Abstract

The photorefractive effect in titanium-in-diffused LiNbO3 waveguides is studied both experimentally and theoretically. Measurements of mode size and transmitted optical power as a function of input optical power are presented. The diffusion constants in the diffusion model and the unknown parameters in Kukhtarev’s model are determined from measurements of the near-field intensity profiles at low and at high intensity levels. These parameters can then be used to predict waveguide behavior as a function of the input power level. The simulated behavior closely resembles that observed experimentally. Calculated corrections for thermally induced index perturbation show that the thermal effects are higher-order corrections to the dominant photorefractive effect.

© 1993 Optical Society of America

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    [CrossRef]
  2. F. S. Chen, “Optically induced change of refractive indices in LiNbO3 and LiTaO3,” J. Appl. Phys. 40, 3389–3396 (1969).
    [CrossRef]
  3. G. E. Peterson, A. M. Glass, T. J. Negran, “Control of the susceptibility of lithium niobate to laser-induced refractive index changes,” Appl. Phys. Lett. 19, 130–132 (1971).
    [CrossRef]
  4. A. M. Glass, D. von der Linde, T. J. Negran, “High-voltage bulk photovoltaic effect and the photorefractive process in LiNbO3,” Appl. Phys. Lett. 25, 233–235 (1974).
    [CrossRef]
  5. N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electro-optic crystals I. Steady-state,” Ferroelectrics 22, 949–960 (1979).
    [CrossRef]
  6. R. L. Holman, P. J. Cressman, J. F. Revelli, “Chemical control of optical damage in lithium niobate,” Appl. Phys. Lett. 32, 280–283 (1978).
    [CrossRef]
  7. R. A. Becker, R. C. Williamson, “Photorefractive effects in LiNbO3 channel waveguides: Model and experimental verification,” Appl. Phys. Lett. 47, 1024–1026 (1985).
    [CrossRef]
  8. T. Fujiwara, S. Sato, H. Mori, “Wavelength dependence of photorefractive effect in Ti-indiffused LiNbO3 waveguides,” Appl. Phys. Lett. 54, 975–977 (1989).
    [CrossRef]
  9. A. M. Glass, I. P. Kaminow, A. A. Ballman, D. H. Olson, “Absorption loss and photorefractive-index changes in Ti:LiNbO3 crystals and waveguides,” Appl. Opt. 19, 276–281 (1980).
    [CrossRef] [PubMed]
  10. M. Fukuma, J. Noda, H. Iwasaki, “Optical properties in titanium-diffused LiNbO3 strip waveguides,” J. Appl. Phys. 49, 3693–3698 (1978).
    [CrossRef]
  11. J. Čtyroký, M. Holfman, J. Janta, J. Schrőfel, “3D analysis of LiNbO3:Ti channel waveguides and directional coupler,” IEEE J Quantum Electron. QE-20, 400–409 (1984).
    [CrossRef]
  12. P. Günter, F. Micheron, “Photorefractive effects and photocurrents in KNbO3:Fe,” Ferroelectrics 18, 27–38 (1978).
    [CrossRef]
  13. E. Krätzig, “Photorefractive effects and photoconductivity in LiNbO3:Fe,” Ferroelectrics 21, 635–636 (1978).
    [CrossRef]
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    [CrossRef]
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  20. W. Charczenko, P. S. Weitzman, H. Klotz, M. Surette, J. M. Dunn, A. R. Mickelson, “Characterization and simulation of proton exchanged integrated optical modulators with various dielectric buffer layers,” J. Lightwave Technol. LT-9, 92–100 (1991).
    [CrossRef]
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  23. A. M. Glass, D. vonder Linde, T. J. Negran, “High-voltage bulk photovoltaic effect and the photorefractive process in LiNbO3,” Appl. Phys. Lett. 25, 233–235 (1974).
    [CrossRef]
  24. H. Kurz, E. Krätzig, W. Keune, H. Engelmann, U. Gonser, B. Dischler, A. Räuber, “Photorefractive centers in LiNbO3, studied by optical-, Mössbauer-, and EPR-methods,” Appl. Phys. 12, 355–368 (1977).
    [CrossRef]
  25. LiNbO3 Optical Grade Substrate Data Sheet (Crystal Technology, Inc., Palo Alto, Calif., 1991).
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    [CrossRef]
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  29. G. D. Boyd, W. L. Bond, H. L. Carter, “Refractive index as a function of temperature in LiNbO3,” J. Appl. Phys. 38, 1941–1943 (1967).
    [CrossRef]
  30. N. P. Barnes, R. C. Eckhardt, D. J. Gettemy, L. B. Edgett, “Absorption coefficients and the temperature variation of the refractive index difference of nonlinear optical crystals,” IEEE J. Quantum Electron. QE-15, 1074–1076 (1979).
    [CrossRef]
  31. D. C. Johnson, “Measurement of low absorption coefficients in crystals,” Appl. Opt. 12, 2192–2197 (1973).
    [CrossRef] [PubMed]
  32. M. J. Weber, Handbook of Laser Science and Technology Volume IV. Optical Materials Part 2 (CRC, Boca Raton, Fla., 1980).

