Abstract

Second-harmonic generation in the Čerenkov configuration is investigated under conditions for which the use of a linear grating fabricated on top of the waveguide reproduces a photonic bandgap structure. The fundamental mode of the guide at the fundamental frequency is tuned at the photonic band-edge resonance, thus producing great confinement and enhancement of the electromagnetic field inside the structure. The conversion efficiency achieved in both the forward and the backward directions is at least 1 order of magnitude greater than that of a conventional Cerenkov emission in a waveguide of the same length. An analysis of the tolerances of the grating period on the conversion efficiency is presented.

© 2002 Optical Society of America

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  1. G. E. Smith, “Phase matching in four-layer optical waveguides,” IEEE J. Quantum Electron. 4, 288–289 (1968).
    [CrossRef]
  2. L. Kuhn, “Nonlinear optics with finite geometries,” IEEE J. Quantum Electron. 5, 383–384 (1969).
    [CrossRef]
  3. M. De Micheli, J. Botineau, S. Neveu, P. Sibillot, D. B. Ostrowsky, and M. Papuchon, “Extension of second-harmonic phase-matching range in lithium niobate guides,” Opt. Lett. 8, 116–118 (1983).
    [CrossRef] [PubMed]
  4. K. S. Buritski, E. M. Zolotov, A. M. Prokhorov, and V. A. Chernykh, “Optimization of the parameters of planar LiNbO3:Ti waveguides for second harmonic generation,” Sov. J. Quantum Electron. 11, 1075–1077 (1981).
    [CrossRef]
  5. Y. Suematsu, “Tunable parametric oscillator using a guided wave structure,” Jpn. J. Appl. Phys. 9, 798–805 (1970).
    [CrossRef]
  6. D. B. Anderson and J. T. Boyd, “Wideband CO2 laser SHG phase matched in GaAs thin films waveguides,” Appl. Phys. Lett. 19, 266–268 (1971).
    [CrossRef]
  7. M. J. Li, M. De Micheli, Q. He, and D. B. Ostrowsky, “Cerenkov configuration second harmonic generation in proton-exchanged lithium niobate guides,” IEEE J. Quantum Electron. 26, 1384–1393 (1990).
    [CrossRef]
  8. A. M. Portis, Electromagnetic Fields: Sources and Media (Wiley, New York, 1978), pp. 567–581.
  9. P. K. Tien, R. Ultich, and R. Martin, “Optical second-harmonic generation in the form of coherent Cerenkov radiation from a thin-film waveguide,” Appl. Phys. Lett. 17, 447–450 (1970).
    [CrossRef]
  10. D. Pezzetta, C. Sibilia, M. Bertolotti, J. W. Haus, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Photonic band-gap structures in planar nonlinear waveguides: application to second-harmonic generation,” J. Opt. Soc. Am. B 18, 1326–1333 (2001).
    [CrossRef]
  11. M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, J. W. Haus, “Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures,” Phys. Rev. A 56, 3166–3174 (1997).
    [CrossRef]
  12. M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite one-dimensional photonic band-gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4898 (1999).
    [CrossRef]
  13. S. Chen, P. Baldi, P. De Micheli, D. B. Ostrowsky, A. Leycuras, G. Tartarini, and P. Bassi, “Hybrid mode in proton exchanged waveguides realized in LiNbO3, and their dependence on fabrication parameters,” J. Lightwave Technol. 12, 862–871 (1994).
    [CrossRef]
  14. G. J. Edwards and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. Quantum Electron. 16, 373–374 (1984).
    [CrossRef]
  15. R. Ramponi, M. Marangoni, and R. Osellame, “Dispersion of the ordinary refractive index change in a proton-exchanged LiNbO3 waveguide,” Appl. Phys. Lett. 78, 2098–2100 (2001).
    [CrossRef]
  16. N. A. Sanford and W. C. Robinson, “Direct measurement of effective indices of guided modes in LiNbO3 waveguides using the Cerenkov second harmonic,” Opt. Lett. 12, 445–447 (1987).
    [CrossRef] [PubMed]
  17. R. Ramponi, R. Osellame, M. Marangoni, and V. Russo, “Near-infrared refractometry of liquids by means of waveguide Cerenkov second-harmonic generation,” Appl. Opt. 37, 1–6 (1998).
  18. R. Ramponi, M. Marangoni, R. Osellame, and V. Russo, “Nonconventional characterization of single-mode planar proton-exchanged LiNbO3 waveguides by Cerenkov second harmonic generation,” Opt. Commun. 159, 37–42 (1999).
    [CrossRef]

