Abstract

We show, for the first time to our knowledge, that the fundamental beam that participates in the process of third-harmonic generation experiences an additional high-order nonlinear phase shift. The magnitude of the shift is proportional to the square of the pump intensity and the length of the sample and depends on the deviation from the exact phase-matched condition. This phase shift arises from cascaded third-order processes. Its value can exceed the value of the phase shift that originates from inherent fifth-order susceptibility of the nonlinear medium. Its sign is controllable by the sign of the phase mismatch of the third-harmonic generation process.

© 1997 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. T. K. Gustafson, P. L. Kelley, R. Y. Chiao, and R. G. Brewer, Appl. Phys. Lett. 12, 165 (1968).
    [Crossref]
  2. R. De Salvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, and E. Van Stryland, Opt. Lett. 17, 28 (1992).
    [Crossref]
  3. S. A. Akhmanov, V. A. Martynov, S. M. Saltiel, and V. G. Tunkin, JETP Lett. 22, 65 (1975).
  4. I. Tomov and M. Richardson, IEEE J. Quantum Electron. QE-12, 521 (1976).
    [Crossref]
  5. M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, IEEE J. Quantum Electron. 28, 2631 (1992).
    [Crossref]
  6. D. Williams, D. West, and T. King, presented at the European Quantum Electronics Conference, September 8–13, 1996, Hamburg, Germany.
  7. Z. A. Tagiev and A. S. Chirkin, Zh. Eksp. Teor. Fiz. 73, 1271 (1977).
  8. S. Saltiel, K. Koynov, and I. Buchvarov, Bulg. J. Phys. 22, 39 (1995).
  9. S. Saltiel, K. Koynov, and I. Buchvarov, Appl. Phys. B 63, 39 (1996).
    [Crossref]
  10. J. E. Midwinter and J. Warner, Br. J. Appl. Phys. 16, 1667 (1965).
    [Crossref]
  11. W. Schmid, T. Vogtman, and M. Schwoerer, Opt. Commun. 121, 55 (1995).
    [Crossref]
  12. B. L. Lawrence, M. Cha, W. E. Torruellas, and G. Stegeman, Appl. Phys. Lett. 64, 2773 (1994).
    [Crossref]
  13. E. M. Wright, B. L. Lawrence, W. Torruellas, and G. Stegeman, Opt. Lett. 20, 2481 (1995).
    [Crossref]
  14. G. Stegeman, A. Villeneuve, J. S. Aitchison, and C. N. Iornside, in Fabrication, Properties and Applications of Low-Dimensional Semi-Conductors, M. Balkanski and I. Yantchev, eds., NATO ASI Ser.3, 415 (1995).
    [Crossref]
  15. S. Gatz and J. Herrmann, J. Opt. Soc. Am. B 8, 2296 (1991).
    [Crossref]
  16. D. I. Pushkarov and S. Tanev, Opt. Commun. 124, 354 (1996).
    [Crossref]
  17. Y. S. Kivshar, V. V. Afanasjev, and A. W. Snyder, Opt. Commun. 126, 348 (1996).
    [Crossref]
  18. K. Hayata, Y. Uehira, and M. Koshiba, Phys. Rev. A 51, 1549 (1995).
    [Crossref] [PubMed]

1996 (3)

S. Saltiel, K. Koynov, and I. Buchvarov, Appl. Phys. B 63, 39 (1996).
[Crossref]

D. I. Pushkarov and S. Tanev, Opt. Commun. 124, 354 (1996).
[Crossref]

Y. S. Kivshar, V. V. Afanasjev, and A. W. Snyder, Opt. Commun. 126, 348 (1996).
[Crossref]

1995 (4)

K. Hayata, Y. Uehira, and M. Koshiba, Phys. Rev. A 51, 1549 (1995).
[Crossref] [PubMed]

S. Saltiel, K. Koynov, and I. Buchvarov, Bulg. J. Phys. 22, 39 (1995).

W. Schmid, T. Vogtman, and M. Schwoerer, Opt. Commun. 121, 55 (1995).
[Crossref]

E. M. Wright, B. L. Lawrence, W. Torruellas, and G. Stegeman, Opt. Lett. 20, 2481 (1995).
[Crossref]

1994 (1)

B. L. Lawrence, M. Cha, W. E. Torruellas, and G. Stegeman, Appl. Phys. Lett. 64, 2773 (1994).
[Crossref]

1992 (2)

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

R. De Salvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, and E. Van Stryland, Opt. Lett. 17, 28 (1992).
[Crossref]

