Abstract

We propose and analyze a novel geometry for all-optical processing of low-power signals that is based on a frequency-nondegenerate counterpropagating parametric amplifier. The stationary response in the cascading regime exhibits multivalued solutions with enhanced nonlinear phase shifts. Implementation in a quasi-phase-matched LiNbO3 waveguide is discussed.

© 2000 Optical Society of America

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References

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  1. G. Assanto, K. Gallo, and C. Conti, in Advanced Photonics with Second-Order Optically Nonlinear Processes, A. Boardman, ed. (Kluwer Academic, London, 1999), pp. 59–87.
    [CrossRef]
  2. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. Lett. 127, 1918 (1962).
  3. X. Gu, R. Korotkov, Y. J. Ding, J. U. Kang, and J. B. Khurgin, J. Opt. Soc. Am. B 15, 1561 (1998).
    [CrossRef]
  4. X. Gu, M. Makarov, Y. J. Ding, J. B. Khurgin, and W. P. Risk, Opt. Lett. 24, 127 (1999).
    [CrossRef]
  5. P. St. J. Russell, IEEE J. Quantum Electron. 27, 830 (1991).
    [CrossRef]
  6. G. D’Alessandro, P. St. J. Russell, and A. A. Wheeler, Phys. Rev. A 55, 3211 (1997).
    [CrossRef]
  7. Y. J. Ding and J. B. Khurgin, Opt. Lett. 21, 1445 (1996).
    [CrossRef] [PubMed]
  8. G. D. Landry and T. Maldonado, Opt. Lett. 22, 1400 (1997); J. Lightwave Technol. 17, 316 (1999).
    [CrossRef]
  9. N. M. Kroll, Phys. Rev. 127, 1207 (1962).
    [CrossRef]
  10. S. E. Harris, Appl. Phys. Lett. 9, 114 (1966).
    [CrossRef]
  11. Y. J. Ding and J. B. Khurgin, IEEE J. Quantum Electron. 32, 1574 (1996).
    [CrossRef]
  12. U. Trutschel, U. Langbein, F. Lederer, and H.-E. Ponath, IEEE J. Quantum Electron. QE-21, 1639 (1985).
    [CrossRef]
  13. P. Baldi, L. Chanvillard, P. Aschiéri, J. Pruvot, M. P. De Micheli, D. B. Ostrowsky, and G. Bellanca, Electron. Lett. 35, 217 (1999).
    [CrossRef]
  14. R. Seydel, Practical Bifurcation and Stability Analysis (Springer, New York, 1994).
  15. P. Baldi, J. Pruvot, M. P. De Micheli, G. Bellanca, and A. C. Cino, Opt. Commun. 164, 307 (1999).
    [CrossRef]
  16. V. Ya Shur, E. L. Rumyantsev, E. V. Nikolaeva, E. I. Shishkin, D. V. Fursov, R. G. Batchko, L. A. Eyres, M. M. Fejer, and R. L. Byer, Appl. Phys. Lett. 76, 143 (2000).
    [CrossRef]

2000 (1)

V. Ya Shur, E. L. Rumyantsev, E. V. Nikolaeva, E. I. Shishkin, D. V. Fursov, R. G. Batchko, L. A. Eyres, M. M. Fejer, and R. L. Byer, Appl. Phys. Lett. 76, 143 (2000).
[CrossRef]

1999 (3)

P. Baldi, L. Chanvillard, P. Aschiéri, J. Pruvot, M. P. De Micheli, D. B. Ostrowsky, and G. Bellanca, Electron. Lett. 35, 217 (1999).
[CrossRef]

P. Baldi, J. Pruvot, M. P. De Micheli, G. Bellanca, and A. C. Cino, Opt. Commun. 164, 307 (1999).
[CrossRef]

X. Gu, M. Makarov, Y. J. Ding, J. B. Khurgin, and W. P. Risk, Opt. Lett. 24, 127 (1999).
[CrossRef]

1998 (1)

X. Gu, R. Korotkov, Y. J. Ding, J. U. Kang, and J. B. Khurgin, J. Opt. Soc. Am. B 15, 1561 (1998).
[CrossRef]

1997 (2)

