Abstract

The second-order susceptibilities (dij) of both ordered and disordered Ga0.5In0.5P semiconductor crystal films epitaxially grown on GaAs substrates are analyzed. Quasi-phase matching based on periodic order–disorder regions is proposed, and the analysis shows that three of the four independent coefficients, namely, d33, d31, and d15, but not d14, can be modulated. Maker-fringe experiments were performed at 1.57 µm to measure these coefficients in the deposited crystals. However, the crystal-film orientation allowed a definitive determination of the d14 coefficient (110 pm/V) only and an upper limit of 60 pm/V for d33. More-sophisticated experimental techniques are proposed for measuring d33.

© 1997 Optical Society of America

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    [CrossRef]
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  24. C GaInP has one C3 axis and three σν planes for symmetry operations. The average owing to the domain mixture causes the crystal to lose the C3 axis and two of the three σν planes and to gain a new (1¯, 1, 0) σν plane and one [0, 0, 1] C2 axis. The (1, 1, 0) σν plane remains. Consequently, a set of symmetry operations with one C2 axis and two σν planes corresponds to the C symmetry.
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    [CrossRef]
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    [CrossRef]
  27. In a few measurements we observed sharp Fabry–Perot fringes corresponding to the distance of 150 μm between GaInP and GaAs surfaces, in addition to Maker fringes, which correspond to the GaInP thickness of 1.2 μm. In most of our measurements, however, the fundamental lights are believed to be incoherently multireflected between GaInP and GaAs surfaces.
  28. D. E. Aspens, S. M. Kelso, R. A. Logan, and R. Bhat, “Optical properties of AlxGa1−xAs,” J. Appl. Phys. 60, 754–767 (1986).
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  30. A. Gomyo, T. Suzuki, S. Iijima, H. Hotta, H. Fujii, S. Kawata, K. Kobayashi, Y. Ueno, and I. Hino, “Nonexistence of long-range order in Ga0.5In0.5P epitaxial layers grown on (111)B and (110)GaAs substrates,” Jpn. J. Appl. Phys. 27, L2370–L2372 (1988).
    [CrossRef]

1996 (1)

A. Moritz, R. Wirth, C. Geng, F. Scholz, and A. Hangleiter, “Birefringence and tilted modes in ordered GaInP/AlGaInP waveguides and lasers,” Appl. Phys. Lett. 68, 1217–1219 (1996).
[CrossRef]

1995 (3)

Y. Kostoulas, K. B. Ucer, G. W. Wicks, and P. M. Fauchet, “Femtosecond carrier dynamics in low-temperature grown Ga0.5In0.5P,” Appl. Phys. Lett. 67, 3756–3758 (1995).
[CrossRef]

See, e.g., L. E. Myers, R. C. Eckardt, M. M. Fejer, R. L. Beyer, W. R. Bosenberg, and J. W. Pierce, “Quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO3,” J. Opt. Soc. Am. B 12, 2102–2116 (1995).
[CrossRef]

P. Ernst, C. Geng, F. Scholz, and H. Schweizer, “Band-gap reduction and valence-band splitting of ordered GaInP2,” Appl. Phys. Lett. 67, 2347–2349 (1995).
[CrossRef]

1994 (1)

1993 (3)

1992 (1)

1991 (1)

E. Ghahramani, D. J. Moss, and J. E. Sipe, “Full-band-structure calculation of first-, second-, and third-harmonic optical response coefficients of ZnSe, ZnTe, and CdTe,” Phys. Rev. B 43, 9700–9710 (1991).
[CrossRef]

1989 (2)

T. Kurimoto and N. Hamada, “Electronic structure of the (GaP)1/(InP)1 (111) strained-layer superlattice,” Phys. Rev. 40, 3889–3895 (1989).
[CrossRef]

A. Mascarenhas, S. Kurtz, A. Kibbler, and J. M. Olson, “Polarized band-edge photoluminescence and ordering in Ga0.52In0.48P,” Phys. Rev. Lett. 63, 2108–2111 (1989).
[CrossRef] [PubMed]

1988 (1)

A. Gomyo, T. Suzuki, S. Iijima, H. Hotta, H. Fujii, S. Kawata, K. Kobayashi, Y. Ueno, and I. Hino, “Nonexistence of long-range order in Ga0.5In0.5P epitaxial layers grown on (111)B and (110)GaAs substrates,” Jpn. J. Appl. Phys. 27, L2370–L2372 (1988).
[CrossRef]