2001

D. Pezzetta, C. Sibilia, M. Bertolotti, J. W. Haus, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Photonic band-gap structures in planar nonlinear waveguides: application to second-harmonic generation,” J. Opt. Soc. Am. B 18, 1326–1333 (2001).
[CrossRef]

R. Ramponi, M. Marangoni, and R. Osellame, “Dispersion of the ordinary refractive index change in a proton-exchanged LiNbO3 waveguide,” Appl. Phys. Lett. 78, 2098–2100 (2001).
[CrossRef]

1999

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite one-dimensional photonic band-gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4898 (1999).
[CrossRef]

R. Ramponi, M. Marangoni, R. Osellame, and V. Russo, “Nonconventional characterization of single-mode planar proton-exchanged LiNbO3 waveguides by Cerenkov second harmonic generation,” Opt. Commun. 159, 37–42 (1999).
[CrossRef]

1998

R. Ramponi, R. Osellame, M. Marangoni, and V. Russo, “Near-infrared refractometry of liquids by means of waveguide Cerenkov second-harmonic generation,” Appl. Opt. 37, 1–6 (1998).

1997

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, J. W. Haus, “Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures,” Phys. Rev. A 56, 3166–3174 (1997).
[CrossRef]

1994

S. Chen, P. Baldi, P. De Micheli, D. B. Ostrowsky, A. Leycuras, G. Tartarini, and P. Bassi, “Hybrid mode in proton exchanged waveguides realized in LiNbO3, and their dependence on fabrication parameters,” J. Lightwave Technol. 12, 862–871 (1994).
[CrossRef]

1990

M. J. Li, M. De Micheli, Q. He, and D. B. Ostrowsky, “Cerenkov configuration second harmonic generation in proton-exchanged lithium niobate guides,” IEEE J. Quantum Electron. 26, 1384–1393 (1990).
[CrossRef]

1987

1984

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

1983

1981

K. S. Buritski, E. M. Zolotov, A. M. Prokhorov, and V. A. Chernykh, “Optimization of the parameters of planar LiNbO3:Ti waveguides for second harmonic generation,” Sov. J. Quantum Electron. 11, 1075–1077 (1981).
[CrossRef]

1971

D. B. Anderson and J. T. Boyd, “Wideband CO2 laser SHG phase matched in GaAs thin films waveguides,” Appl. Phys. Lett. 19, 266–268 (1971).
[CrossRef]

1970

Y. Suematsu, “Tunable parametric oscillator using a guided wave structure,” Jpn. J. Appl. Phys. 9, 798–805 (1970).
[CrossRef]

P. K. Tien, R. Ultich, and R. Martin, “Optical second-harmonic generation in the form of coherent Cerenkov radiation from a thin-film waveguide,” Appl. Phys. Lett. 17, 447–450 (1970).
[CrossRef]

1969

L. Kuhn, “Nonlinear optics with finite geometries,” IEEE J. Quantum Electron. 5, 383–384 (1969).
[CrossRef]

1968

G. E. Smith, “Phase matching in four-layer optical waveguides,” IEEE J. Quantum Electron. 4, 288–289 (1968).
[CrossRef]

Anderson, D. B.

D. B. Anderson and J. T. Boyd, “Wideband CO2 laser SHG phase matched in GaAs thin films waveguides,” Appl. Phys. Lett. 19, 266–268 (1971).
[CrossRef]

Baldi, P.

S. Chen, P. Baldi, P. De Micheli, D. B. Ostrowsky, A. Leycuras, G. Tartarini, and P. Bassi, “Hybrid mode in proton exchanged waveguides realized in LiNbO3, and their dependence on fabrication parameters,” J. Lightwave Technol. 12, 862–871 (1994).
[CrossRef]

Bassi, P.

