Abstract

We present theoretical modeling of a novel configuration for quasi-phase-matched parametric amplification in which the pump and the signal fields form guided waves of a planar waveguide while the idler is radiated into the substrate. We follow a coupled-mode approach to study the parametric amplification in periodically domain-reversed proton-exchanged LiNbO3 waveguides upon a Z-cut substrate and present numerical results relevant to the amplification process. In particular, for given pump and signal wavelengths we have studied the dependence of the gain coefficient on the periodicity of a grating formed by domain inversion. This configuration, which is referred to as the Čerenkov-idler configuration, is shown to provide a large signal gain bandwidth and is more tolerant to variations in pump frequency.

© 1996 Optical Society of America

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References

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  1. Y. Suematsu, Jpn. J. Appl. Phys. 9, 798 (1970).
    [CrossRef]
  2. W. Sohler, H. Suche, in Digest of Third International Conference on Integrated Optics and Optical Fiber Communication (Optical Society of America, Washington, D.C., 1981), pp. 89–90.
  3. B. Hampel, W. Sohler, Proc. SPIE 651, 229 (1986).
  4. J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
    [CrossRef]
  5. P. Baldi, S. Nouh, M. De Micheli, D. B. Ostrowsky, D. Delacourt, X. Banti, M. Papuchon, Electron. Lett. 29, 1539 (1993).
    [CrossRef]
  6. P. Baldi, P. Aschieri, S. Nouh, M. De Micheli, D. B. Ostrowsky, D. Delacourt, M. Papuchon, IEEE J. Quantum Electron. 31, 997 (1995).
    [CrossRef]
  7. M. L. Bortz, M. A. Arbore, M. M. Fejer, in Conference on Lasers and Electro-Optics, Vol. 8 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), paper CPD13.
  8. M. L. Bortz, M. A. Arbore, M. M. Fejer, Opt. Lett. 20, 49 (1995).
    [CrossRef] [PubMed]
  9. T. Taniuchi, K. Yamamoto, Proc. SPIE 864, 36 (1987).
  10. H. Tamada, IEEE J. Quantum Electron. 27, 502 (1991).
    [CrossRef]

1995

P. Baldi, P. Aschieri, S. Nouh, M. De Micheli, D. B. Ostrowsky, D. Delacourt, M. Papuchon, IEEE J. Quantum Electron. 31, 997 (1995).
[CrossRef]

M. L. Bortz, M. A. Arbore, M. M. Fejer, Opt. Lett. 20, 49 (1995).
[CrossRef] [PubMed]

1993

P. Baldi, S. Nouh, M. De Micheli, D. B. Ostrowsky, D. Delacourt, X. Banti, M. Papuchon, Electron. Lett. 29, 1539 (1993).
[CrossRef]

1991

H. Tamada, IEEE J. Quantum Electron. 27, 502 (1991).
[CrossRef]

1987

T. Taniuchi, K. Yamamoto, Proc. SPIE 864, 36 (1987).

1986

B. Hampel, W. Sohler, Proc. SPIE 651, 229 (1986).

1970

Y. Suematsu, Jpn. J. Appl. Phys. 9, 798 (1970).
[CrossRef]

1962

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Arbore, M. A.

M. L. Bortz, M. A. Arbore, M. M. Fejer, Opt. Lett. 20, 49 (1995).
[CrossRef] [PubMed]

M. L. Bortz, M. A. Arbore, M. M. Fejer, in Conference on Lasers and Electro-Optics, Vol. 8 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), paper CPD13.

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Aschieri, P.

P. Baldi, P. Aschieri, S. Nouh, M. De Micheli, D. B. Ostrowsky, D. Delacourt, M. Papuchon, IEEE J. Quantum Electron. 31, 997 (1995).
[CrossRef]

Baldi, P.

P. Baldi, P. Aschieri, S. Nouh, M. De Micheli, D. B. Ostrowsky, D. Delacourt, M. Papuchon, IEEE J. Quantum Electron. 31, 997 (1995).
[CrossRef]

P. Baldi, S. Nouh, M. De Micheli, D. B. Ostrowsky, D. Delacourt, X. Banti, M. Papuchon, Electron. Lett. 29, 1539 (1993).
[CrossRef]

Banti, X.

