Abstract

Magnesium diffusion can be used to optimize the characteristics and performance of a Ti:LiNbO3 Mach–Zehnder modulator. Suitable use of titanium/magnesium double diffusion reduces fiber–waveguide coupling loss, minimizes the modulator size by increasing the bend radius of curvature without increasing bend losses, and decreases separation of the modulator arms. The proposed method also makes it possible to reduce the modulating voltage by improvement of guided-wave lateral confinement. Secondary ion mass spectrometry and m-line techniques are used to characterize Ti/Mg:LiNbO3 waveguides. A numerical optimization procedure based on the full vectorial beam-propagation method is presented.

© 1996 Optical Society of America

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  1. R. C. Alferness, “Guided-wave devices for optical communication,” IEEE J. Quantum Electron. QE-17, 946–959 (1981).
  2. J. Noda, “Ti diffused LiNbO3 waveguides and modulators,” J. Opt. Commun. 1, 64–73 (1980).
  3. M. N. Armenise, “Fabrication techniques of lithium niobate waveguides,” Proc. Inst. Electr. Eng. J 135, 85–91 (1988).
  4. F. Caccavale, P. Chakraborty, A. Capobianco, G. Gianello, I. Mansour, “Characterization and optimization of Ti-diffused LiNbO3 optical waveguides by second diffusion of magnesium,” J. Appl. Phys. 78, 187–193 (1995).
  5. K. Komatsu, S. Yamazaki, M. Kondo, Y. Ohta, “Low-loss broad-band LiNbO3 guided-wave phase modulators using titanium/magnesium double diffusion method,” IEEE J. Lightwave Technol. LT-5, 1239–1245 (1987).
  6. F. Caccavale, P. Chakraborty, I. Mansour, G. Gianello, M. Mazzoleni, M. Elena, “A secondary-ion-mass spectrometry study of magnesium diffusion in lithium niobate,” J. Appl. Phys. 76, 7552–7558 (1994).
  7. C. G. Someda, “Radiation of discrete beams from curved single-mode fibers,” Electron. Lett. 13, 712–713 (1977).
  8. S. K. Korotky, E. A. J. Marcatili, J. J. Veselka, R. H. Besworth, “Greatly reduced losses for small-radius bends in Ti:LiNbO3 waveguides,” Appl. Phys. Lett. 48, 92–94 (1986).
  9. B. Schuüppert, “Reduction of bend losses in Ti:LiNbO3 waveguides through MgO double diffusion,” Electron. Lett. 23, 797–798 (1987).
  10. M. Majd, B. Schuüppert, K. Petermann, “Low-loss Ti:LiNbO3 waveguide bends prepared by MgO in-diffusion,” IEEE J. Lightwave Technol. 8, 1670–1674 (1990).
  11. M. Majd, B. Schüppert, K. Petermann, “90 S-bends in Ti:LiNbO3 waveguides with low losses,” IEEE Photon. Tech-nol. Lett. 5, 806–808 (1993).
  12. I. Mansour, C. G. Someda, “Numerical optimization procedure for low-loss sharp bends in MgO Co-doped Ti:LiNbO3 waveguides,” IEEE Photon. Technol. Lett. 7, 81–83 (1995).
  13. C. De Angelis, “Numerical modelling of bends in optical rib waveguides,” European Transactions on Telecomm. and Related Tech. 3, 73–75 (1992).
  14. E. G. Neumann, W. Richter, “Sharp bends with low losses in dielectric optical waveguides,” Appl. Opt. 22, 1016–1022 (1983).
  15. N. Tanaka, T. Banno, K. Takahashi, T. Shiota, K. Inada, “MgO/Ti bilaterally diffused LiNbO3 optical switch,” Appl. Opt. 29, 5090–5095 (1990).
  16. F. Caccavale, P. Chakraborty, A. Quaranta, I. Mansour, G. Gianello, S. Bosso, R. Corsini, G. Mussi, “Secondary ion mass spectrometry and near field studies of Ti:LiNbO3 optical waveguides,” J. Appl. Phys. 78, 5345–5350 (1995).
  17. F. Gonella, Dipartimento di Fisica, Università Degali Studi di Padova, Padova, Italy35131 (personal communication, 1994).
  18. J. Noda, M. Fukuma, S. Saito, “Effect of Mg diffusion on Ti-diffused LiNbO3 waveguide,” J. Appl. Phys. 49, 3150–3154 (1978).
  19. M. Heiblum, J. H. Harris, “Analysis of curved optical waveguides by conformal transformation,” IEEE J. Quantum Electron. QE-11, 75–84 (1975).
  20. J. A. Nelder, R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1987).
  21. J. Crank, The Mathematics of Diffusion (Oxford University, New York, 1975), pp. 1–21.
  22. M. S. Stern, “Semi-vectorial polarised finite difference method for optical waveguides with arbitrary index profiles,” Proc. Inst. Electr. Eng. J. 135, 56–63 (1988).
  23. S. Steinberg, M. Guntau, R. Göring, W. Karthe, “Calculation of electrooptically induced refractive index changes of integrated optic devices by the finite-element-method,” J. Opt. Commun. 12, 125–129 (1991).