1991 (1)

1977 (1)

Z. A. Tagiev and A. S. Chirkin, Zh. Eksp. Teor. Fiz. 73, 1271 (1977).

1976 (1)

I. Tomov and M. Richardson, IEEE J. Quantum Electron. QE-12, 521 (1976).
[Crossref]

1975 (1)

S. A. Akhmanov, V. A. Martynov, S. M. Saltiel, and V. G. Tunkin, JETP Lett. 22, 65 (1975).

1968 (1)

T. K. Gustafson, P. L. Kelley, R. Y. Chiao, and R. G. Brewer, Appl. Phys. Lett. 12, 165 (1968).
[Crossref]

1965 (1)

J. E. Midwinter and J. Warner, Br. J. Appl. Phys. 16, 1667 (1965).
[Crossref]

Afanasjev, V. V.

Y. S. Kivshar, V. V. Afanasjev, and A. W. Snyder, Opt. Commun. 126, 348 (1996).
[Crossref]

Aitchison, J. S.

G. Stegeman, A. Villeneuve, J. S. Aitchison, and C. N. Iornside, in Fabrication, Properties and Applications of Low-Dimensional Semi-Conductors, M. Balkanski and I. Yantchev, eds., NATO ASI Ser.3, 415 (1995).
[Crossref]

Akhmanov, S. A.

S. A. Akhmanov, V. A. Martynov, S. M. Saltiel, and V. G. Tunkin, JETP Lett. 22, 65 (1975).

Brewer, R. G.

T. K. Gustafson, P. L. Kelley, R. Y. Chiao, and R. G. Brewer, Appl. Phys. Lett. 12, 165 (1968).
[Crossref]

Buchvarov, I.

S. Saltiel, K. Koynov, and I. Buchvarov, Appl. Phys. B 63, 39 (1996).
[Crossref]

S. Saltiel, K. Koynov, and I. Buchvarov, Bulg. J. Phys. 22, 39 (1995).

Byer, R. L.

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

Cha, M.

B. L. Lawrence, M. Cha, W. E. Torruellas, and G. Stegeman, Appl. Phys. Lett. 64, 2773 (1994).
[Crossref]

Chiao, R. Y.

T. K. Gustafson, P. L. Kelley, R. Y. Chiao, and R. G. Brewer, Appl. Phys. Lett. 12, 165 (1968).
[Crossref]

Chirkin, A. S.

Z. A. Tagiev and A. S. Chirkin, Zh. Eksp. Teor. Fiz. 73, 1271 (1977).

De Salvo, R.

Fejer, M. M.

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

Gatz, S.

Gustafson, T. K.

T. K. Gustafson, P. L. Kelley, R. Y. Chiao, and R. G. Brewer, Appl. Phys. Lett. 12, 165 (1968).
[Crossref]

Hagan, D. J.

Hayata, K.

K. Hayata, Y. Uehira, and M. Koshiba, Phys. Rev. A 51, 1549 (1995).
[Crossref] [PubMed]

Herrmann, J.

Iornside, C. N.

G. Stegeman, A. Villeneuve, J. S. Aitchison, and C. N. Iornside, in Fabrication, Properties and Applications of Low-Dimensional Semi-Conductors, M. Balkanski and I. Yantchev, eds., NATO ASI Ser.3, 415 (1995).
[Crossref]

Jundt, D. H.

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

Kelley, P. L.

T. K. Gustafson, P. L. Kelley, R. Y. Chiao, and R. G. Brewer, Appl. Phys. Lett. 12, 165 (1968).
[Crossref]

King, T.

D. Williams, D. West, and T. King, presented at the European Quantum Electronics Conference, September 8–13, 1996, Hamburg, Germany.

Kivshar, Y. S.

Y. S. Kivshar, V. V. Afanasjev, and A. W. Snyder, Opt. Commun. 126, 348 (1996).
[Crossref]

Koshiba, M.

K. Hayata, Y. Uehira, and M. Koshiba, Phys. Rev. A 51, 1549 (1995).
[Crossref] [PubMed]

Koynov, K.

S. Saltiel, K. Koynov, and I. Buchvarov, Appl. Phys. B 63, 39 (1996).
[Crossref]

S. Saltiel, K. Koynov, and I. Buchvarov, Bulg. J. Phys. 22, 39 (1995).

Lawrence, B. L.