G. D’Alessandro, P. St. J. Russell, and A. A. Wheeler, Phys. Rev. A 55, 3211 (1997).
[CrossRef]

G. D. Landry and T. Maldonado, Opt. Lett. 22, 1400 (1997); J. Lightwave Technol. 17, 316 (1999).
[CrossRef]

1996 (2)

Y. J. Ding and J. B. Khurgin, Opt. Lett. 21, 1445 (1996).
[CrossRef] [PubMed]

Y. J. Ding and J. B. Khurgin, IEEE J. Quantum Electron. 32, 1574 (1996).
[CrossRef]

1991 (1)

P. St. J. Russell, IEEE J. Quantum Electron. 27, 830 (1991).
[CrossRef]

1985 (1)

U. Trutschel, U. Langbein, F. Lederer, and H.-E. Ponath, IEEE J. Quantum Electron. QE-21, 1639 (1985).
[CrossRef]

1966 (1)

S. E. Harris, Appl. Phys. Lett. 9, 114 (1966).
[CrossRef]

1962 (2)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. Lett. 127, 1918 (1962).

N. M. Kroll, Phys. Rev. 127, 1207 (1962).
[CrossRef]

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. Lett. 127, 1918 (1962).

Aschiéri, P.

P. Baldi, L. Chanvillard, P. Aschiéri, J. Pruvot, M. P. De Micheli, D. B. Ostrowsky, and G. Bellanca, Electron. Lett. 35, 217 (1999).
[CrossRef]

Assanto, G.

G. Assanto, K. Gallo, and C. Conti, in Advanced Photonics with Second-Order Optically Nonlinear Processes, A. Boardman, ed. (Kluwer Academic, London, 1999), pp. 59–87.
[CrossRef]

Baldi, P.

P. Baldi, L. Chanvillard, P. Aschiéri, J. Pruvot, M. P. De Micheli, D. B. Ostrowsky, and G. Bellanca, Electron. Lett. 35, 217 (1999).
[CrossRef]

P. Baldi, J. Pruvot, M. P. De Micheli, G. Bellanca, and A. C. Cino, Opt. Commun. 164, 307 (1999).
[CrossRef]

Batchko, R. G.

V. Ya Shur, E. L. Rumyantsev, E. V. Nikolaeva, E. I. Shishkin, D. V. Fursov, R. G. Batchko, L. A. Eyres, M. M. Fejer, and R. L. Byer, Appl. Phys. Lett. 76, 143 (2000).
[CrossRef]

Bellanca, G.

P. Baldi, J. Pruvot, M. P. De Micheli, G. Bellanca, and A. C. Cino, Opt. Commun. 164, 307 (1999).
[CrossRef]

P. Baldi, L. Chanvillard, P. Aschiéri, J. Pruvot, M. P. De Micheli, D. B. Ostrowsky, and G. Bellanca, Electron. Lett. 35, 217 (1999).
[CrossRef]

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. Lett. 127, 1918 (1962).

Byer, R. L.

V. Ya Shur, E. L. Rumyantsev, E. V. Nikolaeva, E. I. Shishkin, D. V. Fursov, R. G. Batchko, L. A. Eyres, M. M. Fejer, and R. L. Byer, Appl. Phys. Lett. 76, 143 (2000).
[CrossRef]

Chanvillard, L.

P. Baldi, L. Chanvillard, P. Aschiéri, J. Pruvot, M. P. De Micheli, D. B. Ostrowsky, and G. Bellanca, Electron. Lett. 35, 217 (1999).
[CrossRef]

Cino, A. C.

P. Baldi, J. Pruvot, M. P. De Micheli, G. Bellanca, and A. C. Cino, Opt. Commun. 164, 307 (1999).
[CrossRef]

Conti, C.

G. Assanto, K. Gallo, and C. Conti, in Advanced Photonics with Second-Order Optically Nonlinear Processes, A. Boardman, ed. (Kluwer Academic, London, 1999), pp. 59–87.
[CrossRef]

D’Alessandro, G.

G. D’Alessandro, P. St. J. Russell, and A. A. Wheeler, Phys. Rev. A 55, 3211 (1997).
[CrossRef]

De Micheli, M. P.