1995 (3)

F. Caccavale, P. Chakraborty, A. Capobianco, G. Gianello, I. Mansour, “Characterization and optimization of Ti-diffused LiNbO3 optical waveguides by second diffusion of magnesium,” J. Appl. Phys. 78, 187–193 (1995).

I. Mansour, C. G. Someda, “Numerical optimization procedure for low-loss sharp bends in MgO Co-doped Ti:LiNbO3 waveguides,” IEEE Photon. Technol. Lett. 7, 81–83 (1995).

F. Caccavale, P. Chakraborty, A. Quaranta, I. Mansour, G. Gianello, S. Bosso, R. Corsini, G. Mussi, “Secondary ion mass spectrometry and near field studies of Ti:LiNbO3 optical waveguides,” J. Appl. Phys. 78, 5345–5350 (1995).

1994 (1)

F. Caccavale, P. Chakraborty, I. Mansour, G. Gianello, M. Mazzoleni, M. Elena, “A secondary-ion-mass spectrometry study of magnesium diffusion in lithium niobate,” J. Appl. Phys. 76, 7552–7558 (1994).

1993 (1)

M. Majd, B. Schüppert, K. Petermann, “90 S-bends in Ti:LiNbO3 waveguides with low losses,” IEEE Photon. Tech-nol. Lett. 5, 806–808 (1993).

1992 (1)

C. De Angelis, “Numerical modelling of bends in optical rib waveguides,” European Transactions on Telecomm. and Related Tech. 3, 73–75 (1992).

1991 (1)

S. Steinberg, M. Guntau, R. Göring, W. Karthe, “Calculation of electrooptically induced refractive index changes of integrated optic devices by the finite-element-method,” J. Opt. Commun. 12, 125–129 (1991).

1990 (2)

M. Majd, B. Schuüppert, K. Petermann, “Low-loss Ti:LiNbO3 waveguide bends prepared by MgO in-diffusion,” IEEE J. Lightwave Technol. 8, 1670–1674 (1990).

N. Tanaka, T. Banno, K. Takahashi, T. Shiota, K. Inada, “MgO/Ti bilaterally diffused LiNbO3 optical switch,” Appl. Opt. 29, 5090–5095 (1990).

1988 (2)

M. N. Armenise, “Fabrication techniques of lithium niobate waveguides,” Proc. Inst. Electr. Eng. J 135, 85–91 (1988).

M. S. Stern, “Semi-vectorial polarised finite difference method for optical waveguides with arbitrary index profiles,” Proc. Inst. Electr. Eng. J. 135, 56–63 (1988).

