Abstract

We investigate efficient second harmonic generation in reverse proton exchanged Lithium Niobate waveguides. In z-cut crystals, the resulting buried and surface guides support TM and TE polarizations, respectively, and are coupled through the d31 nonlinear element. Numerically estimated conversion efficiencies in planar structures operating at 1.32µm reach 90% in 2cm or a normalized 14% µm/Wcm.

©2001 Optical Society of America

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  1. See, for example, A. M. Prokhorov, U. S. Kuz’minov, and O. A. Khachaturyan, Ferroelectric Thin Film Waveguides in Integrated Optics and Optoelectronics, Cambridge International Science Publ., 1996
  2. X. F. Cao, R. V. Ramaswamy, and R. Srivastava, “Characterization of annealed proton exchanged LiNbO3 waveguides for nonlinear frequency conversion,” J. Lightw. Technol. 10, 1302–1315 (1992)
    [Crossref]
  3. J. L. Jackel and J. J. Johnson, “Reverse exchange method for burying proton exchanged waveguides,” Electron. Lett. 27, 1360–1361 (1991)
    [Crossref]
  4. J. Olivares and J. M. Cabrera, “Modification of proton exchanged LiNbO3 layers for guiding modes with ordinary polarization,” Fiber Integ. Optics 12, 277–285 (1993)
    [Crossref]
  5. J. Olivares and J. M. Cabrera, “Guided modes with ordinary refractive index in proton exchanged LiNbO3 waveguides,” Appl. Phys. Lett. 62, 2468–2470 (1993)
    [Crossref]
  6. P. Baldi, M. De Micheli, K. El Hadi, A. C. Cino, P. Aschieri, and D. B. Ostrowsky, “Proton exchanged waveguides in LiNbO3 and LiTaO3 for integrated lasers and nonlinear frequency converters,” Opt. Eng. 37, 1193–1202 (1998).
    [Crossref]
  7. K. El Hadi, P. Baldi, M. P. De Micheli, D. B. Ostrowsky, Y. N. Korkishko, V. A. Fedorov, and A. V. Kondrat’ev, “Ordinary and extraordinary waveguides realized by reverse proton exchange on LiTaO3,” Opt. Commun. 140, 23–26 (1997)
    [Crossref]
  8. Y. N. Korkishko, V. A. Fedorov, T. M. Morozova, F. Caccavale, F. Gonella, and F. Segato, “Reverse proton exchange for buried waveguides in LiNbO3,” J. Opt. Soc. Am. A 15, 1838–1842 (1998)
    [Crossref]
  9. J. Rams, J. Olivares, and J. M. Cabrera, “SHG-capabilities of reverse PE-LiNbO3 waveguides,” Electron. Lett. 33, 322–323 (1997)
    [Crossref]
  10. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983)
  11. G. R. Hadley, “Transparent boundary condition for the beam propagation method,” IEEE J. Quantum Electron. 28, 363–370 (1992)
    [Crossref]
  12. G. J. Edwards and M. Lawrence, “A temperature dependent dispersion for congruently grown lithium niobate,” Opt. & Quantum Electron. 16, 373–374 (1984)
    [Crossref]
  13. K. Chikuma and S. Umegaki, “Characteristics of optical second-harmonic generation due to Cerenkov-radiation-type phase matching,” J. Opt. Soc. Am. B 7, 768–775 (1990)
    [Crossref]
  14. M. De Micheli, “Second harmonic generation in Cerenkov configuration” in Guided Wave Nonlinear Optics, D. B. Ostrowsky and R. Reinisch eds. (Kluwer Acad. Publishers., Dordrecht, NL1992)
  15. G. Arvidsson and F. Laurell, “Nonlinear optical wavelength conversion in Ti:LiNbO3 waveguides,” Thin Solid Films 136, 29–36 (1986)
    [Crossref]
  16. N. A. Sanford and J. M. Connors, “Optimization of the Cerenkov sum-frequency generation in proton-exchanged Mg:LiNbO3 channel waveguides,” J. Appl. Phys. 65, 1430–1437 (1989)
    [Crossref]
  17. G. Tohmon, J. Ohya, K. Yamamoto, and T. Taniuchi, “Generation of ultraviolet picosecond pulses by frequency-doubling of laser diode in proton-exchanged MgO:LiNbO3 waveguide,” IEEE Phot. Techn. Lett. 2, 629–631 (1990)
    [Crossref]
  18. W. Sohler and H. Suche, “Second-harmonic generation in Ti-diffused LiNbO3 waveguides with 25% conversion efficiency,” Appl. Phys. Lett. 33, 518–520 (1978)
    [Crossref]