1991

W. Charczenko, P. S. Weitzman, H. Klotz, M. Surette, J. M. Dunn, A. R. Mickelson, “Characterization and simulation of proton exchanged integrated optical modulators with various dielectric buffer layers,” J. Lightwave Technol. LT-9, 92–100 (1991).
[CrossRef]

1989

T. Fujiwara, S. Sato, H. Mori, “Wavelength dependence of photorefractive effect in Ti-indiffused LiNbO3 waveguides,” Appl. Phys. Lett. 54, 975–977 (1989).
[CrossRef]

1985

R. A. Becker, R. C. Williamson, “Photorefractive effects in LiNbO3 channel waveguides: Model and experimental verification,” Appl. Phys. Lett. 47, 1024–1026 (1985).
[CrossRef]

L. M. Walpita, “Solutions for planar optical waveguide equations by selecting zero elements in a characteristic matrix,” J. Opt. Soc. Am. A 2, 595–602 (1985).
[CrossRef]

1984

J. Čtyroký, M. Holfman, J. Janta, J. Schrőfel, “3D analysis of LiNbO3:Ti channel waveguides and directional coupler,” IEEE J Quantum Electron. QE-20, 400–409 (1984).
[CrossRef]

1983

M. D. Feit, J. A. Fleck, “Comparison of calculated and measured performance of diffused channel-waveguide couplers,” J. Opt. Soc. Am. 73, 1296–1304 (1983).
[CrossRef]

M. N. Armenise, C. Canali, M. De Sario, A. Carnera, P. Mazzoldi, G. Celotti, “Characterization of (Ti0.65Nb0.35) O2 compound as a source for Ti diffusion during Ti:LiNbO3 optical waveguide fabrication,” J. Appl. Phys. 54, 62–70 (1983).
[CrossRef]

1980

1979

N. P. Barnes, R. C. Eckhardt, D. J. Gettemy, L. B. Edgett, “Absorption coefficients and the temperature variation of the refractive index difference of nonlinear optical crystals,” IEEE J. Quantum Electron. QE-15, 1074–1076 (1979).
[CrossRef]

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electro-optic crystals I. Steady-state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

1978

R. L. Holman, P. J. Cressman, J. F. Revelli, “Chemical control of optical damage in lithium niobate,” Appl. Phys. Lett. 32, 280–283 (1978).
[CrossRef]

P. Günter, F. Micheron, “Photorefractive effects and photocurrents in KNbO3:Fe,” Ferroelectrics 18, 27–38 (1978).
[CrossRef]

E. Krätzig, “Photorefractive effects and photoconductivity in LiNbO3:Fe,” Ferroelectrics 21, 635–636 (1978).
[CrossRef]

A. M. Glass, “The photorefractive effect,” Opt. Eng. 17, 470–479 (1978).

M. Fukuma, J. Noda, H. Iwasaki, “Optical properties in titanium-diffused LiNbO3 strip waveguides,” J. Appl. Phys. 49, 3693–3698 (1978).
[CrossRef]

1977

H. Kurz, E. Krätzig, W. Keune, H. Engelmann, U. Gonser, B. Dischler, A. Räuber, “Photorefractive centers in LiNbO3, studied by optical-, Mössbauer-, and EPR-methods,” Appl. Phys. 12, 355–368 (1977).
[CrossRef]

C. M. Verber, N. F. Hartman, A. M. Glass, “Formation of integrated optics components by multiphoton photorefractive-effect processes,” Appl. Phys. Lett. 30, 272–273 (1977).
[CrossRef]

1974

A. M. Glass, D. vonder Linde, T. J. Negran, “High-voltage bulk photovoltaic effect and the photorefractive process in LiNbO3,” Appl. Phys. Lett. 25, 233–235 (1974).
[CrossRef]

A. M. Glass, D. von der Linde, T. J. Negran, “High-voltage bulk photovoltaic effect and the photorefractive process in LiNbO3,” Appl. Phys. Lett. 25, 233–235 (1974).
[CrossRef]

D. F. Nelson, R. M. Mikulyak, “Refractive indices of congruently melting lithium niobate,” J. Appl. Phys. 45, 3688–3689 (1974).
[CrossRef]

1973

1971

G. E. Peterson, A. M. Glass, T. J. Negran, “Control of the susceptibility of lithium niobate to laser-induced refractive index changes,” Appl. Phys. Lett. 19, 130–132 (1971).
[CrossRef]

R. T. Smith, F. S. Welsh, “Temperature dependence of the elastic, piezoelectric and dielectric constants of lithium tantalate and lithium niobate,” J. Appl. Phys. 42, 2219–2230 (1971).
[CrossRef]

1969

F. S. Chen, “Optically induced change of refractive indices in LiNbO3 and LiTaO3,” J. Appl. Phys. 40, 3389–3396 (1969).
[CrossRef]

1967

G. D. Boyd, W. L. Bond, H. L. Carter, “Refractive index as a function of temperature in LiNbO3,” J. Appl. Phys. 38, 1941–1943 (1967).
[CrossRef]

1966

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, K. Nassau, “Optically induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[CrossRef]

Armenise, M. N.

