Abstract

Phase-matched electric-field-induced second-harmonic generation is demonstrated in single-mode germania-doped silica fibers. A periodic second-order nonlinearity is induced by a simple interdigitated electrode structure, which can be rotated to permit phase matching between all propagating modes. The most efficient mode interaction between HE11ω and HE112ω is achieved at 1.064 μm by using a Q-switched Nd+3:YAG laser. In principle, phase matching at any propagating wavelength is possible. This technique could be applied to planar as well as cylindrical waveguides and can be used with many non-χ(2) materials. The asymmetry in the applied electric field enhances the optical-field overlaps between modes of dissimilar orders, and this is also demonstrated. A conversion efficiency of 4.0 × 10−4% has been obtained in unoptimized devices. Device optimization is also discussed.

© 1989 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Y. Fujii, B. S. Kawasaki, K. O. Hill, and D. C. Johnson, Opt. Lett. 5, 48 (1980).
    [Crossref]
  2. Y. Sasaki and Y. Ohmori, Appl. Phys. Lett. 39, 466 (1982).
    [Crossref]
  3. U. Osterberg and W. Margulis, in Digest of XIV International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1986), p. 102, paper WBB2; Opt. Lett. 11, 516 (1986).
  4. B. Valk, E. M. Kim, and M. M. Salour, Appl. Phys. Lett. 51, 722 (1987).
    [Crossref]
  5. M. Farries, P. St, J. Russell, M. E. Fermann, and D. N. Payne, Electron. Lett. 23, 322 (1987).
    [Crossref]
  6. R. Stolen and H. W. K. Tom, Opt. Lett. 12, 585 (1987).
    [Crossref] [PubMed]
  7. R. W. Terhune and D. A. Weinberger, J. Opt. Soc. Am. B 4, 661 (1987).
    [Crossref]
  8. F. P. Payne, Electron. Lett. 23, 1215 (1987).
    [Crossref]
  9. A. Krotkus and W. Margulis, Appl. Phys. Lett. 52, 1942 (1988).
    [Crossref]
  10. W. Margulis, Departamento de Fisica, Pontifícia Universidade Católica de São Paulo, São Paulo, SP, Brazil (personal communication).
  11. R. Kashyap, in Molecular and Polymeric Optoelectronic Materials: Fundamentals and Applications, G. Khanarian, ed., Proc. Soc. Photo-Opt. Instrum. Eng.682, 170 (1986).
    [Crossref]
  12. R. Kashyap, in Digest of XVI International Conference on Quantum Electronics, (Japanese Society of Applied Physics, Tokyo, 1988), pp. 110–111, paper MP-25.
  13. S. Kielich, Chem. Phys. Lett. 2, 569 (1968).
    [Crossref]
  14. D. A. Weinberger and R. W. Terhune, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1987), pp. 78–79, paper TUHH3.
  15. C. Elachi, Proc IEEE 64, 1666 (1976).
    [Crossref]
  16. A. Yariv and M. Nakamura, IEEE J. Quantum Electron. QE-13, 233 (1977).
    [Crossref]
  17. C. L. Tang and P. P. Bey, IEEE J. Quantum Electron. QE-9, 9 (1973).
    [Crossref]
  18. R. C. Alferness, IEEE Trans. Microwave Theory Tech. MTT-30, 1121 (1982).
    [Crossref]
  19. D. P. Shelton and A. D. Buckingham, Phys. Rev. A 26, 2787 (1982).
    [Crossref]
  20. B. F. Levine, C. G. Bethea, and R. A. Logan, J. Chem. Phys. 63, 375 (1975).
  21. D. Gloge, Appl. Opt. 10, 2252 (1971).
    [Crossref] [PubMed]
  22. A. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).
  23. J. W. Fleming, Electron. Lett. 14, 326 (1978).
    [Crossref]
  24. See, for example, S. E. Miller and A. G. Chynoweth, Optical Fibre Telecommunications (Academic, New York, 1979), p. 181.
  25. R. Kashyap and J. P. Waite, “Analytic approximation to the fundamental spatial harmonic in a periodic structure,” submitted to Electron. Lett.
  26. A. T. Hunter, R. Kashyap, and J. W. Wright, in Digest of Colloquium on Optical Fibre Measurements (Institution of Electrical Engineers, London, 1987), paper 13.
  27. D. Marcuse, in Theory of Dielectric Optical Waveguides (Academic, New York, 1974).
  28. H. Ito and H. Inaba, Opt. Lett. 2, 139 (1978).
    [Crossref] [PubMed]
  29. N. N. Akhmediev and V. R. Novak, Opt. Spectrosc. (USSR) 58, 558 (1985).
  30. D. C. Hanna, D. Cotter, and M. A. Yuratich, in Non-linear Optics of Free Atoms and Molecules, Vol. 17 of Springer Series in Optical Physics (Springer-Verlag, Berlin, 1979).
    [Crossref]
  31. R. Kashyap and B. K. Nayar, IEEE J. Lightwave Technol. LT-1, 619 (1983).
    [Crossref]
  32. B. K. Nayar, in Proceedings of Third European Conference on Integrated Optics (ECIO), H.-P. Nolting and R. Ulrich, eds. (Springer-Verlag, Heidelberg, 1985).
  33. R. Kashyap, in Technical Digest of Xth International Conference on Lasers, Lasers ’87 (Society of Optical and Quantum Electronics, London, 1987), pp. 859–866.
  34. R. Kashyap and K. J. Blow, Electron. Lett. 24, 47 (1988).
    [Crossref]
  35. V. Mizrahi, U. Osterberg, J. E. Sipe, and G. I. Stegeman, Opt. Lett. 13, 279 (1988).
    [Crossref] [PubMed]
  36. D. W. Hall, N. F. Borrelli, and W. H. Dumbaugh, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper PD27-1; N. F. Borrelli, D. W. Hall, H. J. Holland, and D. W. Smith, J. Appl. Phys. 61, 5399 (1987).
    [Crossref]
  37. V. Mizrahi, U. Osterberg, C. Krautschik, G. I. Stegeman, J. E. Sipe, and T. F. Morse, Appl. Phys. Lett. 53, 557 (1988).
    [Crossref]
  38. C. G. Bethea, Appl. Opt. 14, 2435 (1975).
    [Crossref] [PubMed]
  39. G. R. Meredith, Nonlinear Optical Properties of Organic and Polymeric Materials, D. J. Williams, ed., ACS Symp. Ser.233, 27 (1982), and references therein.
    [Crossref]
  40. M.-V. Bergot, M. C. Farries, M. E. Fermann, L. Li, J. Poyntz-Wright, P. St, J. Russell, and A. Smithson, Opt. Lett. 13, 592 (1988).
    [Crossref]
  41. M. E. Fermann, L. Li, M. C. Farries, and D. N. Payne, in Proceedings of XIV European Conference on Optical Communications, IEEE Conf. Proc.292, 135 (1988).