P. Baldi, J. Pruvot, M. P. De Micheli, G. Bellanca, and A. C. Cino, Opt. Commun. 164, 307 (1999).
[CrossRef]

P. Baldi, L. Chanvillard, P. Aschiéri, J. Pruvot, M. P. De Micheli, D. B. Ostrowsky, and G. Bellanca, Electron. Lett. 35, 217 (1999).
[CrossRef]

Ding, Y. J.

X. Gu, M. Makarov, Y. J. Ding, J. B. Khurgin, and W. P. Risk, Opt. Lett. 24, 127 (1999).
[CrossRef]

X. Gu, R. Korotkov, Y. J. Ding, J. U. Kang, and J. B. Khurgin, J. Opt. Soc. Am. B 15, 1561 (1998).
[CrossRef]

Y. J. Ding and J. B. Khurgin, Opt. Lett. 21, 1445 (1996).
[CrossRef] [PubMed]

Y. J. Ding and J. B. Khurgin, IEEE J. Quantum Electron. 32, 1574 (1996).
[CrossRef]

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. Lett. 127, 1918 (1962).

Eyres, L. A.

V. Ya Shur, E. L. Rumyantsev, E. V. Nikolaeva, E. I. Shishkin, D. V. Fursov, R. G. Batchko, L. A. Eyres, M. M. Fejer, and R. L. Byer, Appl. Phys. Lett. 76, 143 (2000).
[CrossRef]

Fejer, M. M.

V. Ya Shur, E. L. Rumyantsev, E. V. Nikolaeva, E. I. Shishkin, D. V. Fursov, R. G. Batchko, L. A. Eyres, M. M. Fejer, and R. L. Byer, Appl. Phys. Lett. 76, 143 (2000).
[CrossRef]

Fursov, D. V.

V. Ya Shur, E. L. Rumyantsev, E. V. Nikolaeva, E. I. Shishkin, D. V. Fursov, R. G. Batchko, L. A. Eyres, M. M. Fejer, and R. L. Byer, Appl. Phys. Lett. 76, 143 (2000).
[CrossRef]

Gallo, K.

G. Assanto, K. Gallo, and C. Conti, in Advanced Photonics with Second-Order Optically Nonlinear Processes, A. Boardman, ed. (Kluwer Academic, London, 1999), pp. 59–87.
[CrossRef]

Gu, X.

X. Gu, M. Makarov, Y. J. Ding, J. B. Khurgin, and W. P. Risk, Opt. Lett. 24, 127 (1999).
[CrossRef]

X. Gu, R. Korotkov, Y. J. Ding, J. U. Kang, and J. B. Khurgin, J. Opt. Soc. Am. B 15, 1561 (1998).
[CrossRef]

Harris, S. E.

S. E. Harris, Appl. Phys. Lett. 9, 114 (1966).
[CrossRef]

Kang, J. U.

X. Gu, R. Korotkov, Y. J. Ding, J. U. Kang, and J. B. Khurgin, J. Opt. Soc. Am. B 15, 1561 (1998).
[CrossRef]

Khurgin, J. B.

X. Gu, M. Makarov, Y. J. Ding, J. B. Khurgin, and W. P. Risk, Opt. Lett. 24, 127 (1999).
[CrossRef]

X. Gu, R. Korotkov, Y. J. Ding, J. U. Kang, and J. B. Khurgin, J. Opt. Soc. Am. B 15, 1561 (1998).
[CrossRef]

Y. J. Ding and J. B. Khurgin, Opt. Lett. 21, 1445 (1996).
[CrossRef] [PubMed]

Y. J. Ding and J. B. Khurgin, IEEE J. Quantum Electron. 32, 1574 (1996).
[CrossRef]

Korotkov, R.

X. Gu, R. Korotkov, Y. J. Ding, J. U. Kang, and J. B. Khurgin, J. Opt. Soc. Am. B 15, 1561 (1998).
[CrossRef]

Kroll, N. M.

N. M. Kroll, Phys. Rev. 127, 1207 (1962).
[CrossRef]

Landry, G. D.

G. D. Landry and T. Maldonado, Opt. Lett. 22, 1400 (1997); J. Lightwave Technol. 17, 316 (1999).
[CrossRef]

Langbein, U.

