Abstract

We consider the possibility of generating second-harmonic radiation by the interaction of two counter-propagating fundamental waves in a quasi-phase-matched second-order nonlinear medium in a waveguide. The conversion efficiency reaches a maximum at an optimum pump intensity. For a large range of pump intensities below a certain pump intensity the efficiency is larger than that for the copropagating configuration. The saturation intensities at which the efficiency reaches 72% for poled KTiOPO4 and LiNbO3 can be achieved with lasers now available.

© 1996 Optical Society of America

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  1. J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
    [CrossRef]
  2. M. M. Fejer, G. A. Magel, D. H. Jundt, R. L. Byer, IEEE J. Quantum Electron. 28, 2631 (1992).
    [CrossRef]
  3. R. Normandin, R. L. Williams, F. Chatenoud, Electron. Lett. 26, 2088 (1990); D. Vakhshoori, R. J. Fischer, M. Hong, D. L. Sivco, G. J. Zydzic, G. N. S. Chu, Appl. Phys. Lett. 59, 896 (1991).
    [CrossRef]
  4. J. B. Khurgin, Phys. Rev. B 38, 4056 (1988); S. Li, J. Khurgin, Appl. Phys. Lett. 62, 1727 (1993); S. Janz, F. Chatenoud, R. Normandin, Opt. Lett. 19, 622 (1994).
    [CrossRef] [PubMed]
  5. J. R. Meyer, C. A. Hoffman, F. J. Bartoli, L. R. Ram-Mohan, Appl. Phys. Lett. 67, 608 (1995).
    [CrossRef]
  6. A. Yariv, Quantum Electronics (Wiley, New York, 1989).
  7. However, if QPM is not achieved, the conversion efficiency is proportional to [sin(k2ωL)/(k2ωL)]2. The difference of indices of refraction between the fundamental and SH waves has no effect on the conversion efficiency in our scheme.
  8. Y. J. Ding, J. B. Khurgin, “Quasi-phase-matched mirrorless nondegenerate backward optical parametric oscillation,” submitted to Opt. Lett.
  9. J. Jerphagnon, S. K. Kurtz, J. Appl. Phys. 41, 1667 (1970).
    [CrossRef]
  10. Y. J. Ding, J. B. Khurgin, S. J. Lee, J. Opt. Soc. Am. B 12, 1586 (1995).
    [CrossRef]
  11. W. P. Risk, S. D. Lau, M. A. McCord, IEEE Photon. Technol. Lett. 6, 406 (1994).
    [CrossRef]
  12. M. L. Bortz, M. A. Arbore, M. M. Fejer, Opt. Lett. 20, 49 (1995); L. E. Myers, R. C. Eckardt, M. M. Fejer, R. L. Byer, W. R. Bosenberg, in Conference on Lasers and Electro-Optics, Vol. 15 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper CThC3.
    [CrossRef]
  13. J. D. Bierlein, H. Vanherzeele, J. Opt. Soc. Am. B 6, 622 (1989).
    [CrossRef]
  14. J. B. Khurgin, Y. J. Ding, Opt. Lett. 19, 1016 (1994).
    [CrossRef] [PubMed]
  15. S. Janz, E. Frlan, H. Dai, F. Chatenoud, R. L. Williams, in Nonlinear Optics: Materials, Fundamentals, and Applications, Vol. 18 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 263.