M. N. Armenise, C. Canali, M. De Sario, A. Carnera, P. Mazzoldi, G. Celotti, “Characterization of (Ti0.65Nb0.35) O2 compound as a source for Ti diffusion during Ti:LiNbO3 optical waveguide fabrication,” J. Appl. Phys. 54, 62–70 (1983).
[CrossRef]

Ashkin, A.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, K. Nassau, “Optically induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[CrossRef]

Ballman, A. A.

A. M. Glass, I. P. Kaminow, A. A. Ballman, D. H. Olson, “Absorption loss and photorefractive-index changes in Ti:LiNbO3 crystals and waveguides,” Appl. Opt. 19, 276–281 (1980).
[CrossRef] [PubMed]

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, K. Nassau, “Optically induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[CrossRef]

Barnes, N. P.

N. P. Barnes, R. C. Eckhardt, D. J. Gettemy, L. B. Edgett, “Absorption coefficients and the temperature variation of the refractive index difference of nonlinear optical crystals,” IEEE J. Quantum Electron. QE-15, 1074–1076 (1979).
[CrossRef]

Becker, R. A.

R. A. Becker, R. C. Williamson, “Photorefractive effects in LiNbO3 channel waveguides: Model and experimental verification,” Appl. Phys. Lett. 47, 1024–1026 (1985).
[CrossRef]

Bond, W. L.

G. D. Boyd, W. L. Bond, H. L. Carter, “Refractive index as a function of temperature in LiNbO3,” J. Appl. Phys. 38, 1941–1943 (1967).
[CrossRef]

Boyd, G. D.

G. D. Boyd, W. L. Bond, H. L. Carter, “Refractive index as a function of temperature in LiNbO3,” J. Appl. Phys. 38, 1941–1943 (1967).
[CrossRef]

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, K. Nassau, “Optically induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[CrossRef]

Canali, C.

M. N. Armenise, C. Canali, M. De Sario, A. Carnera, P. Mazzoldi, G. Celotti, “Characterization of (Ti0.65Nb0.35) O2 compound as a source for Ti diffusion during Ti:LiNbO3 optical waveguide fabrication,” J. Appl. Phys. 54, 62–70 (1983).
[CrossRef]

Carnera, A.

M. N. Armenise, C. Canali, M. De Sario, A. Carnera, P. Mazzoldi, G. Celotti, “Characterization of (Ti0.65Nb0.35) O2 compound as a source for Ti diffusion during Ti:LiNbO3 optical waveguide fabrication,” J. Appl. Phys. 54, 62–70 (1983).
[CrossRef]

Carter, H. L.

G. D. Boyd, W. L. Bond, H. L. Carter, “Refractive index as a function of temperature in LiNbO3,” J. Appl. Phys. 38, 1941–1943 (1967).
[CrossRef]

Celotti, G.

M. N. Armenise, C. Canali, M. De Sario, A. Carnera, P. Mazzoldi, G. Celotti, “Characterization of (Ti0.65Nb0.35) O2 compound as a source for Ti diffusion during Ti:LiNbO3 optical waveguide fabrication,” J. Appl. Phys. 54, 62–70 (1983).
[CrossRef]

Charczenko, W.

W. Charczenko, P. S. Weitzman, H. Klotz, M. Surette, J. M. Dunn, A. R. Mickelson, “Characterization and simulation of proton exchanged integrated optical modulators with various dielectric buffer layers,” J. Lightwave Technol. LT-9, 92–100 (1991).
[CrossRef]

W. Charczenko, “Coupled mode analysis, fabrication and characterization of microwave integrated optical devices,” Ph.D. dissertation (University of Colorado at Boulder, Boulder, Colo., 1990).

Chen, F. S.

F. S. Chen, “Optically induced change of refractive indices in LiNbO3 and LiTaO3,” J. Appl. Phys. 40, 3389–3396 (1969).
[CrossRef]

Cressman, P. J.

R. L. Holman, P. J. Cressman, J. F. Revelli, “Chemical control of optical damage in lithium niobate,” Appl. Phys. Lett. 32, 280–283 (1978).
[CrossRef]

Ctyroký, J.

J. Čtyroký, M. Holfman, J. Janta, J. Schrőfel, “3D analysis of LiNbO3:Ti channel waveguides and directional coupler,” IEEE J Quantum Electron. QE-20, 400–409 (1984).
[CrossRef]

De Sario, M.

