Abstract

We provide a comprehensive experimental and theoretical study of incoherently coupled photorefractive spatial-soliton pairs in all three possible realizations: bright–bright, dark–dark, and dark–bright. We also show that when the total intensity of two coupled solitons is much lower than the effective dark irradiance, the coupled soliton pair is reduced to Manakov solitons. In all cases, mutual trapping of both components in the coupled soliton pair is verified by analyzing, experimentally and numerically, the beam evolution after decoupling.

© 1997 Optical Society of America

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1997 (9)

1996 (21)

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, Phys. Rev. Lett. 76, 3699 (1996).
[CrossRef] [PubMed]

W. Krolikowski, N. Akhmediev, B. Luther-Davies, and M. Cronin-Golomb, Phys. Rev. E 54, 5761 (1996).
[CrossRef]

M. Chauvet, S. A. Hawkins, G. Salamo, M. Segev, D. F. Bliss, and G. Bryant, Opt. Lett. 21, 1333 (1996).
[CrossRef] [PubMed]

M. Mitchell, Z. Chen, M. Shih, and M. Segev, Phys. Rev. Lett. 77, 490 (1996).
[CrossRef] [PubMed]

S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, Opt. Commun. 130, 288 (1996).
[CrossRef]

M. Taya, M. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, Opt. Lett. 21, 943 (1996).
[CrossRef] [PubMed]

M. I. Carvalho, S. R. Singh, D. N. Christodoulides, and R. I. Joseph, Phys. Rev. E 53, R53 (1996).
[CrossRef]

M. Shih, M. Segev, and G. Salamo, Opt. Lett. 21, 931 (1996).
[CrossRef] [PubMed]

D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, Appl. Phys. Lett. 68, 1763 (1996).
[CrossRef]

W. Krolikowski, N. Akhmediev, and B. Luther-Davies, Opt. Lett. 21, 782 (1996).
[CrossRef]

Z. Chen, M. Segev, T. H. Coskun, and D. N. Christodoulides, Opt. Lett. 21, 1436 (1996).
[CrossRef] [PubMed]

M. Shih and M. Segev, Opt. Lett. 21, 1538 (1996).
[CrossRef] [PubMed]

Z. Chen, M. Segev, T. H. Coskun, D. N. Christodoulides, Y. S. Kivshar, and V. V. Afanasjev, Opt. Lett. 21, 1821 (1996).
[CrossRef] [PubMed]

M. Shih, Z. Chen, M. Segev, T. H. Coskun, and D. N. Christodoulides, Appl. Phys. Lett. 69, 4151 (1996).
[CrossRef]

M. Shih, P. Leach, M. Segev, M. Garrett, G. Salamo, and G. C. Valley, Opt. Lett. 21, R324 (1996).
[CrossRef]

K. Kos, H. Ming, G. Salamo, M. Shih, M. Segev, and G. C. Valley, Phys. Rev. E 53, R4330 (1996).
[CrossRef]

Z. Chen, M. Mitchell, M. Shih, M. Segev, M. Garrett, and G. C. Valley, Opt. Lett. 21, 629 (1996).
[CrossRef] [PubMed]

Z. Chen, M. Mitchell, and M. Segev, Opt. Lett. 21, 716 (1996).
[CrossRef] [PubMed]

V. Tikhonenko, J. Christou, and B. Luther-Davies, Phys. Rev. Lett. 76, 2698 (1996).
[CrossRef] [PubMed]

M. Segev, M. Shih, and G. C. Valley, J. Opt. Soc. Am. B 13, 706 (1996).
[CrossRef]

N. Fressengeas, J. Maufoy, and G. Kugel, Phys. Rev. E 54, 6866 (1996).
[CrossRef]

1995 (12)

M. Morin, G. Duree, G. Salamo, and M. Segev, Opt. Lett. 20, 2066 (1995).
[CrossRef] [PubMed]

G. Duree, M. Morin, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, and E. Sharp, Phys. Rev. Lett. 74, 1978 (1995).
[CrossRef] [PubMed]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

