Jpn. J. Appl. Phys. 19, 1641 (1980).
[CrossRef]

Ishidate, T.

T. Ishidate, K. Inoue, M. Aoki, “SHG of epitaxially-grown GaN crystal,” Jpn. J. Appl. Phys. 19, 1641 (1980).
[CrossRef]

Ito, R.

Y. Hase, K. Kumata, S. S. Kano, M. Ohashi, T. Kondo, R. Ito, Y. Shiraki, “New method for determining the nonlinear optical coefficients of thin films,” Appl. Phys. Lett. 61, 145 (1992).
[CrossRef]

Iwasa, N.

S. Nakamura, N. Iwasa, M. Senoh, T. Mukai, “Hole compensation of p-type GaN films,” Jpn. J. Appl. Phys. 31, 107 (1992).
[CrossRef]

Jerphagnon, J.

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

Kano, S. S.

Y. Hase, K. Kumata, S. S. Kano, M. Ohashi, T. Kondo, R. Ito, Y. Shiraki, “New method for determining the nonlinear optical coefficients of thin films,” Appl. Phys. Lett. 61, 145 (1992).
[CrossRef]

Kasper, H.

G. D. Boyd, H. Kasper, J. H. McFee, “Linear and nonlinear optical properties of AgGaS2, CuGaS2, and CuInS2, and theory of the wedge technique for the measurement of nonlinear coefficients,” IEEE J. Quantum Electron. QE-7, 563 (1971).
[CrossRef]

Khan, M. A.

M. A. Khan, J. M. Van Hove, J. N. Kuznia, D. T. Olsen, “Reflective filters based on single crystal GaN/Alx GaN1−x N multilayers deposited using low pressure MOCVD,” Appl. Phys. Lett. 59, 2408 (1991).
[CrossRef]

Kistenmacher, T. J.

D. K. Wickenden, T. J. Kistenmacher, W. A. Bryden, J. S. Morgan, A. Estes-Wickenden, “The effect of self-nucleation layers on the MOCVD growth of GaN on sapphire,” Mater. Res. Soc. Symp. Proc. 221, 167 (1991).
[CrossRef]

J. S. Morgan, W. A. Bryden, T. J. Kistenmacher, S. A. Ecelberger, T. O. Poehler, “Single-phase aluminum nitride films by dc-magnetron sputtering,” J. Mater. Res. 5, 2677 (1990).
[CrossRef]

T. J. Kistenmacher, W. A. Bryden, J. S. Morgan, T. O. Poehler, “Characterization of rf-sputtered InN films and AlN/InN bilayers on (0001) sapphire by the x-ray precession method,” J. Appl. Phys. 68, 1541 (1990).
[CrossRef]

Kondo, T.

Y. Hase, K. Kumata, S. S. Kano, M. Ohashi, T. Kondo, R. Ito, Y. Shiraki, “New method for determining the nonlinear optical coefficients of thin films,” Appl. Phys. Lett. 61, 145 (1992).
[CrossRef]

Kumata, K.

Y. Hase, K. Kumata, S. S. Kano, M. Ohashi, T. Kondo, R. Ito, Y. Shiraki, “New method for determining the nonlinear optical coefficients of thin films,” Appl. Phys. Lett. 61, 145 (1992).
[CrossRef]

Kuznia, J. N.

M. A. Khan, J. M. Van Hove, J. N. Kuznia, D. T. Olsen, “Reflective filters based on single crystal GaN/Alx GaN1−x N multilayers deposited using low pressure MOCVD,” Appl. Phys. Lett. 59, 2408 (1991).
[CrossRef]

Levine, B. F.

B. F. Levine, “Bond-charge calculation of nonlinear optical susceptibilities for various crystal structures,” Phys. Rev. B 7, 2600 (1973).
[CrossRef]

B. F. Levine, “d-Electron effects on bond susceptibilities and ionicities,” Phys. Rev. B 7, 2591 (1973).
[CrossRef]

B. F. Levine, “A new contribution to the nonlinear optical susceptibility arising from unequal atomic radii,” Phys. Rev. Lett. 25, 440 (1970).
[CrossRef]

Li, Y.