1998 (2)

Y. N. Korkishko, V. A. Fedorov, T. M. Morozova, F. Caccavale, F. Gonella, and F. Segato, “Reverse proton exchange for buried waveguides in LiNbO3,” J. Opt. Soc. Am. A 15, 1838–1842 (1998)
[Crossref]

P. Baldi, M. De Micheli, K. El Hadi, A. C. Cino, P. Aschieri, and D. B. Ostrowsky, “Proton exchanged waveguides in LiNbO3 and LiTaO3 for integrated lasers and nonlinear frequency converters,” Opt. Eng. 37, 1193–1202 (1998).
[Crossref]

1997 (2)

K. El Hadi, P. Baldi, M. P. De Micheli, D. B. Ostrowsky, Y. N. Korkishko, V. A. Fedorov, and A. V. Kondrat’ev, “Ordinary and extraordinary waveguides realized by reverse proton exchange on LiTaO3,” Opt. Commun. 140, 23–26 (1997)
[Crossref]

J. Rams, J. Olivares, and J. M. Cabrera, “SHG-capabilities of reverse PE-LiNbO3 waveguides,” Electron. Lett. 33, 322–323 (1997)
[Crossref]

1993 (2)

J. Olivares and J. M. Cabrera, “Modification of proton exchanged LiNbO3 layers for guiding modes with ordinary polarization,” Fiber Integ. Optics 12, 277–285 (1993)
[Crossref]

J. Olivares and J. M. Cabrera, “Guided modes with ordinary refractive index in proton exchanged LiNbO3 waveguides,” Appl. Phys. Lett. 62, 2468–2470 (1993)
[Crossref]

1992 (2)

X. F. Cao, R. V. Ramaswamy, and R. Srivastava, “Characterization of annealed proton exchanged LiNbO3 waveguides for nonlinear frequency conversion,” J. Lightw. Technol. 10, 1302–1315 (1992)
[Crossref]

G. R. Hadley, “Transparent boundary condition for the beam propagation method,” IEEE J. Quantum Electron. 28, 363–370 (1992)
[Crossref]

1991 (1)

J. L. Jackel and J. J. Johnson, “Reverse exchange method for burying proton exchanged waveguides,” Electron. Lett. 27, 1360–1361 (1991)
[Crossref]

1990 (2)

K. Chikuma and S. Umegaki, “Characteristics of optical second-harmonic generation due to Cerenkov-radiation-type phase matching,” J. Opt. Soc. Am. B 7, 768–775 (1990)
[Crossref]

G. Tohmon, J. Ohya, K. Yamamoto, and T. Taniuchi, “Generation of ultraviolet picosecond pulses by frequency-doubling of laser diode in proton-exchanged MgO:LiNbO3 waveguide,” IEEE Phot. Techn. Lett. 2, 629–631 (1990)
[Crossref]

1989 (1)

N. A. Sanford and J. M. Connors, “Optimization of the Cerenkov sum-frequency generation in proton-exchanged Mg:LiNbO3 channel waveguides,” J. Appl. Phys. 65, 1430–1437 (1989)
[Crossref]

1986 (1)