A. W. Snyder, D. J. Mitchell, and Y. S. Kivshar, Mod. Phys. Lett. B 9, 1479 (1995).
[CrossRef]

D. N. Christodoulides and M. I. Carvalho, J. Opt. Soc. Am. B 12, 1628 (1995).
[CrossRef]

M. Segev, G. C. Valley, S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, Opt. Lett. 20, 1764 (1995).
[CrossRef]

S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, Opt. Lett. 20, 2177 (1995).
[CrossRef]

S. R. Singh and D. N. Christodoulides, Opt. Commun. 118, 569 (1995).
[CrossRef]

Steady-state screening solitons in biased photorefractive media was first observed by M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, Electron. Lett. 31, 826 (1995).
[CrossRef]

M. Taya, M. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, Phys. Rev. A 52, 3095 (1995).
[CrossRef] [PubMed]

R. Radhakrishnan and M. Lakshmanan, J. Phys. A 28, 2683 (1995).
[CrossRef]

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, Opt. Commun. 120, 311 (1995).
[CrossRef]

1994 (3)

Steady-state self-focusing in biased photorefractive media was first observed by M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sánchez-Mondragón, S. I. Stepanov, and V. A. Vysloukh, Appl. Phys. Lett. 64, 408 (1994).
[CrossRef]

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. Bashaw, Phys. Rev. A 50, R4457 (1994).
[CrossRef]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

1993 (2)

G. Duree, J. L. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. Sharp, and R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef] [PubMed]

Y. Kivshar, IEEE J. Quantum Electron. 29, 250 (1993).
[CrossRef]

1992 (3)

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992).
[CrossRef] [PubMed]

R. De La Fuente and A. Barthelemy, Opt. Commun. 88, 419 (1992).
[CrossRef]

M. Shalaby and A. J. Barthelemy, IEEE J. Quantum Electron. 28, 2736 (1992).
[CrossRef]

1991 (2)

1989 (1)

1988 (2)

1974 (2)

S. V. Manakov, Sov. Phys. JETP 38, 248 (1974).

V. E. Zakharov and A. Rubenchik, Sov. Phys. JETP 38, 494 (1974).

1972 (1)

V. E. Zakharov and A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

1964 (1)

R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

Afanasjev, V. V.

Aitchison, J. S.

Akhmediev, N.

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, Phys. Rev. Lett. 76, 3699 (1996).
[CrossRef] [PubMed]

W. Krolikowski, N. Akhmediev, B. Luther-Davies, and M. Cronin-Golomb, Phys. Rev. E 54, 5761 (1996).
[CrossRef]

W. Krolikowski, N. Akhmediev, and B. Luther-Davies, Opt. Lett. 21, 782 (1996).
[CrossRef]

Barthelemy, A.

Barthelemy, A. J.

M. Shalaby and A. J. Barthelemy, IEEE J. Quantum Electron. 28, 2736 (1992).
[CrossRef]

Bashaw, M.

M. Taya, M. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, Opt. Lett. 21, 943 (1996).
[CrossRef] [PubMed]

M. Taya, M. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, Phys. Rev. A 52, 3095 (1995).
[CrossRef] [PubMed]

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. Bashaw, Phys. Rev. A 50, R4457 (1994).
[CrossRef]

Bashaw, M. C.

Bliss, D. F.

Bryant, G.

Carcia-Quirino, G. S.

Carvalho, M. I.

D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, Appl. Phys. Lett. 68, 1763 (1996).
[CrossRef]

S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, Opt. Commun. 130, 288 (1996).
[CrossRef]

M. I. Carvalho, S. R. Singh, D. N. Christodoulides, and R. I. Joseph, Phys. Rev. E 53, R53 (1996).
[CrossRef]

M. Segev, G. C. Valley, S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, Opt. Lett. 20, 1764 (1995).
[CrossRef]

S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, Opt. Lett. 20, 2177 (1995).
[CrossRef]

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, Opt. Commun. 120, 311 (1995).
[CrossRef]

D. N. Christodoulides and M. I. Carvalho, J. Opt. Soc. Am. B 12, 1628 (1995).
[CrossRef]

Chauvet, M.