M. N. Armenise, C. Canali, M. De Sario, A. Carnera, P. Mazzoldi, G. Celotti, “Characterization of (Ti0.65Nb0.35) O2 compound as a source for Ti diffusion during Ti:LiNbO3 optical waveguide fabrication,” J. Appl. Phys. 54, 62–70 (1983).
[CrossRef]

Dischler, B.

H. Kurz, E. Krätzig, W. Keune, H. Engelmann, U. Gonser, B. Dischler, A. Räuber, “Photorefractive centers in LiNbO3, studied by optical-, Mössbauer-, and EPR-methods,” Appl. Phys. 12, 355–368 (1977).
[CrossRef]

Dunn, J. M.

W. Charczenko, P. S. Weitzman, H. Klotz, M. Surette, J. M. Dunn, A. R. Mickelson, “Characterization and simulation of proton exchanged integrated optical modulators with various dielectric buffer layers,” J. Lightwave Technol. LT-9, 92–100 (1991).
[CrossRef]

Dziedzic, J. M.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, K. Nassau, “Optically induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[CrossRef]

Eckhardt, R. C.

N. P. Barnes, R. C. Eckhardt, D. J. Gettemy, L. B. Edgett, “Absorption coefficients and the temperature variation of the refractive index difference of nonlinear optical crystals,” IEEE J. Quantum Electron. QE-15, 1074–1076 (1979).
[CrossRef]

Edgett, L. B.

N. P. Barnes, R. C. Eckhardt, D. J. Gettemy, L. B. Edgett, “Absorption coefficients and the temperature variation of the refractive index difference of nonlinear optical crystals,” IEEE J. Quantum Electron. QE-15, 1074–1076 (1979).
[CrossRef]

Engelmann, H.

H. Kurz, E. Krätzig, W. Keune, H. Engelmann, U. Gonser, B. Dischler, A. Räuber, “Photorefractive centers in LiNbO3, studied by optical-, Mössbauer-, and EPR-methods,” Appl. Phys. 12, 355–368 (1977).
[CrossRef]

Feit, M. D.

Fleck, J. A.

Fujiwara, T.

T. Fujiwara, S. Sato, H. Mori, “Wavelength dependence of photorefractive effect in Ti-indiffused LiNbO3 waveguides,” Appl. Phys. Lett. 54, 975–977 (1989).
[CrossRef]

Fukuma, M.

M. Fukuma, J. Noda, H. Iwasaki, “Optical properties in titanium-diffused LiNbO3 strip waveguides,” J. Appl. Phys. 49, 3693–3698 (1978).
[CrossRef]

Gettemy, D. J.

N. P. Barnes, R. C. Eckhardt, D. J. Gettemy, L. B. Edgett, “Absorption coefficients and the temperature variation of the refractive index difference of nonlinear optical crystals,” IEEE J. Quantum Electron. QE-15, 1074–1076 (1979).
[CrossRef]

Glass, A. M.

A. M. Glass, I. P. Kaminow, A. A. Ballman, D. H. Olson, “Absorption loss and photorefractive-index changes in Ti:LiNbO3 crystals and waveguides,” Appl. Opt. 19, 276–281 (1980).
[CrossRef] [PubMed]

A. M. Glass, “The photorefractive effect,” Opt. Eng. 17, 470–479 (1978).

C. M. Verber, N. F. Hartman, A. M. Glass, “Formation of integrated optics components by multiphoton photorefractive-effect processes,” Appl. Phys. Lett. 30, 272–273 (1977).
[CrossRef]

A. M. Glass, D. von der Linde, T. J. Negran, “High-voltage bulk photovoltaic effect and the photorefractive process in LiNbO3,” Appl. Phys. Lett. 25, 233–235 (1974).
[CrossRef]

A. M. Glass, D. vonder Linde, T. J. Negran, “High-voltage bulk photovoltaic effect and the photorefractive process in LiNbO3,” Appl. Phys. Lett. 25, 233–235 (1974).
[CrossRef]

G. E. Peterson, A. M. Glass, T. J. Negran, “Control of the susceptibility of lithium niobate to laser-induced refractive index changes,” Appl. Phys. Lett. 19, 130–132 (1971).
[CrossRef]

Gonser, U.

H. Kurz, E. Krätzig, W. Keune, H. Engelmann, U. Gonser, B. Dischler, A. Räuber, “Photorefractive centers in LiNbO3, studied by optical-, Mössbauer-, and EPR-methods,” Appl. Phys. 12, 355–368 (1977).
[CrossRef]

Günter, P.

P. Günter, F. Micheron, “Photorefractive effects and photocurrents in KNbO3:Fe,” Ferroelectrics 18, 27–38 (1978).
[CrossRef]

P. Günter, J. P. Huignard, Photorefractive Materials and Their Application (Springer-Verlag, Berlin, 1988), Vol. I, p. 21.

Hartman, N. F.

C. M. Verber, N. F. Hartman, A. M. Glass, “Formation of integrated optics components by multiphoton photorefractive-effect processes,” Appl. Phys. Lett. 30, 272–273 (1977).
[CrossRef]

Holfman, M.

