Abstract

Second-harmonic generation (SHG) is investigated in a planar waveguide geometry 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, which coincides with the fundamental pump frequency, is tuned at the photonic band-edge resonance in order to enhance field-localization effects. However, the linear grating alone is not able to produce both field confinement and phase matching of the second-harmonic-generation process. Phase matching is obtained with the additional modulation of the nonlinear susceptibility χ(2), as in conventional quasi-phase-matching schemes. The conversion efficiency achieved with both linear and nonlinear gratings is orders of magnitude greater than that of a quasi-phase-matched device of the same length.

© 2001 Optical Society of America

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  1. R. A. Andrews, “Crystal symmetry effects on nonlinear optical processes in optical waveguides,” IEEE J. Quantum Electron. 7, 523–529 (1971).
    [Crossref]
  2. J. T. Boyd, “Theory of parametric oscillation phase matched in GaAs thin film waveguides,” IEEE J. Quantum Electron. 8, 788–796 (1972).
    [Crossref]
  3. M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
    [Crossref]
  4. M. Fejer, “Nonlinear frequency conversion in periodically-poled ferroelectric waveguides,” in Guided Wave Nonlinear Optics (Kluwer Academic, Dordrecht, The Netherlands, 1992).
  5. T. Sugita, K. Mizuuchi, Y. Kitaoka, and K. Yamamoto, “31%-efficient blue second-harmonic generation in a periodically poled MgO:LiNbO3 waveguide by frequency doubling of an AlGaAs laser diode,” Opt. Lett. 24, 1590–1592 (1996).
    [Crossref]
  6. C. L. Tang and P. B. Bey, “Phase matching in second harmonic generation using artificial periodic structure,” IEEE J. Quantum Electron. 9, 9–17 (1973).
    [Crossref]
  7. T. Suhara and H. Nishihara, “Theoretical analysis of waveguide second-harmonic generation phase matched with uniform and chirped gratings,” IEEE J. Quantum Electron. 26, 1265–1276 (1990).
    [Crossref]
  8. M. Yokota, S. Takaishi, and J. Yamane, “Second-harmonic generation in nonlinear grating coupler,” J. Appl. Phys. 84, 5913–5921 (1998).
    [Crossref]
  9. J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures,” Phys. Rev. E 53, 4107–4121 (1996).
    [Crossref]
  10. M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures,” Phys. Rev. A 56, 3166–3174 (1997).
    [Crossref]
  11. 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]
  12. V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Photonic band-structure effects in the reflectivity of periodically patterned waveguides,” Phys. Rev. B 60, R16255–R16258 (1999).
    [Crossref]
  13. M. Bertolotti, P. Masciulli, C. Sibilia, F. Wijnands, and H. Hoekstra, “Transmission properties of a Cantor corrugated waveguide,” J. Opt. Soc. Am. B 13, 628–634 (1996).
    [Crossref]
  14. H. Nishiara, M. Haruna, and T. Suhara, Optical Integrated Circuits (McGraw-Hill, New York, 1989).
  15. 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]
  16. J. W. Haus, R. Viswanathan, M. Scalora, A. G. Kalocsai, J. D. Cole, and J. Theimer, “Enhanced second-harmonic generation in media with a weak periodicity,” Phys. Rev. A 57, 2120–2128 (1998).
    [Crossref]
  17. G. D’Aguanno, M. Centini, C. Sibilia, M. Bertolotti, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Enhancement of χ(2) cascading processes in one-dimensional photonic bandgap structures,” Opt. Lett. 24, 1663–1665 (1999).
    [Crossref]
  18. 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]
  19. A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).
  20. M. Marangoni, “Guide d’onda planari in niobato di litio per generazione di seconda armonica: modellistica, caratterizzazione e misure non lineari,” Ph.D. dissertation (Politecnico di Milano, Milan, 1998).