S. Chen, P. Baldi, P. De Micheli, D. B. Ostrowsky, A. Leycuras, G. Tartarini, and P. Bassi, “Hybrid mode in proton exchanged waveguides realized in LiNbO3, and their dependence on fabrication parameters,” J. Lightwave Technol. 12, 862–871 (1994).
[CrossRef]

Bertolotti, M.

D. Pezzetta, C. Sibilia, M. Bertolotti, J. W. Haus, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Photonic band-gap structures in planar nonlinear waveguides: application to second-harmonic generation,” J. Opt. Soc. Am. B 18, 1326–1333 (2001).
[CrossRef]

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite one-dimensional photonic band-gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4898 (1999).
[CrossRef]

Bloemer, M. J.

D. Pezzetta, C. Sibilia, M. Bertolotti, J. W. Haus, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Photonic band-gap structures in planar nonlinear waveguides: application to second-harmonic generation,” J. Opt. Soc. Am. B 18, 1326–1333 (2001).
[CrossRef]

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite one-dimensional photonic band-gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4898 (1999).
[CrossRef]

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, J. W. Haus, “Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures,” Phys. Rev. A 56, 3166–3174 (1997).
[CrossRef]

Botineau, J.

Bowden, C. M.

D. Pezzetta, C. Sibilia, M. Bertolotti, J. W. Haus, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Photonic band-gap structures in planar nonlinear waveguides: application to second-harmonic generation,” J. Opt. Soc. Am. B 18, 1326–1333 (2001).
[CrossRef]

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite one-dimensional photonic band-gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4898 (1999).
[CrossRef]

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, J. W. Haus, “Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures,” Phys. Rev. A 56, 3166–3174 (1997).
[CrossRef]

Boyd, J. T.

D. B. Anderson and J. T. Boyd, “Wideband CO2 laser SHG phase matched in GaAs thin films waveguides,” Appl. Phys. Lett. 19, 266–268 (1971).
[CrossRef]

Buritski, K. S.

K. S. Buritski, E. M. Zolotov, A. M. Prokhorov, and V. A. Chernykh, “Optimization of the parameters of planar LiNbO3:Ti waveguides for second harmonic generation,” Sov. J. Quantum Electron. 11, 1075–1077 (1981).
[CrossRef]

Centini, M.

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite one-dimensional photonic band-gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4898 (1999).
[CrossRef]

Chen, S.

S. Chen, P. Baldi, P. De Micheli, D. B. Ostrowsky, A. Leycuras, G. Tartarini, and P. Bassi, “Hybrid mode in proton exchanged waveguides realized in LiNbO3, and their dependence on fabrication parameters,” J. Lightwave Technol. 12, 862–871 (1994).
[CrossRef]

Chernykh, V. A.

K. S. Buritski, E. M. Zolotov, A. M. Prokhorov, and V. A. Chernykh, “Optimization of the parameters of planar LiNbO3:Ti waveguides for second harmonic generation,” Sov. J. Quantum Electron. 11, 1075–1077 (1981).
[CrossRef]

D’Aguanno, G.

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite one-dimensional photonic band-gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4898 (1999).
[CrossRef]

De Micheli, M.

M. J. Li, M. De Micheli, Q. He, and D. B. Ostrowsky, “Cerenkov configuration second harmonic generation in proton-exchanged lithium niobate guides,” IEEE J. Quantum Electron. 26, 1384–1393 (1990).
[CrossRef]

M. De Micheli, J. Botineau, S. Neveu, P. Sibillot, D. B. Ostrowsky, and M. Papuchon, “Extension of second-harmonic phase-matching range in lithium niobate guides,” Opt. Lett. 8, 116–118 (1983).
[CrossRef] [PubMed]

De Micheli, P.

S. Chen, P. Baldi, P. De Micheli, D. B. Ostrowsky, A. Leycuras, G. Tartarini, and P. Bassi, “Hybrid mode in proton exchanged waveguides realized in LiNbO3, and their dependence on fabrication parameters,” J. Lightwave Technol. 12, 862–871 (1994).
[CrossRef]

Dowling, J. P.