P. Baldi, S. Nouh, M. De Micheli, D. B. Ostrowsky, D. Delacourt, X. Banti, M. Papuchon, Electron. Lett. 29, 1539 (1993).
[CrossRef]

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Bortz, M. L.

M. L. Bortz, M. A. Arbore, M. M. Fejer, Opt. Lett. 20, 49 (1995).
[CrossRef] [PubMed]

M. L. Bortz, M. A. Arbore, M. M. Fejer, in Conference on Lasers and Electro-Optics, Vol. 8 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), paper CPD13.

De Micheli, M.

P. Baldi, P. Aschieri, S. Nouh, M. De Micheli, D. B. Ostrowsky, D. Delacourt, M. Papuchon, IEEE J. Quantum Electron. 31, 997 (1995).
[CrossRef]

P. Baldi, S. Nouh, M. De Micheli, D. B. Ostrowsky, D. Delacourt, X. Banti, M. Papuchon, Electron. Lett. 29, 1539 (1993).
[CrossRef]

Delacourt, D.

P. Baldi, P. Aschieri, S. Nouh, M. De Micheli, D. B. Ostrowsky, D. Delacourt, M. Papuchon, IEEE J. Quantum Electron. 31, 997 (1995).
[CrossRef]

P. Baldi, S. Nouh, M. De Micheli, D. B. Ostrowsky, D. Delacourt, X. Banti, M. Papuchon, Electron. Lett. 29, 1539 (1993).
[CrossRef]

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Fejer, M. M.

M. L. Bortz, M. A. Arbore, M. M. Fejer, Opt. Lett. 20, 49 (1995).
[CrossRef] [PubMed]

M. L. Bortz, M. A. Arbore, M. M. Fejer, in Conference on Lasers and Electro-Optics, Vol. 8 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), paper CPD13.

Hampel, B.

B. Hampel, W. Sohler, Proc. SPIE 651, 229 (1986).

Nouh, S.

P. Baldi, P. Aschieri, S. Nouh, M. De Micheli, D. B. Ostrowsky, D. Delacourt, M. Papuchon, IEEE J. Quantum Electron. 31, 997 (1995).
[CrossRef]

P. Baldi, S. Nouh, M. De Micheli, D. B. Ostrowsky, D. Delacourt, X. Banti, M. Papuchon, Electron. Lett. 29, 1539 (1993).
[CrossRef]

Ostrowsky, D. B.

P. Baldi, P. Aschieri, S. Nouh, M. De Micheli, D. B. Ostrowsky, D. Delacourt, M. Papuchon, IEEE J. Quantum Electron. 31, 997 (1995).
[CrossRef]

P. Baldi, S. Nouh, M. De Micheli, D. B. Ostrowsky, D. Delacourt, X. Banti, M. Papuchon, Electron. Lett. 29, 1539 (1993).
[CrossRef]

Papuchon, M.

P. Baldi, P. Aschieri, S. Nouh, M. De Micheli, D. B. Ostrowsky, D. Delacourt, M. Papuchon, IEEE J. Quantum Electron. 31, 997 (1995).
[CrossRef]

P. Baldi, S. Nouh, M. De Micheli, D. B. Ostrowsky, D. Delacourt, X. Banti, M. Papuchon, Electron. Lett. 29, 1539 (1993).
[CrossRef]

Pershan, P. S.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Sohler, W.

B. Hampel, W. Sohler, Proc. SPIE 651, 229 (1986).

W. Sohler, H. Suche, in Digest of Third International Conference on Integrated Optics and Optical Fiber Communication (Optical Society of America, Washington, D.C., 1981), pp. 89–90.

Suche, H.

W. Sohler, H. Suche, in Digest of Third International Conference on Integrated Optics and Optical Fiber Communication (Optical Society of America, Washington, D.C., 1981), pp. 89–90.

Suematsu, Y.

Y. Suematsu, Jpn. J. Appl. Phys. 9, 798 (1970).
[CrossRef]

Tamada, H.

H. Tamada, IEEE J. Quantum Electron. 27, 502 (1991).
[CrossRef]

Taniuchi, T.