1999 (3)

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]

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Photonic band-structure effects in the reflectivity of periodically patterned waveguides,” Phys. Rev. B 60, R16255–R16258 (1999).
[Crossref]

G. D’Aguanno, M. Centini, C. Sibilia, M. Bertolotti, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Enhancement of χ(2) cascading processes in one-dimensional photonic bandgap structures,” Opt. Lett. 24, 1663–1665 (1999).
[Crossref]

1998 (2)

J. W. Haus, R. Viswanathan, M. Scalora, A. G. Kalocsai, J. D. Cole, and J. Theimer, “Enhanced second-harmonic generation in media with a weak periodicity,” Phys. Rev. A 57, 2120–2128 (1998).
[Crossref]

M. Yokota, S. Takaishi, and J. Yamane, “Second-harmonic generation in nonlinear grating coupler,” J. Appl. Phys. 84, 5913–5921 (1998).
[Crossref]

1997 (1)

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

1996 (3)

1994 (1)

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]

1992 (1)

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[Crossref]

1990 (2)

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]

T. Suhara and H. Nishihara, “Theoretical analysis of waveguide second-harmonic generation phase matched with uniform and chirped gratings,” IEEE J. Quantum Electron. 26, 1265–1276 (1990).
[Crossref]

1973 (1)

C. L. Tang and P. B. Bey, “Phase matching in second harmonic generation using artificial periodic structure,” IEEE J. Quantum Electron. 9, 9–17 (1973).
[Crossref]

1972 (1)

J. T. Boyd, “Theory of parametric oscillation phase matched in GaAs thin film waveguides,” IEEE J. Quantum Electron. 8, 788–796 (1972).
[Crossref]

1971 (1)

R. A. Andrews, “Crystal symmetry effects on nonlinear optical processes in optical waveguides,” IEEE J. Quantum Electron. 7, 523–529 (1971).
[Crossref]

Andrews, R. A.

R. A. Andrews, “Crystal symmetry effects on nonlinear optical processes in optical waveguides,” IEEE J. Quantum Electron. 7, 523–529 (1971).
[Crossref]

Astratov, V. N.

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Photonic band-structure effects in the reflectivity of periodically patterned waveguides,” Phys. Rev. B 60, R16255–R16258 (1999).
[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]

Bendickson, J. M.

J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures,” Phys. Rev. E 53, 4107–4121 (1996).
[Crossref]

Bertolotti, M.

Bey, P. B.

C. L. Tang and P. B. Bey, “Phase matching in second harmonic generation using artificial periodic structure,” IEEE J. Quantum Electron. 9, 9–17 (1973).
[Crossref]

Bloemer, M. J.

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]

G. D’Aguanno, M. Centini, C. Sibilia, M. Bertolotti, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Enhancement of χ(2) cascading processes in one-dimensional photonic bandgap structures,” Opt. Lett. 24, 1663–1665 (1999).
[Crossref]

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

Bowden, C. 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]

G. D’Aguanno, M. Centini, C. Sibilia, M. Bertolotti, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Enhancement of χ(2) cascading processes in one-dimensional photonic bandgap structures,” Opt. Lett. 24, 1663–1665 (1999).
[Crossref]

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

Boyd, J. T.

J. T. Boyd, “Theory of parametric oscillation phase matched in GaAs thin film waveguides,” IEEE J. Quantum Electron. 8, 788–796 (1972).
[Crossref]

Byer, R. L.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[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]

G. D’Aguanno, M. Centini, C. Sibilia, M. Bertolotti, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Enhancement of χ(2) cascading processes in one-dimensional photonic bandgap structures,” Opt. Lett. 24, 1663–1665 (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]

Cole, J. D.

J. W. Haus, R. Viswanathan, M. Scalora, A. G. Kalocsai, J. D. Cole, and J. Theimer, “Enhanced second-harmonic generation in media with a weak periodicity,” Phys. Rev. A 57, 2120–2128 (1998).
[Crossref]

Culshaw, I. S.

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Photonic band-structure effects in the reflectivity of periodically patterned waveguides,” Phys. Rev. B 60, R16255–R16258 (1999).
[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]

G. D’Aguanno, M. Centini, C. Sibilia, M. Bertolotti, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Enhancement of χ(2) cascading processes in one-dimensional photonic bandgap structures,” Opt. Lett. 24, 1663–1665 (1999).
[Crossref]

De La Rue, R. M.

