Abstract

Harmonic generation of light in thin-film optical waveguides is analyzed theoretically by evaluating the total electromagnetic fields that satisfy the polarization driven wave equation and the electromagnetic boundary conditions at both interfaces. Analytical expressions are given for the amplitude of the growing wave component of the total fields. The results agree with those of normal mode analysis only in the limit of phase-matched harmonic generation. This analysis is believed to be applicable to a large range of wave interaction phenomena in integrated optics.

© 1979 Optical Society of America

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  1. Y. Suematsu, "Tunable Parametric Oscillator Using a Guided Wave Structure," Jpn. J. Appl. Phys. 9, 798–805 (1970).
  2. D. B. Anderson and J. T. Boyd, "Wideband CO2 Laser Second Harmonic Generation Phase Matched in GaAs Thin-Film Waveguides," Appl. Phys. Lett. 19, 266–268 (1971).
  3. J. T. Boyd, "Theory of Parametric Oscillation Phase Matched in GaAs Thin-Film Waveguides," IEEE J. Quantum Electron. QE-8, 788–796 (1972).
  4. E. M. Conwell, "Theory of Second-Harmonic Generation in Optical Waveguides," IEEE J. Quantum Electron. QE-9, 867–879 (1973).
  5. Y. Suematsu, Y. Sasaki, K. Furuya, K. Shibata, and S. Ibukuro, "Optical Second-Harmonic Generation Due to Guided Wave Structure Consisting of Quartz and Glass Film," IEEE J. Quantum Electron. QE-10, 222–229 (1974).
  6. H. Ito, N. Uesugi, and H. Inaba, "Phase-Matched Guided Optical Second Harmonic Wave Generation in Oriented ZnS Polycrystalline Thin-Film Waveguides," Appl. Phys. Lett. 25, 385–387 (1974).
  7. B. U. Chen, C. L. Tang, and J. M. Telle, "CW Harmonic Generation in the UV Using a Thin-Film Waveguide on a Nonlinear Substrate," Appl. Phys. Lett. 9, 495–498 (1974).
  8. A. T. Reutov and P. P. Taraschenko, "Generation of a Sum Frequency Wave in a Microscopic Optically Nonlinear Waveguide Made of Lithium Niobate," Sov. J. Quantum Electron. 4, 910–911 (1975).
  9. B. U. Chen, C. C. Ghizoni, and C. L. Tang, "Phase Matched Second-Harmonic Generation in Solid Thin Films Using Modulation of the Nonlinear Susceptibilities," Appl. Phys. Lett. 28, 651–653 (1976).
  10. N. Uesugi and T. Kimura, "Efficient Second-Harmonic Generation in Three Dimensional LiNbO3 Optical Waveguide," Appl. Phys. Lett. 29, 572–574 (1976).
  11. J. P. vander Ziel, M. Ilegems, P. W. Foy, and R. M. Mikulyak, "Phase-Matched Second-Harmonic Generation in a Periodic GaAs Waveguide," Appl. Phys. Lett. 29, 775–777 (1976).
  12. M. Fukui and G. I. Stegeman, "Theory of Non Phase-Matched Second-Harmonic Generation of Surface Plasmons," Solid State Commun. 26, 239–241 (1978).
  13. R. Normandin, M. Fukui, and G. I. Stegeman, "Analysis of Parametric Mixing and Harmonic Generation of Surface Acoustic Waves," J. Appl. Phys. 50, 81–86 (1979).
  14. R. Normandin, V. C. Y. So, N. Rowell, and G. I. Stegeman, "The Scattering of Guided Optical Beams by Surface Acoustic Waves in Thin Films," J. Opt. Soc. Am. 69, 1153–1165 (1979).
  15. See, for example, A. Yariv, Quantum Electronics, (Wiley, New York 1975).

1979 (2)

R. Normandin, M. Fukui, and G. I. Stegeman, "Analysis of Parametric Mixing and Harmonic Generation of Surface Acoustic Waves," J. Appl. Phys. 50, 81–86 (1979).

R. Normandin, V. C. Y. So, N. Rowell, and G. I. Stegeman, "The Scattering of Guided Optical Beams by Surface Acoustic Waves in Thin Films," J. Opt. Soc. Am. 69, 1153–1165 (1979).

1978 (1)

M. Fukui and G. I. Stegeman, "Theory of Non Phase-Matched Second-Harmonic Generation of Surface Plasmons," Solid State Commun. 26, 239–241 (1978).

1976 (3)

B. U. Chen, C. C. Ghizoni, and C. L. Tang, "Phase Matched Second-Harmonic Generation in Solid Thin Films Using Modulation of the Nonlinear Susceptibilities," Appl. Phys. Lett. 28, 651–653 (1976).