1987 (3)

J. A. Nelder, R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1987).

K. Komatsu, S. Yamazaki, M. Kondo, Y. Ohta, “Low-loss broad-band LiNbO3 guided-wave phase modulators using titanium/magnesium double diffusion method,” IEEE J. Lightwave Technol. LT-5, 1239–1245 (1987).

B. Schuüppert, “Reduction of bend losses in Ti:LiNbO3 waveguides through MgO double diffusion,” Electron. Lett. 23, 797–798 (1987).

1986 (1)

S. K. Korotky, E. A. J. Marcatili, J. J. Veselka, R. H. Besworth, “Greatly reduced losses for small-radius bends in Ti:LiNbO3 waveguides,” Appl. Phys. Lett. 48, 92–94 (1986).

1983 (1)

1981 (1)

R. C. Alferness, “Guided-wave devices for optical communication,” IEEE J. Quantum Electron. QE-17, 946–959 (1981).

1980 (1)

J. Noda, “Ti diffused LiNbO3 waveguides and modulators,” J. Opt. Commun. 1, 64–73 (1980).

1978 (1)

J. Noda, M. Fukuma, S. Saito, “Effect of Mg diffusion on Ti-diffused LiNbO3 waveguide,” J. Appl. Phys. 49, 3150–3154 (1978).

1977 (1)

C. G. Someda, “Radiation of discrete beams from curved single-mode fibers,” Electron. Lett. 13, 712–713 (1977).

1975 (1)

M. Heiblum, J. H. Harris, “Analysis of curved optical waveguides by conformal transformation,” IEEE J. Quantum Electron. QE-11, 75–84 (1975).

Alferness, R. C.

R. C. Alferness, “Guided-wave devices for optical communication,” IEEE J. Quantum Electron. QE-17, 946–959 (1981).

Armenise, M. N.

M. N. Armenise, “Fabrication techniques of lithium niobate waveguides,” Proc. Inst. Electr. Eng. J 135, 85–91 (1988).

Banno, T.

Besworth, R. H.

S. K. Korotky, E. A. J. Marcatili, J. J. Veselka, R. H. Besworth, “Greatly reduced losses for small-radius bends in Ti:LiNbO3 waveguides,” Appl. Phys. Lett. 48, 92–94 (1986).

Bosso, S.

F. Caccavale, P. Chakraborty, A. Quaranta, I. Mansour, G. Gianello, S. Bosso, R. Corsini, G. Mussi, “Secondary ion mass spectrometry and near field studies of Ti:LiNbO3 optical waveguides,” J. Appl. Phys. 78, 5345–5350 (1995).

Caccavale, F.

F. Caccavale, P. Chakraborty, A. Quaranta, I. Mansour, G. Gianello, S. Bosso, R. Corsini, G. Mussi, “Secondary ion mass spectrometry and near field studies of Ti:LiNbO3 optical waveguides,” J. Appl. Phys. 78, 5345–5350 (1995).

F. Caccavale, P. Chakraborty, A. Capobianco, G. Gianello, I. Mansour, “Characterization and optimization of Ti-diffused LiNbO3 optical waveguides by second diffusion of magnesium,” J. Appl. Phys. 78, 187–193 (1995).

F. Caccavale, P. Chakraborty, I. Mansour, G. Gianello, M. Mazzoleni, M. Elena, “A secondary-ion-mass spectrometry study of magnesium diffusion in lithium niobate,” J. Appl. Phys. 76, 7552–7558 (1994).

Capobianco, A.

F. Caccavale, P. Chakraborty, A. Capobianco, G. Gianello, I. Mansour, “Characterization and optimization of Ti-diffused LiNbO3 optical waveguides by second diffusion of magnesium,” J. Appl. Phys. 78, 187–193 (1995).

Chakraborty, P.

F. Caccavale, P. Chakraborty, A. Capobianco, G. Gianello, I. Mansour, “Characterization and optimization of Ti-diffused LiNbO3 optical waveguides by second diffusion of magnesium,” J. Appl. Phys. 78, 187–193 (1995).