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Photonic band-structure effects in the reflectivity of periodically patterned waveguides,” Phys. Rev. B 60, R16255–R16258 (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]

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, and J. W. Haus, “Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures,” Phys. Rev. A 56, 3166–3174 (1997).
[Crossref]

J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures,” Phys. Rev. E 53, 4107–4121 (1996).
[Crossref]

Fejer, M.

M. Fejer, “Nonlinear frequency conversion in periodically-poled ferroelectric waveguides,” in Guided Wave Nonlinear Optics (Kluwer Academic, Dordrecht, The Netherlands, 1992).

Fejer, M. M.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[Crossref]

Haruna, M.

H. Nishiara, M. Haruna, and T. Suhara, Optical Integrated Circuits (McGraw-Hill, New York, 1989).

Haus, J. W.

J. W. Haus, R. Viswanathan, M. Scalora, A. G. Kalocsai, J. D. Cole, and J. Theimer, “Enhanced second-harmonic generation in media with a weak periodicity,” Phys. Rev. A 57, 2120–2128 (1998).
[Crossref]

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and 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]

Hoekstra, H.

Jundt, D. H.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[Crossref]

Kalocsai, A. G.

J. W. Haus, R. Viswanathan, M. Scalora, A. G. Kalocsai, J. D. Cole, and J. Theimer, “Enhanced second-harmonic generation in media with a weak periodicity,” Phys. Rev. A 57, 2120–2128 (1998).
[Crossref]

Kitaoka, Y.

Krauss, T. F.

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Photonic band-structure effects in the reflectivity of periodically patterned waveguides,” Phys. Rev. B 60, R16255–R16258 (1999).
[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]

Magel, G. A.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[Crossref]

Manka, A. S.

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

Marangoni, M.

M. Marangoni, “Guide d’onda planari in niobato di litio per generazione di seconda armonica: modellistica, caratterizzazione e misure non lineari,” Ph.D. dissertation (Politecnico di Milano, Milan, 1998).

Masciulli, P.

Mizuuchi, K.

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]

Nishiara, H.

H. Nishiara, M. Haruna, and T. Suhara, Optical Integrated Circuits (McGraw-Hill, New York, 1989).

Nishihara, H.

T. Suhara and H. Nishihara, “Theoretical analysis of waveguide second-harmonic generation phase matched with uniform and chirped gratings,” IEEE J. Quantum Electron. 26, 1265–1276 (1990).
[Crossref]

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]

Scalora, 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]

G. D’Aguanno, M. Centini, C. Sibilia, M. Bertolotti, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Enhancement of χ(2) cascading processes in one-dimensional photonic bandgap structures,” Opt. Lett. 24, 1663–1665 (1999).
[Crossref]

J. W. Haus, R. Viswanathan, M. Scalora, A. G. Kalocsai, J. D. Cole, and J. Theimer, “Enhanced second-harmonic generation in media with a weak periodicity,” Phys. Rev. A 57, 2120–2128 (1998).
[Crossref]

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

J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures,” Phys. Rev. E 53, 4107–4121 (1996).
[Crossref]

Sibilia, C.

Skolnick, M. S.

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Photonic band-structure effects in the reflectivity of periodically patterned waveguides,” Phys. Rev. B 60, R16255–R16258 (1999).
[Crossref]

Stevenson, R. M.

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Photonic band-structure effects in the reflectivity of periodically patterned waveguides,” Phys. Rev. B 60, R16255–R16258 (1999).
[Crossref]

Sugita, T.

Suhara, T.

T. Suhara and H. Nishihara, “Theoretical analysis of waveguide second-harmonic generation phase matched with uniform and chirped gratings,” IEEE J. Quantum Electron. 26, 1265–1276 (1990).
[Crossref]

H. Nishiara, M. Haruna, and T. Suhara, Optical Integrated Circuits (McGraw-Hill, New York, 1989).

Takaishi, S.

M. Yokota, S. Takaishi, and J. Yamane, “Second-harmonic generation in nonlinear grating coupler,” J. Appl. Phys. 84, 5913–5921 (1998).
[Crossref]

Tang, C. L.

