Abstract

Second-harmonic generation (SHG) in channel waveguides fabricated by titanium diffusion into MgO-doped lithium niobate is studied. A conversion efficiency for SHG of 2.4%/W has been obtained for a 16-mm-long waveguide by using a Nd:YAG laser as pump source. The conversion efficiency is lower than the theoretical prediction. This difference is attributed to inhomogeneities along the waveguide. The channel waveguides used carried several modes at the second-harmonic wavelength; those modes, phase matched above room temperature (~80°C), showed substantially lower sensitivity for photorefractive damage than others phase matched at room temperature.

© 1988 Optical Society of America

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References

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  1. G. I. Stegeman and C. T. Seaton, “Nonlinear integrated optics,” J. Appl. Phys. 58, R57 (1985).
    [CrossRef]
  2. See, for example, H. Suche, R. Ricken, and W. Sohler, “Integrated optical parametric oscillator of low threshold and high power conversion efficiency,” in Proceedings of the Fourth European Conference on Integrated Optics, C. D. W. Wilkinson and J. Lamb, eds. (SETG, Glasgow, 1987), p. 202; R. Regener and W. Sohler, “Efficient second harmonic generator in matched waveguide resonators,” in Technical Digest of European Conference on Optical Communication (Telefónica, Madrid, 1986), Vol. III Postdeadline Papers, p. 49.
  3. W. Sohler, B. Hampel, R. Regener, R. Ricken, H. Suche, and R. Volk, “Integrated optical parametric devices,” IEEE J. Lightwave Technol. LT-4, 772 (1986).
    [CrossRef]
  4. G. G. Zhong, J. Jian, and Z. K. Wu, “Measurement of optically induced refractive-index damage of lithium niobate doped with different concentrations of MgO,” in Digest of XI International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1980), p. 631.
  5. D. A. Bryan, R. R. Rice, R. Gerson, H. E. Tomaschke, K. L. Sweeney, and L. E. Halliburton, “Magnesium-doped lithium niobate for higher optical power applications,” Opt. Eng. 24, 138 (1985).
    [CrossRef]
  6. R. A. Becker, “Methods of characterizing photorefractive susceptibility of LiNbO3waveguides,” Proc. Soc. Photo-Opt. Instrum. Eng. 578, 12 (1985).
  7. R. L. Byer, Y. K. Park, R. S. Feigelson, and W. L. Kway, “Efficient second-harmonic generation of Nd:YAG laser radiation using warm phasematching LiNbO3,” Appl. Phys. Lett. 39, 17 (1981).
    [CrossRef]
  8. F. A. Hopf and M. Cervantes, “Nonlinear optical interferometer,” Appl. Opt. 21, 668 (1982).
    [CrossRef] [PubMed]
  9. M. M. Fejer, M. J. F. Digonnet, and R. L. Byer, “Generation of 22 mW of 532-nm radiation by frequency doubling in Ti:MgO:LiNbO3waveguides,” Opt. Lett. 11, 230 (1986).
    [CrossRef]
  10. G. Arvidsson, A. Sjöberg, A. A. Lipovskii, and F. Laurell, “Titanium-diffused waveguides in magnesium-doped lithium niobate for nonlinear frequency conversion,” in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1986), p. 228.
  11. A. Yariv, “Coupled-mode theory for guided wave optics,” IEEE J. Quantum Electron. QE-9, 919 (1973).
    [CrossRef]
  12. W. Sohler, “Nonlinear integrated optics,” in New Directions in Guided Wave and Coherent Optics, D. B. Ostrowsky and E. Spitz, eds., No. 79 of NATO ASI Series E (NATO, Brussels, 1984), p. 449.
  13. V. C. Y. So, R. Normandin, and G. I. Stegeman, “Field analysis of harmonic generation in thin-film integrated optics,” J. Opt. Soc. Am. 69, 1166 (1979).
    [CrossRef]
  14. G. P. Bava, I. Montrosset, W. Sohler, and H. Suche, “Numerical modeling of Ti:LiNbO3integrated optical parametric oscillators,” IEEE J. Quantum Electron. QE-23, 42 (1987).
    [CrossRef]
  15. A. Sjöberg, G. Arvidsson, and A. A. Lipovskii, “Characterization of waveguides fabricated by titanium diffusion in magnesium-doped lithium niobate,” J. Opt. Soc. Am. B 5, 285 (1988).
    [CrossRef]
  16. Y. Handa, M. Miyawaki, and S. Ogura, “Guided-wave characteristics and optical damage in LiNbO3waveguides,” Proc. Soc. Photo-Opt. Instrum. Eng. 460, 101 (1984).
  17. F. Laurell, Laserskador i dielektriska material, speciellt litiumniobat, (Institute of Optical Research, Stockholm, 1985, in Swedish).
  18. A. M. Glass, “The photorefractive effect,” Opt. Eng. 17, 470 (1978).
    [CrossRef]
  19. G. Arvidsson and F. Laurell, “Non-linear optical wavelength conversion in Ti:LiNbO3waveguides,” Thin Solid Films 136, 29 (1986).
    [CrossRef]