G. Arvidsson and F. Laurell, “Nonlinear optical wavelength conversion in Ti:LiNbO3 waveguides,” Thin Solid Films 136, 29–36 (1986)
[Crossref]

1984 (1)

G. J. Edwards and M. Lawrence, “A temperature dependent dispersion for congruently grown lithium niobate,” Opt. & Quantum Electron. 16, 373–374 (1984)
[Crossref]

1978 (1)

W. Sohler and H. Suche, “Second-harmonic generation in Ti-diffused LiNbO3 waveguides with 25% conversion efficiency,” Appl. Phys. Lett. 33, 518–520 (1978)
[Crossref]

Arvidsson, G.

G. Arvidsson and F. Laurell, “Nonlinear optical wavelength conversion in Ti:LiNbO3 waveguides,” Thin Solid Films 136, 29–36 (1986)
[Crossref]

Aschieri, P.

P. Baldi, M. De Micheli, K. El Hadi, A. C. Cino, P. Aschieri, and D. B. Ostrowsky, “Proton exchanged waveguides in LiNbO3 and LiTaO3 for integrated lasers and nonlinear frequency converters,” Opt. Eng. 37, 1193–1202 (1998).
[Crossref]

Baldi, P.

P. Baldi, M. De Micheli, K. El Hadi, A. C. Cino, P. Aschieri, and D. B. Ostrowsky, “Proton exchanged waveguides in LiNbO3 and LiTaO3 for integrated lasers and nonlinear frequency converters,” Opt. Eng. 37, 1193–1202 (1998).
[Crossref]

K. El Hadi, P. Baldi, M. P. De Micheli, D. B. Ostrowsky, Y. N. Korkishko, V. A. Fedorov, and A. V. Kondrat’ev, “Ordinary and extraordinary waveguides realized by reverse proton exchange on LiTaO3,” Opt. Commun. 140, 23–26 (1997)
[Crossref]

Cabrera, J. M.

J. Rams, J. Olivares, and J. M. Cabrera, “SHG-capabilities of reverse PE-LiNbO3 waveguides,” Electron. Lett. 33, 322–323 (1997)
[Crossref]

J. Olivares and J. M. Cabrera, “Guided modes with ordinary refractive index in proton exchanged LiNbO3 waveguides,” Appl. Phys. Lett. 62, 2468–2470 (1993)
[Crossref]

J. Olivares and J. M. Cabrera, “Modification of proton exchanged LiNbO3 layers for guiding modes with ordinary polarization,” Fiber Integ. Optics 12, 277–285 (1993)
[Crossref]

Caccavale, F.

Cao, X. F.

X. F. Cao, R. V. Ramaswamy, and R. Srivastava, “Characterization of annealed proton exchanged LiNbO3 waveguides for nonlinear frequency conversion,” J. Lightw. Technol. 10, 1302–1315 (1992)
[Crossref]

Chikuma, K.

Cino, A. C.

P. Baldi, M. De Micheli, K. El Hadi, A. C. Cino, P. Aschieri, and D. B. Ostrowsky, “Proton exchanged waveguides in LiNbO3 and LiTaO3 for integrated lasers and nonlinear frequency converters,” Opt. Eng. 37, 1193–1202 (1998).
[Crossref]

Connors, J. M.

N. A. Sanford and J. M. Connors, “Optimization of the Cerenkov sum-frequency generation in proton-exchanged Mg:LiNbO3 channel waveguides,” J. Appl. Phys. 65, 1430–1437 (1989)
[Crossref]

De Micheli, M.

P. Baldi, M. De Micheli, K. El Hadi, A. C. Cino, P. Aschieri, and D. B. Ostrowsky, “Proton exchanged waveguides in LiNbO3 and LiTaO3 for integrated lasers and nonlinear frequency converters,” Opt. Eng. 37, 1193–1202 (1998).
[Crossref]

M. De Micheli, “Second harmonic generation in Cerenkov configuration” in Guided Wave Nonlinear Optics, D. B. Ostrowsky and R. Reinisch eds. (Kluwer Acad. Publishers., Dordrecht, NL1992)

De Micheli, M. P.