1988 (5)

A. Krotkus and W. Margulis, Appl. Phys. Lett. 52, 1942 (1988).
[Crossref]

R. Kashyap and K. J. Blow, Electron. Lett. 24, 47 (1988).
[Crossref]

V. Mizrahi, U. Osterberg, J. E. Sipe, and G. I. Stegeman, Opt. Lett. 13, 279 (1988).
[Crossref] [PubMed]

V. Mizrahi, U. Osterberg, C. Krautschik, G. I. Stegeman, J. E. Sipe, and T. F. Morse, Appl. Phys. Lett. 53, 557 (1988).
[Crossref]

M.-V. Bergot, M. C. Farries, M. E. Fermann, L. Li, J. Poyntz-Wright, P. St, J. Russell, and A. Smithson, Opt. Lett. 13, 592 (1988).
[Crossref]

1987 (5)

B. Valk, E. M. Kim, and M. M. Salour, Appl. Phys. Lett. 51, 722 (1987).
[Crossref]

M. Farries, P. St, J. Russell, M. E. Fermann, and D. N. Payne, Electron. Lett. 23, 322 (1987).
[Crossref]

R. Stolen and H. W. K. Tom, Opt. Lett. 12, 585 (1987).
[Crossref] [PubMed]

R. W. Terhune and D. A. Weinberger, J. Opt. Soc. Am. B 4, 661 (1987).
[Crossref]

F. P. Payne, Electron. Lett. 23, 1215 (1987).
[Crossref]

1985 (1)

N. N. Akhmediev and V. R. Novak, Opt. Spectrosc. (USSR) 58, 558 (1985).

1983 (1)

R. Kashyap and B. K. Nayar, IEEE J. Lightwave Technol. LT-1, 619 (1983).
[Crossref]

1982 (3)

Y. Sasaki and Y. Ohmori, Appl. Phys. Lett. 39, 466 (1982).
[Crossref]

R. C. Alferness, IEEE Trans. Microwave Theory Tech. MTT-30, 1121 (1982).
[Crossref]

D. P. Shelton and A. D. Buckingham, Phys. Rev. A 26, 2787 (1982).
[Crossref]

1980 (1)

1978 (2)

1977 (1)

A. Yariv and M. Nakamura, IEEE J. Quantum Electron. QE-13, 233 (1977).
[Crossref]

1976 (1)

C. Elachi, Proc IEEE 64, 1666 (1976).
[Crossref]

1975 (2)

C. G. Bethea, Appl. Opt. 14, 2435 (1975).
[Crossref] [PubMed]

B. F. Levine, C. G. Bethea, and R. A. Logan, J. Chem. Phys. 63, 375 (1975).

1973 (1)

C. L. Tang and P. P. Bey, IEEE J. Quantum Electron. QE-9, 9 (1973).
[Crossref]

1971 (1)

1968 (1)

S. Kielich, Chem. Phys. Lett. 2, 569 (1968).
[Crossref]

Akhmediev, N. N.

N. N. Akhmediev and V. R. Novak, Opt. Spectrosc. (USSR) 58, 558 (1985).

Alferness, R. C.

R. C. Alferness, IEEE Trans. Microwave Theory Tech. MTT-30, 1121 (1982).
[Crossref]

Bergot, M.-V.

Bethea, C. G.

C. G. Bethea, Appl. Opt. 14, 2435 (1975).
[Crossref] [PubMed]

B. F. Levine, C. G. Bethea, and R. A. Logan, J. Chem. Phys. 63, 375 (1975).

Bey, P. P.