Y. Li, G. Eichmann, X. Luo, P. P. Ho, R. R. Alfano, “Noncollinear SHG-based ultrafast optical signal processing for optical digital computing,” Opt. Commun. 64, 322 (1987).
[CrossRef]

Lugara, M.

I. M. Catalano, A. Cingolani, M. Lugara, A. Minafra, “Nonlinear optical properties of GaN,” Opt. Commun. 23, 419 (1977).
[CrossRef]

Luo, X.

Y. Li, G. Eichmann, X. Luo, P. P. Ho, R. R. Alfano, “Noncollinear SHG-based ultrafast optical signal processing for optical digital computing,” Opt. Commun. 64, 322 (1987).
[CrossRef]

Maker, P. D.

P. D. Maker, R. W. Terhune, M. Nisenoff, C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8, 21 (1962).
[CrossRef]

Malitson, I. H.

McFee, J. H.

G. D. Boyd, H. Kasper, J. H. McFee, “Linear and nonlinear optical properties of AgGaS2, CuGaS2, and CuInS2, and theory of the wedge technique for the measurement of nonlinear coefficients,” IEEE J. Quantum Electron. QE-7, 563 (1971).
[CrossRef]

Minafra, A.

I. M. Catalano, A. Cingolani, M. Lugara, A. Minafra, “Nonlinear optical properties of GaN,” Opt. Commun. 23, 419 (1977).
[CrossRef]

Morgan, J. S.

D. K. Wickenden, T. J. Kistenmacher, W. A. Bryden, J. S. Morgan, A. Estes-Wickenden, “The effect of self-nucleation layers on the MOCVD growth of GaN on sapphire,” Mater. Res. Soc. Symp. Proc. 221, 167 (1991).
[CrossRef]

T. J. Kistenmacher, W. A. Bryden, J. S. Morgan, T. O. Poehler, “Characterization of rf-sputtered InN films and AlN/InN bilayers on (0001) sapphire by the x-ray precession method,” J. Appl. Phys. 68, 1541 (1990).
[CrossRef]

J. S. Morgan, W. A. Bryden, T. J. Kistenmacher, S. A. Ecelberger, T. O. Poehler, “Single-phase aluminum nitride films by dc-magnetron sputtering,” J. Mater. Res. 5, 2677 (1990).
[CrossRef]

Morkoc, H.

S. Strite, H. Morkoc, “GaN, AlN, and InN: a review,” J. Vac. Sci. Tech. B 10, 1238 (1992).
[CrossRef]

Mukai, T.

S. Nakamura, N. Iwasa, M. Senoh, T. Mukai, “Hole compensation of p-type GaN films,” Jpn. J. Appl. Phys. 31, 107 (1992).
[CrossRef]

Nakamura, S.

S. Nakamura, N. Iwasa, M. Senoh, T. Mukai, “Hole compensation of p-type GaN films,” Jpn. J. Appl. Phys. 31, 107 (1992).
[CrossRef]

Nisenoff, M.

P. D. Maker, R. W. Terhune, M. Nisenoff, C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8, 21 (1962).
[CrossRef]

Ohashi, M.

Y. Hase, K. Kumata, S. S. Kano, M. Ohashi, T. Kondo, R. Ito, Y. Shiraki, “New method for determining the nonlinear optical coefficients of thin films,” Appl. Phys. Lett. 61, 145 (1992).
[CrossRef]

Olsen, D. T.

M. A. Khan, J. M. Van Hove, J. N. Kuznia, D. T. Olsen, “Reflective filters based on single crystal GaN/Alx GaN1−x N multilayers deposited using low pressure MOCVD,” Appl. Phys. Lett. 59, 2408 (1991).
[CrossRef]

Pershan, P. S.

N. Bloembergen, P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev. 128, 606 (1962).
[CrossRef]

Poehler, T. O.

T. J. Kistenmacher, W. A. Bryden, J. S. Morgan, T. O. Poehler, “Characterization of rf-sputtered InN films and AlN/InN bilayers on (0001) sapphire by the x-ray precession method,” J. Appl. Phys. 68, 1541 (1990).
[CrossRef]

J. S. Morgan, W. A. Bryden, T. J. Kistenmacher, S. A. Ecelberger, T. O. Poehler, “Single-phase aluminum nitride films by dc-magnetron sputtering,” J. Mater. Res. 5, 2677 (1990).
[CrossRef]

Savage, C. M.