N. Uesugi and T. Kimura, "Efficient Second-Harmonic Generation in Three Dimensional LiNbO3 Optical Waveguide," Appl. Phys. Lett. 29, 572–574 (1976).

J. P. vander Ziel, M. Ilegems, P. W. Foy, and R. M. Mikulyak, "Phase-Matched Second-Harmonic Generation in a Periodic GaAs Waveguide," Appl. Phys. Lett. 29, 775–777 (1976).

1975 (1)

A. T. Reutov and P. P. Taraschenko, "Generation of a Sum Frequency Wave in a Microscopic Optically Nonlinear Waveguide Made of Lithium Niobate," Sov. J. Quantum Electron. 4, 910–911 (1975).

1974 (3)

Y. Suematsu, Y. Sasaki, K. Furuya, K. Shibata, and S. Ibukuro, "Optical Second-Harmonic Generation Due to Guided Wave Structure Consisting of Quartz and Glass Film," IEEE J. Quantum Electron. QE-10, 222–229 (1974).

H. Ito, N. Uesugi, and H. Inaba, "Phase-Matched Guided Optical Second Harmonic Wave Generation in Oriented ZnS Polycrystalline Thin-Film Waveguides," Appl. Phys. Lett. 25, 385–387 (1974).

B. U. Chen, C. L. Tang, and J. M. Telle, "CW Harmonic Generation in the UV Using a Thin-Film Waveguide on a Nonlinear Substrate," Appl. Phys. Lett. 9, 495–498 (1974).

1973 (1)

E. M. Conwell, "Theory of Second-Harmonic Generation in Optical Waveguides," IEEE J. Quantum Electron. QE-9, 867–879 (1973).

1972 (1)

J. T. Boyd, "Theory of Parametric Oscillation Phase Matched in GaAs Thin-Film Waveguides," IEEE J. Quantum Electron. QE-8, 788–796 (1972).

1971 (1)

D. B. Anderson and J. T. Boyd, "Wideband CO2 Laser Second Harmonic Generation Phase Matched in GaAs Thin-Film Waveguides," Appl. Phys. Lett. 19, 266–268 (1971).

1970 (1)

Y. Suematsu, "Tunable Parametric Oscillator Using a Guided Wave Structure," Jpn. J. Appl. Phys. 9, 798–805 (1970).

Anderson, D. B.

D. B. Anderson and J. T. Boyd, "Wideband CO2 Laser Second Harmonic Generation Phase Matched in GaAs Thin-Film Waveguides," Appl. Phys. Lett. 19, 266–268 (1971).

Boyd, J. T.

J. T. Boyd, "Theory of Parametric Oscillation Phase Matched in GaAs Thin-Film Waveguides," IEEE J. Quantum Electron. QE-8, 788–796 (1972).

D. B. Anderson and J. T. Boyd, "Wideband CO2 Laser Second Harmonic Generation Phase Matched in GaAs Thin-Film Waveguides," Appl. Phys. Lett. 19, 266–268 (1971).

Chen, B. U.

B. U. Chen, C. C. Ghizoni, and C. L. Tang, "Phase Matched Second-Harmonic Generation in Solid Thin Films Using Modulation of the Nonlinear Susceptibilities," Appl. Phys. Lett. 28, 651–653 (1976).

B. U. Chen, C. L. Tang, and J. M. Telle, "CW Harmonic Generation in the UV Using a Thin-Film Waveguide on a Nonlinear Substrate," Appl. Phys. Lett. 9, 495–498 (1974).

Conwell, E. M.

E. M. Conwell, "Theory of Second-Harmonic Generation in Optical Waveguides," IEEE J. Quantum Electron. QE-9, 867–879 (1973).

Foy, P. W.

J. P. vander Ziel, M. Ilegems, P. W. Foy, and R. M. Mikulyak, "Phase-Matched Second-Harmonic Generation in a Periodic GaAs Waveguide," Appl. Phys. Lett. 29, 775–777 (1976).

Fukui, M.

R. Normandin, M. Fukui, and G. I. Stegeman, "Analysis of Parametric Mixing and Harmonic Generation of Surface Acoustic Waves," J. Appl. Phys. 50, 81–86 (1979).

M. Fukui and G. I. Stegeman, "Theory of Non Phase-Matched Second-Harmonic Generation of Surface Plasmons," Solid State Commun. 26, 239–241 (1978).

Furuya, K.

Y. Suematsu, Y. Sasaki, K. Furuya, K. Shibata, and S. Ibukuro, "Optical Second-Harmonic Generation Due to Guided Wave Structure Consisting of Quartz and Glass Film," IEEE J. Quantum Electron. QE-10, 222–229 (1974).

Ghizoni, C. C.