1995 (3)

1994 (2)

W. P. Risk, S. D. Lau, M. A. McCord, IEEE Photon. Technol. Lett. 6, 406 (1994).
[CrossRef]

J. B. Khurgin, Y. J. Ding, Opt. Lett. 19, 1016 (1994).
[CrossRef] [PubMed]

1992 (1)

M. M. Fejer, G. A. Magel, D. H. Jundt, R. L. Byer, IEEE J. Quantum Electron. 28, 2631 (1992).
[CrossRef]

1990 (1)

R. Normandin, R. L. Williams, F. Chatenoud, Electron. Lett. 26, 2088 (1990); D. Vakhshoori, R. J. Fischer, M. Hong, D. L. Sivco, G. J. Zydzic, G. N. S. Chu, Appl. Phys. Lett. 59, 896 (1991).
[CrossRef]

1989 (1)

1988 (1)

J. B. Khurgin, Phys. Rev. B 38, 4056 (1988); S. Li, J. Khurgin, Appl. Phys. Lett. 62, 1727 (1993); S. Janz, F. Chatenoud, R. Normandin, Opt. Lett. 19, 622 (1994).
[CrossRef] [PubMed]

1970 (1)

J. Jerphagnon, S. K. Kurtz, J. Appl. Phys. 41, 1667 (1970).
[CrossRef]

1962 (1)

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

Arbore, M. A.

Armstrong, J. A.

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

Bartoli, F. J.

J. R. Meyer, C. A. Hoffman, F. J. Bartoli, L. R. Ram-Mohan, Appl. Phys. Lett. 67, 608 (1995).
[CrossRef]

Bierlein, J. D.

Bloembergen, N.

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

Bortz, M. L.

Byer, R. L.

M. M. Fejer, G. A. Magel, D. H. Jundt, R. L. Byer, IEEE J. Quantum Electron. 28, 2631 (1992).
[CrossRef]

Chatenoud, F.

R. Normandin, R. L. Williams, F. Chatenoud, Electron. Lett. 26, 2088 (1990); D. Vakhshoori, R. J. Fischer, M. Hong, D. L. Sivco, G. J. Zydzic, G. N. S. Chu, Appl. Phys. Lett. 59, 896 (1991).
[CrossRef]

S. Janz, E. Frlan, H. Dai, F. Chatenoud, R. L. Williams, in Nonlinear Optics: Materials, Fundamentals, and Applications, Vol. 18 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 263.

Dai, H.

S. Janz, E. Frlan, H. Dai, F. Chatenoud, R. L. Williams, in Nonlinear Optics: Materials, Fundamentals, and Applications, Vol. 18 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 263.

Ding, Y. J.

Y. J. Ding, J. B. Khurgin, S. J. Lee, J. Opt. Soc. Am. B 12, 1586 (1995).
[CrossRef]

J. B. Khurgin, Y. J. Ding, Opt. Lett. 19, 1016 (1994).
[CrossRef] [PubMed]

Y. J. Ding, J. B. Khurgin, “Quasi-phase-matched mirrorless nondegenerate backward optical parametric oscillation,” submitted to Opt. Lett.

Ducuing, J.

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

Fejer, M. M.

Frlan, E.

S. Janz, E. Frlan, H. Dai, F. Chatenoud, R. L. Williams, in Nonlinear Optics: Materials, Fundamentals, and Applications, Vol. 18 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 263.

Hoffman, C. A.

J. R. Meyer, C. A. Hoffman, F. J. Bartoli, L. R. Ram-Mohan, Appl. Phys. Lett. 67, 608 (1995).
[CrossRef]

Janz, S.

S. Janz, E. Frlan, H. Dai, F. Chatenoud, R. L. Williams, in Nonlinear Optics: Materials, Fundamentals, and Applications, Vol. 18 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 263.

Jerphagnon, J.

J. Jerphagnon, S. K. Kurtz, J. Appl. Phys. 41, 1667 (1970).
[CrossRef]

Jundt, D. H.

M. M. Fejer, G. A. Magel, D. H. Jundt, R. L. Byer, IEEE J. Quantum Electron. 28, 2631 (1992).
[CrossRef]

Khurgin, J. B.