K. El Hadi, P. Baldi, M. P. De Micheli, D. B. Ostrowsky, Y. N. Korkishko, V. A. Fedorov, and A. V. Kondrat’ev, “Ordinary and extraordinary waveguides realized by reverse proton exchange on LiTaO3,” Opt. Commun. 140, 23–26 (1997)
[Crossref]

Edwards, G. J.

G. J. Edwards and M. Lawrence, “A temperature dependent dispersion for congruently grown lithium niobate,” Opt. & Quantum Electron. 16, 373–374 (1984)
[Crossref]

El Hadi, K.

P. Baldi, M. De Micheli, K. El Hadi, A. C. Cino, P. Aschieri, and D. B. Ostrowsky, “Proton exchanged waveguides in LiNbO3 and LiTaO3 for integrated lasers and nonlinear frequency converters,” Opt. Eng. 37, 1193–1202 (1998).
[Crossref]

K. El Hadi, P. Baldi, M. P. De Micheli, D. B. Ostrowsky, Y. N. Korkishko, V. A. Fedorov, and A. V. Kondrat’ev, “Ordinary and extraordinary waveguides realized by reverse proton exchange on LiTaO3,” Opt. Commun. 140, 23–26 (1997)
[Crossref]

Fedorov, V. A.

Y. N. Korkishko, V. A. Fedorov, T. M. Morozova, F. Caccavale, F. Gonella, and F. Segato, “Reverse proton exchange for buried waveguides in LiNbO3,” J. Opt. Soc. Am. A 15, 1838–1842 (1998)
[Crossref]

K. El Hadi, P. Baldi, M. P. De Micheli, D. B. Ostrowsky, Y. N. Korkishko, V. A. Fedorov, and A. V. Kondrat’ev, “Ordinary and extraordinary waveguides realized by reverse proton exchange on LiTaO3,” Opt. Commun. 140, 23–26 (1997)
[Crossref]

Gonella, F.

Hadley, G. R.

G. R. Hadley, “Transparent boundary condition for the beam propagation method,” IEEE J. Quantum Electron. 28, 363–370 (1992)
[Crossref]

Jackel, J. L.

J. L. Jackel and J. J. Johnson, “Reverse exchange method for burying proton exchanged waveguides,” Electron. Lett. 27, 1360–1361 (1991)
[Crossref]

Johnson, J. J.

J. L. Jackel and J. J. Johnson, “Reverse exchange method for burying proton exchanged waveguides,” Electron. Lett. 27, 1360–1361 (1991)
[Crossref]

Khachaturyan, O. A.

See, for example, A. M. Prokhorov, U. S. Kuz’minov, and O. A. Khachaturyan, Ferroelectric Thin Film Waveguides in Integrated Optics and Optoelectronics, Cambridge International Science Publ., 1996

Kondrat’ev, A. V.

K. El Hadi, P. Baldi, M. P. De Micheli, D. B. Ostrowsky, Y. N. Korkishko, V. A. Fedorov, and A. V. Kondrat’ev, “Ordinary and extraordinary waveguides realized by reverse proton exchange on LiTaO3,” Opt. Commun. 140, 23–26 (1997)
[Crossref]

Korkishko, Y. N.

Y. N. Korkishko, V. A. Fedorov, T. M. Morozova, F. Caccavale, F. Gonella, and F. Segato, “Reverse proton exchange for buried waveguides in LiNbO3,” J. Opt. Soc. Am. A 15, 1838–1842 (1998)
[Crossref]

K. El Hadi, P. Baldi, M. P. De Micheli, D. B. Ostrowsky, Y. N. Korkishko, V. A. Fedorov, and A. V. Kondrat’ev, “Ordinary and extraordinary waveguides realized by reverse proton exchange on LiTaO3,” Opt. Commun. 140, 23–26 (1997)
[Crossref]

Kuz’minov, U. S.