C. L. Tang and P. P. Bey, IEEE J. Quantum Electron. QE-9, 9 (1973).
[Crossref]

Blow, K. J.

R. Kashyap and K. J. Blow, Electron. Lett. 24, 47 (1988).
[Crossref]

Borrelli, N. F.

D. W. Hall, N. F. Borrelli, and W. H. Dumbaugh, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper PD27-1; N. F. Borrelli, D. W. Hall, H. J. Holland, and D. W. Smith, J. Appl. Phys. 61, 5399 (1987).
[Crossref]

Buckingham, A. D.

D. P. Shelton and A. D. Buckingham, Phys. Rev. A 26, 2787 (1982).
[Crossref]

Chynoweth, A. G.

See, for example, S. E. Miller and A. G. Chynoweth, Optical Fibre Telecommunications (Academic, New York, 1979), p. 181.

Cotter, D.

D. C. Hanna, D. Cotter, and M. A. Yuratich, in Non-linear Optics of Free Atoms and Molecules, Vol. 17 of Springer Series in Optical Physics (Springer-Verlag, Berlin, 1979).
[Crossref]

Dumbaugh, W. H.

D. W. Hall, N. F. Borrelli, and W. H. Dumbaugh, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper PD27-1; N. F. Borrelli, D. W. Hall, H. J. Holland, and D. W. Smith, J. Appl. Phys. 61, 5399 (1987).
[Crossref]

Elachi, C.

C. Elachi, Proc IEEE 64, 1666 (1976).
[Crossref]

Farries, M.

M. Farries, P. St, J. Russell, M. E. Fermann, and D. N. Payne, Electron. Lett. 23, 322 (1987).
[Crossref]

Farries, M. C.

M.-V. Bergot, M. C. Farries, M. E. Fermann, L. Li, J. Poyntz-Wright, P. St, J. Russell, and A. Smithson, Opt. Lett. 13, 592 (1988).
[Crossref]

M. E. Fermann, L. Li, M. C. Farries, and D. N. Payne, in Proceedings of XIV European Conference on Optical Communications, IEEE Conf. Proc.292, 135 (1988).

Fermann, M. E.

M.-V. Bergot, M. C. Farries, M. E. Fermann, L. Li, J. Poyntz-Wright, P. St, J. Russell, and A. Smithson, Opt. Lett. 13, 592 (1988).
[Crossref]

M. Farries, P. St, J. Russell, M. E. Fermann, and D. N. Payne, Electron. Lett. 23, 322 (1987).
[Crossref]

M. E. Fermann, L. Li, M. C. Farries, and D. N. Payne, in Proceedings of XIV European Conference on Optical Communications, IEEE Conf. Proc.292, 135 (1988).

Fleming, J. W.

J. W. Fleming, Electron. Lett. 14, 326 (1978).
[Crossref]

Fujii, Y.

Gloge, D.

Hall, D. W.

D. W. Hall, N. F. Borrelli, and W. H. Dumbaugh, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper PD27-1; N. F. Borrelli, D. W. Hall, H. J. Holland, and D. W. Smith, J. Appl. Phys. 61, 5399 (1987).
[Crossref]

Hanna, D. C.

D. C. Hanna, D. Cotter, and M. A. Yuratich, in Non-linear Optics of Free Atoms and Molecules, Vol. 17 of Springer Series in Optical Physics (Springer-Verlag, Berlin, 1979).
[Crossref]

Hill, K. O.

Hunter, A. T.

A. T. Hunter, R. Kashyap, and J. W. Wright, in Digest of Colloquium on Optical Fibre Measurements (Institution of Electrical Engineers, London, 1987), paper 13.

Inaba, H.

Ito, H.

Johnson, D. C.

Kashyap, R.

R. Kashyap and K. J. Blow, Electron. Lett. 24, 47 (1988).
[Crossref]

R. Kashyap and B. K. Nayar, IEEE J. Lightwave Technol. LT-1, 619 (1983).
[Crossref]

R. Kashyap, in Technical Digest of Xth International Conference on Lasers, Lasers ’87 (Society of Optical and Quantum Electronics, London, 1987), pp. 859–866.

A. T. Hunter, R. Kashyap, and J. W. Wright, in Digest of Colloquium on Optical Fibre Measurements (Institution of Electrical Engineers, London, 1987), paper 13.

R. Kashyap and J. P. Waite, “Analytic approximation to the fundamental spatial harmonic in a periodic structure,” submitted to Electron. Lett.

R. Kashyap, in Molecular and Polymeric Optoelectronic Materials: Fundamentals and Applications, G. Khanarian, ed., Proc. Soc. Photo-Opt. Instrum. Eng.682, 170 (1986).
[Crossref]

R. Kashyap, in Digest of XVI International Conference on Quantum Electronics, (Japanese Society of Applied Physics, Tokyo, 1988), pp. 110–111, paper MP-25.

Kawasaki, B. S.

Kielich, S.

S. Kielich, Chem. Phys. Lett. 2, 569 (1968).
[Crossref]

Kim, E. M.

B. Valk, E. M. Kim, and M. M. Salour, Appl. Phys. Lett. 51, 722 (1987).
[Crossref]

Krautschik, C.

V. Mizrahi, U. Osterberg, C. Krautschik, G. I. Stegeman, J. E. Sipe, and T. F. Morse, Appl. Phys. Lett. 53, 557 (1988).
[Crossref]

Krotkus, A.

