Abstract

We predict that the combination of space and time modulational instabilities that occur by means of parametric wave mixing in quadratic media leads to colored conical emission. This phenomenon should be observed under conditions usually employed in second-harmonic experiments.

© 2002 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K. Tai, A. Hasegawa, and A. Tomita, Phys. Rev. Lett. 56, 135 (1986).
    [CrossRef] [PubMed]
  2. R. Malendevich, L. Jankovic, G. I. Stegeman, and J. S. Aitchison, Opt. Lett. 26, 1879 (2001).
    [CrossRef]
  3. S. Trillo and P. Ferro, Opt. Lett. 20, 438 (1995).
    [CrossRef] [PubMed]
  4. R. Schiek, H. Fang, R. Malendevich, and G. I. Stegeman, Phys. Rev. Lett. 86, 4528 (2001).
    [CrossRef] [PubMed]
  5. R. A. Fuerst, D. M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).
    [CrossRef]
  6. S. Trillo and S. Wabnitz, Phys. Rev. E 55, R4897 (1997).
    [CrossRef]
  7. H. Fang, R. Malendevich, R. Schiek, and G. I. Stegeman, Opt. Lett. 25, 1786 (2000).
    [CrossRef]
  8. L. W. Liou, X. D. Cao, C. J. McKinstrie, and G. P. Agrawal, Phys. Rev. A 46, 4202 (1992).
    [CrossRef] [PubMed]
  9. G. G. Luther, A. C. Newell, J. V. Moloney, and E. M. Wright, Opt. Lett. 19, 789 (1994).
    [CrossRef] [PubMed]
  10. E. J. Fonseca, B. S. Cavalcanti, and J. M. Hickmann, Opt. Commun. 169, 199 (1999).
    [CrossRef]
  11. A. De Rossi, S. Trillo, A. V. Buryak, and Yu. S. Kivshar, Phys. Rev. E 56, R4959 (1997).
    [CrossRef]
  12. J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
    [CrossRef] [PubMed]
  13. R. J. Gehr, M. W. Kimmel, and A. V. Smith, Opt. Lett. 23, 1298 (1998).
    [CrossRef]
  14. C. Conti, P. Di Trapani, S. Trillo, G. Valiulis, S. Minardi, and O. Jedrkiewicz, in Quantum Electronics and Laser Science Conference (Optical Society of America, Washington, D.C., 2002), paper QTuJ6.
  15. P. Saari and K. Reivelt, Phys. Rev. Lett. 79, 4135 (1997).
    [CrossRef]
  16. K. D. Moll, D. Homoelle, A. L. Gaeta, and R. W. Boyd, Phys. Rev. Lett. 88, 153901 (2002).
    [CrossRef]

2002 (1)

K. D. Moll, D. Homoelle, A. L. Gaeta, and R. W. Boyd, Phys. Rev. Lett. 88, 153901 (2002).
[CrossRef]

2001 (2)

R. Malendevich, L. Jankovic, G. I. Stegeman, and J. S. Aitchison, Opt. Lett. 26, 1879 (2001).
[CrossRef]

R. Schiek, H. Fang, R. Malendevich, and G. I. Stegeman, Phys. Rev. Lett. 86, 4528 (2001).
[CrossRef] [PubMed]

2000 (1)

1999 (1)

E. J. Fonseca, B. S. Cavalcanti, and J. M. Hickmann, Opt. Commun. 169, 199 (1999).
[CrossRef]

1998 (1)

1997 (4)

A. De Rossi, S. Trillo, A. V. Buryak, and Yu. S. Kivshar, Phys. Rev. E 56, R4959 (1997).
[CrossRef]

P. Saari and K. Reivelt, Phys. Rev. Lett. 79, 4135 (1997).
[CrossRef]

R. A. Fuerst, D. M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).
[CrossRef]

S. Trillo and S. Wabnitz, Phys. Rev. E 55, R4897 (1997).
[CrossRef]

1995 (1)

1994 (1)

1992 (1)

L. W. Liou, X. D. Cao, C. J. McKinstrie, and G. P. Agrawal, Phys. Rev. A 46, 4202 (1992).
[CrossRef] [PubMed]

1987 (1)

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

1986 (1)

K. Tai, A. Hasegawa, and A. Tomita, Phys. Rev. Lett. 56, 135 (1986).
[CrossRef] [PubMed]

Agrawal, G. P.

L. W. Liou, X. D. Cao, C. J. McKinstrie, and G. P. Agrawal, Phys. Rev. A 46, 4202 (1992).
[CrossRef] [PubMed]

Aitchison, J. S.

Baboiu, D. M.

R. A. Fuerst, D. M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).
[CrossRef]

Boyd, R. W.

K. D. Moll, D. Homoelle, A. L. Gaeta, and R. W. Boyd, Phys. Rev. Lett. 88, 153901 (2002).
[CrossRef]

Buryak, A. V.

A. De Rossi, S. Trillo, A. V. Buryak, and Yu. S. Kivshar, Phys. Rev. E 56, R4959 (1997).
[CrossRef]

Cao, X. D.