1986 (2)

H. Tanaka, Y. Kawamura, and H. Asahi, “Refractive indices of In0.49Ga0.51−xAlxP lattice matched to GaAs,” J. Appl. Phys. 59, 985–986 (1986).
[CrossRef]

D. E. Aspens, S. M. Kelso, R. A. Logan, and R. Bhat, “Optical properties of AlxGa1−xAs,” J. Appl. Phys. 60, 754–767 (1986).
[CrossRef]

1970 (1)

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

Asahi, H.

H. Tanaka, Y. Kawamura, and H. Asahi, “Refractive indices of In0.49Ga0.51−xAlxP lattice matched to GaAs,” J. Appl. Phys. 59, 985–986 (1986).
[CrossRef]

Aspens, D. E.

D. E. Aspens, S. M. Kelso, R. A. Logan, and R. Bhat, “Optical properties of AlxGa1−xAs,” J. Appl. Phys. 60, 754–767 (1986).
[CrossRef]

Assanto, G.

Baek, Y.

Beyer, R. L.

Bhat, R.

D. E. Aspens, S. M. Kelso, R. A. Logan, and R. Bhat, “Optical properties of AlxGa1−xAs,” J. Appl. Phys. 60, 754–767 (1986).
[CrossRef]

Bierlein, J. D.

Bosenberg, W. R.

Bosshard, Ch.

DeSalvo, R.

Eckardt, R. C.

Endo, K.

Y. Ueno, H. Fujii, H. Sawano, K. Kobayashi, K. Hara, A. Gomyo, and K. Endo, “30-mW 690-nm high-power strained-quantum-well AlGaInP laser,” IEEE J. Quantum Electron. 29, 1851–1856 (1993).
[CrossRef]

Ernst, P.

P. Ernst, C. Geng, F. Scholz, and H. Schweizer, “Band-gap reduction and valence-band splitting of ordered GaInP2,” Appl. Phys. Lett. 67, 2347–2349 (1995).
[CrossRef]

Fauchet, P. M.

Y. Kostoulas, K. B. Ucer, G. W. Wicks, and P. M. Fauchet, “Femtosecond carrier dynamics in low-temperature grown Ga0.5In0.5P,” Appl. Phys. Lett. 67, 3756–3758 (1995).
[CrossRef]

Fejer, M. M.

Fujii, H.

Y. Ueno, H. Fujii, H. Sawano, K. Kobayashi, K. Hara, A. Gomyo, and K. Endo, “30-mW 690-nm high-power strained-quantum-well AlGaInP laser,” IEEE J. Quantum Electron. 29, 1851–1856 (1993).
[CrossRef]

A. Gomyo, T. Suzuki, S. Iijima, H. Hotta, H. Fujii, S. Kawata, K. Kobayashi, Y. Ueno, and I. Hino, “Nonexistence of long-range order in Ga0.5In0.5P epitaxial layers grown on (111)B and (110)GaAs substrates,” Jpn. J. Appl. Phys. 27, L2370–L2372 (1988).
[CrossRef]

Geng, C.

A. Moritz, R. Wirth, C. Geng, F. Scholz, and A. Hangleiter, “Birefringence and tilted modes in ordered GaInP/AlGaInP waveguides and lasers,” Appl. Phys. Lett. 68, 1217–1219 (1996).
[CrossRef]

P. Ernst, C. Geng, F. Scholz, and H. Schweizer, “Band-gap reduction and valence-band splitting of ordered GaInP2,” Appl. Phys. Lett. 67, 2347–2349 (1995).
[CrossRef]

Ghahramani, E.

E. Ghahramani, D. J. Moss, and J. E. Sipe, “Full-band-structure calculation of first-, second-, and third-harmonic optical response coefficients of ZnSe, ZnTe, and CdTe,” Phys. Rev. B 43, 9700–9710 (1991).
[CrossRef]

Gomyo, A.