J. Čtyroký, M. Holfman, J. Janta, J. Schrőfel, “3D analysis of LiNbO3:Ti channel waveguides and directional coupler,” IEEE J Quantum Electron. QE-20, 400–409 (1984).
[CrossRef]

Holman, R. L.

R. L. Holman, P. J. Cressman, J. F. Revelli, “Chemical control of optical damage in lithium niobate,” Appl. Phys. Lett. 32, 280–283 (1978).
[CrossRef]

Huignard, J. P.

P. Günter, J. P. Huignard, Photorefractive Materials and Their Application (Springer-Verlag, Berlin, 1988), Vol. I, p. 21.

Iwasaki, H.

M. Fukuma, J. Noda, H. Iwasaki, “Optical properties in titanium-diffused LiNbO3 strip waveguides,” J. Appl. Phys. 49, 3693–3698 (1978).
[CrossRef]

Janta, J.

J. Čtyroký, M. Holfman, J. Janta, J. Schrőfel, “3D analysis of LiNbO3:Ti channel waveguides and directional coupler,” IEEE J Quantum Electron. QE-20, 400–409 (1984).
[CrossRef]

Johnson, D. C.

Kaminow, I. P.

Keune, W.

H. Kurz, E. Krätzig, W. Keune, H. Engelmann, U. Gonser, B. Dischler, A. Räuber, “Photorefractive centers in LiNbO3, studied by optical-, Mössbauer-, and EPR-methods,” Appl. Phys. 12, 355–368 (1977).
[CrossRef]

Klotz, H.

W. Charczenko, P. S. Weitzman, H. Klotz, M. Surette, J. M. Dunn, A. R. Mickelson, “Characterization and simulation of proton exchanged integrated optical modulators with various dielectric buffer layers,” J. Lightwave Technol. LT-9, 92–100 (1991).
[CrossRef]

Krätzig, E.

E. Krätzig, “Photorefractive effects and photoconductivity in LiNbO3:Fe,” Ferroelectrics 21, 635–636 (1978).
[CrossRef]

H. Kurz, E. Krätzig, W. Keune, H. Engelmann, U. Gonser, B. Dischler, A. Räuber, “Photorefractive centers in LiNbO3, studied by optical-, Mössbauer-, and EPR-methods,” Appl. Phys. 12, 355–368 (1977).
[CrossRef]

Kukhtarev, N. V.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electro-optic crystals I. Steady-state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Kurz, H.

H. Kurz, E. Krätzig, W. Keune, H. Engelmann, U. Gonser, B. Dischler, A. Räuber, “Photorefractive centers in LiNbO3, studied by optical-, Mössbauer-, and EPR-methods,” Appl. Phys. 12, 355–368 (1977).
[CrossRef]

Levinstein, J. J.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, K. Nassau, “Optically induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[CrossRef]

Markov, V. B.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electro-optic crystals I. Steady-state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Mazzoldi, P.

M. N. Armenise, C. Canali, M. De Sario, A. Carnera, P. Mazzoldi, G. Celotti, “Characterization of (Ti0.65Nb0.35) O2 compound as a source for Ti diffusion during Ti:LiNbO3 optical waveguide fabrication,” J. Appl. Phys. 54, 62–70 (1983).
[CrossRef]

Micheron, F.

P. Günter, F. Micheron, “Photorefractive effects and photocurrents in KNbO3:Fe,” Ferroelectrics 18, 27–38 (1978).
[CrossRef]

Mickelson, A. R.

W. Charczenko, P. S. Weitzman, H. Klotz, M. Surette, J. M. Dunn, A. R. Mickelson, “Characterization and simulation of proton exchanged integrated optical modulators with various dielectric buffer layers,” J. Lightwave Technol. LT-9, 92–100 (1991).
[CrossRef]

A. R. Mickelson, Guided Wave Optics, (Van Nostrand Reinhold, 1993).
[CrossRef]

Mikulyak, R. M.

D. F. Nelson, R. M. Mikulyak, “Refractive indices of congruently melting lithium niobate,” J. Appl. Phys. 45, 3688–3689 (1974).
[CrossRef]

Mori, H.

T. Fujiwara, S. Sato, H. Mori, “Wavelength dependence of photorefractive effect in Ti-indiffused LiNbO3 waveguides,” Appl. Phys. Lett. 54, 975–977 (1989).
[CrossRef]

Nassau, K.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, K. Nassau, “Optically induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[CrossRef]

Negran, T. J.

A. M. Glass, D. vonder Linde, T. J. Negran, “High-voltage bulk photovoltaic effect and the photorefractive process in LiNbO3,” Appl. Phys. Lett. 25, 233–235 (1974).
[CrossRef]

A. M. Glass, D. von der Linde, T. J. Negran, “High-voltage bulk photovoltaic effect and the photorefractive process in LiNbO3,” Appl. Phys. Lett. 25, 233–235 (1974).
[CrossRef]

G. E. Peterson, A. M. Glass, T. J. Negran, “Control of the susceptibility of lithium niobate to laser-induced refractive index changes,” Appl. Phys. Lett. 19, 130–132 (1971).
[CrossRef]

Nelson, D. F.