1988 (1)

1987 (1)

G. P. Bava, I. Montrosset, W. Sohler, and H. Suche, “Numerical modeling of Ti:LiNbO3integrated optical parametric oscillators,” IEEE J. Quantum Electron. QE-23, 42 (1987).
[CrossRef]

1986 (3)

G. Arvidsson and F. Laurell, “Non-linear optical wavelength conversion in Ti:LiNbO3waveguides,” Thin Solid Films 136, 29 (1986).
[CrossRef]

W. Sohler, B. Hampel, R. Regener, R. Ricken, H. Suche, and R. Volk, “Integrated optical parametric devices,” IEEE J. Lightwave Technol. LT-4, 772 (1986).
[CrossRef]

M. M. Fejer, M. J. F. Digonnet, and R. L. Byer, “Generation of 22 mW of 532-nm radiation by frequency doubling in Ti:MgO:LiNbO3waveguides,” Opt. Lett. 11, 230 (1986).
[CrossRef]

1985 (3)

G. I. Stegeman and C. T. Seaton, “Nonlinear integrated optics,” J. Appl. Phys. 58, R57 (1985).
[CrossRef]

D. A. Bryan, R. R. Rice, R. Gerson, H. E. Tomaschke, K. L. Sweeney, and L. E. Halliburton, “Magnesium-doped lithium niobate for higher optical power applications,” Opt. Eng. 24, 138 (1985).
[CrossRef]

R. A. Becker, “Methods of characterizing photorefractive susceptibility of LiNbO3waveguides,” Proc. Soc. Photo-Opt. Instrum. Eng. 578, 12 (1985).

1984 (1)

Y. Handa, M. Miyawaki, and S. Ogura, “Guided-wave characteristics and optical damage in LiNbO3waveguides,” Proc. Soc. Photo-Opt. Instrum. Eng. 460, 101 (1984).

1982 (1)

1981 (1)

R. L. Byer, Y. K. Park, R. S. Feigelson, and W. L. Kway, “Efficient second-harmonic generation of Nd:YAG laser radiation using warm phasematching LiNbO3,” Appl. Phys. Lett. 39, 17 (1981).
[CrossRef]

1979 (1)

1978 (1)

A. M. Glass, “The photorefractive effect,” Opt. Eng. 17, 470 (1978).
[CrossRef]

1973 (1)

A. Yariv, “Coupled-mode theory for guided wave optics,” IEEE J. Quantum Electron. QE-9, 919 (1973).
[CrossRef]

Arvidsson, G.

A. Sjöberg, G. Arvidsson, and A. A. Lipovskii, “Characterization of waveguides fabricated by titanium diffusion in magnesium-doped lithium niobate,” J. Opt. Soc. Am. B 5, 285 (1988).
[CrossRef]

G. Arvidsson and F. Laurell, “Non-linear optical wavelength conversion in Ti:LiNbO3waveguides,” Thin Solid Films 136, 29 (1986).
[CrossRef]

G. Arvidsson, A. Sjöberg, A. A. Lipovskii, and F. Laurell, “Titanium-diffused waveguides in magnesium-doped lithium niobate for nonlinear frequency conversion,” in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1986), p. 228.

Bava, G. P.

G. P. Bava, I. Montrosset, W. Sohler, and H. Suche, “Numerical modeling of Ti:LiNbO3integrated optical parametric oscillators,” IEEE J. Quantum Electron. QE-23, 42 (1987).
[CrossRef]

Becker, R. A.

R. A. Becker, “Methods of characterizing photorefractive susceptibility of LiNbO3waveguides,” Proc. Soc. Photo-Opt. Instrum. Eng. 578, 12 (1985).

Bryan, D. A.