A. Krotkus and W. Margulis, Appl. Phys. Lett. 52, 1942 (1988).
[Crossref]

Levine, B. F.

B. F. Levine, C. G. Bethea, and R. A. Logan, J. Chem. Phys. 63, 375 (1975).

Li, L.

M.-V. Bergot, M. C. Farries, M. E. Fermann, L. Li, J. Poyntz-Wright, P. St, J. Russell, and A. Smithson, Opt. Lett. 13, 592 (1988).
[Crossref]

M. E. Fermann, L. Li, M. C. Farries, and D. N. Payne, in Proceedings of XIV European Conference on Optical Communications, IEEE Conf. Proc.292, 135 (1988).

Logan, R. A.

B. F. Levine, C. G. Bethea, and R. A. Logan, J. Chem. Phys. 63, 375 (1975).

Love, J. D.

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

Marcuse, D.

D. Marcuse, in Theory of Dielectric Optical Waveguides (Academic, New York, 1974).

Margulis, W.

A. Krotkus and W. Margulis, Appl. Phys. Lett. 52, 1942 (1988).
[Crossref]

W. Margulis, Departamento de Fisica, Pontifícia Universidade Católica de São Paulo, São Paulo, SP, Brazil (personal communication).

U. Osterberg and W. Margulis, in Digest of XIV International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1986), p. 102, paper WBB2; Opt. Lett. 11, 516 (1986).

Meredith, G. R.

G. R. Meredith, Nonlinear Optical Properties of Organic and Polymeric Materials, D. J. Williams, ed., ACS Symp. Ser.233, 27 (1982), and references therein.
[Crossref]

Miller, S. E.

See, for example, S. E. Miller and A. G. Chynoweth, Optical Fibre Telecommunications (Academic, New York, 1979), p. 181.

Mizrahi, V.

V. Mizrahi, U. Osterberg, C. Krautschik, G. I. Stegeman, J. E. Sipe, and T. F. Morse, Appl. Phys. Lett. 53, 557 (1988).
[Crossref]

V. Mizrahi, U. Osterberg, J. E. Sipe, and G. I. Stegeman, Opt. Lett. 13, 279 (1988).
[Crossref] [PubMed]

Morse, T. F.

V. Mizrahi, U. Osterberg, C. Krautschik, G. I. Stegeman, J. E. Sipe, and T. F. Morse, Appl. Phys. Lett. 53, 557 (1988).
[Crossref]

Nakamura, M.

A. Yariv and M. Nakamura, IEEE J. Quantum Electron. QE-13, 233 (1977).
[Crossref]

Nayar, B. K.

R. Kashyap and B. K. Nayar, IEEE J. Lightwave Technol. LT-1, 619 (1983).
[Crossref]

B. K. Nayar, in Proceedings of Third European Conference on Integrated Optics (ECIO), H.-P. Nolting and R. Ulrich, eds. (Springer-Verlag, Heidelberg, 1985).

Novak, V. R.

N. N. Akhmediev and V. R. Novak, Opt. Spectrosc. (USSR) 58, 558 (1985).

Ohmori, Y.

Y. Sasaki and Y. Ohmori, Appl. Phys. Lett. 39, 466 (1982).
[Crossref]

Osterberg, U.

V. Mizrahi, U. Osterberg, C. Krautschik, G. I. Stegeman, J. E. Sipe, and T. F. Morse, Appl. Phys. Lett. 53, 557 (1988).
[Crossref]

V. Mizrahi, U. Osterberg, J. E. Sipe, and G. I. Stegeman, Opt. Lett. 13, 279 (1988).
[Crossref] [PubMed]

U. Osterberg and W. Margulis, in Digest of XIV International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1986), p. 102, paper WBB2; Opt. Lett. 11, 516 (1986).

Payne, D. N.

M. Farries, P. St, J. Russell, M. E. Fermann, and D. N. Payne, Electron. Lett. 23, 322 (1987).
[Crossref]

M. E. Fermann, L. Li, M. C. Farries, and D. N. Payne, in Proceedings of XIV European Conference on Optical Communications, IEEE Conf. Proc.292, 135 (1988).

Payne, F. P.

F. P. Payne, Electron. Lett. 23, 1215 (1987).
[Crossref]

Poyntz-Wright, J.

Russell, J.

Salour, M. M.

B. Valk, E. M. Kim, and M. M. Salour, Appl. Phys. Lett. 51, 722 (1987).
[Crossref]

Sasaki, Y.

Y. Sasaki and Y. Ohmori, Appl. Phys. Lett. 39, 466 (1982).
[Crossref]

Shelton, D. P.

D. P. Shelton and A. D. Buckingham, Phys. Rev. A 26, 2787 (1982).
[Crossref]

Sipe, J. E.

V. Mizrahi, U. Osterberg, C. Krautschik, G. I. Stegeman, J. E. Sipe, and T. F. Morse, Appl. Phys. Lett. 53, 557 (1988).
[Crossref]

V. Mizrahi, U. Osterberg, J. E. Sipe, and G. I. Stegeman, Opt. Lett. 13, 279 (1988).
[Crossref] [PubMed]

Smithson, A.

Snyder, A.

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

St, P.