E. M. Wright, B. L. Lawrence, W. Torruellas, and G. Stegeman, Opt. Lett. 20, 2481 (1995).
[Crossref]

B. L. Lawrence, M. Cha, W. E. Torruellas, and G. Stegeman, Appl. Phys. Lett. 64, 2773 (1994).
[Crossref]

Magel, G. A.

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

Martynov, V. A.

S. A. Akhmanov, V. A. Martynov, S. M. Saltiel, and V. G. Tunkin, JETP Lett. 22, 65 (1975).

Midwinter, J. E.

J. E. Midwinter and J. Warner, Br. J. Appl. Phys. 16, 1667 (1965).
[Crossref]

Pushkarov, D. I.

D. I. Pushkarov and S. Tanev, Opt. Commun. 124, 354 (1996).
[Crossref]

Richardson, M.

I. Tomov and M. Richardson, IEEE J. Quantum Electron. QE-12, 521 (1976).
[Crossref]

Saltiel, S.

S. Saltiel, K. Koynov, and I. Buchvarov, Appl. Phys. B 63, 39 (1996).
[Crossref]

S. Saltiel, K. Koynov, and I. Buchvarov, Bulg. J. Phys. 22, 39 (1995).

Saltiel, S. M.

S. A. Akhmanov, V. A. Martynov, S. M. Saltiel, and V. G. Tunkin, JETP Lett. 22, 65 (1975).

Schmid, W.

W. Schmid, T. Vogtman, and M. Schwoerer, Opt. Commun. 121, 55 (1995).
[Crossref]

Schwoerer, M.

W. Schmid, T. Vogtman, and M. Schwoerer, Opt. Commun. 121, 55 (1995).
[Crossref]

Sheik-Bahae, M.

Snyder, A. W.

Y. S. Kivshar, V. V. Afanasjev, and A. W. Snyder, Opt. Commun. 126, 348 (1996).
[Crossref]

Stegeman, G.

E. M. Wright, B. L. Lawrence, W. Torruellas, and G. Stegeman, Opt. Lett. 20, 2481 (1995).
[Crossref]

B. L. Lawrence, M. Cha, W. E. Torruellas, and G. Stegeman, Appl. Phys. Lett. 64, 2773 (1994).
[Crossref]

R. De Salvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, and E. Van Stryland, Opt. Lett. 17, 28 (1992).
[Crossref]

G. Stegeman, A. Villeneuve, J. S. Aitchison, and C. N. Iornside, in Fabrication, Properties and Applications of Low-Dimensional Semi-Conductors, M. Balkanski and I. Yantchev, eds., NATO ASI Ser.3, 415 (1995).
[Crossref]

Tagiev, Z. A.

Z. A. Tagiev and A. S. Chirkin, Zh. Eksp. Teor. Fiz. 73, 1271 (1977).

Tanev, S.

D. I. Pushkarov and S. Tanev, Opt. Commun. 124, 354 (1996).
[Crossref]

Tomov, I.

I. Tomov and M. Richardson, IEEE J. Quantum Electron. QE-12, 521 (1976).
[Crossref]

Torruellas, W.

Torruellas, W. E.

B. L. Lawrence, M. Cha, W. E. Torruellas, and G. Stegeman, Appl. Phys. Lett. 64, 2773 (1994).
[Crossref]

Tunkin, V. G.

S. A. Akhmanov, V. A. Martynov, S. M. Saltiel, and V. G. Tunkin, JETP Lett. 22, 65 (1975).

Uehira, Y.

K. Hayata, Y. Uehira, and M. Koshiba, Phys. Rev. A 51, 1549 (1995).
[Crossref] [PubMed]

Van Stryland, E.

Villeneuve, A.

G. Stegeman, A. Villeneuve, J. S. Aitchison, and C. N. Iornside, in Fabrication, Properties and Applications of Low-Dimensional Semi-Conductors, M. Balkanski and I. Yantchev, eds., NATO ASI Ser.3, 415 (1995).
[Crossref]

Vogtman, T.

W. Schmid, T. Vogtman, and M. Schwoerer, Opt. Commun. 121, 55 (1995).
[Crossref]

Warner, J.

J. E. Midwinter and J. Warner, Br. J. Appl. Phys. 16, 1667 (1965).
[Crossref]

West, D.

D. Williams, D. West, and T. King, presented at the European Quantum Electronics Conference, September 8–13, 1996, Hamburg, Germany.

Williams, D.

D. Williams, D. West, and T. King, presented at the European Quantum Electronics Conference, September 8–13, 1996, Hamburg, Germany.

Wright, E. M.