Y. J. Ding, J. B. Khurgin, S. J. Lee, J. Opt. Soc. Am. B 12, 1586 (1995).
[CrossRef]

J. B. Khurgin, Y. J. Ding, Opt. Lett. 19, 1016 (1994).
[CrossRef] [PubMed]

J. B. Khurgin, Phys. Rev. B 38, 4056 (1988); S. Li, J. Khurgin, Appl. Phys. Lett. 62, 1727 (1993); S. Janz, F. Chatenoud, R. Normandin, Opt. Lett. 19, 622 (1994).
[CrossRef] [PubMed]

Y. J. Ding, J. B. Khurgin, “Quasi-phase-matched mirrorless nondegenerate backward optical parametric oscillation,” submitted to Opt. Lett.

Kurtz, S. K.

J. Jerphagnon, S. K. Kurtz, J. Appl. Phys. 41, 1667 (1970).
[CrossRef]

Lau, S. D.

W. P. Risk, S. D. Lau, M. A. McCord, IEEE Photon. Technol. Lett. 6, 406 (1994).
[CrossRef]

Lee, S. J.

Magel, G. A.

M. M. Fejer, G. A. Magel, D. H. Jundt, R. L. Byer, IEEE J. Quantum Electron. 28, 2631 (1992).
[CrossRef]

McCord, M. A.

W. P. Risk, S. D. Lau, M. A. McCord, IEEE Photon. Technol. Lett. 6, 406 (1994).
[CrossRef]

Meyer, J. R.

J. R. Meyer, C. A. Hoffman, F. J. Bartoli, L. R. Ram-Mohan, Appl. Phys. Lett. 67, 608 (1995).
[CrossRef]

Normandin, R.

R. Normandin, R. L. Williams, F. Chatenoud, Electron. Lett. 26, 2088 (1990); D. Vakhshoori, R. J. Fischer, M. Hong, D. L. Sivco, G. J. Zydzic, G. N. S. Chu, Appl. Phys. Lett. 59, 896 (1991).
[CrossRef]

Pershan, P. S.

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

Ram-Mohan, L. R.

J. R. Meyer, C. A. Hoffman, F. J. Bartoli, L. R. Ram-Mohan, Appl. Phys. Lett. 67, 608 (1995).
[CrossRef]

Risk, W. P.

W. P. Risk, S. D. Lau, M. A. McCord, IEEE Photon. Technol. Lett. 6, 406 (1994).
[CrossRef]

Vanherzeele, H.

Williams, R. L.

R. Normandin, R. L. Williams, F. Chatenoud, Electron. Lett. 26, 2088 (1990); D. Vakhshoori, R. J. Fischer, M. Hong, D. L. Sivco, G. J. Zydzic, G. N. S. Chu, Appl. Phys. Lett. 59, 896 (1991).
[CrossRef]

S. Janz, E. Frlan, H. Dai, F. Chatenoud, R. L. Williams, in Nonlinear Optics: Materials, Fundamentals, and Applications, Vol. 18 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 263.

Yariv, A.

A. Yariv, Quantum Electronics (Wiley, New York, 1989).

Appl. Phys. Lett. (1)

J. R. Meyer, C. A. Hoffman, F. J. Bartoli, L. R. Ram-Mohan, Appl. Phys. Lett. 67, 608 (1995).
[CrossRef]

Electron. Lett. (1)

R. Normandin, R. L. Williams, F. Chatenoud, Electron. Lett. 26, 2088 (1990); D. Vakhshoori, R. J. Fischer, M. Hong, D. L. Sivco, G. J. Zydzic, G. N. S. Chu, Appl. Phys. Lett. 59, 896 (1991).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. M. Fejer, G. A. Magel, D. H. Jundt, R. L. Byer, IEEE J. Quantum Electron. 28, 2631 (1992).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

W. P. Risk, S. D. Lau, M. A. McCord, IEEE Photon. Technol. Lett. 6, 406 (1994).
[CrossRef]

J. Appl. Phys. (1)

J. Jerphagnon, S. K. Kurtz, J. Appl. Phys. 41, 1667 (1970).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Lett. (2)

Phys. Rev. (1)

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

Phys. Rev. B (1)