U. Trutschel, U. Langbein, F. Lederer, and H.-E. Ponath, IEEE J. Quantum Electron. QE-21, 1639 (1985).
[CrossRef]

Lederer, F.

U. Trutschel, U. Langbein, F. Lederer, and H.-E. Ponath, IEEE J. Quantum Electron. QE-21, 1639 (1985).
[CrossRef]

Makarov, M.

X. Gu, M. Makarov, Y. J. Ding, J. B. Khurgin, and W. P. Risk, Opt. Lett. 24, 127 (1999).
[CrossRef]

Maldonado, T.

G. D. Landry and T. Maldonado, Opt. Lett. 22, 1400 (1997); J. Lightwave Technol. 17, 316 (1999).
[CrossRef]

Nikolaeva, E. V.

V. Ya Shur, E. L. Rumyantsev, E. V. Nikolaeva, E. I. Shishkin, D. V. Fursov, R. G. Batchko, L. A. Eyres, M. M. Fejer, and R. L. Byer, Appl. Phys. Lett. 76, 143 (2000).
[CrossRef]

Ostrowsky, D. B.

P. Baldi, L. Chanvillard, P. Aschiéri, J. Pruvot, M. P. De Micheli, D. B. Ostrowsky, and G. Bellanca, Electron. Lett. 35, 217 (1999).
[CrossRef]

Pershan, P. S.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. Lett. 127, 1918 (1962).

Ponath, H.-E.

U. Trutschel, U. Langbein, F. Lederer, and H.-E. Ponath, IEEE J. Quantum Electron. QE-21, 1639 (1985).
[CrossRef]

Pruvot, J.

P. Baldi, L. Chanvillard, P. Aschiéri, J. Pruvot, M. P. De Micheli, D. B. Ostrowsky, and G. Bellanca, Electron. Lett. 35, 217 (1999).
[CrossRef]

P. Baldi, J. Pruvot, M. P. De Micheli, G. Bellanca, and A. C. Cino, Opt. Commun. 164, 307 (1999).
[CrossRef]

Risk, W. P.

X. Gu, M. Makarov, Y. J. Ding, J. B. Khurgin, and W. P. Risk, Opt. Lett. 24, 127 (1999).
[CrossRef]

Rumyantsev, E. L.

V. Ya Shur, E. L. Rumyantsev, E. V. Nikolaeva, E. I. Shishkin, D. V. Fursov, R. G. Batchko, L. A. Eyres, M. M. Fejer, and R. L. Byer, Appl. Phys. Lett. 76, 143 (2000).
[CrossRef]

Russell, P. St. J.

G. D’Alessandro, P. St. J. Russell, and A. A. Wheeler, Phys. Rev. A 55, 3211 (1997).
[CrossRef]

P. St. J. Russell, IEEE J. Quantum Electron. 27, 830 (1991).
[CrossRef]

Seydel, R.

R. Seydel, Practical Bifurcation and Stability Analysis (Springer, New York, 1994).

Shishkin, E. I.

V. Ya Shur, E. L. Rumyantsev, E. V. Nikolaeva, E. I. Shishkin, D. V. Fursov, R. G. Batchko, L. A. Eyres, M. M. Fejer, and R. L. Byer, Appl. Phys. Lett. 76, 143 (2000).
[CrossRef]

Shur, V. Ya

V. Ya Shur, E. L. Rumyantsev, E. V. Nikolaeva, E. I. Shishkin, D. V. Fursov, R. G. Batchko, L. A. Eyres, M. M. Fejer, and R. L. Byer, Appl. Phys. Lett. 76, 143 (2000).
[CrossRef]

Trutschel, U.

U. Trutschel, U. Langbein, F. Lederer, and H.-E. Ponath, IEEE J. Quantum Electron. QE-21, 1639 (1985).
[CrossRef]

Wheeler, A. A.