F. Caccavale, P. Chakraborty, A. Quaranta, I. Mansour, G. Gianello, S. Bosso, R. Corsini, G. Mussi, “Secondary ion mass spectrometry and near field studies of Ti:LiNbO3 optical waveguides,” J. Appl. Phys. 78, 5345–5350 (1995).

F. Caccavale, P. Chakraborty, I. Mansour, G. Gianello, M. Mazzoleni, M. Elena, “A secondary-ion-mass spectrometry study of magnesium diffusion in lithium niobate,” J. Appl. Phys. 76, 7552–7558 (1994).

Corsini, R.

F. Caccavale, P. Chakraborty, A. Quaranta, I. Mansour, G. Gianello, S. Bosso, R. Corsini, G. Mussi, “Secondary ion mass spectrometry and near field studies of Ti:LiNbO3 optical waveguides,” J. Appl. Phys. 78, 5345–5350 (1995).

Crank, J.

J. Crank, The Mathematics of Diffusion (Oxford University, New York, 1975), pp. 1–21.

De Angelis, C.

C. De Angelis, “Numerical modelling of bends in optical rib waveguides,” European Transactions on Telecomm. and Related Tech. 3, 73–75 (1992).

Elena, M.

F. Caccavale, P. Chakraborty, I. Mansour, G. Gianello, M. Mazzoleni, M. Elena, “A secondary-ion-mass spectrometry study of magnesium diffusion in lithium niobate,” J. Appl. Phys. 76, 7552–7558 (1994).

Fukuma, M.

J. Noda, M. Fukuma, S. Saito, “Effect of Mg diffusion on Ti-diffused LiNbO3 waveguide,” J. Appl. Phys. 49, 3150–3154 (1978).

Gianello, G.

F. Caccavale, P. Chakraborty, A. Quaranta, I. Mansour, G. Gianello, S. Bosso, R. Corsini, G. Mussi, “Secondary ion mass spectrometry and near field studies of Ti:LiNbO3 optical waveguides,” J. Appl. Phys. 78, 5345–5350 (1995).

F. Caccavale, P. Chakraborty, A. Capobianco, G. Gianello, I. Mansour, “Characterization and optimization of Ti-diffused LiNbO3 optical waveguides by second diffusion of magnesium,” J. Appl. Phys. 78, 187–193 (1995).

F. Caccavale, P. Chakraborty, I. Mansour, G. Gianello, M. Mazzoleni, M. Elena, “A secondary-ion-mass spectrometry study of magnesium diffusion in lithium niobate,” J. Appl. Phys. 76, 7552–7558 (1994).

Gonella, F.

F. Gonella, Dipartimento di Fisica, Università Degali Studi di Padova, Padova, Italy35131 (personal communication, 1994).

Göring, R.

S. Steinberg, M. Guntau, R. Göring, W. Karthe, “Calculation of electrooptically induced refractive index changes of integrated optic devices by the finite-element-method,” J. Opt. Commun. 12, 125–129 (1991).

Guntau, M.

S. Steinberg, M. Guntau, R. Göring, W. Karthe, “Calculation of electrooptically induced refractive index changes of integrated optic devices by the finite-element-method,” J. Opt. Commun. 12, 125–129 (1991).

Harris, J. H.

M. Heiblum, J. H. Harris, “Analysis of curved optical waveguides by conformal transformation,” IEEE J. Quantum Electron. QE-11, 75–84 (1975).

Heiblum, M.

M. Heiblum, J. H. Harris, “Analysis of curved optical waveguides by conformal transformation,” IEEE J. Quantum Electron. QE-11, 75–84 (1975).

Inada, K.

Karthe, W.

S. Steinberg, M. Guntau, R. Göring, W. Karthe, “Calculation of electrooptically induced refractive index changes of integrated optic devices by the finite-element-method,” J. Opt. Commun. 12, 125–129 (1991).

Komatsu, K.