L. W. Liou, X. D. Cao, C. J. McKinstrie, and G. P. Agrawal, Phys. Rev. A 46, 4202 (1992).
[CrossRef] [PubMed]

Cavalcanti, B. S.

E. J. Fonseca, B. S. Cavalcanti, and J. M. Hickmann, Opt. Commun. 169, 199 (1999).
[CrossRef]

Conti, C.

C. Conti, P. Di Trapani, S. Trillo, G. Valiulis, S. Minardi, and O. Jedrkiewicz, in Quantum Electronics and Laser Science Conference (Optical Society of America, Washington, D.C., 2002), paper QTuJ6.

De Rossi, A.

A. De Rossi, S. Trillo, A. V. Buryak, and Yu. S. Kivshar, Phys. Rev. E 56, R4959 (1997).
[CrossRef]

Di Trapani, P.

C. Conti, P. Di Trapani, S. Trillo, G. Valiulis, S. Minardi, and O. Jedrkiewicz, in Quantum Electronics and Laser Science Conference (Optical Society of America, Washington, D.C., 2002), paper QTuJ6.

Durnin, J.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Eberly, J. H.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Fang, H.

R. Schiek, H. Fang, R. Malendevich, and G. I. Stegeman, Phys. Rev. Lett. 86, 4528 (2001).
[CrossRef] [PubMed]

H. Fang, R. Malendevich, R. Schiek, and G. I. Stegeman, Opt. Lett. 25, 1786 (2000).
[CrossRef]

Ferro, P.

Fonseca, E. J.

E. J. Fonseca, B. S. Cavalcanti, and J. M. Hickmann, Opt. Commun. 169, 199 (1999).
[CrossRef]

Fuerst, R. A.

R. A. Fuerst, D. M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).
[CrossRef]

Gaeta, A. L.

K. D. Moll, D. Homoelle, A. L. Gaeta, and R. W. Boyd, Phys. Rev. Lett. 88, 153901 (2002).
[CrossRef]

Gehr, R. J.

Hasegawa, A.

K. Tai, A. Hasegawa, and A. Tomita, Phys. Rev. Lett. 56, 135 (1986).
[CrossRef] [PubMed]

Hickmann, J. M.

E. J. Fonseca, B. S. Cavalcanti, and J. M. Hickmann, Opt. Commun. 169, 199 (1999).
[CrossRef]

Homoelle, D.

K. D. Moll, D. Homoelle, A. L. Gaeta, and R. W. Boyd, Phys. Rev. Lett. 88, 153901 (2002).
[CrossRef]

Jankovic, L.

Jedrkiewicz, O.

C. Conti, P. Di Trapani, S. Trillo, G. Valiulis, S. Minardi, and O. Jedrkiewicz, in Quantum Electronics and Laser Science Conference (Optical Society of America, Washington, D.C., 2002), paper QTuJ6.

Kimmel, M. W.

Kivshar, Yu. S.

A. De Rossi, S. Trillo, A. V. Buryak, and Yu. S. Kivshar, Phys. Rev. E 56, R4959 (1997).
[CrossRef]

Lawrence, B.

R. A. Fuerst, D. M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).
[CrossRef]

Liou, L. W.

L. W. Liou, X. D. Cao, C. J. McKinstrie, and G. P. Agrawal, Phys. Rev. A 46, 4202 (1992).
[CrossRef] [PubMed]

Luther, G. G.

Malendevich, R.

McKinstrie, C. J.

L. W. Liou, X. D. Cao, C. J. McKinstrie, and G. P. Agrawal, Phys. Rev. A 46, 4202 (1992).
[CrossRef] [PubMed]

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Minardi, S.

C. Conti, P. Di Trapani, S. Trillo, G. Valiulis, S. Minardi, and O. Jedrkiewicz, in Quantum Electronics and Laser Science Conference (Optical Society of America, Washington, D.C., 2002), paper QTuJ6.

Moll, K. D.

K. D. Moll, D. Homoelle, A. L. Gaeta, and R. W. Boyd, Phys. Rev. Lett. 88, 153901 (2002).
[CrossRef]

Moloney, J. V.

Newell, A. C.

Reivelt, K.

P. Saari and K. Reivelt, Phys. Rev. Lett. 79, 4135 (1997).
[CrossRef]

Saari, P.

P. Saari and K. Reivelt, Phys. Rev. Lett. 79, 4135 (1997).
[CrossRef]

Schiek, R.

R. Schiek, H. Fang, R. Malendevich, and G. I. Stegeman, Phys. Rev. Lett. 86, 4528 (2001).
[CrossRef] [PubMed]

H. Fang, R. Malendevich, R. Schiek, and G. I. Stegeman, Opt. Lett. 25, 1786 (2000).
[CrossRef]

Smith, A. V.

Stegeman, G. I.