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, J. W. Haus, “Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures,” Phys. Rev. A 56, 3166–3174 (1997).
[CrossRef]

Edwards, G. J.

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

Haus, J. W.

D. Pezzetta, C. Sibilia, M. Bertolotti, J. W. Haus, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Photonic band-gap structures in planar nonlinear waveguides: application to second-harmonic generation,” J. Opt. Soc. Am. B 18, 1326–1333 (2001).
[CrossRef]

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, J. W. Haus, “Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures,” Phys. Rev. A 56, 3166–3174 (1997).
[CrossRef]

He, Q.

M. J. Li, M. De Micheli, Q. He, and D. B. Ostrowsky, “Cerenkov configuration second harmonic generation in proton-exchanged lithium niobate guides,” IEEE J. Quantum Electron. 26, 1384–1393 (1990).
[CrossRef]

Kuhn, L.

L. Kuhn, “Nonlinear optics with finite geometries,” IEEE J. Quantum Electron. 5, 383–384 (1969).
[CrossRef]

Lawrence, M.

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

Leycuras, A.

S. Chen, P. Baldi, P. De Micheli, D. B. Ostrowsky, A. Leycuras, G. Tartarini, and P. Bassi, “Hybrid mode in proton exchanged waveguides realized in LiNbO3, and their dependence on fabrication parameters,” J. Lightwave Technol. 12, 862–871 (1994).
[CrossRef]

Li, M. J.

M. J. Li, M. De Micheli, Q. He, and D. B. Ostrowsky, “Cerenkov configuration second harmonic generation in proton-exchanged lithium niobate guides,” IEEE J. Quantum Electron. 26, 1384–1393 (1990).
[CrossRef]

Manka, A. S.

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, J. W. Haus, “Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures,” Phys. Rev. A 56, 3166–3174 (1997).
[CrossRef]

Marangoni, M.

R. Ramponi, M. Marangoni, and R. Osellame, “Dispersion of the ordinary refractive index change in a proton-exchanged LiNbO3 waveguide,” Appl. Phys. Lett. 78, 2098–2100 (2001).
[CrossRef]

R. Ramponi, M. Marangoni, R. Osellame, and V. Russo, “Nonconventional characterization of single-mode planar proton-exchanged LiNbO3 waveguides by Cerenkov second harmonic generation,” Opt. Commun. 159, 37–42 (1999).
[CrossRef]

R. Ramponi, R. Osellame, M. Marangoni, and V. Russo, “Near-infrared refractometry of liquids by means of waveguide Cerenkov second-harmonic generation,” Appl. Opt. 37, 1–6 (1998).

Martin, R.

P. K. Tien, R. Ultich, and R. Martin, “Optical second-harmonic generation in the form of coherent Cerenkov radiation from a thin-film waveguide,” Appl. Phys. Lett. 17, 447–450 (1970).
[CrossRef]

Nefedov, I.

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite one-dimensional photonic band-gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4898 (1999).
[CrossRef]

Neveu, S.

Osellame, R.

R. Ramponi, M. Marangoni, and R. Osellame, “Dispersion of the ordinary refractive index change in a proton-exchanged LiNbO3 waveguide,” Appl. Phys. Lett. 78, 2098–2100 (2001).
[CrossRef]

R. Ramponi, M. Marangoni, R. Osellame, and V. Russo, “Nonconventional characterization of single-mode planar proton-exchanged LiNbO3 waveguides by Cerenkov second harmonic generation,” Opt. Commun. 159, 37–42 (1999).
[CrossRef]

R. Ramponi, R. Osellame, M. Marangoni, and V. Russo, “Near-infrared refractometry of liquids by means of waveguide Cerenkov second-harmonic generation,” Appl. Opt. 37, 1–6 (1998).

Ostrowsky, D. B.