P. D. Maker, R. W. Terhune, M. Nisenoff, C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8, 21 (1962).
[CrossRef]

Senoh, M.

S. Nakamura, N. Iwasa, M. Senoh, T. Mukai, “Hole compensation of p-type GaN films,” Jpn. J. Appl. Phys. 31, 107 (1992).
[CrossRef]

Shen, Y. R.

Y. R. Shen, Principles of Nonlinear Optics, 1st ed. (Wiley, New York, 1984), Chap. 2.

Shiraki, Y.

Y. Hase, K. Kumata, S. S. Kano, M. Ohashi, T. Kondo, R. Ito, Y. Shiraki, “New method for determining the nonlinear optical coefficients of thin films,” Appl. Phys. Lett. 61, 145 (1992).
[CrossRef]

Stegeman, G. I.

G. I. Stegeman, “Nonlinear guided waves,” in Contemporary Nonlinear Optics, G. P. Agrawal, R. W. Boyd, eds. (Academic, San Diego, 1992), p. 1.
[CrossRef]

Strite, S.

S. Strite, H. Morkoc, “GaN, AlN, and InN: a review,” J. Vac. Sci. Tech. B 10, 1238 (1992).
[CrossRef]

Terhune, R. W.

P. D. Maker, R. W. Terhune, M. Nisenoff, C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8, 21 (1962).
[CrossRef]

Ulrich, D. R.

D. R. Ulrich, “Overview: nonlinear optical organics and devices,” in Organic Materials for Nonlinear Materials, R. A. Hann, D. Bloor, eds. (Royal Society of Chemistry, London, 1989), p. 241.

Van Hove, J. M.

M. A. Khan, J. M. Van Hove, J. N. Kuznia, D. T. Olsen, “Reflective filters based on single crystal GaN/Alx GaN1−x N multilayers deposited using low pressure MOCVD,” Appl. Phys. Lett. 59, 2408 (1991).
[CrossRef]

Wickenden, D. K.

D. K. Wickenden, T. J. Kistenmacher, W. A. Bryden, J. S. Morgan, A. Estes-Wickenden, “The effect of self-nucleation layers on the MOCVD growth of GaN on sapphire,” Mater. Res. Soc. Symp. Proc. 221, 167 (1991).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980).

Appl. Phys. Lett. (2)

M. A. Khan, J. M. Van Hove, J. N. Kuznia, D. T. Olsen, “Reflective filters based on single crystal GaN/Alx GaN1−x N multilayers deposited using low pressure MOCVD,” Appl. Phys. Lett. 59, 2408 (1991).
[CrossRef]

Y. Hase, K. Kumata, S. S. Kano, M. Ohashi, T. Kondo, R. Ito, Y. Shiraki, “New method for determining the nonlinear optical coefficients of thin films,” Appl. Phys. Lett. 61, 145 (1992).
[CrossRef]

IEEE J. Quantum Electron. (1)

G. D. Boyd, H. Kasper, J. H. McFee, “Linear and nonlinear optical properties of AgGaS2, CuGaS2, and CuInS2, and theory of the wedge technique for the measurement of nonlinear coefficients,” IEEE J. Quantum Electron. QE-7, 563 (1971).
[CrossRef]

J. Appl. Phys. (2)

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

T. J. Kistenmacher, W. A. Bryden, J. S. Morgan, T. O. Poehler, “Characterization of rf-sputtered InN films and AlN/InN bilayers on (0001) sapphire by the x-ray precession method,” J. Appl. Phys. 68, 1541 (1990).
[CrossRef]

J. Mater. Res. (1)

J. S. Morgan, W. A. Bryden, T. J. Kistenmacher, S. A. Ecelberger, T. O. Poehler, “Single-phase aluminum nitride films by dc-magnetron sputtering,” J. Mater. Res. 5, 2677 (1990).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (2)

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[CrossRef]

Jpn. J. Appl. Phys. (2)

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[CrossRef]

T. Ishidate, K. Inoue, M. Aoki, “SHG of epitaxially-grown GaN crystal,” Jpn. J. Appl. Phys. 19, 1641 (1980).
[CrossRef]

Mater. Res. Soc. Symp. Proc. (1)