J. B. Khurgin, Phys. Rev. B 38, 4056 (1988); S. Li, J. Khurgin, Appl. Phys. Lett. 62, 1727 (1993); S. Janz, F. Chatenoud, R. Normandin, Opt. Lett. 19, 622 (1994).
[CrossRef] [PubMed]

Other (4)

A. Yariv, Quantum Electronics (Wiley, New York, 1989).

However, if QPM is not achieved, the conversion efficiency is proportional to [sin(k2ωL)/(k2ωL)]2. The difference of indices of refraction between the fundamental and SH waves has no effect on the conversion efficiency in our scheme.

Y. J. Ding, J. B. Khurgin, “Quasi-phase-matched mirrorless nondegenerate backward optical parametric oscillation,” submitted to Opt. Lett.

S. Janz, E. Frlan, H. Dai, F. Chatenoud, R. L. Williams, in Nonlinear Optics: Materials, Fundamentals, and Applications, Vol. 18 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 263.

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Figures (3)

Fig. 1
Fig. 1

Configuration for generation of two counterpropagating SH waves in the presence of a mirror for the fundamental and SH waves next to the right-side facet. For QPM the spatial period of the domains must be λ2ω /n, where λ2ω is the SH wavelength in vacuum.

Fig. 2
Fig. 2

(a) Conversion efficiency for a backward SH wave as a function of the normalized pump intensity for the configuration shown in Fig. 1 (solid curve) and for the copropagating configuration (dashed curve). (b) Relative increase of the conversion efficiency for our scheme with respect to that for the copropagating configuration: (ηη′)/η′ [corresponding to the curves in (a)] versus the normalized pump intensity.

Fig. 3
Fig. 3

Normalized output SH intensity versus the normalized pump intensity for the configuration shown in Fig. 1.

Equations (14)

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2 E ω ± n ω 2 c 2 2 E ω ± t 2 = 1 c 2 2 t 2 [ χ F ( 2 ) E ω ( E 2 ω + + E 2 ω ) ] ,
2 ( E 2 ω + + E 2 ω ) n 2 ω 2 c 2 2 ( E 2 ω + + E 2 ω ) t 2 = 1 c 2 2 t 2 [ χ F ( 2 ) E ω + + E ω ] ,
E ω ± = A ω ± ( z ) exp [ i ( ± k ω z ω t ) ] + c . c . ,
E 2 ω ± = A 2 ω ± ( z ) exp [ i ( ± k 2 ω z 2 ω t ) ] + c . c . ,
d A ω ± d z = ± i Γ ω ( A ω ) * ( A 2 ω + + A 2 ω ) ,
d A 2 ω ± d z = ± i Γ 2 ω A ω + A ω ,
A 2 ω + + A 2 ω = A 0 ,
A ω + = a 0 cos ( Γ ω A 0 z + δ ) , A ω = i ( A 0 / A 0 * ) a 0 * sin ( Γ ω A 0 z + δ ) ,
A 2 ω + = ( Γ 2 ω a 0 2 / 4 Γ ω A 0 * ) × [ cos ( 2 Γ ω A 0 z + 2 δ )     cos ( 2 δ ) ] .
A 0 2 = ( Γ 2 ω / 4 Γ ω ) a 0 2 ( 1 + R ω ) cos ( 2 δ ) .
η = I 2 ω / I 0 = [ ( 1 + R 2 ω ) / 2 ] × [ 1 tan 2 ( π / 4 Γ ω A 0 L ) ] ,
I 0 / I s = 8 ( Γ ω A 0 L ) 2 / [ 1 tan 2 ( π / 4 Γ ω A 0 L ) ] ,
I s = λ 2 n ω 2 n 2 ω 32 [ χ 0 ( 2 ) ] 2 L 2 ( 1 + R 2 ω ) η 0
P s , SE P s , B 8 π 2 d eff , SE d SE W SE W L 2 d L SE ,

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