Stegeman, G. I.

V. Mizrahi, U. Osterberg, C. Krautschik, G. I. Stegeman, J. E. Sipe, and T. F. Morse, Appl. Phys. Lett. 53, 557 (1988).
[Crossref]

V. Mizrahi, U. Osterberg, J. E. Sipe, and G. I. Stegeman, Opt. Lett. 13, 279 (1988).
[Crossref] [PubMed]

Stolen, R.

Tang, C. L.

C. L. Tang and P. P. Bey, IEEE J. Quantum Electron. QE-9, 9 (1973).
[Crossref]

Terhune, R. W.

R. W. Terhune and D. A. Weinberger, J. Opt. Soc. Am. B 4, 661 (1987).
[Crossref]

D. A. Weinberger and R. W. Terhune, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1987), pp. 78–79, paper TUHH3.

Tom, H. W. K.

Valk, B.

B. Valk, E. M. Kim, and M. M. Salour, Appl. Phys. Lett. 51, 722 (1987).
[Crossref]

Waite, J. P.

R. Kashyap and J. P. Waite, “Analytic approximation to the fundamental spatial harmonic in a periodic structure,” submitted to Electron. Lett.

Weinberger, D. A.

R. W. Terhune and D. A. Weinberger, J. Opt. Soc. Am. B 4, 661 (1987).
[Crossref]

D. A. Weinberger and R. W. Terhune, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1987), pp. 78–79, paper TUHH3.

Wright, J. W.

A. T. Hunter, R. Kashyap, and J. W. Wright, in Digest of Colloquium on Optical Fibre Measurements (Institution of Electrical Engineers, London, 1987), paper 13.

Yariv, A.

A. Yariv and M. Nakamura, IEEE J. Quantum Electron. QE-13, 233 (1977).
[Crossref]

Yuratich, M. A.

D. C. Hanna, D. Cotter, and M. A. Yuratich, in Non-linear Optics of Free Atoms and Molecules, Vol. 17 of Springer Series in Optical Physics (Springer-Verlag, Berlin, 1979).
[Crossref]

Appl. Opt. (2)

Appl. Phys. Lett. (4)

V. Mizrahi, U. Osterberg, C. Krautschik, G. I. Stegeman, J. E. Sipe, and T. F. Morse, Appl. Phys. Lett. 53, 557 (1988).
[Crossref]

Y. Sasaki and Y. Ohmori, Appl. Phys. Lett. 39, 466 (1982).
[Crossref]

B. Valk, E. M. Kim, and M. M. Salour, Appl. Phys. Lett. 51, 722 (1987).
[Crossref]

A. Krotkus and W. Margulis, Appl. Phys. Lett. 52, 1942 (1988).
[Crossref]

Chem. Phys. Lett. (1)

S. Kielich, Chem. Phys. Lett. 2, 569 (1968).
[Crossref]

Electron. Lett. (4)

M. Farries, P. St, J. Russell, M. E. Fermann, and D. N. Payne, Electron. Lett. 23, 322 (1987).
[Crossref]

R. Kashyap and K. J. Blow, Electron. Lett. 24, 47 (1988).
[Crossref]

F. P. Payne, Electron. Lett. 23, 1215 (1987).
[Crossref]

J. W. Fleming, Electron. Lett. 14, 326 (1978).
[Crossref]

IEEE J. Lightwave Technol. (1)

R. Kashyap and B. K. Nayar, IEEE J. Lightwave Technol. LT-1, 619 (1983).
[Crossref]

IEEE J. Quantum Electron. (2)

A. Yariv and M. Nakamura, IEEE J. Quantum Electron. QE-13, 233 (1977).
[Crossref]

C. L. Tang and P. P. Bey, IEEE J. Quantum Electron. QE-9, 9 (1973).
[Crossref]

IEEE Trans. Microwave Theory Tech. (1)

R. C. Alferness, IEEE Trans. Microwave Theory Tech. MTT-30, 1121 (1982).
[Crossref]

J. Chem. Phys. (1)

B. F. Levine, C. G. Bethea, and R. A. Logan, J. Chem. Phys. 63, 375 (1975).

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

Opt. Lett. (5)

Opt. Spectrosc. (USSR) (1)

N. N. Akhmediev and V. R. Novak, Opt. Spectrosc. (USSR) 58, 558 (1985).

Phys. Rev. A (1)

D. P. Shelton and A. D. Buckingham, Phys. Rev. A 26, 2787 (1982).
[Crossref]

Proc IEEE (1)

C. Elachi, Proc IEEE 64, 1666 (1976).
[Crossref]

Other (16)

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

See, for example, S. E. Miller and A. G. Chynoweth, Optical Fibre Telecommunications (Academic, New York, 1979), p. 181.

R. Kashyap and J. P. Waite, “Analytic approximation to the fundamental spatial harmonic in a periodic structure,” submitted to Electron. Lett.

A. T. Hunter, R. Kashyap, and J. W. Wright, in Digest of Colloquium on Optical Fibre Measurements (Institution of Electrical Engineers, London, 1987), paper 13.