S. Chen, P. Baldi, P. De Micheli, D. B. Ostrowsky, A. Leycuras, G. Tartarini, and P. Bassi, “Hybrid mode in proton exchanged waveguides realized in LiNbO3, and their dependence on fabrication parameters,” J. Lightwave Technol. 12, 862–871 (1994).
[CrossRef]

M. J. Li, M. De Micheli, Q. He, and D. B. Ostrowsky, “Cerenkov configuration second harmonic generation in proton-exchanged lithium niobate guides,” IEEE J. Quantum Electron. 26, 1384–1393 (1990).
[CrossRef]

M. De Micheli, J. Botineau, S. Neveu, P. Sibillot, D. B. Ostrowsky, and M. Papuchon, “Extension of second-harmonic phase-matching range in lithium niobate guides,” Opt. Lett. 8, 116–118 (1983).
[CrossRef] [PubMed]

Papuchon, M.

Pezzetta, D.

Prokhorov, A. M.

K. S. Buritski, E. M. Zolotov, A. M. Prokhorov, and V. A. Chernykh, “Optimization of the parameters of planar LiNbO3:Ti waveguides for second harmonic generation,” Sov. J. Quantum Electron. 11, 1075–1077 (1981).
[CrossRef]

Ramponi, R.

R. Ramponi, M. Marangoni, and R. Osellame, “Dispersion of the ordinary refractive index change in a proton-exchanged LiNbO3 waveguide,” Appl. Phys. Lett. 78, 2098–2100 (2001).
[CrossRef]

R. Ramponi, M. Marangoni, R. Osellame, and V. Russo, “Nonconventional characterization of single-mode planar proton-exchanged LiNbO3 waveguides by Cerenkov second harmonic generation,” Opt. Commun. 159, 37–42 (1999).
[CrossRef]

R. Ramponi, R. Osellame, M. Marangoni, and V. Russo, “Near-infrared refractometry of liquids by means of waveguide Cerenkov second-harmonic generation,” Appl. Opt. 37, 1–6 (1998).

Robinson, W. C.

Russo, V.

R. Ramponi, M. Marangoni, R. Osellame, and V. Russo, “Nonconventional characterization of single-mode planar proton-exchanged LiNbO3 waveguides by Cerenkov second harmonic generation,” Opt. Commun. 159, 37–42 (1999).
[CrossRef]

R. Ramponi, R. Osellame, M. Marangoni, and V. Russo, “Near-infrared refractometry of liquids by means of waveguide Cerenkov second-harmonic generation,” Appl. Opt. 37, 1–6 (1998).

Sanford, N. A.

Scalora, M.

D. Pezzetta, C. Sibilia, M. Bertolotti, J. W. Haus, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Photonic band-gap structures in planar nonlinear waveguides: application to second-harmonic generation,” J. Opt. Soc. Am. B 18, 1326–1333 (2001).
[CrossRef]

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite one-dimensional photonic band-gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4898 (1999).
[CrossRef]

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, J. W. Haus, “Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures,” Phys. Rev. A 56, 3166–3174 (1997).
[CrossRef]

Sibilia, C.

D. Pezzetta, C. Sibilia, M. Bertolotti, J. W. Haus, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Photonic band-gap structures in planar nonlinear waveguides: application to second-harmonic generation,” J. Opt. Soc. Am. B 18, 1326–1333 (2001).
[CrossRef]

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite one-dimensional photonic band-gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4898 (1999).
[CrossRef]

Sibillot, P.

Smith, G. E.

G. E. Smith, “Phase matching in four-layer optical waveguides,” IEEE J. Quantum Electron. 4, 288–289 (1968).
[CrossRef]

Suematsu, Y.

Y. Suematsu, “Tunable parametric oscillator using a guided wave structure,” Jpn. J. Appl. Phys. 9, 798–805 (1970).
[CrossRef]

Tartarini, G.

S. Chen, P. Baldi, P. De Micheli, D. B. Ostrowsky, A. Leycuras, G. Tartarini, and P. Bassi, “Hybrid mode in proton exchanged waveguides realized in LiNbO3, and their dependence on fabrication parameters,” J. Lightwave Technol. 12, 862–871 (1994).
[CrossRef]

Tien, P. K.