D. A. Bryan, R. R. Rice, R. Gerson, H. E. Tomaschke, K. L. Sweeney, and L. E. Halliburton, “Magnesium-doped lithium niobate for higher optical power applications,” Opt. Eng. 24, 138 (1985).
[CrossRef]

Byer, R. L.

M. M. Fejer, M. J. F. Digonnet, and R. L. Byer, “Generation of 22 mW of 532-nm radiation by frequency doubling in Ti:MgO:LiNbO3waveguides,” Opt. Lett. 11, 230 (1986).
[CrossRef]

R. L. Byer, Y. K. Park, R. S. Feigelson, and W. L. Kway, “Efficient second-harmonic generation of Nd:YAG laser radiation using warm phasematching LiNbO3,” Appl. Phys. Lett. 39, 17 (1981).
[CrossRef]

Cervantes, M.

Digonnet, M. J. F.

Feigelson, R. S.

R. L. Byer, Y. K. Park, R. S. Feigelson, and W. L. Kway, “Efficient second-harmonic generation of Nd:YAG laser radiation using warm phasematching LiNbO3,” Appl. Phys. Lett. 39, 17 (1981).
[CrossRef]

Fejer, M. M.

Gerson, R.

D. A. Bryan, R. R. Rice, R. Gerson, H. E. Tomaschke, K. L. Sweeney, and L. E. Halliburton, “Magnesium-doped lithium niobate for higher optical power applications,” Opt. Eng. 24, 138 (1985).
[CrossRef]

Glass, A. M.

A. M. Glass, “The photorefractive effect,” Opt. Eng. 17, 470 (1978).
[CrossRef]

Halliburton, L. E.

D. A. Bryan, R. R. Rice, R. Gerson, H. E. Tomaschke, K. L. Sweeney, and L. E. Halliburton, “Magnesium-doped lithium niobate for higher optical power applications,” Opt. Eng. 24, 138 (1985).
[CrossRef]

Hampel, B.

W. Sohler, B. Hampel, R. Regener, R. Ricken, H. Suche, and R. Volk, “Integrated optical parametric devices,” IEEE J. Lightwave Technol. LT-4, 772 (1986).
[CrossRef]

Handa, Y.

Y. Handa, M. Miyawaki, and S. Ogura, “Guided-wave characteristics and optical damage in LiNbO3waveguides,” Proc. Soc. Photo-Opt. Instrum. Eng. 460, 101 (1984).

Hopf, F. A.

Jian, J.

G. G. Zhong, J. Jian, and Z. K. Wu, “Measurement of optically induced refractive-index damage of lithium niobate doped with different concentrations of MgO,” in Digest of XI International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1980), p. 631.

Kway, W. L.

R. L. Byer, Y. K. Park, R. S. Feigelson, and W. L. Kway, “Efficient second-harmonic generation of Nd:YAG laser radiation using warm phasematching LiNbO3,” Appl. Phys. Lett. 39, 17 (1981).
[CrossRef]

Laurell, F.

G. Arvidsson and F. Laurell, “Non-linear optical wavelength conversion in Ti:LiNbO3waveguides,” Thin Solid Films 136, 29 (1986).
[CrossRef]

F. Laurell, Laserskador i dielektriska material, speciellt litiumniobat, (Institute of Optical Research, Stockholm, 1985, in Swedish).

G. Arvidsson, A. Sjöberg, A. A. Lipovskii, and F. Laurell, “Titanium-diffused waveguides in magnesium-doped lithium niobate for nonlinear frequency conversion,” in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1986), p. 228.

Lipovskii, A. A.

A. Sjöberg, G. Arvidsson, and A. A. Lipovskii, “Characterization of waveguides fabricated by titanium diffusion in magnesium-doped lithium niobate,” J. Opt. Soc. Am. B 5, 285 (1988).
[CrossRef]

G. Arvidsson, A. Sjöberg, A. A. Lipovskii, and F. Laurell, “Titanium-diffused waveguides in magnesium-doped lithium niobate for nonlinear frequency conversion,” in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1986), p. 228.

Miyawaki, M.

Y. Handa, M. Miyawaki, and S. Ogura, “Guided-wave characteristics and optical damage in LiNbO3waveguides,” Proc. Soc. Photo-Opt. Instrum. Eng. 460, 101 (1984).

Montrosset, I.