K. Komatsu, S. Yamazaki, M. Kondo, Y. Ohta, “Low-loss broad-band LiNbO3 guided-wave phase modulators using titanium/magnesium double diffusion method,” IEEE J. Lightwave Technol. LT-5, 1239–1245 (1987).

Kondo, M.

K. Komatsu, S. Yamazaki, M. Kondo, Y. Ohta, “Low-loss broad-band LiNbO3 guided-wave phase modulators using titanium/magnesium double diffusion method,” IEEE J. Lightwave Technol. LT-5, 1239–1245 (1987).

Korotky, S. K.

S. K. Korotky, E. A. J. Marcatili, J. J. Veselka, R. H. Besworth, “Greatly reduced losses for small-radius bends in Ti:LiNbO3 waveguides,” Appl. Phys. Lett. 48, 92–94 (1986).

Majd, M.

M. Majd, B. Schüppert, K. Petermann, “90 S-bends in Ti:LiNbO3 waveguides with low losses,” IEEE Photon. Tech-nol. Lett. 5, 806–808 (1993).

M. Majd, B. Schuüppert, K. Petermann, “Low-loss Ti:LiNbO3 waveguide bends prepared by MgO in-diffusion,” IEEE J. Lightwave Technol. 8, 1670–1674 (1990).

Mansour, I.

I. Mansour, C. G. Someda, “Numerical optimization procedure for low-loss sharp bends in MgO Co-doped Ti:LiNbO3 waveguides,” IEEE Photon. Technol. Lett. 7, 81–83 (1995).

F. Caccavale, P. Chakraborty, A. Capobianco, G. Gianello, I. Mansour, “Characterization and optimization of Ti-diffused LiNbO3 optical waveguides by second diffusion of magnesium,” J. Appl. Phys. 78, 187–193 (1995).

F. Caccavale, P. Chakraborty, A. Quaranta, I. Mansour, G. Gianello, S. Bosso, R. Corsini, G. Mussi, “Secondary ion mass spectrometry and near field studies of Ti:LiNbO3 optical waveguides,” J. Appl. Phys. 78, 5345–5350 (1995).

F. Caccavale, P. Chakraborty, I. Mansour, G. Gianello, M. Mazzoleni, M. Elena, “A secondary-ion-mass spectrometry study of magnesium diffusion in lithium niobate,” J. Appl. Phys. 76, 7552–7558 (1994).

Marcatili, E. A. J.

S. K. Korotky, E. A. J. Marcatili, J. J. Veselka, R. H. Besworth, “Greatly reduced losses for small-radius bends in Ti:LiNbO3 waveguides,” Appl. Phys. Lett. 48, 92–94 (1986).

Mazzoleni, M.

F. Caccavale, P. Chakraborty, I. Mansour, G. Gianello, M. Mazzoleni, M. Elena, “A secondary-ion-mass spectrometry study of magnesium diffusion in lithium niobate,” J. Appl. Phys. 76, 7552–7558 (1994).

Mead, R.

J. A. Nelder, R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1987).

Mussi, G.

F. Caccavale, P. Chakraborty, A. Quaranta, I. Mansour, G. Gianello, S. Bosso, R. Corsini, G. Mussi, “Secondary ion mass spectrometry and near field studies of Ti:LiNbO3 optical waveguides,” J. Appl. Phys. 78, 5345–5350 (1995).

Nelder, J. A.

J. A. Nelder, R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1987).

Neumann, E. G.

Noda, J.

J. Noda, “Ti diffused LiNbO3 waveguides and modulators,” J. Opt. Commun. 1, 64–73 (1980).

J. Noda, M. Fukuma, S. Saito, “Effect of Mg diffusion on Ti-diffused LiNbO3 waveguide,” J. Appl. Phys. 49, 3150–3154 (1978).

Ohta, Y.