D. Marcuse, in Theory of Dielectric Optical Waveguides (Academic, New York, 1974).

D. C. Hanna, D. Cotter, and M. A. Yuratich, in Non-linear Optics of Free Atoms and Molecules, Vol. 17 of Springer Series in Optical Physics (Springer-Verlag, Berlin, 1979).
[Crossref]

B. K. Nayar, in Proceedings of Third European Conference on Integrated Optics (ECIO), H.-P. Nolting and R. Ulrich, eds. (Springer-Verlag, Heidelberg, 1985).

R. Kashyap, in Technical Digest of Xth International Conference on Lasers, Lasers ’87 (Society of Optical and Quantum Electronics, London, 1987), pp. 859–866.

D. W. Hall, N. F. Borrelli, and W. H. Dumbaugh, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1988), paper PD27-1; N. F. Borrelli, D. W. Hall, H. J. Holland, and D. W. Smith, J. Appl. Phys. 61, 5399 (1987).
[Crossref]

D. A. Weinberger and R. W. Terhune, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1987), pp. 78–79, paper TUHH3.

U. Osterberg and W. Margulis, in Digest of XIV International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1986), p. 102, paper WBB2; Opt. Lett. 11, 516 (1986).

W. Margulis, Departamento de Fisica, Pontifícia Universidade Católica de São Paulo, São Paulo, SP, Brazil (personal communication).

R. Kashyap, in Molecular and Polymeric Optoelectronic Materials: Fundamentals and Applications, G. Khanarian, ed., Proc. Soc. Photo-Opt. Instrum. Eng.682, 170 (1986).
[Crossref]

R. Kashyap, in Digest of XVI International Conference on Quantum Electronics, (Japanese Society of Applied Physics, Tokyo, 1988), pp. 110–111, paper MP-25.

M. E. Fermann, L. Li, M. C. Farries, and D. N. Payne, in Proceedings of XIV European Conference on Optical Communications, IEEE Conf. Proc.292, 135 (1988).

G. R. Meredith, Nonlinear Optical Properties of Organic and Polymeric Materials, D. J. Williams, ed., ACS Symp. Ser.233, 27 (1982), and references therein.
[Crossref]

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (15)

Fig. 1
Fig. 1

Schematic of a periodic EFISH fiber device. The electric field modulates the third-order susceptibility χ(3) to give a spatially periodic effective second-order nonlinearity, χ(3)E0.

Fig. 2
Fig. 2

Modal dispersion of the fundamental and second-harmonic wavelength modes for a germania-doped silica fiber with a core–cladding index difference of 4.5 × 10−3. The LP mode designations are marked, and the absence of intersections between the fundamental and second-harmonic wavelength modes shows that phase matching is not possible.

Fig. 3
Fig. 3

Phase-match pitch as a function of the core radius for mode interactions is shown for the two propagating fundamental wavelength modes and supported second-harmonic wavelength modes. For a grating with a 35-μm pitch, all mode combinations can be achieved by rotating the grating. The numbering scheme shown applies also to Figs. 35 and 8.

Fig. 4
Fig. 4

Variation of the pitch Λ as a function of the core–cladding index difference Δn. The numbering of curves is identical to that in Fig. 3. For most of the interactions with the LP01ω mode, the dependence is weak. LP01ω → LP112ω shows virtually no dependence on Δn.

Fig. 5
Fig. 5

Wavelength dependence of the phase-matching pitch Λ for with an index difference of 4.5 × 10−3. The numbering of a fiber curves is identical to that in Fig. 3.

Fig. 6
Fig. 6

(a) Cross section of the fiber core and electrodes. In the calculations, R is chosen to be a maximum of 2a. grating in (b) Critical dimensions of the a schematic along the propagation direction.

Fig. 7
Fig. 7

Square of the overlap integral for the dc spatial field (assuming that B1 = 0.776) and the optical fields for the fundamental wavelength LP01ω and second-harmonic LP112ω modes for different values of the electrode–HCB surface distance d. With no asymmetry in the dc field (Γ = 0), the overlap is also zero. At larger values of d (as great as 4 μm), there is a substantial change in the overlap. The square of the overlap integral varies as ~exp(−4πd/Λ). The units of the vertical axis are 1/(377)3 Ω3μm−2.

Fig. 8
Fig. 8

Square of the overlap integral for measured interaction between LP01ω and LP11ω, with all second-harmonic modes for d= 4 μm for a fiber with Δn = 4.5 × 10−3. At 4 μm the ratio between the two strongest interactions, LP01ω → LP012ω and LP11ω → LP212ω, is ~0.15. Note the change in scale for LP01ω → LP012ω,. The numbering of curves is identical to that in Fig. 3. The units of the vertical axis are 1/(377)3 Ω3μm−2.

Fig. 9
Fig. 9

Representation of the overlap between modes. All the interactions shown, apart from (c), were observed in this study. The figures show the mode and static fields as a function of radial distance from the axis of the fiber. The overlap is the integral of the product of the three profiles shown. The exponential decay of the static field away from the electrode shows how part of the overlap integral is diminished. Thus as the integral changes sign its contribution is reduced. (a) Interacting field for LP01ω → LP012ω, where the overall integral is reduced, as is it for LP11ω → LP012ω, which is shown in (c). For LP01ω → LP012ω and LP11ω → LP112ω, shown in (b) and (d), respectively, the integral is zero for a uniform static field. However, with the exponential decaying field, the symmetry is reduced, thus enhancing the overlap.