D. K. Wickenden, T. J. Kistenmacher, W. A. Bryden, J. S. Morgan, A. Estes-Wickenden, “The effect of self-nucleation layers on the MOCVD growth of GaN on sapphire,” Mater. Res. Soc. Symp. Proc. 221, 167 (1991).
[CrossRef]

Opt. Commun. (2)

Y. Li, G. Eichmann, X. Luo, P. P. Ho, R. R. Alfano, “Noncollinear SHG-based ultrafast optical signal processing for optical digital computing,” Opt. Commun. 64, 322 (1987).
[CrossRef]

I. M. Catalano, A. Cingolani, M. Lugara, A. Minafra, “Nonlinear optical properties of GaN,” Opt. Commun. 23, 419 (1977).
[CrossRef]

Phys. Rev. (1)

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Schematic of SHG in a thin GaN film on a sapphire substrate. The wave vectors of each field are discussed in the text. The refracted angle for the transmitted beams is exaggerated. Only the harmonic fields are shown in the film and sapphire substrate. The unit vectors x ˆ and z ˆ define the plane of incidence. The unit vector ŷ points out of the page and is along the GaN surface.

Fig. 2
Fig. 2

Linear transmission profiles for a GaN film generated (a) by using p-polarized incident radiation at 514.5 nm and varying the incident angle and (b) by using unpolarized radiation at normal incidence from 500 to 1200 nm. The solid curves are the experimental data, and the dashed curves are fitted by using a classical approach in determining the transmitted intensity.

Fig. 3
Fig. 3

Comparison of p-polarized SH signals at 532 nm from a 1.09-μm GaN film generated by using (a) p-polarized and (b) s-polarized incident light at 1.064 μm. The solid curves are the experimental data, and the dashed curves were generated by fitting to Eq. (16).

Fig. 4
Fig. 4

Comparison of p-polarized SH signals at 532 nm, generated with p-polarized incident radiation at 1.064 μm for (a) 1.09-μm and (b) 1.30-μm films. The solid curves are the experimental data, and the dashed curves are the curve fitting analysis from Eq. (16).

Fig. 5
Fig. 5

Comparison of p-polarized SH signals at 532 nm, generated with p-polarized incident radiation at 1.064 μm for (a) 0.74-, (b) 2.25-, and (c) 5.31-μm GaN films. The solid curves are the experimental data, and the dashed curves are the curve fitting analysis from Eq. (16).

Fig. 6
Fig. 6

SH transmitted power generated from a proposed multilayer film structure, which is shown in the inset. In the device the hatched regions are 2.2-μm. GaN films (nonlinear) and the shaded regions are sapphire films (linear). The plot shows the SH transmitted power (normalized to the SH power from a single 2.2-μm GaN film) as a function of the sapphire film thickness. The fringes superimposed upon the profile are due to multiple-beam interference in the device.

Tables (2)

Tables Icon

Table 1 Film Thickness and Curve-Fitting Parameters Used in the Cauchy Dispersion Formula for Determining the Refractive Index of the GaN Films

Tables Icon

Table 2 Nonlinear Coefficients (Normalized to χ x x x in Quartz), Coherence Lengths, and Tilt Angles for the GaN Films

Equations (20)