Y. Ueno, H. Fujii, H. Sawano, K. Kobayashi, K. Hara, A. Gomyo, and K. Endo, “30-mW 690-nm high-power strained-quantum-well AlGaInP laser,” IEEE J. Quantum Electron. 29, 1851–1856 (1993).
[CrossRef]

A. Gomyo, T. Suzuki, S. Iijima, H. Hotta, H. Fujii, S. Kawata, K. Kobayashi, Y. Ueno, and I. Hino, “Nonexistence of long-range order in Ga0.5In0.5P epitaxial layers grown on (111)B and (110)GaAs substrates,” Jpn. J. Appl. Phys. 27, L2370–L2372 (1988).
[CrossRef]

Hagan, D. J.

Hamada, N.

T. Kurimoto and N. Hamada, “Electronic structure of the (GaP)1/(InP)1 (111) strained-layer superlattice,” Phys. Rev. 40, 3889–3895 (1989).
[CrossRef]

Hangleiter, A.

A. Moritz, R. Wirth, C. Geng, F. Scholz, and A. Hangleiter, “Birefringence and tilted modes in ordered GaInP/AlGaInP waveguides and lasers,” Appl. Phys. Lett. 68, 1217–1219 (1996).
[CrossRef]

Hara, K.

Y. Ueno, H. Fujii, H. Sawano, K. Kobayashi, K. Hara, A. Gomyo, and K. Endo, “30-mW 690-nm high-power strained-quantum-well AlGaInP laser,” IEEE J. Quantum Electron. 29, 1851–1856 (1993).
[CrossRef]

Hino, I.

A. Gomyo, T. Suzuki, S. Iijima, H. Hotta, H. Fujii, S. Kawata, K. Kobayashi, Y. Ueno, and I. Hino, “Nonexistence of long-range order in Ga0.5In0.5P epitaxial layers grown on (111)B and (110)GaAs substrates,” Jpn. J. Appl. Phys. 27, L2370–L2372 (1988).
[CrossRef]

Hotta, H.

A. Gomyo, T. Suzuki, S. Iijima, H. Hotta, H. Fujii, S. Kawata, K. Kobayashi, Y. Ueno, and I. Hino, “Nonexistence of long-range order in Ga0.5In0.5P epitaxial layers grown on (111)B and (110)GaAs substrates,” Jpn. J. Appl. Phys. 27, L2370–L2372 (1988).
[CrossRef]

Iijima, S.

A. Gomyo, T. Suzuki, S. Iijima, H. Hotta, H. Fujii, S. Kawata, K. Kobayashi, Y. Ueno, and I. Hino, “Nonexistence of long-range order in Ga0.5In0.5P epitaxial layers grown on (111)B and (110)GaAs substrates,” Jpn. J. Appl. Phys. 27, L2370–L2372 (1988).
[CrossRef]

Jerphagnon, J.

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

Kawamura, Y.

H. Tanaka, Y. Kawamura, and H. Asahi, “Refractive indices of In0.49Ga0.51−xAlxP lattice matched to GaAs,” J. Appl. Phys. 59, 985–986 (1986).
[CrossRef]

Kawata, S.

A. Gomyo, T. Suzuki, S. Iijima, H. Hotta, H. Fujii, S. Kawata, K. Kobayashi, Y. Ueno, and I. Hino, “Nonexistence of long-range order in Ga0.5In0.5P epitaxial layers grown on (111)B and (110)GaAs substrates,” Jpn. J. Appl. Phys. 27, L2370–L2372 (1988).
[CrossRef]

Kelso, S. M.

D. E. Aspens, S. M. Kelso, R. A. Logan, and R. Bhat, “Optical properties of AlxGa1−xAs,” J. Appl. Phys. 60, 754–767 (1986).
[CrossRef]

Kibbler, A.

A. Mascarenhas, S. Kurtz, A. Kibbler, and J. M. Olson, “Polarized band-edge photoluminescence and ordering in Ga0.52In0.48P,” Phys. Rev. Lett. 63, 2108–2111 (1989).
[CrossRef] [PubMed]

Kim, D. Y.

Kobayashi, K.

Y. Ueno, H. Fujii, H. Sawano, K. Kobayashi, K. Hara, A. Gomyo, and K. Endo, “30-mW 690-nm high-power strained-quantum-well AlGaInP laser,” IEEE J. Quantum Electron. 29, 1851–1856 (1993).
[CrossRef]

A. Gomyo, T. Suzuki, S. Iijima, H. Hotta, H. Fujii, S. Kawata, K. Kobayashi, Y. Ueno, and I. Hino, “Nonexistence of long-range order in Ga0.5In0.5P epitaxial layers grown on (111)B and (110)GaAs substrates,” Jpn. J. Appl. Phys. 27, L2370–L2372 (1988).
[CrossRef]

Kostoulas, Y.