Fig. 10
Fig. 10

Schematic of the periodic static field applied by the grating. (a) Top view of the device. The components of the grating static field Eg0 , resolved into two directions, y and z, are shown. Ez0 and Ey0 exist only between the electrodes, whereas Ex0 is present below the grating. Thus the fields are out of phase, as shown in (b) and (c). The field lines shown in (c) are only a pictorial representation of the actual field. The computed potential distribution has been published elsewhere.12

Fig. 11
Fig. 11

Experimental layout of periodic EFISH in optical fibers. The total fiber length used was approximately 1 m: λ/2’s, half-wave plates (1.064 μm); P1, polarizer; f1, visible block filter; f2, IR filter; HRM, high-reflection mirror; HTM, high-transmission mirror; BPF1, BPF2, bandpass filters (0.532 μm);L1–L4, lenses;PD1, photodiode; PMT, photomultiplier tube.

Fig. 12
Fig. 12

Second-harmonic signal versus electrode rotation angle, θ, for D1. The 19× expanded vertical scale selects the major observed phase-matched interactions, summarized in Table 4. Notice the relative strength of the LP01ω → LP012ω interaction (marked 2). LP11ω → LP012ω and LP01ω → LP312ω were not observed. The former interaction requires a shorter pitch than was possible with the grating, whereas the latter interaction has a small overlap integral. All second-harmonic mode patterns shown in the figure were observed visually. The interactions are as follows: 1, LP11ω → LP112ω; 2, LP01ω → LP012ω and LP11ω → LP212ω; 3, LP11ω → LP022ω; 4, LP01ω → LP112ω; 5, ? → LP212ω; 6, ? → LP022ω; 7, ? → LP022ω; 8, LP01ω → LP212ω; 9, LP11ω → LP312ω; 10, ? → LP312ω; 11, LP01ω → LP022ω.

Fig. 13
Fig. 13

Second-harmonic signal from D1 as it is translated across the electrode grating at the peak of LP01ω → LP012ω. The increase in the signal appears to be a square law. The curvature does affect the overlap integral substantially for this experiment. However, the growth of the second-harmonic power is dependent on the square of the overlap integral integrated as a function of z. The calculated second-harmonic power evolution [from relation (26)] over the initial half of the interaction is also shown in the figure. For clarity, it is slightly displaced from the measured data. The agreement can be seen to be excellent.

Fig. 14
Fig. 14

Phase-matched output for device D2. The expected three interactions are shown. The major peak displays a shape similar to a sinc2 function because fiber curvature has little effect on this 8-mm-long flat device. Mode patterns shown are of the generated second harmonic. The three interactions resolved in this measurement are shown.

Fig. 15
Fig. 15

Inset shows a fitted sinc2 function to the main LP01ω → LP012ω for device D3. The asymmetry in the structure of the tuning curve is clearly visible for both the computed and measured data, owing to the small angle θ of the electrode grating at phase matching. The effective interaction length is calculated to be 9.8 mm. No other mode interaction was resolved in this measurement. The pattern shown is that of the second-harmonic mode.

Tables (5)

Tables Icon

Table 1 Sensitivity of the Phase-Matching Pitch Λ on the Core Radius a, Core–Cladding Index Difference Δn, and Wavelength λ, for a = 4.0 μm, Δn = 4.5 × 10−3, and λ = 1.064 μm

Tables Icon

Table 2 Magnitudes and Phases of the Active χijkl(3)El0 Tensor Elements as a Result of the Components of the Applied dc Electric Field Relative to χxxxx(3)Ex0 and Grouped as in Eqs. (21a) and (21b)a

Tables Icon

Table 3 Dimensions of Periodic Electrode Structures Used in Experiments

Tables Icon

Table 4 Measured and Computed Coherence Lengths and Overlap Integrals Ratios for Seven Mode Interactions Are Compared Using Data from Device D1a

Tables Icon

Table 5 Measurement Data on Devices Used in the Experiments

Equations (46)