G. P. Bava, I. Montrosset, W. Sohler, and H. Suche, “Numerical modeling of Ti:LiNbO3integrated optical parametric oscillators,” IEEE J. Quantum Electron. QE-23, 42 (1987).
[CrossRef]

Normandin, R.

Ogura, S.

Y. Handa, M. Miyawaki, and S. Ogura, “Guided-wave characteristics and optical damage in LiNbO3waveguides,” Proc. Soc. Photo-Opt. Instrum. Eng. 460, 101 (1984).

Park, Y. K.

R. L. Byer, Y. K. Park, R. S. Feigelson, and W. L. Kway, “Efficient second-harmonic generation of Nd:YAG laser radiation using warm phasematching LiNbO3,” Appl. Phys. Lett. 39, 17 (1981).
[CrossRef]

Regener, R.

W. Sohler, B. Hampel, R. Regener, R. Ricken, H. Suche, and R. Volk, “Integrated optical parametric devices,” IEEE J. Lightwave Technol. LT-4, 772 (1986).
[CrossRef]

Rice, R. R.

D. A. Bryan, R. R. Rice, R. Gerson, H. E. Tomaschke, K. L. Sweeney, and L. E. Halliburton, “Magnesium-doped lithium niobate for higher optical power applications,” Opt. Eng. 24, 138 (1985).
[CrossRef]

Ricken, R.

W. Sohler, B. Hampel, R. Regener, R. Ricken, H. Suche, and R. Volk, “Integrated optical parametric devices,” IEEE J. Lightwave Technol. LT-4, 772 (1986).
[CrossRef]

See, for example, H. Suche, R. Ricken, and W. Sohler, “Integrated optical parametric oscillator of low threshold and high power conversion efficiency,” in Proceedings of the Fourth European Conference on Integrated Optics, C. D. W. Wilkinson and J. Lamb, eds. (SETG, Glasgow, 1987), p. 202; R. Regener and W. Sohler, “Efficient second harmonic generator in matched waveguide resonators,” in Technical Digest of European Conference on Optical Communication (Telefónica, Madrid, 1986), Vol. III Postdeadline Papers, p. 49.

Seaton, C. T.

G. I. Stegeman and C. T. Seaton, “Nonlinear integrated optics,” J. Appl. Phys. 58, R57 (1985).
[CrossRef]

Sjöberg, A.

A. Sjöberg, G. Arvidsson, and A. A. Lipovskii, “Characterization of waveguides fabricated by titanium diffusion in magnesium-doped lithium niobate,” J. Opt. Soc. Am. B 5, 285 (1988).
[CrossRef]

G. Arvidsson, A. Sjöberg, A. A. Lipovskii, and F. Laurell, “Titanium-diffused waveguides in magnesium-doped lithium niobate for nonlinear frequency conversion,” in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1986), p. 228.

So, V. C. Y.

Sohler, W.

G. P. Bava, I. Montrosset, W. Sohler, and H. Suche, “Numerical modeling of Ti:LiNbO3integrated optical parametric oscillators,” IEEE J. Quantum Electron. QE-23, 42 (1987).
[CrossRef]

W. Sohler, B. Hampel, R. Regener, R. Ricken, H. Suche, and R. Volk, “Integrated optical parametric devices,” IEEE J. Lightwave Technol. LT-4, 772 (1986).
[CrossRef]

See, for example, H. Suche, R. Ricken, and W. Sohler, “Integrated optical parametric oscillator of low threshold and high power conversion efficiency,” in Proceedings of the Fourth European Conference on Integrated Optics, C. D. W. Wilkinson and J. Lamb, eds. (SETG, Glasgow, 1987), p. 202; R. Regener and W. Sohler, “Efficient second harmonic generator in matched waveguide resonators,” in Technical Digest of European Conference on Optical Communication (Telefónica, Madrid, 1986), Vol. III Postdeadline Papers, p. 49.

W. Sohler, “Nonlinear integrated optics,” in New Directions in Guided Wave and Coherent Optics, D. B. Ostrowsky and E. Spitz, eds., No. 79 of NATO ASI Series E (NATO, Brussels, 1984), p. 449.

Stegeman, G. I.

Suche, H.