P. K. Tien, R. Ultich, and R. Martin, “Optical second-harmonic generation in the form of coherent Cerenkov radiation from a thin-film waveguide,” Appl. Phys. Lett. 17, 447–450 (1970).
[CrossRef]

Ultich, R.

P. K. Tien, R. Ultich, and R. Martin, “Optical second-harmonic generation in the form of coherent Cerenkov radiation from a thin-film waveguide,” Appl. Phys. Lett. 17, 447–450 (1970).
[CrossRef]

Viswanathan, R.

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, J. W. Haus, “Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures,” Phys. Rev. A 56, 3166–3174 (1997).
[CrossRef]

Zolotov, E. M.

K. S. Buritski, E. M. Zolotov, A. M. Prokhorov, and V. A. Chernykh, “Optimization of the parameters of planar LiNbO3:Ti waveguides for second harmonic generation,” Sov. J. Quantum Electron. 11, 1075–1077 (1981).
[CrossRef]

Appl. Opt.

R. Ramponi, R. Osellame, M. Marangoni, and V. Russo, “Near-infrared refractometry of liquids by means of waveguide Cerenkov second-harmonic generation,” Appl. Opt. 37, 1–6 (1998).

Appl. Phys. Lett.

R. Ramponi, M. Marangoni, and R. Osellame, “Dispersion of the ordinary refractive index change in a proton-exchanged LiNbO3 waveguide,” Appl. Phys. Lett. 78, 2098–2100 (2001).
[CrossRef]

D. B. Anderson and J. T. Boyd, “Wideband CO2 laser SHG phase matched in GaAs thin films waveguides,” Appl. Phys. Lett. 19, 266–268 (1971).
[CrossRef]

P. K. Tien, R. Ultich, and R. Martin, “Optical second-harmonic generation in the form of coherent Cerenkov radiation from a thin-film waveguide,” Appl. Phys. Lett. 17, 447–450 (1970).
[CrossRef]

IEEE J. Quantum Electron.

M. J. Li, M. De Micheli, Q. He, and D. B. Ostrowsky, “Cerenkov configuration second harmonic generation in proton-exchanged lithium niobate guides,” IEEE J. Quantum Electron. 26, 1384–1393 (1990).
[CrossRef]

G. E. Smith, “Phase matching in four-layer optical waveguides,” IEEE J. Quantum Electron. 4, 288–289 (1968).
[CrossRef]

L. Kuhn, “Nonlinear optics with finite geometries,” IEEE J. Quantum Electron. 5, 383–384 (1969).
[CrossRef]

J. Lightwave Technol.

S. Chen, P. Baldi, P. De Micheli, D. B. Ostrowsky, A. Leycuras, G. Tartarini, and P. Bassi, “Hybrid mode in proton exchanged waveguides realized in LiNbO3, and their dependence on fabrication parameters,” J. Lightwave Technol. 12, 862–871 (1994).
[CrossRef]

J. Opt. Soc. Am. B

Jpn. J. Appl. Phys.

Y. Suematsu, “Tunable parametric oscillator using a guided wave structure,” Jpn. J. Appl. Phys. 9, 798–805 (1970).
[CrossRef]

Opt. Commun.

R. Ramponi, M. Marangoni, R. Osellame, and V. Russo, “Nonconventional characterization of single-mode planar proton-exchanged LiNbO3 waveguides by Cerenkov second harmonic generation,” Opt. Commun. 159, 37–42 (1999).
[CrossRef]

Opt. Lett.

Opt. Quantum Electron.

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

Phys. Rev. A

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, J. W. Haus, “Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures,” Phys. Rev. A 56, 3166–3174 (1997).
[CrossRef]

Phys. Rev. E

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite one-dimensional photonic band-gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4898 (1999).
[CrossRef]

Sov. J. Quantum Electron.