See, for example, A. M. Prokhorov, U. S. Kuz’minov, and O. A. Khachaturyan, Ferroelectric Thin Film Waveguides in Integrated Optics and Optoelectronics, Cambridge International Science Publ., 1996

Laurell, F.

G. Arvidsson and F. Laurell, “Nonlinear optical wavelength conversion in Ti:LiNbO3 waveguides,” Thin Solid Films 136, 29–36 (1986)
[Crossref]

Lawrence, M.

G. J. Edwards and M. Lawrence, “A temperature dependent dispersion for congruently grown lithium niobate,” Opt. & Quantum Electron. 16, 373–374 (1984)
[Crossref]

Love, J. D.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983)

Morozova, T. M.

Ohya, J.

G. Tohmon, J. Ohya, K. Yamamoto, and T. Taniuchi, “Generation of ultraviolet picosecond pulses by frequency-doubling of laser diode in proton-exchanged MgO:LiNbO3 waveguide,” IEEE Phot. Techn. Lett. 2, 629–631 (1990)
[Crossref]

Olivares, J.

J. Rams, J. Olivares, and J. M. Cabrera, “SHG-capabilities of reverse PE-LiNbO3 waveguides,” Electron. Lett. 33, 322–323 (1997)
[Crossref]

J. Olivares and J. M. Cabrera, “Modification of proton exchanged LiNbO3 layers for guiding modes with ordinary polarization,” Fiber Integ. Optics 12, 277–285 (1993)
[Crossref]

J. Olivares and J. M. Cabrera, “Guided modes with ordinary refractive index in proton exchanged LiNbO3 waveguides,” Appl. Phys. Lett. 62, 2468–2470 (1993)
[Crossref]

Ostrowsky, D. B.

P. Baldi, M. De Micheli, K. El Hadi, A. C. Cino, P. Aschieri, and D. B. Ostrowsky, “Proton exchanged waveguides in LiNbO3 and LiTaO3 for integrated lasers and nonlinear frequency converters,” Opt. Eng. 37, 1193–1202 (1998).
[Crossref]

K. El Hadi, P. Baldi, M. P. De Micheli, D. B. Ostrowsky, Y. N. Korkishko, V. A. Fedorov, and A. V. Kondrat’ev, “Ordinary and extraordinary waveguides realized by reverse proton exchange on LiTaO3,” Opt. Commun. 140, 23–26 (1997)
[Crossref]

Prokhorov, A. M.

See, for example, A. M. Prokhorov, U. S. Kuz’minov, and O. A. Khachaturyan, Ferroelectric Thin Film Waveguides in Integrated Optics and Optoelectronics, Cambridge International Science Publ., 1996

Ramaswamy, R. V.

X. F. Cao, R. V. Ramaswamy, and R. Srivastava, “Characterization of annealed proton exchanged LiNbO3 waveguides for nonlinear frequency conversion,” J. Lightw. Technol. 10, 1302–1315 (1992)
[Crossref]

Rams, J.

J. Rams, J. Olivares, and J. M. Cabrera, “SHG-capabilities of reverse PE-LiNbO3 waveguides,” Electron. Lett. 33, 322–323 (1997)
[Crossref]

Sanford, N. A.

N. A. Sanford and J. M. Connors, “Optimization of the Cerenkov sum-frequency generation in proton-exchanged Mg:LiNbO3 channel waveguides,” J. Appl. Phys. 65, 1430–1437 (1989)
[Crossref]

Segato, F.

Snyder, A. W.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983)

Sohler, W.

W. Sohler and H. Suche, “Second-harmonic generation in Ti-diffused LiNbO3 waveguides with 25% conversion efficiency,” Appl. Phys. Lett. 33, 518–520 (1978)
[Crossref]

Srivastava, R.