G. P. Bava, I. Montrosset, W. Sohler, and H. Suche, “Numerical modeling of Ti:LiNbO3integrated optical parametric oscillators,” IEEE J. Quantum Electron. QE-23, 42 (1987).
[CrossRef]

W. Sohler, B. Hampel, R. Regener, R. Ricken, H. Suche, and R. Volk, “Integrated optical parametric devices,” IEEE J. Lightwave Technol. LT-4, 772 (1986).
[CrossRef]

See, for example, H. Suche, R. Ricken, and W. Sohler, “Integrated optical parametric oscillator of low threshold and high power conversion efficiency,” in Proceedings of the Fourth European Conference on Integrated Optics, C. D. W. Wilkinson and J. Lamb, eds. (SETG, Glasgow, 1987), p. 202; R. Regener and W. Sohler, “Efficient second harmonic generator in matched waveguide resonators,” in Technical Digest of European Conference on Optical Communication (Telefónica, Madrid, 1986), Vol. III Postdeadline Papers, p. 49.

Sweeney, K. L.

D. A. Bryan, R. R. Rice, R. Gerson, H. E. Tomaschke, K. L. Sweeney, and L. E. Halliburton, “Magnesium-doped lithium niobate for higher optical power applications,” Opt. Eng. 24, 138 (1985).
[CrossRef]

Tomaschke, H. E.

D. A. Bryan, R. R. Rice, R. Gerson, H. E. Tomaschke, K. L. Sweeney, and L. E. Halliburton, “Magnesium-doped lithium niobate for higher optical power applications,” Opt. Eng. 24, 138 (1985).
[CrossRef]

Volk, R.

W. Sohler, B. Hampel, R. Regener, R. Ricken, H. Suche, and R. Volk, “Integrated optical parametric devices,” IEEE J. Lightwave Technol. LT-4, 772 (1986).
[CrossRef]

Wu, Z. K.

G. G. Zhong, J. Jian, and Z. K. Wu, “Measurement of optically induced refractive-index damage of lithium niobate doped with different concentrations of MgO,” in Digest of XI International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1980), p. 631.

Yariv, A.

A. Yariv, “Coupled-mode theory for guided wave optics,” IEEE J. Quantum Electron. QE-9, 919 (1973).
[CrossRef]

Zhong, G. G.

G. G. Zhong, J. Jian, and Z. K. Wu, “Measurement of optically induced refractive-index damage of lithium niobate doped with different concentrations of MgO,” in Digest of XI International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1980), p. 631.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

R. L. Byer, Y. K. Park, R. S. Feigelson, and W. L. Kway, “Efficient second-harmonic generation of Nd:YAG laser radiation using warm phasematching LiNbO3,” Appl. Phys. Lett. 39, 17 (1981).
[CrossRef]

IEEE J. Lightwave Technol. (1)

W. Sohler, B. Hampel, R. Regener, R. Ricken, H. Suche, and R. Volk, “Integrated optical parametric devices,” IEEE J. Lightwave Technol. LT-4, 772 (1986).
[CrossRef]

IEEE J. Quantum Electron. (2)

A. Yariv, “Coupled-mode theory for guided wave optics,” IEEE J. Quantum Electron. QE-9, 919 (1973).
[CrossRef]

G. P. Bava, I. Montrosset, W. Sohler, and H. Suche, “Numerical modeling of Ti:LiNbO3integrated optical parametric oscillators,” IEEE J. Quantum Electron. QE-23, 42 (1987).
[CrossRef]

J. Appl. Phys. (1)

G. I. Stegeman and C. T. Seaton, “Nonlinear integrated optics,” J. Appl. Phys. 58, R57 (1985).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Opt. Eng. (2)

D. A. Bryan, R. R. Rice, R. Gerson, H. E. Tomaschke, K. L. Sweeney, and L. E. Halliburton, “Magnesium-doped lithium niobate for higher optical power applications,” Opt. Eng. 24, 138 (1985).
[CrossRef]

A. M. Glass, “The photorefractive effect,” Opt. Eng. 17, 470 (1978).
[CrossRef]

Opt. Lett. (1)

Proc. Soc. Photo-Opt. Instrum. Eng. (2)

R. A. Becker, “Methods of characterizing photorefractive susceptibility of LiNbO3waveguides,” Proc. Soc. Photo-Opt. Instrum. Eng. 578, 12 (1985).

Y. Handa, M. Miyawaki, and S. Ogura, “Guided-wave characteristics and optical damage in LiNbO3waveguides,” Proc. Soc. Photo-Opt. Instrum. Eng. 460, 101 (1984).