D. F. Nelson, R. M. Mikulyak, “Refractive indices of congruently melting lithium niobate,” J. Appl. Phys. 45, 3688–3689 (1974).
[CrossRef]

Noda, J.

M. Fukuma, J. Noda, H. Iwasaki, “Optical properties in titanium-diffused LiNbO3 strip waveguides,” J. Appl. Phys. 49, 3693–3698 (1978).
[CrossRef]

Odulov, S. G.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electro-optic crystals I. Steady-state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Olson, D. H.

Peterson, G. E.

G. E. Peterson, A. M. Glass, T. J. Negran, “Control of the susceptibility of lithium niobate to laser-induced refractive index changes,” Appl. Phys. Lett. 19, 130–132 (1971).
[CrossRef]

Räuber, A.

H. Kurz, E. Krätzig, W. Keune, H. Engelmann, U. Gonser, B. Dischler, A. Räuber, “Photorefractive centers in LiNbO3, studied by optical-, Mössbauer-, and EPR-methods,” Appl. Phys. 12, 355–368 (1977).
[CrossRef]

Revelli, J. F.

R. L. Holman, P. J. Cressman, J. F. Revelli, “Chemical control of optical damage in lithium niobate,” Appl. Phys. Lett. 32, 280–283 (1978).
[CrossRef]

Sato, S.

T. Fujiwara, S. Sato, H. Mori, “Wavelength dependence of photorefractive effect in Ti-indiffused LiNbO3 waveguides,” Appl. Phys. Lett. 54, 975–977 (1989).
[CrossRef]

Schrofel, J.

J. Čtyroký, M. Holfman, J. Janta, J. Schrőfel, “3D analysis of LiNbO3:Ti channel waveguides and directional coupler,” IEEE J Quantum Electron. QE-20, 400–409 (1984).
[CrossRef]

Smith, R. G.

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, K. Nassau, “Optically induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[CrossRef]

Smith, R. T.

R. T. Smith, F. S. Welsh, “Temperature dependence of the elastic, piezoelectric and dielectric constants of lithium tantalate and lithium niobate,” J. Appl. Phys. 42, 2219–2230 (1971).
[CrossRef]

Soskin, M. S.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electro-optic crystals I. Steady-state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Surette, M.

W. Charczenko, P. S. Weitzman, H. Klotz, M. Surette, J. M. Dunn, A. R. Mickelson, “Characterization and simulation of proton exchanged integrated optical modulators with various dielectric buffer layers,” J. Lightwave Technol. LT-9, 92–100 (1991).
[CrossRef]

Verber, C. M.

C. M. Verber, N. F. Hartman, A. M. Glass, “Formation of integrated optics components by multiphoton photorefractive-effect processes,” Appl. Phys. Lett. 30, 272–273 (1977).
[CrossRef]

Vinetskii, V. L.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electro-optic crystals I. Steady-state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

von der Linde, D.

A. M. Glass, D. von der Linde, T. J. Negran, “High-voltage bulk photovoltaic effect and the photorefractive process in LiNbO3,” Appl. Phys. Lett. 25, 233–235 (1974).
[CrossRef]

vonder Linde, D.

A. M. Glass, D. vonder Linde, T. J. Negran, “High-voltage bulk photovoltaic effect and the photorefractive process in LiNbO3,” Appl. Phys. Lett. 25, 233–235 (1974).
[CrossRef]

Walpita, L. M.

Weber, M. J.

M. J. Weber, Handbook of Laser Science and Technology Volume IV. Optical Materials Part 2 (CRC, Boca Raton, Fla., 1980).

Weitzman, P. S.

W. Charczenko, P. S. Weitzman, H. Klotz, M. Surette, J. M. Dunn, A. R. Mickelson, “Characterization and simulation of proton exchanged integrated optical modulators with various dielectric buffer layers,” J. Lightwave Technol. LT-9, 92–100 (1991).
[CrossRef]

Welsh, F. S.

R. T. Smith, F. S. Welsh, “Temperature dependence of the elastic, piezoelectric and dielectric constants of lithium tantalate and lithium niobate,” J. Appl. Phys. 42, 2219–2230 (1971).
[CrossRef]

Williamson, R. C.

R. A. Becker, R. C. Williamson, “Photorefractive effects in LiNbO3 channel waveguides: Model and experimental verification,” Appl. Phys. Lett. 47, 1024–1026 (1985).
[CrossRef]

Yariv, A.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), p. 232.

Yeh, P.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), p. 232.

Appl. Opt.

Appl. Phys.

H. Kurz, E. Krätzig, W. Keune, H. Engelmann, U. Gonser, B. Dischler, A. Räuber, “Photorefractive centers in LiNbO3, studied by optical-, Mössbauer-, and EPR-methods,” Appl. Phys. 12, 355–368 (1977).
[CrossRef]

Appl. Phys. Lett.