K. S. Buritski, E. M. Zolotov, A. M. Prokhorov, and V. A. Chernykh, “Optimization of the parameters of planar LiNbO3:Ti waveguides for second harmonic generation,” Sov. J. Quantum Electron. 11, 1075–1077 (1981).
[CrossRef]

Other

A. M. Portis, Electromagnetic Fields: Sources and Media (Wiley, New York, 1978), pp. 567–581.

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Figures (8)

Fig. 1
Fig. 1

Geometry of the planar guide with respect to the crystal axes in the case of a Z-cut LiNbO3 substrate. The only guided modes in the Z-cut substrate are the TM modes because, in the TE case, the only nonvanishing electric field component Ey is parallel to the ordinary component of the dielectric constant tensor: The ordinary component of the refractive index is reduced by the proton-exchange technique, and the TE wave is no longer totally reflected at the film–substrate interface.

Fig. 2
Fig. 2

Linear grating obtained by the etching of part of the film layer or, alternatively, the deposition of an additional cladding material and the periodic etching of this additional layer.

Fig. 3
Fig. 3

Forward SHG relative conversion efficiency for the 0.92-µm-deep waveguide plotted as a function of the linear grating’s number of periods N and of the grating thickness h. In the Čerenkov configuration, the forward and the backward nonlinear processes no longer have the same conversion efficiency: The forward-propagating field is increased far more by the presence of the linear grating. The relative conversion efficiencies are set to zero when the linewidth of the transmission spectrum becomes less than 3 GHz.

Fig. 4
Fig. 4

Waveguide PBG transmission spectrum for the 0.92-µm-deep waveguide with N=4500 and h=0.25 µm. The band-edge transmission resonance occurs at exactly the fundamental field frequency and is 3 GHz wide.

Fig. 5
Fig. 5

Period of the linear grating (in nanometers) plotted as a function of the fundamental wavelength tuned at the BER when the fundamental wavelength is in the C band (1528.77–1569.59 nm).

Fig. 6
Fig. 6

(a) Backward and (b) forward relative conversion efficiencies when the period of the linear grating corresponds to the tuning of the fundamental frequency at the BER and the fundamental frequency is in the C band. As the fundamental wavelength increases to more than 1.55 µm, the forward and the backward relative conversion efficiencies become greater than the expected values given in Table 3 because the PBG transmission bandwidth becomes smaller than the design value of 3 GHz (see Fig. 7).

Fig. 7
Fig. 7

PBG transmission spectrum bandwidth plotted as a function of the fundamental wavelength. The dashed curve shows that the transmission bandwidth is less than 3 GHz.

Fig. 8
Fig. 8

Normalized conversion efficiency plotted as a function of the duty cycle of the linear grating.

Tables (4)

Tables Icon

Table 1 Refractive Indices14 Used in the Numerical Calculations and Index Steps15 for the Ordinary and the Extraordinary Refractive Indicesa

Tables Icon

Table 2 Sample Waveguides Considered in the Numerical Calculations: Film Depths and Effective Refractive Indices for the TM0 and the TM1 Guided Modes at the Fundamental and the Second-Harmonic Wavelengthsa

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Table 3 Comparison of the Results Obtained for the Three Waveguidesa

Tables Icon

Table 4 Sensitivity of the Fundamental Wavelength with Respect to Various Parameters

Equations (53)