Thin Solid Films (1)

G. Arvidsson and F. Laurell, “Non-linear optical wavelength conversion in Ti:LiNbO3waveguides,” Thin Solid Films 136, 29 (1986).
[CrossRef]

Other (5)

F. Laurell, Laserskador i dielektriska material, speciellt litiumniobat, (Institute of Optical Research, Stockholm, 1985, in Swedish).

W. Sohler, “Nonlinear integrated optics,” in New Directions in Guided Wave and Coherent Optics, D. B. Ostrowsky and E. Spitz, eds., No. 79 of NATO ASI Series E (NATO, Brussels, 1984), p. 449.

G. Arvidsson, A. Sjöberg, A. A. Lipovskii, and F. Laurell, “Titanium-diffused waveguides in magnesium-doped lithium niobate for nonlinear frequency conversion,” in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1986), p. 228.

See, for example, H. Suche, R. Ricken, and W. Sohler, “Integrated optical parametric oscillator of low threshold and high power conversion efficiency,” in Proceedings of the Fourth European Conference on Integrated Optics, C. D. W. Wilkinson and J. Lamb, eds. (SETG, Glasgow, 1987), p. 202; R. Regener and W. Sohler, “Efficient second harmonic generator in matched waveguide resonators,” in Technical Digest of European Conference on Optical Communication (Telefónica, Madrid, 1986), Vol. III Postdeadline Papers, p. 49.

G. G. Zhong, J. Jian, and Z. K. Wu, “Measurement of optically induced refractive-index damage of lithium niobate doped with different concentrations of MgO,” in Digest of XI International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1980), p. 631.

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Figures (8)

Fig. 1
Fig. 1

Comparison between calculated and measured near-field intensity distribution for the TE10 mode in a 10-μm channel waveguide (680-Å Ti, 25 h) at 532 nm.

Fig. 2
Fig. 2

Comparison between calculated and measured near-field intensity distribution at 1.064 μm for the TM00 mode in the same waveguide as in Fig. 1.

Fig. 3
Fig. 3

The experimental setup used for the conversion-efficiency measurements.

Fig. 4
Fig. 4

Measured SH power for a 10-μm channel waveguide (680-Å Ti, 16 h) as a function of temperature. The ripple at temperatures below the main peaks is assumed to have its origin in inhomogeneities in the waveguide.

Fig. 5
Fig. 5

(a) Calculated diagram illustrating the phase-matching condition for a 10-μm channel waveguide (680-Å Ti, 25 h). The waveguide is single mode for TM polarization at 1.064 μm and multimode for TE at 532 nm. The TM00 mode is phase matched to the TE modes at different temperatures. The crossing points (open circles) correspond to the phase matching. For clarity, not all modes are shown. (b) Photographs of the observed near-field patterns at the SH frequency. The corresponding measured phase-matching temperatures are also given. They are in good agreement with the calculated values.

Fig. 6
Fig. 6

Square root of the SH power plotted versus input power for the TE00 (a), TE10 (b), and TE20 (c) modes.

Fig. 7
Fig. 7

Simulation of the phase-matched power as a function of temperature deviation from the optimal phase-matching point in the unperturbed case. a, A homogeneous waveguide, that is, a waveguide with Δβ constant along its length. b and c, Δβ varies parabolically along the waveguide. Δβmax = 8 × 10−4μm−1 and Δβmax = 47 × 10−4μm−1 are equivalent to temperature deviations of 1 and 6°C, respectively; for a typical 10-μm-wide channel waveguide the same values for Δβmax would correspond to a perturbation of the Ti stripe width of 0.3 and 1.7 μm, respectively.

Fig. 8
Fig. 8

The phase-matching temperature as function of SH power for the TE00 (a), TB10 (b), and TB20 (c) modes.

Tables (1)

Tables Icon

Table 1 Normalized Conversion Efficiencies—Experimental versus Calculated Values for Various Mode Combinations

Equations (7)

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

E ( x , y , z ) = A E ( x , y ) e - i β z + c . c . ,
- + - + E ( x , y ) 2 d x d y = 1 ,
I OVL = - + - + E ω E ω E 2 ω * d x d y
A OVL = ( I OVL ) - 2 ,
η = P 2 ω P ω = C 1 ( d eff 2 N e o N o 2 ) L 2 P ω A OVL sinc 2 ( Δ β L 2 ) ,
Δ β = β 2 ω - 2 β ω = 4 π λ ( N e o 2 ω - N o ω ) ,
C 1 = 2 ω 2 c 2 o = 8 π 2 c 0 λ 2 .

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