C. L. Tang and P. B. Bey, “Phase matching in second harmonic generation using artificial periodic structure,” IEEE J. Quantum Electron. 9, 9–17 (1973).
[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]

Theimer, J.

J. W. Haus, R. Viswanathan, M. Scalora, A. G. Kalocsai, J. D. Cole, and J. Theimer, “Enhanced second-harmonic generation in media with a weak periodicity,” Phys. Rev. A 57, 2120–2128 (1998).
[Crossref]

Viswanathan, R.

J. W. Haus, R. Viswanathan, M. Scalora, A. G. Kalocsai, J. D. Cole, and J. Theimer, “Enhanced second-harmonic generation in media with a weak periodicity,” Phys. Rev. A 57, 2120–2128 (1998).
[Crossref]

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

Whittaker, D. M.

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Photonic band-structure effects in the reflectivity of periodically patterned waveguides,” Phys. Rev. B 60, R16255–R16258 (1999).
[Crossref]

Wijnands, F.

Yamamoto, K.

Yamane, J.

M. Yokota, S. Takaishi, and J. Yamane, “Second-harmonic generation in nonlinear grating coupler,” J. Appl. Phys. 84, 5913–5921 (1998).
[Crossref]

Yariv, A.

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

Yeh, P.

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

Yokota, M.

M. Yokota, S. Takaishi, and J. Yamane, “Second-harmonic generation in nonlinear grating coupler,” J. Appl. Phys. 84, 5913–5921 (1998).
[Crossref]

IEEE J. Quantum Electron. (6)

R. A. Andrews, “Crystal symmetry effects on nonlinear optical processes in optical waveguides,” IEEE J. Quantum Electron. 7, 523–529 (1971).
[Crossref]

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Figures (7)

Fig. 1
Fig. 1

Geometry of the planar guide with respect to the crystal axis, in the case of a z-cut LiNbO3 substrate. The only guided modes in the z-cut substrate are TM polarized, since in the TE case the only nonvanishing electric field component, Ey, is parallel to the ordinary component of the dielectric-constant tensor.

Fig. 2
Fig. 2

Linear and nonlinear gratings. The linear grating is obtained by etching part of the film layer, or alternatively, by depositing an additional cladding material and by periodically etching this additional layer. The nonlinear grating is obtained by periodically inverting the orientation of the nonlinear-susceptibility tensor. The domains are assumed to be infinite and uniform along the transverse direction, x, perpendicular to the plane of the page.

Fig. 3
Fig. 3

(a) Refractive indices used in the numerical calculations.20 (b) Index step for ordinary and extraordinary refractive indices: only the extraordinary index is increased by the proton exchange, whereas the ordinary index decreases after the proton-exchange bath, thus avoiding the presence of hybrid modes in the z-cut case.

Fig. 4
Fig. 4

Transmission spectrum (a) in the strong linear-coupling case and (b) in the weak linear coupling case. The strong coupling produces a wide gap and a deep band-edge transmission resonance, which in our case is 3 GHz wide. The weak coupling produces a narrower gap and a shallower transmission resonances. The x axis is normalized with respect to the wavelength fixed at λ0=1064 nm. The band-edge transmission resonance occurs exactly at the fundamental-field frequency.

Fig. 5
Fig. 5

(a) Conversion efficiency as a function of the number of periods in the strong linear-coupling case. The structure whose transmission spectrum is shown in Fig. 4 has N=3400 periods. The normalized conversion efficiency, defined by Eq. (30), is equal to 75. (b) FWHM as a function of the number of periods for the band-edge transmission resonance denoted by the arrow in Fig. 4.

Fig. 6
Fig. 6

(a) Conversion efficiency as a function of the number of periods in the weak linear-coupling case. The structure whose transmission spectrum is shown in Fig. 5 is obtained when N=9200, where the normalized conversion efficiency is equal to 10. (b) FWHM as a function of the number of periods for the band-edge transmission resonance shown by an arrow in Fig. 5.