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

P i 2 ω = [ κ P ω E i 0 L sinc ( Δ β L / 2 ) ] 2 ,
κ = - ³ / 0 χ i j k l ( 3 ) I
Δ β = 2 β ω - β 2 ω - β 0 ,
β ω = 2 π n eff ω / λ ω ,
β 2 ω = 2 π n eff 2 ω / λ 2 ω ,
l c = π 2 β ω - β 2 ω .
β 0 = 2 π N / Λ             N = 1 , 2 , ,
v = 2 π a λ ( n core 2 - n clad 2 ) 1 / 2 ,
u = 2 π a λ ( n core 2 - n eff ) 1 / 2 ,
w 2 = v 2 - u 2 ,
b = w 2 v 2 ,
Δ n = n core - n clad ,
β 0 = 2 β ω - β 2 ω .
2 π N Λ = 2 β ω - β 2 ω ,
Δ n mismatch = n clad 2 ω - n clad ω + b 2 ω Δ n 2 ω - b ω Δ n ω ,
Λ = Λ a Δ a + Λ Δ n δ Δ n + Λ λ Δ λ .
Δ β L / 2 = ( π l c - 2 π cos θ Λ ) L grating 2 cos θ ,
2 Δ β = 5.6 L .
Δ θ = 5.6 l c cos 2 θ π L grating sin θ ,
2 l c = Λ N cos θ .
Δ θ = 2.8 Λ π L grating N tan θ .
E 0 = E x 0 i ^ + E z 0 k ^ ,
E x 0 = E g 0 B N , x ( z ) exp { - [ ( cos ϕ ) r / ρ + 1 ] Γ } ,
Γ = 2 π ρ N Λ ,
B N , x ( z ) = B N cos ( N β 0 z ) ,
I = cross section ( E μ ω ) 2 E ν 2 ω E 0 d x d y ,
I core = ( C μ ω ) 2 C ν 2 ω B N , x 0 a 0 2 π [ J μ ω ( u ω r / a ) ] 2 J ν 2 ω ( u 2 ω r / a ) × cos 2 μ ϕ cos ν ϕ exp { - [ ( cos ϕ ) r / ρ + 1 ] Γ } r d r d ϕ ,
I clad = ( C μ ω ) 2 C ν 2 ω B N , x a R + d 0 2 π [ K μ ω ( w ω r / a ) ] 2 K ν 2 ω ( w 2 ω r / a ) × cos 2 μ ϕ cos ν ϕ exp { - [ ( cos ϕ ) r / ρ + 1 ] Γ } r d r d ϕ ,
C μ ω = 2 w ω a v ω [ ( μ 0 0 ) 1 / 2 n eff ω π e μ J μ - 1 ω ( u ) J μ + 1 ω ( u ) ] 1 / 2 ,
E ^ ( r ^ , t ) = ½ [ E ^ ω exp ( - i ω t ) + E ^ * ω exp ( + i ω t ) + 2 E ^ 0 ] ,
P ^ ( r ^ , t ) = ½ [ P 2 ω exp ( - 2 i ω t ) + P ^ * 2 ω exp ( + 2 i ω t ) ] ,
P x 2 ω 0 = ½ { 3 χ x x x x ( 3 ) ( E x ω ) 2 E x 0 + [ χ x x y y ( 3 ) + χ x y x y ( 3 ) + χ x y y x ( 3 ) ] × [ 2 E x ω E y ω E y 0 + ( E y ω ) 2 E x 0 ] }
P y 2 ω 0 = ½ { 3 χ y y y y ( 3 ) ( E y ω ) 2 E y 0 + [ χ y y x x ( 3 ) + χ y x y x ( 3 ) + χ y x x y ( 3 ) ] × [ 2 E x ω E y ω E x 0 + ( E x ω ) 2 E y 0 ] } ,
χ ( 3 ) = χ x x x x ( 3 ) + χ y y y y ( 3 ) = χ x x y y ( 3 ) + χ x y x y ( 3 ) + χ y x x y ( 3 )
χ x x y y ( 3 ) = χ x y x y ( 3 ) = χ y x x y ( 3 ) = χ x x x x ( 3 ) .
E x 0 = 1 2 - + A N ξ x 0 exp ( i β 0 z ) , E y 0 = 1 2 - + B N ξ y 0 exp [ i ( β 0 z + π / 2 ) ] ,
E x ω = ξ x ω exp ( + i β ω z ) , E y ω = ξ x ω exp ( + i β ω z ) ,
P x 2 ω 0 = χ ( 3 ) 4 [ 3 ( ξ x ω ) 2 A 1 ξ x 0 + 2 ξ x ω ξ y ω B 1 ξ y 0 × exp ( i π / 2 ) + ( ξ y ω ) 2 A 1 ξ x 0 ] × { exp [ i ( 2 β ω z + β 0 z ) ] + exp [ i ( 2 β ω z - β 0 z ) ] } ,
P y 2 ω 0 = χ ( 3 ) 4 [ 3 ( ξ y ω ) 2 B 1 ξ y 0 exp ( i π / 2 ) + 2 ξ y ω ξ x ω A 1 ξ x 0 + ( ξ x ω ) 2 B 1 ξ y 0 exp ( i π / 2 ) ] × { exp [ i ( 2 β ω z + β 0 z ) ] + exp [ i ( 2 β ω z - β 0 z ) ] } .
ξ x 2 ω 0 χ ( 3 ) 4 [ 3 ( ξ x ω ) 2 A 1 ξ x 0 + 2 ξ x ω ξ y ω B 1 ξ y 0 + i ( ξ y ω ) 2 A 1 ξ x 0 ] × - L / 2 + L / 2 exp ( i Δ β z ) d z ,
ξ y 2 ω 0 χ ( 3 ) 4 [ i [ 3 ( ξ y ω ) 2 B 1 ξ y 0 + 2 ξ x ω ξ y ω A 1 ξ x 0 ] + ( ξ x ω ) 2 B 1 ξ y 0 ] × - L / 2 + L / 2 exp ( i Δ β z ) d z ,
Δ β = ( 2 β ω - β 2 ω ± β 0 )
E x 0 = E y 0 = E 0 2 .
Power ( 2 ω ) ξ x 2 ω 2 + ξ y 2 ω 2 .
Power ( 2 ω ) / [ χ ( 3 ) 0 E 0 ] 2 [ ( ξ x ω ) 2 + ( ξ y ω ) 2 ] 2 .
power 2 ω [ - L / 2 + L / 2 exp ( - π z 2 Λ Ψ ) d z ] 2 ,

Metrics