Y. Kostoulas, K. B. Ucer, G. W. Wicks, and P. M. Fauchet, “Femtosecond carrier dynamics in low-temperature grown Ga0.5In0.5P,” Appl. Phys. Lett. 67, 3756–3758 (1995).
[CrossRef]

Kurimoto, T.

T. Kurimoto and N. Hamada, “Electronic structure of the (GaP)1/(InP)1 (111) strained-layer superlattice,” Phys. Rev. 40, 3889–3895 (1989).
[CrossRef]

Kurtz, S.

A. Mascarenhas, S. Kurtz, A. Kibbler, and J. M. Olson, “Polarized band-edge photoluminescence and ordering in Ga0.52In0.48P,” Phys. Rev. Lett. 63, 2108–2111 (1989).
[CrossRef] [PubMed]

Kurtz, S. K.

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

Logan, R. A.

D. E. Aspens, S. M. Kelso, R. A. Logan, and R. Bhat, “Optical properties of AlxGa1−xAs,” J. Appl. Phys. 60, 754–767 (1986).
[CrossRef]

Mascarenhas, A.

A. Mascarenhas, S. Kurtz, A. Kibbler, and J. M. Olson, “Polarized band-edge photoluminescence and ordering in Ga0.52In0.48P,” Phys. Rev. Lett. 63, 2108–2111 (1989).
[CrossRef] [PubMed]

Moritz, A.

A. Moritz, R. Wirth, C. Geng, F. Scholz, and A. Hangleiter, “Birefringence and tilted modes in ordered GaInP/AlGaInP waveguides and lasers,” Appl. Phys. Lett. 68, 1217–1219 (1996).
[CrossRef]

Moss, D. J.

E. Ghahramani, D. J. Moss, and J. E. Sipe, “Full-band-structure calculation of first-, second-, and third-harmonic optical response coefficients of ZnSe, ZnTe, and CdTe,” Phys. Rev. B 43, 9700–9710 (1991).
[CrossRef]

Myers, L. E.

Olson, J. M.

A. Mascarenhas, S. Kurtz, A. Kibbler, and J. M. Olson, “Polarized band-edge photoluminescence and ordering in Ga0.52In0.48P,” Phys. Rev. Lett. 63, 2108–2111 (1989).
[CrossRef] [PubMed]

Pierce, J. W.

Sawano, H.

Y. Ueno, H. Fujii, H. Sawano, K. Kobayashi, K. Hara, A. Gomyo, and K. Endo, “30-mW 690-nm high-power strained-quantum-well AlGaInP laser,” IEEE J. Quantum Electron. 29, 1851–1856 (1993).
[CrossRef]

Schiek, R.

Scholz, F.

A. Moritz, R. Wirth, C. Geng, F. Scholz, and A. Hangleiter, “Birefringence and tilted modes in ordered GaInP/AlGaInP waveguides and lasers,” Appl. Phys. Lett. 68, 1217–1219 (1996).
[CrossRef]

P. Ernst, C. Geng, F. Scholz, and H. Schweizer, “Band-gap reduction and valence-band splitting of ordered GaInP2,” Appl. Phys. Lett. 67, 2347–2349 (1995).
[CrossRef]

Schweizer, H.

P. Ernst, C. Geng, F. Scholz, and H. Schweizer, “Band-gap reduction and valence-band splitting of ordered GaInP2,” Appl. Phys. Lett. 67, 2347–2349 (1995).
[CrossRef]

Seibert, H.

Sheik-Bahae, M.

Sipe, J. E.

E. Ghahramani, D. J. Moss, and J. E. Sipe, “Full-band-structure calculation of first-, second-, and third-harmonic optical response coefficients of ZnSe, ZnTe, and CdTe,” Phys. Rev. B 43, 9700–9710 (1991).
[CrossRef]

Sohler, W.

Stegeman, G. I.

Sundheimer, M. L.

Suzuki, T.