T. Taniuchi, K. Yamamoto, Proc. SPIE 864, 36 (1987).

Yamamoto, K.

T. Taniuchi, K. Yamamoto, Proc. SPIE 864, 36 (1987).

Electron. Lett.

P. Baldi, S. Nouh, M. De Micheli, D. B. Ostrowsky, D. Delacourt, X. Banti, M. Papuchon, Electron. Lett. 29, 1539 (1993).
[CrossRef]

IEEE J. Quantum Electron.

P. Baldi, P. Aschieri, S. Nouh, M. De Micheli, D. B. Ostrowsky, D. Delacourt, M. Papuchon, IEEE J. Quantum Electron. 31, 997 (1995).
[CrossRef]

H. Tamada, IEEE J. Quantum Electron. 27, 502 (1991).
[CrossRef]

Jpn. J. Appl. Phys.

Y. Suematsu, Jpn. J. Appl. Phys. 9, 798 (1970).
[CrossRef]

Opt. Lett.

Phys. Rev.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Proc. SPIE

B. Hampel, W. Sohler, Proc. SPIE 651, 229 (1986).

T. Taniuchi, K. Yamamoto, Proc. SPIE 864, 36 (1987).

Other

M. L. Bortz, M. A. Arbore, M. M. Fejer, in Conference on Lasers and Electro-Optics, Vol. 8 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), paper CPD13.

W. Sohler, H. Suche, in Digest of Third International Conference on Integrated Optics and Optical Fiber Communication (Optical Society of America, Washington, D.C., 1981), pp. 89–90.

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Figures (4)

Fig. 1
Fig. 1

Waveguide configuration for quasi-phase-matched parametric amplification in the Čerenkov-idler configuration. X, Y, Z, are the principal axes of the crystal and x, y, and z correspond to the waveguide coordinate system. (b) Phase-vector diagram for phase-matched parametric amplification in the Čerenkov-idler configuration.

Fig. 2
Fig. 2

Variation of output signal power with Λ corresponding to a pump power of 1000 kW/m and an input signal power of 1 mW/m for three different interaction lengths: a, 1.0 mm; b, 5.0 mm; c, 10.0 mm; the dotted curve shows the corresponding variation of the idler radiation angle (θ) with Λ.

Fig. 3
Fig. 3

Variation of output signal power with signal wavelength for a pump power of 1000 kW/m and an input signal power of 1.0 mW/m. The dotted curves correspond to the Čerenkov-idler configuration for two different grating periods: a, Λ = 8.99 μm, the optimum period; and b, Λ = 8.90 μm for an interaction length of 10 mm; the continuous curve corresponds to the all-guided configuration for an interaction length of 2.6 mm.

Fig. 4
Fig. 4

Variation of output signal power with signal wavelength for a pump power of 1000 kW/m and an input signal power of 1.0 mW/m; the continuous curve corresponds to the all-guided configuration for an interaction length of 2.6 mm, and the dotted curve corresponds to the Čerenkov-idler configuration for an interaction length of 10.0 mm.

Equations (8)

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ω p = ω s + ω i , β p = β s + k i cos θ + ( 2 π / Λ ) ,
E x = E xp + E xs + E xi = 1 2 ( { A p ( z ) E p ( x ) exp [ i ( ω p t β p z ) ] + A s ( z ) E s ( x ) × exp [ i ( ω s t β s z ) ] + A i ( β i , z ) E i ( β i , x ) × exp [ i ( ω i t β i z ) ] d β i } + c . c . ) ,
2 E xj x 2 + n o 2 ( ω j ) n e 2 ( ω j ) 2 E xj z 2 μ 0 0 n o 2 ( ω j ) 2 E xj t 2 = μ 0 n o 2 ( ω j ) n e 2 ( ω j ) 2 P xj t 2 ,
P x 2 0 d 33 E x 2 .
d A i d z = i ω i γ ( β i ) A p A s * ( z ) exp ( i Δ β i z ) ,
d A s d z = i ω s A p γ ( β i ) A i * ( β i , z ) exp ( i Δ β i z ) d β i ,
Δ β i = β p β s β i ( 2 π / Λ ) ,
γ ( β i ) = 0 2 d ¯ 33 E p E s * E i * d x ,

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