K. Komatsu, S. Yamazaki, M. Kondo, Y. Ohta, “Low-loss broad-band LiNbO3 guided-wave phase modulators using titanium/magnesium double diffusion method,” IEEE J. Lightwave Technol. LT-5, 1239–1245 (1987).

Petermann, K.

M. Majd, B. Schüppert, K. Petermann, “90 S-bends in Ti:LiNbO3 waveguides with low losses,” IEEE Photon. Tech-nol. Lett. 5, 806–808 (1993).

M. Majd, B. Schuüppert, K. Petermann, “Low-loss Ti:LiNbO3 waveguide bends prepared by MgO in-diffusion,” IEEE J. Lightwave Technol. 8, 1670–1674 (1990).

Quaranta, A.

F. Caccavale, P. Chakraborty, A. Quaranta, I. Mansour, G. Gianello, S. Bosso, R. Corsini, G. Mussi, “Secondary ion mass spectrometry and near field studies of Ti:LiNbO3 optical waveguides,” J. Appl. Phys. 78, 5345–5350 (1995).

Richter, W.

Saito, S.

J. Noda, M. Fukuma, S. Saito, “Effect of Mg diffusion on Ti-diffused LiNbO3 waveguide,” J. Appl. Phys. 49, 3150–3154 (1978).

Schüppert, B.

M. Majd, B. Schüppert, K. Petermann, “90 S-bends in Ti:LiNbO3 waveguides with low losses,” IEEE Photon. Tech-nol. Lett. 5, 806–808 (1993).

Schuüppert, B.

M. Majd, B. Schuüppert, K. Petermann, “Low-loss Ti:LiNbO3 waveguide bends prepared by MgO in-diffusion,” IEEE J. Lightwave Technol. 8, 1670–1674 (1990).

B. Schuüppert, “Reduction of bend losses in Ti:LiNbO3 waveguides through MgO double diffusion,” Electron. Lett. 23, 797–798 (1987).

Shiota, T.

Someda, C. G.

I. Mansour, C. G. Someda, “Numerical optimization procedure for low-loss sharp bends in MgO Co-doped Ti:LiNbO3 waveguides,” IEEE Photon. Technol. Lett. 7, 81–83 (1995).

C. G. Someda, “Radiation of discrete beams from curved single-mode fibers,” Electron. Lett. 13, 712–713 (1977).

Steinberg, S.

S. Steinberg, M. Guntau, R. Göring, W. Karthe, “Calculation of electrooptically induced refractive index changes of integrated optic devices by the finite-element-method,” J. Opt. Commun. 12, 125–129 (1991).

Stern, M. S.

M. S. Stern, “Semi-vectorial polarised finite difference method for optical waveguides with arbitrary index profiles,” Proc. Inst. Electr. Eng. J. 135, 56–63 (1988).

Takahashi, K.

Tanaka, N.

Veselka, J. J.

S. K. Korotky, E. A. J. Marcatili, J. J. Veselka, R. H. Besworth, “Greatly reduced losses for small-radius bends in Ti:LiNbO3 waveguides,” Appl. Phys. Lett. 48, 92–94 (1986).

Yamazaki, S.

K. Komatsu, S. Yamazaki, M. Kondo, Y. Ohta, “Low-loss broad-band LiNbO3 guided-wave phase modulators using titanium/magnesium double diffusion method,” IEEE J. Lightwave Technol. LT-5, 1239–1245 (1987).

Appl. Opt. (2)

Appl. Phys. Lett. (1)

S. K. Korotky, E. A. J. Marcatili, J. J. Veselka, R. H. Besworth, “Greatly reduced losses for small-radius bends in Ti:LiNbO3 waveguides,” Appl. Phys. Lett. 48, 92–94 (1986).

Comput. J. (1)

J. A. Nelder, R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1987).

Electron. Lett. (2)

B. Schuüppert, “Reduction of bend losses in Ti:LiNbO3 waveguides through MgO double diffusion,” Electron. Lett. 23, 797–798 (1987).