A. Gomyo, T. Suzuki, S. Iijima, H. Hotta, H. Fujii, S. Kawata, K. Kobayashi, Y. Ueno, and I. Hino, “Nonexistence of long-range order in Ga0.5In0.5P epitaxial layers grown on (111)B and (110)GaAs substrates,” Jpn. J. Appl. Phys. 27, L2370–L2372 (1988).
[CrossRef]

Tanaka, H.

H. Tanaka, Y. Kawamura, and H. Asahi, “Refractive indices of In0.49Ga0.51−xAlxP lattice matched to GaAs,” J. Appl. Phys. 59, 985–986 (1986).
[CrossRef]

Ucer, K. B.

Y. Kostoulas, K. B. Ucer, G. W. Wicks, and P. M. Fauchet, “Femtosecond carrier dynamics in low-temperature grown Ga0.5In0.5P,” Appl. Phys. Lett. 67, 3756–3758 (1995).
[CrossRef]

Ueno, Y.

Y. Ueno, H. Fujii, H. Sawano, K. Kobayashi, K. Hara, A. Gomyo, and K. Endo, “30-mW 690-nm high-power strained-quantum-well AlGaInP laser,” IEEE J. Quantum Electron. 29, 1851–1856 (1993).
[CrossRef]

A. Gomyo, T. Suzuki, S. Iijima, H. Hotta, H. Fujii, S. Kawata, K. Kobayashi, Y. Ueno, and I. Hino, “Nonexistence of long-range order in Ga0.5In0.5P epitaxial layers grown on (111)B and (110)GaAs substrates,” Jpn. J. Appl. Phys. 27, L2370–L2372 (1988).
[CrossRef]

Van Stryland, E.

Van Stryland, E. W.

Wicks, G. W.

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[CrossRef]

Wirth, R.

A. Moritz, R. Wirth, C. Geng, F. Scholz, and A. Hangleiter, “Birefringence and tilted modes in ordered GaInP/AlGaInP waveguides and lasers,” Appl. Phys. Lett. 68, 1217–1219 (1996).
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Appl. Phys. Lett. (3)

A. Moritz, R. Wirth, C. Geng, F. Scholz, and A. Hangleiter, “Birefringence and tilted modes in ordered GaInP/AlGaInP waveguides and lasers,” Appl. Phys. Lett. 68, 1217–1219 (1996).
[CrossRef]

Y. Kostoulas, K. B. Ucer, G. W. Wicks, and P. M. Fauchet, “Femtosecond carrier dynamics in low-temperature grown Ga0.5In0.5P,” Appl. Phys. Lett. 67, 3756–3758 (1995).
[CrossRef]

P. Ernst, C. Geng, F. Scholz, and H. Schweizer, “Band-gap reduction and valence-band splitting of ordered GaInP2,” Appl. Phys. Lett. 67, 2347–2349 (1995).
[CrossRef]

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Y. Ueno, H. Fujii, H. Sawano, K. Kobayashi, K. Hara, A. Gomyo, and K. Endo, “30-mW 690-nm high-power strained-quantum-well AlGaInP laser,” IEEE J. Quantum Electron. 29, 1851–1856 (1993).
[CrossRef]

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H. Tanaka, Y. Kawamura, and H. Asahi, “Refractive indices of In0.49Ga0.51−xAlxP lattice matched to GaAs,” J. Appl. Phys. 59, 985–986 (1986).
[CrossRef]

D. E. Aspens, S. M. Kelso, R. A. Logan, and R. Bhat, “Optical properties of AlxGa1−xAs,” J. Appl. Phys. 60, 754–767 (1986).
[CrossRef]

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[CrossRef]

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A. Gomyo, T. Suzuki, S. Iijima, H. Hotta, H. Fujii, S. Kawata, K. Kobayashi, Y. Ueno, and I. Hino, “Nonexistence of long-range order in Ga0.5In0.5P epitaxial layers grown on (111)B and (110)GaAs substrates,” Jpn. J. Appl. Phys. 27, L2370–L2372 (1988).
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H. Fujii, Y. Ueno, A. Gomyo, K. Endo, and T. Suzuki, “Observation of stripe-direction dependence of threshold current density for AlGaInP laser diodes with CuPt-type natural superlattice in Ga0.5In0.5P active layer,” Appl. Phys. Lett. 61, 737–739 (1992); Y. Ueno, “Oscillator strength enhancement for [110]-polarized light in compressively strained GaInP ordered crystals used in AlGaInP laser,” Appl. Phys. Lett. 62, 553–555 (1993).
[CrossRef]