X. F. Cao, R. V. Ramaswamy, and R. Srivastava, “Characterization of annealed proton exchanged LiNbO3 waveguides for nonlinear frequency conversion,” J. Lightw. Technol. 10, 1302–1315 (1992)
[Crossref]

Suche, H.

W. Sohler and H. Suche, “Second-harmonic generation in Ti-diffused LiNbO3 waveguides with 25% conversion efficiency,” Appl. Phys. Lett. 33, 518–520 (1978)
[Crossref]

Taniuchi, T.

G. Tohmon, J. Ohya, K. Yamamoto, and T. Taniuchi, “Generation of ultraviolet picosecond pulses by frequency-doubling of laser diode in proton-exchanged MgO:LiNbO3 waveguide,” IEEE Phot. Techn. Lett. 2, 629–631 (1990)
[Crossref]

Tohmon, G.

G. Tohmon, J. Ohya, K. Yamamoto, and T. Taniuchi, “Generation of ultraviolet picosecond pulses by frequency-doubling of laser diode in proton-exchanged MgO:LiNbO3 waveguide,” IEEE Phot. Techn. Lett. 2, 629–631 (1990)
[Crossref]

Umegaki, S.

Yamamoto, K.

G. Tohmon, J. Ohya, K. Yamamoto, and T. Taniuchi, “Generation of ultraviolet picosecond pulses by frequency-doubling of laser diode in proton-exchanged MgO:LiNbO3 waveguide,” IEEE Phot. Techn. Lett. 2, 629–631 (1990)
[Crossref]

Appl. Phys. Lett. (2)

J. Olivares and J. M. Cabrera, “Guided modes with ordinary refractive index in proton exchanged LiNbO3 waveguides,” Appl. Phys. Lett. 62, 2468–2470 (1993)
[Crossref]

W. Sohler and H. Suche, “Second-harmonic generation in Ti-diffused LiNbO3 waveguides with 25% conversion efficiency,” Appl. Phys. Lett. 33, 518–520 (1978)
[Crossref]

Electron. Lett. (2)

J. L. Jackel and J. J. Johnson, “Reverse exchange method for burying proton exchanged waveguides,” Electron. Lett. 27, 1360–1361 (1991)
[Crossref]

J. Rams, J. Olivares, and J. M. Cabrera, “SHG-capabilities of reverse PE-LiNbO3 waveguides,” Electron. Lett. 33, 322–323 (1997)
[Crossref]

Fiber Integ. Optics (1)

J. Olivares and J. M. Cabrera, “Modification of proton exchanged LiNbO3 layers for guiding modes with ordinary polarization,” Fiber Integ. Optics 12, 277–285 (1993)
[Crossref]

IEEE J. Quantum Electron. (1)

G. R. Hadley, “Transparent boundary condition for the beam propagation method,” IEEE J. Quantum Electron. 28, 363–370 (1992)
[Crossref]

IEEE Phot. Techn. Lett. (1)

G. Tohmon, J. Ohya, K. Yamamoto, and T. Taniuchi, “Generation of ultraviolet picosecond pulses by frequency-doubling of laser diode in proton-exchanged MgO:LiNbO3 waveguide,” IEEE Phot. Techn. Lett. 2, 629–631 (1990)
[Crossref]

J. Appl. Phys. (1)

N. A. Sanford and J. M. Connors, “Optimization of the Cerenkov sum-frequency generation in proton-exchanged Mg:LiNbO3 channel waveguides,” J. Appl. Phys. 65, 1430–1437 (1989)
[Crossref]

J. Lightw. Technol. (1)

X. F. Cao, R. V. Ramaswamy, and R. Srivastava, “Characterization of annealed proton exchanged LiNbO3 waveguides for nonlinear frequency conversion,” J. Lightw. Technol. 10, 1302–1315 (1992)
[Crossref]

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

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

Opt. & Quantum Electron. (1)

G. J. Edwards and M. Lawrence, “A temperature dependent dispersion for congruently grown lithium niobate,” Opt. & Quantum Electron. 16, 373–374 (1984)
[Crossref]