C. G. Someda, “Radiation of discrete beams from curved single-mode fibers,” Electron. Lett. 13, 712–713 (1977).

European Transactions on Telecomm. and Related Tech. (1)

C. De Angelis, “Numerical modelling of bends in optical rib waveguides,” European Transactions on Telecomm. and Related Tech. 3, 73–75 (1992).

IEEE J. Lightwave Technol. (2)

M. Majd, B. Schuüppert, K. Petermann, “Low-loss Ti:LiNbO3 waveguide bends prepared by MgO in-diffusion,” IEEE J. Lightwave Technol. 8, 1670–1674 (1990).

K. Komatsu, S. Yamazaki, M. Kondo, Y. Ohta, “Low-loss broad-band LiNbO3 guided-wave phase modulators using titanium/magnesium double diffusion method,” IEEE J. Lightwave Technol. LT-5, 1239–1245 (1987).

IEEE J. Quantum Electron. (2)

R. C. Alferness, “Guided-wave devices for optical communication,” IEEE J. Quantum Electron. QE-17, 946–959 (1981).

M. Heiblum, J. H. Harris, “Analysis of curved optical waveguides by conformal transformation,” IEEE J. Quantum Electron. QE-11, 75–84 (1975).

IEEE Photon. Tech-nol. Lett. (1)

M. Majd, B. Schüppert, K. Petermann, “90 S-bends in Ti:LiNbO3 waveguides with low losses,” IEEE Photon. Tech-nol. Lett. 5, 806–808 (1993).

IEEE Photon. Technol. Lett. (1)

I. Mansour, C. G. Someda, “Numerical optimization procedure for low-loss sharp bends in MgO Co-doped Ti:LiNbO3 waveguides,” IEEE Photon. Technol. Lett. 7, 81–83 (1995).

J. Appl. Phys. (4)

F. Caccavale, P. Chakraborty, I. Mansour, G. Gianello, M. Mazzoleni, M. Elena, “A secondary-ion-mass spectrometry study of magnesium diffusion in lithium niobate,” J. Appl. Phys. 76, 7552–7558 (1994).

J. Noda, M. Fukuma, S. Saito, “Effect of Mg diffusion on Ti-diffused LiNbO3 waveguide,” J. Appl. Phys. 49, 3150–3154 (1978).

F. Caccavale, P. Chakraborty, A. Capobianco, G. Gianello, I. Mansour, “Characterization and optimization of Ti-diffused LiNbO3 optical waveguides by second diffusion of magnesium,” J. Appl. Phys. 78, 187–193 (1995).

F. Caccavale, P. Chakraborty, A. Quaranta, I. Mansour, G. Gianello, S. Bosso, R. Corsini, G. Mussi, “Secondary ion mass spectrometry and near field studies of Ti:LiNbO3 optical waveguides,” J. Appl. Phys. 78, 5345–5350 (1995).

J. Opt. Commun. (2)

J. Noda, “Ti diffused LiNbO3 waveguides and modulators,” J. Opt. Commun. 1, 64–73 (1980).

S. Steinberg, M. Guntau, R. Göring, W. Karthe, “Calculation of electrooptically induced refractive index changes of integrated optic devices by the finite-element-method,” J. Opt. Commun. 12, 125–129 (1991).

Proc. Inst. Electr. Eng. J (1)

M. N. Armenise, “Fabrication techniques of lithium niobate waveguides,” Proc. Inst. Electr. Eng. J 135, 85–91 (1988).

Proc. Inst. Electr. Eng. J. (1)

M. S. Stern, “Semi-vectorial polarised finite difference method for optical waveguides with arbitrary index profiles,” Proc. Inst. Electr. Eng. J. 135, 56–63 (1988).

Other (2)

J. Crank, The Mathematics of Diffusion (Oxford University, New York, 1975), pp. 1–21.

F. Gonella, Dipartimento di Fisica, Università Degali Studi di Padova, Padova, Italy35131 (personal communication, 1994).