Y. Ueno, K. Endo, H. Fujii, K. Kobayashi, K. Hara, and T. Yuasa, “Continuous-wave high-power (75 mW) operation of a transverse-mode stabilized window structure 680-nm AlGaInP visible laser diode,” Electron. Lett. 26, 1726–1727 (1990); Y. Hämisch, R. Steffen, P. Röntgen, and A. Forchel, “Implantation induced order-disorder transition in Ga0.52In0.48P/(Al0.35Ga0.65)0.5In0.5P heterostructures,” Jpn. J.Appl. Phys. 32, L1492–L1495 (1993).
[CrossRef]

Y. Ueno, V. Ricci, and G. I. Stegeman, “Phase-matchable second-order susceptibility of GaInP crystals at 1.5-μm,” 7th Topical Meeting of the European Optical Society, Vol. 7 of EOS Topical Meetings Digest Series (European Optical Society, Orsay, France, 1996), pp. 185–186; V. Ricci, Y. Ueno, and G. I. Stegeman, “Measurement of the second-order susceptibility of GaInP films at 1.5 μm,” in Quantum Electronics and Laser Science Conference (QELS’96), Vol. 10 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 21–22.

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A. Gomyo, T. Suzuki, and S. Iijima, “Observation of strong ordering in GaxIn1−xP alloy semiconductors,” Phys. Rev. Lett. 60, 2645–2648 (1988); A. Gomyo, T. Suzuki, K. Kobayashi, S. Kawata, and I. Hino, “Evidence for the existence of an ordered state in Ga0.5In0.5P grown by metalorganic vapor phase epitaxy and its relation to band-gap energy,” Appl. Phys. Lett. 50, 673–675 (1987); O. Ueda, M. Takikawa, J. Komeno, and I. Umebu, “Atomic structure of ordered InGaP crystals on (0, 0, 1) GaAs substrates by metalorganic chemical vapor deposition,” Jpn. J. Appl. Phys. JAPNDE 26, L1824–L1827 (1987).
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See, e.g., F. A. Hopf and G. I. Stegeman, Applied Classical Electrodynamics (Wiley, New York, 1986), Vol. 2, p. 14; R. W. Boyd, Nonlinear Optics (Academic, Boston, 1992), p. 46.

Td crystals have three IC4 axes and four C3 axes. Because of the Ga–In ordering, ordered GaInP loses all IC4 axes and three of the four C3 axes, which causes symmetry breakdown to C.

In a few measurements we observed sharp Fabry–Perot fringes corresponding to the distance of 150 μm between GaInP and GaAs surfaces, in addition to Maker fringes, which correspond to the GaInP thickness of 1.2 μm. In most of our measurements, however, the fundamental lights are believed to be incoherently multireflected between GaInP and GaAs surfaces.

Domain-mixed ordered GaInP crystal has been used as the active layer for the above-mentioned red lasers in Ref. 10. Thus the domain-mixed crystal is supposed to be stable, even under a high-density carrier injection of approximately 2 kA/cm2.

The volume of the one domain equals that of the other, because these two domains are equivalent with respect to the (001) surface. In contrast, the one domain dominates the other when grown on surfaces tilted from (001). Refer to A. Gomyo, T. Suzuki, K. Kobayashi, S. Kawata, H. Hotta, and I. Hino, “Effects of GaAs-substrate surface misorientation from (001) on band-gap energy in Ga0.5In0.5P,” NEC Res. Dev. 35, 134–143 (1994).

C GaInP has one C3 axis and three σν planes for symmetry operations. The average owing to the domain mixture causes the crystal to lose the C3 axis and two of the three σν planes and to gain a new (1¯, 1, 0) σν plane and one [0, 0, 1] C2 axis. The (1, 1, 0) σν plane remains. Consequently, a set of symmetry operations with one C2 axis and two σν planes corresponds to the C symmetry.

V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, eds., Handbook of Nonlinear Optical Crystals (Springer-Verlag, Berlin, 1991).

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Figures (10)

Fig. 1
Fig. 1

Ordered Ga0.5In0.5P crystal grown on GaAs.9 The crystal symmetry is C3ν. The [1̅, 1, 1] symmetry axis is tilted 54.7° from the [0, 0, 1] growth direction. The band-gap energy is 1.8–1.9 eV, which is more than twice as large as the 1.55-µm photon energy of 0.8 eV.