B. U. Chen, C. C. Ghizoni, and C. L. Tang, "Phase Matched Second-Harmonic Generation in Solid Thin Films Using Modulation of the Nonlinear Susceptibilities," Appl. Phys. Lett. 28, 651–653 (1976).

Ibukuro, S.

Y. Suematsu, Y. Sasaki, K. Furuya, K. Shibata, and S. Ibukuro, "Optical Second-Harmonic Generation Due to Guided Wave Structure Consisting of Quartz and Glass Film," IEEE J. Quantum Electron. QE-10, 222–229 (1974).

Ilegems, M.

J. P. vander Ziel, M. Ilegems, P. W. Foy, and R. M. Mikulyak, "Phase-Matched Second-Harmonic Generation in a Periodic GaAs Waveguide," Appl. Phys. Lett. 29, 775–777 (1976).

Inaba, H.

H. Ito, N. Uesugi, and H. Inaba, "Phase-Matched Guided Optical Second Harmonic Wave Generation in Oriented ZnS Polycrystalline Thin-Film Waveguides," Appl. Phys. Lett. 25, 385–387 (1974).

Ito, H.

H. Ito, N. Uesugi, and H. Inaba, "Phase-Matched Guided Optical Second Harmonic Wave Generation in Oriented ZnS Polycrystalline Thin-Film Waveguides," Appl. Phys. Lett. 25, 385–387 (1974).

Kimura, T.

N. Uesugi and T. Kimura, "Efficient Second-Harmonic Generation in Three Dimensional LiNbO3 Optical Waveguide," Appl. Phys. Lett. 29, 572–574 (1976).

Mikulyak, R. M.

J. P. vander Ziel, M. Ilegems, P. W. Foy, and R. M. Mikulyak, "Phase-Matched Second-Harmonic Generation in a Periodic GaAs Waveguide," Appl. Phys. Lett. 29, 775–777 (1976).

Normandin, R.

R. Normandin, V. C. Y. So, N. Rowell, and G. I. Stegeman, "The Scattering of Guided Optical Beams by Surface Acoustic Waves in Thin Films," J. Opt. Soc. Am. 69, 1153–1165 (1979).

R. Normandin, M. Fukui, and G. I. Stegeman, "Analysis of Parametric Mixing and Harmonic Generation of Surface Acoustic Waves," J. Appl. Phys. 50, 81–86 (1979).

Reutov, A. T.

A. T. Reutov and P. P. Taraschenko, "Generation of a Sum Frequency Wave in a Microscopic Optically Nonlinear Waveguide Made of Lithium Niobate," Sov. J. Quantum Electron. 4, 910–911 (1975).

Rowell, N.

Sasaki, Y.

Y. Suematsu, Y. Sasaki, K. Furuya, K. Shibata, and S. Ibukuro, "Optical Second-Harmonic Generation Due to Guided Wave Structure Consisting of Quartz and Glass Film," IEEE J. Quantum Electron. QE-10, 222–229 (1974).

Shibata, K.

Y. Suematsu, Y. Sasaki, K. Furuya, K. Shibata, and S. Ibukuro, "Optical Second-Harmonic Generation Due to Guided Wave Structure Consisting of Quartz and Glass Film," IEEE J. Quantum Electron. QE-10, 222–229 (1974).

So, V. C. Y.

Stegeman, G. I.

R. Normandin, V. C. Y. So, N. Rowell, and G. I. Stegeman, "The Scattering of Guided Optical Beams by Surface Acoustic Waves in Thin Films," J. Opt. Soc. Am. 69, 1153–1165 (1979).

R. Normandin, M. Fukui, and G. I. Stegeman, "Analysis of Parametric Mixing and Harmonic Generation of Surface Acoustic Waves," J. Appl. Phys. 50, 81–86 (1979).

M. Fukui and G. I. Stegeman, "Theory of Non Phase-Matched Second-Harmonic Generation of Surface Plasmons," Solid State Commun. 26, 239–241 (1978).

Suematsu, Y.

Y. Suematsu, Y. Sasaki, K. Furuya, K. Shibata, and S. Ibukuro, "Optical Second-Harmonic Generation Due to Guided Wave Structure Consisting of Quartz and Glass Film," IEEE J. Quantum Electron. QE-10, 222–229 (1974).

Y. Suematsu, "Tunable Parametric Oscillator Using a Guided Wave Structure," Jpn. J. Appl. Phys. 9, 798–805 (1970).

Tang, C. L.

B. U. Chen, C. C. Ghizoni, and C. L. Tang, "Phase Matched Second-Harmonic Generation in Solid Thin Films Using Modulation of the Nonlinear Susceptibilities," Appl. Phys. Lett. 28, 651–653 (1976).