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Figures (11)

Fig. 1.
Fig. 1.

Schematic of a Mach–Zehnder Ti:LiNbO3 modulator with the application of Mg indiffusion: (a) coupling-loss reduction, (b) bend-loss reduction, (c) waveguide-separation reduction and modulation-efficiency improvement.

Fig. 2.
Fig. 2.

Dopant secondary ion mass spectrometry concentration profiles of a z-cut Ti/Mg:LiNbO3 waveguide.

Fig. 3.
Fig. 3.

Refractive-index profiles of a Ti/Mg:LiNbO3 buried waveguide: (a) Ti indiffusion, m-line measurement; (b) Mg indiffusion, simulated; (c) Ti + Mg indiffusion, simulated.

Fig. 4.
Fig. 4.

Coupling loss as a function of burying depth δ.

Fig. 5.
Fig. 5.

Cross section of the refractive-index profiles for a Ti: LiNbO3 waveguide: (a) conventional straight waveguide; (b) equivalent straight waveguide, as derived from Eq. (3) (see the text); (c) distorted profile in the bend [its equivalent straight index is shown in (a)].

Fig. 6.
Fig. 6.

Cross section of the bend refractive-index profiles, distorted by Ti: (a) actual Ti-distorted index profile, (b) equivalent straight waveguide index profile. The inset shows a Ti stripe on Ti:LiNbO3 before diffusion; typical values are thickness τ = 44 nm, width w = 8.8 μm, shift l = 14 μm.

Fig. 7.
Fig. 7.

Cross section of the bend refractive-index profiles, distorted by Mg: (a) actual Mg-distorted index profile, (b) equivalent straight waveguide index profile. The inset shows a MgO stripe on Ti:LiNbO3 before diffusion; typical values are thickness τ = 13 nm, width w = 8.8 μm, shift l = 14 μm.

Fig. 8.
Fig. 8.

Accumulated bend losses (transition and curvature) versus propagation distance for different index profiles (bend radius = 5 mm, ζ is the end of the π/4 rad deflection). (a) standard Ti:LiNbO3 bend, (b) bend distorted by Mg indiffusion.

Fig. 9.
Fig. 9.

Output-field profile of a standard Ti:LiNbO3 bent waveguide: A, x component; B, y component. Bend radius R = 5 mm, and ζ is the end of the π/4 rad deflection.

Fig. 10.
Fig. 10.

Output-field profile of a Mg-distorted Ti:LiNbO3 bent waveguide: A, x component; B, y component. Bend radius R = 5 mm, and ζ is the end of the π/4 rad deflection.

Fig. 11.
Fig. 11.

Optical bilateral confinement by Mg diffusion in a Ti:LiNbO3 waveguide (cross section): A, index profiles; B, mode profiles. The inset shows MgO stripes on Ti:LiNbO3 before diffusion.

Equations (9)

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n ( x , y ) = { n s + Δ n 2 ( erf x + w a x erf x w a x ) exp [ ( y + δ ) 2 a y 2 ] y 0 1 y > 0 ,
n ( x , y ) = { n s + Δ n 2 ( erf x + w a x erf x w a x ) exp ( y 2 / a y 2 ) y 0 1 y > 0 ,
n ˜ ( x , y ) = n ( x , y ) ( r R ) = n ( x , y ) ( 1 + x R ) ,
n d ( x , y ) = n ( x , y ) [ 1 + ( x / R ) ] .
loss ( dB ) = 10    log [ | E * ( x , y , z ) E ( x , y , 0 ) d x d y | | E ( x , y , 0 ) | 2 d x d y ] .
η m = P o ( max ) P o ( min ) P o ( max ) ,
E r = 10    log P o ( max ) P o ( min ) = 10    log ( 1 + r p 1 r p ) ( dB ) ,
V π 1 2 λ 0 4 L 1.14 × 10 5 Γ ,
Γ = g V π s E a | E opt | 2 d s s | E opt | 2 d s ,

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