Appl. Phys. B (1)

S. Saltiel, K. Koynov, and I. Buchvarov, Appl. Phys. B 63, 39 (1996).
[Crossref]

Appl. Phys. Lett. (2)

T. K. Gustafson, P. L. Kelley, R. Y. Chiao, and R. G. Brewer, Appl. Phys. Lett. 12, 165 (1968).
[Crossref]

B. L. Lawrence, M. Cha, W. E. Torruellas, and G. Stegeman, Appl. Phys. Lett. 64, 2773 (1994).
[Crossref]

Br. J. Appl. Phys. (1)

J. E. Midwinter and J. Warner, Br. J. Appl. Phys. 16, 1667 (1965).
[Crossref]

Bulg. J. Phys. (1)

S. Saltiel, K. Koynov, and I. Buchvarov, Bulg. J. Phys. 22, 39 (1995).

IEEE J. Quantum Electron. (2)

I. Tomov and M. Richardson, IEEE J. Quantum Electron. QE-12, 521 (1976).
[Crossref]

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

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

JETP Lett. (1)

S. A. Akhmanov, V. A. Martynov, S. M. Saltiel, and V. G. Tunkin, JETP Lett. 22, 65 (1975).

Opt. Commun. (3)

W. Schmid, T. Vogtman, and M. Schwoerer, Opt. Commun. 121, 55 (1995).
[Crossref]

D. I. Pushkarov and S. Tanev, Opt. Commun. 124, 354 (1996).
[Crossref]

Y. S. Kivshar, V. V. Afanasjev, and A. W. Snyder, Opt. Commun. 126, 348 (1996).
[Crossref]

Opt. Lett. (2)

Phys. Rev. A (1)

K. Hayata, Y. Uehira, and M. Koshiba, Phys. Rev. A 51, 1549 (1995).
[Crossref] [PubMed]

Zh. Eksp. Teor. Fiz. (1)

Z. A. Tagiev and A. S. Chirkin, Zh. Eksp. Teor. Fiz. 73, 1271 (1977).

Other (2)

D. Williams, D. West, and T. King, presented at the European Quantum Electronics Conference, September 8–13, 1996, Hamburg, Germany.

G. Stegeman, A. Villeneuve, J. S. Aitchison, and C. N. Iornside, in Fabrication, Properties and Applications of Low-Dimensional Semi-Conductors, M. Balkanski and I. Yantchev, eds., NATO ASI Ser.3, 415 (1995).
[Crossref]

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (2)

Fig. 1
Fig. 1

High-order NLPS (owing to cascading) as a function of the normalized phase mismatch ΔkL. The parameter is the value of the normalized input intensity γ13|A1|2L.

Fig. 2
Fig. 2

Normalized effective coefficient n˜4 as a function of the normalized pump intensity γ13|A1|2L. The parameter is the normalized phase mismatch ΔkL (in radians) with the following values: a, -π/2; b, -π; c, -3π/2; d, -2π.

Tables (2)

Tables Icon

Table 1 Nonlinear Coupling Coefficients

Tables Icon

Table 2 Numerical Values of the Nonlinear Refractive-Index Coefficients n2, n4, and n4,maxcase for Various Materials and Wavelengths

Equations (10)

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

n=n0+n2I+n4I2+n6I3+.
n2=3χ(3)/(40cn02), n4=5χ(5)/(402c2n03),n6=35χ(7)/(1603c3n04).
E={eˆ1A1 exp[-i(ωt-k1z)]+ eˆ3A3 exp[-i(3ωt-k3z)]+c.c.},
dA1dz=i(γ1|A1|2+γ2|A3|2+δ|A1|4)×A1+iγ13A1*2A3 exp(iΔkz),dA3dz=iγ4|A1|2A3+iγ31A13 exp(-iΔkz),
d2A3dz2+iΔdA3dz+SA3=0,
a3(z)=γ31a13 sinc(Λz)z,φ3(z)=(π/2)+3φ10-(Δ/2)z,
dφ1dz=γ1a12+δa14+γ2a32+ (γ13/γ31)(a3/a1)2(Δ/2+γ4a12).
Δφ1=(γ1a12+δa14)L-[γ13γ31(Δ/2)-γ31(γ2γ31-γ4γ13)a12]a14L2Λ2[1-sinc(2ΛL)].
n4casc=ωcn22Δ4Λ2[1-sinc(2ΛL)].
n4casc(2ΛL=±π)=-sgn(Δk)2n22L/λ.

Metrics