Fig. 2
Fig. 2

Two equivalent domains of Ga0.5In0.5P grown on a (0, 0, 1) GaAs substrate.22,23

Fig. 3
Fig. 3

Possible quasi-phase-matched waveguide structure using an AlGaInP–GaInP–AlGaInP double heterostructure. Area-selective impurity implantation or diffusion periodically disorders GaInP and therefore modulates the dij matrix. The QPM period for the 1.5-µm light is approximately 2.5 µm.

Fig. 4
Fig. 4

Maker-fringe measurement setup at 1.579 µm. The pulse width was 11 ns, the repetition rate was 10 Hz, and the typical pulse energy used for GaInP samples was 10 mJ.

Fig. 5
Fig. 5

Ga0.5In0.5P sample structure, grown lattice matched on a (0, 0, 1) GaAs substrate by metallorganic vapor phase epitaxy. The GaInP thickness of 1.2 µm is close to the coherence length of 1.36 µm. After the growth, the GaAs substrate was wrapped and polished for the measurements.

Fig. 6
Fig. 6

Photoluminescence from our GaInP sample at room temperature shows the typical spectrum and a peak at 675 nm (1.84 eV).

Fig. 7
Fig. 7

Measured TE-polarized d14 signal obtained by focusing the TM-polarized fundamental beam. The d14 coefficient of GaInP was calculated as 110 pm/V, assuming a d14 of 130 pm/V in GaAs6 and a linear absorption coefficient of 20 000 cm-1 for the SH wave in GaAs.

Fig. 8
Fig. 8

Measured SH signals obtained by setting the polarizer and analyzer along the TM direction. The solid curve shows a simulated d33 signal assuming d33=60 pm/V. Coexistence of a d31+2d15 component changes the signal shape. For example, the dotted curve shows a simulated signal assuming both d31 +2d15=-2.9 pm/V and d33=34 pm/V, which is not distinguishable from d14 leakage (dashed curve) assuming only a 1° misfit (ψ1,2=1°). Thus our detection limit for the d33 coefficient was approximately 60 pm/V.

Fig. 9
Fig. 9

Signal intensities measured at a fixed incidence angle (θ) of 40° obtained by rotating the polarizer (ψ1) and the analyzer (ψ2) synchronously (i.e., ψ1=ψ2=ψ1,2). The calculated d14 signal (dashed curve) reproduced well both the magnitude and shape of the measured data. This d14 signal leakage in the vicinity of ψ1,2=0 was much stronger than we had originally expected (dotted curve).

Fig. 10
Fig. 10

Polarizer (ψ1) and analyzer (ψ2) rotations with respect to the sample axis.

Tables (3)

Tables Icon

Table 1 Projection Factors for Domain-Mixed GaInP Crystalsa

Tables Icon

Table 2 Material Parameters Used for the Analyses

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Table 3 Modulation Detection Signalsa

Equations (11)

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dij(O:C3ν)=0000d15-d22-d22d220d1500d31d31d33000,
dij(DO:Td)=000d14000000d14000000d14,
dij(O:Td)=-d33-d31-d31d14d15d15d31d33d31d15d14-d15d31d31d33d15-d15d14,
d33d31d14d15=394d15+d33-22d22+2d31-2d15+d33+2d22+2d312d15-d33+22d22+d31d15+d33+2d22-d310.77d15+0.19d33-0.54d22+0.38d31-0.38d15+0.19d33+0.27d22+0.38d310.38d15-0.19d33+0.54d22+0.19d310.19d15+0.19d33+0.27d22-0.19d31.
dij(Mix:Td)=000d14d150000d15d140d31d31d3300d14,
dij(O:C3ν¯)=0000d15d22d22-d220d1500d31d31d33000,
dij(O:wg)=0000d15+d14d33-d312d33+d31-2d152d33+d31+2d1522d31d15-d1400d31+d14d31-d14d332d1500,
dij(Mix:wg)=0000d15+d140000d15-d1400d31+d14d31-d14d33000,
dij(DO:wg)=0000d140000-d1400d14-d140000,
O(|d33d14|)O(|d14|2)=O(|d33|)O(|d14|),
O(|d33|2)O(|d14|2).

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