Opt. Commun. (1)

K. El Hadi, P. Baldi, M. P. De Micheli, D. B. Ostrowsky, Y. N. Korkishko, V. A. Fedorov, and A. V. Kondrat’ev, “Ordinary and extraordinary waveguides realized by reverse proton exchange on LiTaO3,” Opt. Commun. 140, 23–26 (1997)
[Crossref]

Opt. Eng. (1)

P. Baldi, M. De Micheli, K. El Hadi, A. C. Cino, P. Aschieri, and D. B. Ostrowsky, “Proton exchanged waveguides in LiNbO3 and LiTaO3 for integrated lasers and nonlinear frequency converters,” Opt. Eng. 37, 1193–1202 (1998).
[Crossref]

Thin Solid Films (1)

G. Arvidsson and F. Laurell, “Nonlinear optical wavelength conversion in Ti:LiNbO3 waveguides,” Thin Solid Films 136, 29–36 (1986)
[Crossref]

Other (3)

M. De Micheli, “Second harmonic generation in Cerenkov configuration” in Guided Wave Nonlinear Optics, D. B. Ostrowsky and R. Reinisch eds. (Kluwer Acad. Publishers., Dordrecht, NL1992)

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983)

See, for example, A. M. Prokhorov, U. S. Kuz’minov, and O. A. Khachaturyan, Ferroelectric Thin Film Waveguides in Integrated Optics and Optoelectronics, Cambridge International Science Publ., 1996

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Figures (7)

Fig. 1.
Fig. 1. RPE geometry with graphs of ordinary and extraordinary index distributions in z-cut LN.

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Fig. 2.
Fig. 2. Computed SHG conversion efficiency versus input power for a 1cm sample at 25°C. (a) CMT and (b) EFDBPM results in case of Gaussian excitation.

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Fig. 3.
Fig. 3. Contour maps of (a) FF and (b) SH intensity versus z and y for a Gaussian input at 10W/µm in a sample at temperature 25°C.

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Fig. 4.
Fig. 4. Phase-matching diagram at 25°C versus modal order m at SH. The horizontal lines refer to the FF modes, TE0 and leaky (or quasi-mode), respectively. The inset shows the corresponding TMm-TE0 overlap integral.

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Fig. 5.
Fig. 5. Contour maps of (a) FF and (b) SH intensity versus z and y for a TE0 input at 10W/µm.

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Fig. 6.
Fig. 6. Conversion efficiency versus input FF power (TE0 excitation) at (a) 25 and (b) 85°C, for samples 1cm (dashed line) and 2cm (solid line) in length.

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Fig. 7.
Fig. 7. Conversion efficiency versus temperature (TE0 excitation) at input powers of (a) 1W/µm and (b) 10W/µm, for samples 1cm (dashed line) and 2cm (solid line) in length.

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Equations (4)

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

E TE ω ( z , y ) = A ( y ) f ω ( z ) e − i k 0 N ω y , E TM 2 ω ( z , y ) = ∑ ν B ν ( y ) f 2 ω ν ( z ) e − i 2 k 0 N 2 ω ν y
∂ 2 E TE ω ∂ y 2 + ∂ 2 E TE ω ∂ z 2 + k 0 2 ( n o ω ( z ) ) 2 E TE ω + 2 k 0 2 d 15 E TM 2 ω ( E TE ω ) * = 0
∂ 2 E TM 2 ω ∂ y 2 + ( n es 2 ω ) 2 ( n os 2 ω ) 2 ∂ 2 E TM 2 ω ∂ z 2 + 4 k 0 2 ( n e 2 ω ( z ) ) 2 E TM 2 ω + 4 k 0 2 d 31 ( E TE ω ) 2 = 0
n o , e qω ( z ) = n os , es qω + Δ n o , e qω exp ( − z − z 0 σ oi , ei ) 2

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