Fig. 7
Fig. 7

Forward- and backward-propagating field intensities as a function of position when the fundamental field is tuned at the first transmission maximum at the low-frequency band edge. The parameters correspond (a) to Fig. 4(a), and (b) to Fig. 4(b). The intensities are normalized with respect to the input forward intensity. There is no backward-propagating field because of the transmission resonance tuning conditions.

Tables (1)

Tables Icon

Table 1 Comparison of the Results Obtained in the Strong and Weak Linear-Coupling Regimes

Equations (49)

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×E=iωμH, ×H=-iωε0(εr+Δεr)E,
±ddzaμ(z)=i ωε04 SEμ*·P exp(-iβμz)dxdy,
PNL(ω)=2dE(2ω)E(ω)*,
PNL(2ω)=dE(ω)E(ω),
ΔεrL(x, y, z)
=(no/e, f2-1)fα(z)0txt+hx<0orx>t+h,
d=0df[2 fα(z)-1]ds[2 fα(z)-1] x>t0<x<tx<0,
fα(z)=12+m=-+ sin(π/2+mπ)(2m+1)π expi2π2m+1Λαz.
dA+dz=iKL(z)A- exp(-i2βFFz)+iKNL(z)B+(A+)* exp(iΔβz),
dA-dz=-iKL(z)A+ exp(i2βFFz)+iKNL(z)B-(A-)* exp(-iΔβz),
dB+dz=iKNL(z)(A+)2 exp(-iΔβz),
dB-dz=iKNL(z)(A-)2 exp(iΔβz),
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.
2πΛL=βSH.
a+(z)=C1 cos(Δ1z)+C2 sin(Δ1z),
a-(z)=C2 Δ1iKL1+C1 δ1KL1cos(Δ1z)+C2 δ1KL1-C1 Δ1iKL1sin(Δ1z),
Δ12δ12-KL12.
a-(0)=a-(L=NΛL)=0C2C1=-i δ1Δ1,Δ1NΛL=mπ,
KL1=12 Δβ2-βSHN2.
da+dz+iδ˜1a+=iKL1a-+iKNL1b+(a+)*×exp[i(Δβ-2δ˜1-δ˜2-2π/ΛNL)z],
da-dz-iδ˜1a-=-iKL1a++iKNL1b-(a-)*×exp[-i(Δβ-2δ˜1-δ˜2-2π/ΛNL)z],
db+dz-iδ˜2b+=iKNL1(a+)2×exp[-i(Δβ-2δ˜1-δ˜2-2π/ΛNL)z],
db-dz+iδ˜2b-=iKNL1(a-)2×exp[i(Δβ-2δ˜1-δ˜2-2π/ΛNL)z].
δ˜2=Δβ-2δ˜1-2πΛNL,
δ˜2=0,
2πΛNL+2πΛL=βSH.
2πΛL=2 βFF+(βFF/N)2+(1-1/N2)KL121-1/N2.
 b+(0)=0,
b-(L=NΛL)=0.
a+(z)=Acos(Δ˜1z)-i δ˜iΔ˜1 sin(Δ˜1z),
a-(z)=-iA KL1Δ˜1 sin(Δ˜1z),
b+(z)=iKNL1 A22 -KL1Δ˜12z+1+δ˜1Δ˜12 sin(2Δ˜1z)2Δ˜1+i δ˜1Δ˜12[cos(2Δ˜1z)-1],
b-(z)=-iKNL1 A22 KL1Δ˜12z-NΛL-sin(2Δ˜1z)Δ˜1.
η+=b+(L=NΛL)a+(0)2=η-=b-(0)a+(0)2=KNL12 A24 1δ˜1KL12-12(NΛL)2,
η+=η-N1KNL12 A24 NKL1βFF+KL14(NΛL)2N6.
ηQPM=KNL12A2L2.
ηrel=η+,-ηQPM.
Δνπcng,FF 1KL12L3,
ng,FF=βFFk0,
KL=ζ04k0 tt+h(no,fFF)2-1(no,fFF)2 d HyFFdx2-[(ne,fFF)2-1](βFFHyFF)2dx,
KNL=ζ02k02βFF2βSH-td33,i(z) HySH(ne,iSH)2 HyFF(ne,iFF)22dx,

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