G. D’Alessandro, P. St. J. Russell, and A. A. Wheeler, Phys. Rev. A 55, 3211 (1997).
[CrossRef]

Appl. Phys. Lett. (2)

S. E. Harris, Appl. Phys. Lett. 9, 114 (1966).
[CrossRef]

V. Ya Shur, E. L. Rumyantsev, E. V. Nikolaeva, E. I. Shishkin, D. V. Fursov, R. G. Batchko, L. A. Eyres, M. M. Fejer, and R. L. Byer, Appl. Phys. Lett. 76, 143 (2000).
[CrossRef]

Electron. Lett. (1)

P. Baldi, L. Chanvillard, P. Aschiéri, J. Pruvot, M. P. De Micheli, D. B. Ostrowsky, and G. Bellanca, Electron. Lett. 35, 217 (1999).
[CrossRef]

IEEE J. Quantum Electron. (3)

Y. J. Ding and J. B. Khurgin, IEEE J. Quantum Electron. 32, 1574 (1996).
[CrossRef]

U. Trutschel, U. Langbein, F. Lederer, and H.-E. Ponath, IEEE J. Quantum Electron. QE-21, 1639 (1985).
[CrossRef]

P. St. J. Russell, IEEE J. Quantum Electron. 27, 830 (1991).
[CrossRef]

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

X. Gu, R. Korotkov, Y. J. Ding, J. U. Kang, and J. B. Khurgin, J. Opt. Soc. Am. B 15, 1561 (1998).
[CrossRef]

Opt. Commun. (1)

P. Baldi, J. Pruvot, M. P. De Micheli, G. Bellanca, and A. C. Cino, Opt. Commun. 164, 307 (1999).
[CrossRef]

Opt. Lett. (3)

X. Gu, M. Makarov, Y. J. Ding, J. B. Khurgin, and W. P. Risk, Opt. Lett. 24, 127 (1999).
[CrossRef]

Y. J. Ding and J. B. Khurgin, Opt. Lett. 21, 1445 (1996).
[CrossRef] [PubMed]

G. D. Landry and T. Maldonado, Opt. Lett. 22, 1400 (1997); J. Lightwave Technol. 17, 316 (1999).
[CrossRef]

Phys. Rev. (1)

N. M. Kroll, Phys. Rev. 127, 1207 (1962).
[CrossRef]

Phys. Rev. A (1)

G. D’Alessandro, P. St. J. Russell, and A. A. Wheeler, Phys. Rev. A 55, 3211 (1997).
[CrossRef]

Phys. Rev. Lett. (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. Lett. 127, 1918 (1962).

Other (2)

G. Assanto, K. Gallo, and C. Conti, in Advanced Photonics with Second-Order Optically Nonlinear Processes, A. Boardman, ed. (Kluwer Academic, London, 1999), pp. 59–87.
[CrossRef]

R. Seydel, Practical Bifurcation and Stability Analysis (Springer, New York, 1994).

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Figures (4)

Fig. 1
Fig. 1

Scheme of the COPA.

Fig. 2
Fig. 2

(a) Signal transmission T1=P1z=0/P1L and (b) nonlinear phase shift φ10=φ1z=0 at the output versus normalized input pump power Γ2=κ02L2P30 for a given phase mismatch ΔβL=0.01π, with r1=1.05 and κ02L2P1L=0.07. On the uppermost horizontal axis we show the corresponding pump powers P30 for first-order QPM in a SPE LiNbO3 waveguide of length L=3 cm, with a normalized efficiency κ02=1.3 W-1 cm-2. The asterisks on the lower horizontal axis in (a) indicate the values Γ2|n=0,1 given by Eq (2) in the text.

Fig. 3
Fig. 3

(A), (B), (C) Evolution of the signal [idler] normalized power, P1z/P1LP2z/P1L, and phase, φ1zφ2z, along the waveguide, shown as solid (dashed) curves that correspond to points A, B, and C in Fig. 2.

Fig. 4
Fig. 4

(a) Signal transmission and (b) output signal phase shift versus mismatch ΔβL, calculated for Γ-2=4.32 (dashed curves) and Γ+2=5.04 (solid curves with symbols), i.e., below and above the value Γth2 in Fig. 2, respectively. Here r1=1.05 and κ02L2P1L=0.07. The open circle indicates the solution described in Ref. 11.

Equations (2)

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

dA1/dz=+ir1κ0A2*A3 exp-iΔβz,  dA2/dz=-i2-r1κ0A1*A3 exp-iΔβz,  dA3/dz=-i2κ0A1A2 exp+iΔβz,
Γ2|n=κ02L2P30n=π/2+nπ2-ΔβL/22/r12-r1,

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