B. U. Chen, C. L. Tang, and J. M. Telle, "CW Harmonic Generation in the UV Using a Thin-Film Waveguide on a Nonlinear Substrate," Appl. Phys. Lett. 9, 495–498 (1974).

Taraschenko, P. P.

A. T. Reutov and P. P. Taraschenko, "Generation of a Sum Frequency Wave in a Microscopic Optically Nonlinear Waveguide Made of Lithium Niobate," Sov. J. Quantum Electron. 4, 910–911 (1975).

Telle, J. M.

B. U. Chen, C. L. Tang, and J. M. Telle, "CW Harmonic Generation in the UV Using a Thin-Film Waveguide on a Nonlinear Substrate," Appl. Phys. Lett. 9, 495–498 (1974).

Uesugi, N.

N. Uesugi and T. Kimura, "Efficient Second-Harmonic Generation in Three Dimensional LiNbO3 Optical Waveguide," Appl. Phys. Lett. 29, 572–574 (1976).

H. Ito, N. Uesugi, and H. Inaba, "Phase-Matched Guided Optical Second Harmonic Wave Generation in Oriented ZnS Polycrystalline Thin-Film Waveguides," Appl. Phys. Lett. 25, 385–387 (1974).

Yariv, A.

See, for example, A. Yariv, Quantum Electronics, (Wiley, New York 1975).

Ziel, J. P. vander

J. P. vander Ziel, M. Ilegems, P. W. Foy, and R. M. Mikulyak, "Phase-Matched Second-Harmonic Generation in a Periodic GaAs Waveguide," Appl. Phys. Lett. 29, 775–777 (1976).

Appl. Phys. Lett. (6)

D. B. Anderson and J. T. Boyd, "Wideband CO2 Laser Second Harmonic Generation Phase Matched in GaAs Thin-Film Waveguides," Appl. Phys. Lett. 19, 266–268 (1971).

B. U. Chen, C. C. Ghizoni, and C. L. Tang, "Phase Matched Second-Harmonic Generation in Solid Thin Films Using Modulation of the Nonlinear Susceptibilities," Appl. Phys. Lett. 28, 651–653 (1976).

N. Uesugi and T. Kimura, "Efficient Second-Harmonic Generation in Three Dimensional LiNbO3 Optical Waveguide," Appl. Phys. Lett. 29, 572–574 (1976).

J. P. vander Ziel, M. Ilegems, P. W. Foy, and R. M. Mikulyak, "Phase-Matched Second-Harmonic Generation in a Periodic GaAs Waveguide," Appl. Phys. Lett. 29, 775–777 (1976).

H. Ito, N. Uesugi, and H. Inaba, "Phase-Matched Guided Optical Second Harmonic Wave Generation in Oriented ZnS Polycrystalline Thin-Film Waveguides," Appl. Phys. Lett. 25, 385–387 (1974).

B. U. Chen, C. L. Tang, and J. M. Telle, "CW Harmonic Generation in the UV Using a Thin-Film Waveguide on a Nonlinear Substrate," Appl. Phys. Lett. 9, 495–498 (1974).

IEEE J. Quantum Electron. (3)

J. T. Boyd, "Theory of Parametric Oscillation Phase Matched in GaAs Thin-Film Waveguides," IEEE J. Quantum Electron. QE-8, 788–796 (1972).

E. M. Conwell, "Theory of Second-Harmonic Generation in Optical Waveguides," IEEE J. Quantum Electron. QE-9, 867–879 (1973).

Y. Suematsu, Y. Sasaki, K. Furuya, K. Shibata, and S. Ibukuro, "Optical Second-Harmonic Generation Due to Guided Wave Structure Consisting of Quartz and Glass Film," IEEE J. Quantum Electron. QE-10, 222–229 (1974).

J. Appl. Phys. (1)

R. Normandin, M. Fukui, and G. I. Stegeman, "Analysis of Parametric Mixing and Harmonic Generation of Surface Acoustic Waves," J. Appl. Phys. 50, 81–86 (1979).

J. Opt. Soc. Am. (1)

Jpn. J. Appl. Phys. (1)

Y. Suematsu, "Tunable Parametric Oscillator Using a Guided Wave Structure," Jpn. J. Appl. Phys. 9, 798–805 (1970).

Solid State Commun. (1)

M. Fukui and G. I. Stegeman, "Theory of Non Phase-Matched Second-Harmonic Generation of Surface Plasmons," Solid State Commun. 26, 239–241 (1978).

Sov. J. Quantum Electron. (1)

A. T. Reutov and P. P. Taraschenko, "Generation of a Sum Frequency Wave in a Microscopic Optically Nonlinear Waveguide Made of Lithium Niobate," Sov. J. Quantum Electron. 4, 910–911 (1975).

Other (1)

See, for example, A. Yariv, Quantum Electronics, (Wiley, New York 1975).

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