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E inc ω ( x , y ) = E 0 exp [ ( x d f tan θ 2 ) 2 ( cos θ 1 w 0 ) 2 ] exp [ ( y w 0 ) 2 ] ,
P x ( 2 ) ( 2 ω ) = 2 χ x z x ( 2 ω ) E z ( ω ) E x ( ω ) , P y ( 2 ) ( 2 ω ) = 2 χ x z x ( 2 ω ) E z ( ω ) E y ( ω ) , P z ( 2 ) ( 2 ω ) = χ z x x ( 2 ω ) [ E x ( ω ) 2 + E y ( ω ) 2 ] + χ z z z ( 2 ω ) E z ( ω ) 2 ,
χ x z x = χ z x x , χ z x x = χ z z z / 2 .
P x lab ( 2 ) = i = x , y , z A x i P i xtal ( 2 ) , P y lab ( 2 ) = i = x , y , z A y i P i xtal ( 2 ) , P z lab ( 2 ) = i = x , y , z A z i P i xtal ( 2 ) ,
P x lab ( 2 ) P x xtal ( 2 ) , P y lab ( 2 ) P y xtal ( 2 ) , P z lab ( 2 ) P z xtal ( 2 ) .
P ( 2 ) = P z ( 2 ) ( cos θ s ) + P x ( 2 ) ( sin θ s ) , P ( 2 ) = P z ( 2 ) ( sin θ s ) + P x ( 2 ) ( cos θ s ) ,
E t 2 ω ( x , y ) = π [ A 1 g ( x ) + B 1 h ( x ) ] × exp [ 2 ( cos θ 1 w 0 ) 2 ] exp [ ( y w 0 ) 2 ] ,
g ( x ) = exp { 2 [ d f ( tan θ f ) ( cos θ 1 ) w 0 ] 2 } exp [ 4 d f x ( tan θ f ) ( cos 2 θ 1 ) w 0 2 ] , h ( x ) = exp { 2 [ d f ( tan θ 2 ) ( cos θ 1 ) w 0 ] 2 } exp [ 4 d f x ( tan θ 2 ) ( cos 2 θ 1 ) w 0 2 ] ,
A 1 = exp ( i ϕ f ) [ n t ( cos θ f ) + n f ( cos θ t ) ] [ Q 1 n f + Q 2 ( cos θ f ) ] ( n f cos θ t ) ( n t cos θ f ) exp ( i ϕ f ) [ n f ( cos θ t ) n t ( cos θ f ) ] [ Q 2 ( cos θ f ) Q 1 n f ] ( n f cos θ t ) ( n t cos θ f ) + { [ n f ( cos θ t ) n t ( cos θ f ) ] [ Q 1 n f + Q 2 ( cos θ f ) ] exp ( i ϕ f ) D ( n f cos θ t ) ( n t cos θ f ) + [ n t ( cos θ f ) + n f ( cos θ t ) ] [ Q 2 ( cos θ f ) Q 1 n f ] exp ( i ϕ f ) D ( n f cos θ t ) ( n t cos θ f ) } × { [ n r ( cos θ f ) n f ( cos θ r ) ] [ n f ( cos θ t ) + n t ( cos θ f ) ] exp ( i ϕ f ) + [ n f ( cos θ t ) n t ( cos θ f ) ] × [ n r ( cos θ f ) + n f ( cos θ r ) ] exp ( i ϕ f ) } ,
B 1 = 2 ( Q 3 n t + Q 4 cos θ t ) n t cos θ t 2 [ Q 4 ( cos θ t ) Q 3 n t ] n t cos θ t { [ n f ( cos θ t ) n r ( cos θ r ) ] [ n t ( cos θ f ) + n f ( cos θ t ) ] exp ( i ϕ f ) D + [ n f ( cos θ t ) n t ( cos θ f ) ] [ n r ( cos θ f ) + n f ( cos θ r ) ] exp ( i ϕ f ) D } ,
D = [ n f ( cos θ t ) n t ( cos θ f ) ] [ n r ( cos θ f ) n f ( cos r ) ] × exp ( i ϕ f ) + [ n f ( cos θ t ) + n t ( cos θ f ) ] × [ n r ( cos θ f ) + n f ( cos θ r ) ] exp ( i ϕ f ) .
Q 1 ( 3 ) = ( cos θ s ) P ( 2 ) n s 2 n f 2 ( sin θ s ) P ( 2 ) n f 2 ,
Q 2 ( 4 ) = n s P ( 2 ) n s 2 n f 2 ,
ϕ f = 2 n f ω d f ( cos θ f ) / c ,
I 2 ω ( E t 2 ω ) * ( E t 2 ω ) ,
P 2 ω = F 1 ( A 1 * A 1 + B 1 * B + ( A 1 * B + B 1 * A 1 ) × exp { ( d f cos θ 1 ) 2 [ ( tan θ 2 ) ( tan θ f ) ] 2 w 0 2 } ) ,
F 1 = [ 2 n t cos θ t n t ( cos θ 1 ) + n 1 ( cos θ t ) ] 2 .
n ( θ film ) n o { 1 + ( sin 2 θ 1 ) [ n e n o ( n e n o ) 2 ] } 1 / 2 ,
n f = A + ( B / λ inc 2 ) ,
l c = λ inc 4 | n 2 ω n ω | ,

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