A. M. Glass, D. vonder Linde, T. J. Negran, “High-voltage bulk photovoltaic effect and the photorefractive process in LiNbO3,” Appl. Phys. Lett. 25, 233–235 (1974).
[CrossRef]

A. Ashkin, G. D. Boyd, J. M. Dziedzic, R. G. Smith, A. A. Ballman, J. J. Levinstein, K. Nassau, “Optically induced refractive index inhomogeneities in LiNbO3 and LiTaO3,” Appl. Phys. Lett. 9, 72–74 (1966).
[CrossRef]

G. E. Peterson, A. M. Glass, T. J. Negran, “Control of the susceptibility of lithium niobate to laser-induced refractive index changes,” Appl. Phys. Lett. 19, 130–132 (1971).
[CrossRef]

A. M. Glass, D. von der Linde, T. J. Negran, “High-voltage bulk photovoltaic effect and the photorefractive process in LiNbO3,” Appl. Phys. Lett. 25, 233–235 (1974).
[CrossRef]

R. L. Holman, P. J. Cressman, J. F. Revelli, “Chemical control of optical damage in lithium niobate,” Appl. Phys. Lett. 32, 280–283 (1978).
[CrossRef]

R. A. Becker, R. C. Williamson, “Photorefractive effects in LiNbO3 channel waveguides: Model and experimental verification,” Appl. Phys. Lett. 47, 1024–1026 (1985).
[CrossRef]

T. Fujiwara, S. Sato, H. Mori, “Wavelength dependence of photorefractive effect in Ti-indiffused LiNbO3 waveguides,” Appl. Phys. Lett. 54, 975–977 (1989).
[CrossRef]

C. M. Verber, N. F. Hartman, A. M. Glass, “Formation of integrated optics components by multiphoton photorefractive-effect processes,” Appl. Phys. Lett. 30, 272–273 (1977).
[CrossRef]

Ferroelectrics

P. Günter, F. Micheron, “Photorefractive effects and photocurrents in KNbO3:Fe,” Ferroelectrics 18, 27–38 (1978).
[CrossRef]

E. Krätzig, “Photorefractive effects and photoconductivity in LiNbO3:Fe,” Ferroelectrics 21, 635–636 (1978).
[CrossRef]

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electro-optic crystals I. Steady-state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

IEEE J Quantum Electron.

J. Čtyroký, M. Holfman, J. Janta, J. Schrőfel, “3D analysis of LiNbO3:Ti channel waveguides and directional coupler,” IEEE J Quantum Electron. QE-20, 400–409 (1984).
[CrossRef]

IEEE J. Quantum Electron.

N. P. Barnes, R. C. Eckhardt, D. J. Gettemy, L. B. Edgett, “Absorption coefficients and the temperature variation of the refractive index difference of nonlinear optical crystals,” IEEE J. Quantum Electron. QE-15, 1074–1076 (1979).
[CrossRef]

J. Appl. Phys.

M. Fukuma, J. Noda, H. Iwasaki, “Optical properties in titanium-diffused LiNbO3 strip waveguides,” J. Appl. Phys. 49, 3693–3698 (1978).
[CrossRef]

G. D. Boyd, W. L. Bond, H. L. Carter, “Refractive index as a function of temperature in LiNbO3,” J. Appl. Phys. 38, 1941–1943 (1967).
[CrossRef]

M. N. Armenise, C. Canali, M. De Sario, A. Carnera, P. Mazzoldi, G. Celotti, “Characterization of (Ti0.65Nb0.35) O2 compound as a source for Ti diffusion during Ti:LiNbO3 optical waveguide fabrication,” J. Appl. Phys. 54, 62–70 (1983).
[CrossRef]

D. F. Nelson, R. M. Mikulyak, “Refractive indices of congruently melting lithium niobate,” J. Appl. Phys. 45, 3688–3689 (1974).
[CrossRef]

F. S. Chen, “Optically induced change of refractive indices in LiNbO3 and LiTaO3,” J. Appl. Phys. 40, 3389–3396 (1969).
[CrossRef]

R. T. Smith, F. S. Welsh, “Temperature dependence of the elastic, piezoelectric and dielectric constants of lithium tantalate and lithium niobate,” J. Appl. Phys. 42, 2219–2230 (1971).
[CrossRef]

J. Lightwave Technol.

W. Charczenko, P. S. Weitzman, H. Klotz, M. Surette, J. M. Dunn, A. R. Mickelson, “Characterization and simulation of proton exchanged integrated optical modulators with various dielectric buffer layers,” J. Lightwave Technol. LT-9, 92–100 (1991).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Eng.

A. M. Glass, “The photorefractive effect,” Opt. Eng. 17, 470–479 (1978).

Other

W. Charczenko, “Coupled mode analysis, fabrication and characterization of microwave integrated optical devices,” Ph.D. dissertation (University of Colorado at Boulder, Boulder, Colo., 1990).