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×E=iωμH,×H=-iω0(r+Δr)E,
dA+d=iKL(z)A- exp(-i2βFFz)+iKNL(z)B+(A+)*exp(iΔβz),
dA-dz=-iKL(z)A+ exp(i2βFPz)+iKNL(z)B-(A-)*exp(-iΔβz),
dB+dz=iKNL(z)(A+)2exp(-iΔβz),
dB-dz=iKNL(z)(A-)2exp(iΔβz),
Δr(x, y, z)
=(no/e,f2-nc2)f(z)txt+h0x<t,x>t+h,
f(z)=12+m=-+ sin(π/2+mπ)(2m+1)π expi2π 2m+1ΛLz.
A+(z)=a+(z)exp(iδ1z),A-(z)=a-(z)exp(-iδ1z), 
B+(z)=b+(z)exp(-iδ2z),B-(z)=b-(z)exp(iδ2z), 
2δ1=2πΛL-2βFF,
da+dz+iδ1a+=iKL1a-+iKNLb+(a+)*×exp[i(Δβ-2δ1-δ2)z],
da-dz-iδ1a-=-iKL1a++iKNLb-(a-)*×exp[-i(Δβ-2δ1-δ2)z],
db+dz-iδ2b+=iKNL(a+)2×exp[-i(Δβ-2δ1-δ2)z],
db-dz+iδ2b-=iKNL(a-)2×exp[i(Δβ-2δ1-δ2)z].
δ2=Δβ-2δ1
δ2=0.
Δβ=2δ1
βSH=2πΛL.
a+(z)=C1 cos(Δ1z)+C2 sin(Δ1z),
a-(z)=C2 Δ1iKL1+C1 δ1KL1cos(Δ1z)+C2 δ1KL1-C1 Δ1iKL1sin(Δ1z),
Δ12=δ12-KL12.
a-(0)=a-(L=NΛL)=0C2C1=-i δ1Δ1Δ1NΛL=mπ,
2πΛL=2βFF+βFFN2+1-1N2KL12.
θCˇerenkovOut=cos-1δ02ΛL 1ne,sSH,
b+(0)=0,
b-(L=NΛL)=0.
a+(z)=Acos(Δ1z)-i δ1Δ1 sin(Δ1z),
a-(z)=-iA KL1Δ1 sin(Δ1z),
b+(z)=-iKNL1 A22 exp-i Δβ¯z2z-KL1Δ12×sincΔβ¯z2+exp(Δ1z) 12 1+δ1Δ12-δ1Δ1×sinc(2Δ1-Δβ¯) z2+exp(-Δ1z) 12 1+δ1Δ12+δ1Δ1×sinc(2Δ1+Δβ¯) z2,
b-(z)=-iKNL1 A22 KL1Δ12 expi Δβ¯z2zsincΔβ¯z2-12 exp(Δ1z)sinc(2Δ1-Δβ¯) z2-12 exp(-Δ1z)sinc(2Δ1+Δβ¯) z2,
PSH+=0k0SHne,sSH|b+(L)|2dβSH,
PSH-=-k0SHne,sSH0|b-(L)|2dβSH,
PSH+=KNL2A2KL1Δ14L ξ+2,
PSH-=KNL2A4KL1Δ14L ξ-2,
nref=K˜NL2A22πL,
ηrel+=n+nref=KNLK˜NL2KL1Δ14 ξ+4π,
nrel-=η-ηref=KNLK˜NL2KL1Δ14 ξ-4π.
GPBGBack/Forward=LPBGLCSHGηrelBack/Forward
ΛL>λ02ne,sSH.
λ0FF|BER=f(N, t, ΛL).
SNλ0FF|BER=(λ0FF|BER)N Nλ0FF|BER,
Shλ0FF|BER=(λ0FF|BER)h hλ0FF|BER,
SΛLλ0FF|BER=(λ0FF|BER)ΛL ΛLλ0FF|BER.
ηrel±sin4(πδΛL).
βSH=k0SHne,sSH cos(θCˇerenkovOut).
PSH-=KNL2 A44 KL1Δ14L20k0SHne,sSHsincΔβ¯L2+12 sincΔβ¯L2+π+12 sincΔβ¯L2-π2dβSH,
ξ-=-+sinc(x)+12 sinc(x+π)+12 sinc(x-π)2dx32π,
PSH+=KNL2 A44 KL1Δ14L20k0SHne,sSHsincΔβ¯L2+Δ12+δ12+Δ1δ1KL12 sincΔβ¯L2+π+Δ12+δ12-Δ1δ1KL12 sincΔβ¯L2-π2dβSH.
ξ+=-+sinc(x)+Δ12+δ12+Δ1δ1KL12 sinc(x+π)+Δ12+δ12-Δ1δ1KL12 sinc(x-π)2dx=fβFF,2πΛL,h.
ddzbref+=iK˜NLA2 exp(-iΔβz),
bref+(L=NΛL)=iK˜NLA2 exp-i ΔβL2sincΔβL2L.
PSHref=0k0SHne,sSH|bref+(L)|2dβSH=K˜NL2A42πL.

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