R. Malendevich, L. Jankovic, G. I. Stegeman, and J. S. Aitchison, Opt. Lett. 26, 1879 (2001).
[CrossRef]

R. Schiek, H. Fang, R. Malendevich, and G. I. Stegeman, Phys. Rev. Lett. 86, 4528 (2001).
[CrossRef] [PubMed]

H. Fang, R. Malendevich, R. Schiek, and G. I. Stegeman, Opt. Lett. 25, 1786 (2000).
[CrossRef]

R. A. Fuerst, D. M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).
[CrossRef]

Tai, K.

K. Tai, A. Hasegawa, and A. Tomita, Phys. Rev. Lett. 56, 135 (1986).
[CrossRef] [PubMed]

Tomita, A.

K. Tai, A. Hasegawa, and A. Tomita, Phys. Rev. Lett. 56, 135 (1986).
[CrossRef] [PubMed]

Torruellas, W. E.

R. A. Fuerst, D. M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).
[CrossRef]

Trillo, S.

R. A. Fuerst, D. M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).
[CrossRef]

A. De Rossi, S. Trillo, A. V. Buryak, and Yu. S. Kivshar, Phys. Rev. E 56, R4959 (1997).
[CrossRef]

S. Trillo and S. Wabnitz, Phys. Rev. E 55, R4897 (1997).
[CrossRef]

S. Trillo and P. Ferro, Opt. Lett. 20, 438 (1995).
[CrossRef] [PubMed]

C. Conti, P. Di Trapani, S. Trillo, G. Valiulis, S. Minardi, and O. Jedrkiewicz, in Quantum Electronics and Laser Science Conference (Optical Society of America, Washington, D.C., 2002), paper QTuJ6.

Valiulis, G.

C. Conti, P. Di Trapani, S. Trillo, G. Valiulis, S. Minardi, and O. Jedrkiewicz, in Quantum Electronics and Laser Science Conference (Optical Society of America, Washington, D.C., 2002), paper QTuJ6.

Wabnitz, S.

R. A. Fuerst, D. M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).
[CrossRef]

S. Trillo and S. Wabnitz, Phys. Rev. E 55, R4897 (1997).
[CrossRef]

Wright, E. M.

Opt. Commun. (1)

E. J. Fonseca, B. S. Cavalcanti, and J. M. Hickmann, Opt. Commun. 169, 199 (1999).
[CrossRef]

Opt. Lett. (5)

Phys. Rev. A (1)

L. W. Liou, X. D. Cao, C. J. McKinstrie, and G. P. Agrawal, Phys. Rev. A 46, 4202 (1992).
[CrossRef] [PubMed]

Phys. Rev. E (2)

A. De Rossi, S. Trillo, A. V. Buryak, and Yu. S. Kivshar, Phys. Rev. E 56, R4959 (1997).
[CrossRef]

S. Trillo and S. Wabnitz, Phys. Rev. E 55, R4897 (1997).
[CrossRef]

Phys. Rev. Lett. (6)

K. Tai, A. Hasegawa, and A. Tomita, Phys. Rev. Lett. 56, 135 (1986).
[CrossRef] [PubMed]

R. Schiek, H. Fang, R. Malendevich, and G. I. Stegeman, Phys. Rev. Lett. 86, 4528 (2001).
[CrossRef] [PubMed]

R. A. Fuerst, D. M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).
[CrossRef]

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

P. Saari and K. Reivelt, Phys. Rev. Lett. 79, 4135 (1997).
[CrossRef]

K. D. Moll, D. Homoelle, A. L. Gaeta, and R. W. Boyd, Phys. Rev. Lett. 88, 153901 (2002).
[CrossRef]

Other (1)

C. Conti, P. Di Trapani, S. Trillo, G. Valiulis, S. Minardi, and O. Jedrkiewicz, in Quantum Electronics and Laser Science Conference (Optical Society of America, Washington, D.C., 2002), paper QTuJ6.

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 (4)

Fig. 1
Fig. 1

MI gain gΩ,K in the anomalous GVD regime for the in-phase eigenmode at phase matching δk=0.

Fig. 2
Fig. 2

Normal GVD regime β1,2=1: (a) level plot of conical emission gain gΩ,K for the ϕ=0 eigenmode (similar plot holds for ϕ=π); (b) peak value of g versus δk.

Fig. 3
Fig. 3

Level plot of CCE dimensional gain G for the in-phase eigenmode in a lithium triborate crystal (see text for data).

Fig. 4
Fig. 4

Spectrally selective amplification of white noise seen at z=15 from unseeded collinearly phase matched SHG [δk=0 in Eqs. (1)] pumped by a cw plane-wave pump at ω: (a) u1K,Ω and (b) u2K,Ω.

Equations (6)

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

iu1z+σ122u1-β122u1t2+u2u1*=0, iu2z+σ222u2+iδu2t-β222u2t2+δku2+u122=0,
umr,t,z=um0+amr,t,zexpimβz, m=1,2,
fm±r,t=-0Fm±K,ΩJ0KrexpiΩtKdKdΩ.
Ω1+iλu20u100u20Ω1-iλ0u10u100Ω2-δΩ+iλ00u100Ω2+δΩ-iλ×F=0,
λ=λK,Ω=±f0±f02-f11/21/2.
k1δω2-k1-1kt2=Δk.

Metrics