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), p. 232.

LiNbO3 Optical Grade Substrate Data Sheet (Crystal Technology, Inc., Palo Alto, Calif., 1991).

P. Günter, J. P. Huignard, Photorefractive Materials and Their Application (Springer-Verlag, Berlin, 1988), Vol. I, p. 21.

A. R. Mickelson, Guided Wave Optics, (Van Nostrand Reinhold, 1993).
[CrossRef]

M. J. Weber, Handbook of Laser Science and Technology Volume IV. Optical Materials Part 2 (CRC, Boca Raton, Fla., 1980).

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Figures (11)

Fig. 1
Fig. 1

Energy-band diagram of Fe:LiNbO3 crystal at room temperature.

Fig. 2
Fig. 2

Arrangement for making the photorefractive near-field and power measurements.

Fig. 3
Fig. 3

(a) Magnified near-field (×400) image from the CCD camera. (b) Intensity scan along the horizontal direction across the maximum intensity point. (c) Intensity scan along the vertical direction across the maximum intensity point. (TM mode, z-cut, 3-μm-wide and 200-Å-thick TiO2 strip, 1000-°C diffusion temperature, 6-h diffusion time, and λ = 0.53 μm.)

Fig. 4
Fig. 4

Measured (●) and calculated (○) FWHM for different strip widths: (a) for TE excitation, (b) for TM excitation.

Fig. 5
Fig. 5

(a) Measured (●) and calculated (○) FWHM variations as a function of coupled-in intensity. (b) Measured (●) and calculated (○) coupled-out power variations as a function of coupled-in intensity. (TM excitation, z-cut, 200-Å-thick and 3-μm-wide TiO2 strip, 1000-°C diffusion temperature, and 6-h diffusion time).

Fig. 6
Fig. 6

(a) Prototype Ti:LiNbO3 channel waveguide. (b) Geometry of TiO2 strip used to fabricate a Ti:LiNbO3 channel waveguide and the choice of coordinate axes.

Fig. 7
Fig. 7

Cross section of a Ti:LiNbO3 channel waveguide of diffused waveguide shape, and the defined coordinate used in the photorefractive calculations.

Fig. 8
Fig. 8

Normalized three-dimensional plot of the intensity distribution for the TM mode of a 3-μm-wide and 200-Å-thick TiO2 strip, z-cut Ti:LiNbO3 channel waveguide with diffusion temperature at 1000 °C and 6-h diffusion time at low input intensity (< 10 W/cm2).

Fig. 9
Fig. 9

Normalized three-dimensional plot for the ionized-donor and free-electron number density difference (ND+ncarrier) under the illumination I(x, y) shown in Fig. 8. (Input intensity 60 W/cm2).

Fig. 10
Fig. 10

Normalized three-dimensional plot for the space-charge field (ESCz) calculated by integrating the function (ND+ncarrier) (Fig. 9) along the crystal’s z axis.

Fig. 11
Fig. 11

Normalized 3-D plot of a new TM mode profile of the channel waveguide of Fig. 9, after the electro-optic effect caused by the space-charge field ESCz in Fig. 10.

Equations (19)

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

Fe 2 + + h ν Fe 3 + + e -
C ( x , y , t ) = C p H ( x ) G ( y ) ,
H ( x ) = 1 2 [ erf ( w 2 + x B x ) + erf ( w 2 - x B x ) ] .
G ( y ) = exp ( - y 2 B y 2 ) .
Δ n = ( d n / d c )             ( weight - percent ratio of TiO 2 and LiNbO 3 ) = ( d n / d c ) [ 9.3 × 10 - 2 τ ( nm ) B y ( μ m ) H ( x ) G ( y ) ] ,
n ( x , y ) = n b + Δ n ( x , y ) ,
n c t = N D + t - 1 e j
N D + t = ( S I + β ) ( N D - N D + ) - γ R n c N D +
j = e μ n c [ E SC - K T e log ( n c ) ] + p I e c
( E SC ) = - 4 π e ( n c + N A - N D + )
N D + I N D γ R S n c + I
E sc K T e 1 n c n c y e c - p I e μ n c e c = E s c y e c
E sc y - ( 4 π e ) ( n c - S I N D γ R n c + S I ) e c = E s c y y e c
2 n c y 2 = [ 4 π e ( K T e ) ] ( n c ) [ N D 1 + ( γ R S I ) n c - n c ] + ( p μ K T ) ( I y - I n c n c y ) + 1 n c ( n c y ) 2 .
Δ n PR = - ½ n o 3 r 13 E s c y ,
Δ n PR = - ½ n e 3 r 33 E s c y ,
κ = - + 0 + ψ calculated ( x , y ) - ψ measured ( x , y ) 2 d x d y - + 0 + ψ measured ( x , y ) 2 d x d y .
Δ T τ L P T β a C P m ,
Δ T = 1.444 × 10 4 × P T ( watts ) .

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