Chen, Z.

Chiao, R. Y.

R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

Christodoulides, D. N.

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997).
[CrossRef]

Z. Chen, M. Segev, S. R. Singh, T. H. Coskun, and D. N. Christodoulides, J. Opt. Soc. Am. B 14, 1407 (1997).
[CrossRef]

Z. Chen, M. Segev, T. H. Coskun, D. N. Christodoulides, Y. S. Kivshar, and V. V. Afanasjev, Opt. Lett. 21, 1821 (1996).
[CrossRef] [PubMed]

M. Shih, Z. Chen, M. Segev, T. H. Coskun, and D. N. Christodoulides, Appl. Phys. Lett. 69, 4151 (1996).
[CrossRef]

Z. Chen, M. Segev, T. H. Coskun, and D. N. Christodoulides, Opt. Lett. 21, 1436 (1996).
[CrossRef] [PubMed]

D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, Appl. Phys. Lett. 68, 1763 (1996).
[CrossRef]

S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, Opt. Commun. 130, 288 (1996).
[CrossRef]

M. I. Carvalho, S. R. Singh, D. N. Christodoulides, and R. I. Joseph, Phys. Rev. E 53, R53 (1996).
[CrossRef]

S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, Opt. Lett. 20, 2177 (1995).
[CrossRef]

M. Segev, G. C. Valley, S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, Opt. Lett. 20, 1764 (1995).
[CrossRef]

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, Opt. Commun. 120, 311 (1995).
[CrossRef]

S. R. Singh and D. N. Christodoulides, Opt. Commun. 118, 569 (1995).
[CrossRef]

D. N. Christodoulides and M. I. Carvalho, J. Opt. Soc. Am. B 12, 1628 (1995).
[CrossRef]

D. N. Christodoulides, Phys. Lett. A 132, 451 (1988).
[CrossRef]

Christou, J.

V. Tikhonenko, J. Christou, and B. Luther-Davies, Phys. Rev. Lett. 76, 2698 (1996).
[CrossRef] [PubMed]

Coskun, T. H.

Cronin-Golomb, M.

W. Krolikowski, N. Akhmediev, B. Luther-Davies, and M. Cronin-Golomb, Phys. Rev. E 54, 5761 (1996).
[CrossRef]

Crosignani, B.

Steady-state screening solitons in biased photorefractive media was first observed by M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, Electron. Lett. 31, 826 (1995).
[CrossRef]

G. Duree, M. Morin, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, and E. Sharp, Phys. Rev. Lett. 74, 1978 (1995).
[CrossRef] [PubMed]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. Bashaw, Phys. Rev. A 50, R4457 (1994).
[CrossRef]

G. Duree, J. L. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. Sharp, and R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef] [PubMed]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, Phys. Rev. Lett. 68, 923 (1992).
[CrossRef] [PubMed]

De La Fuente, R.

DiPorto, P.

G. Duree, M. Morin, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, and E. Sharp, Phys. Rev. Lett. 74, 1978 (1995).
[CrossRef] [PubMed]

Steady-state screening solitons in biased photorefractive media was first observed by M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, Electron. Lett. 31, 826 (1995).
[CrossRef]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

G. Duree, J. L. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. Sharp, and R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef] [PubMed]

Duree, G.

M. Morin, G. Duree, G. Salamo, and M. Segev, Opt. Lett. 20, 2066 (1995).
[CrossRef] [PubMed]

G. Duree, M. Morin, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, and E. Sharp, Phys. Rev. Lett. 74, 1978 (1995).
[CrossRef] [PubMed]

G. Duree, J. L. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. DiPorto, E. Sharp, and R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef] [PubMed]

Fejer, M. M.

M. Segev, G. C. Valley, M. C. Bashaw, M. Taya, and M. M. Fejer, J. Opt. Soc. Am. B 14, 1772 (1997).
[CrossRef]

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Other (1)

A. P. Sheppard and Y. S. Kivshar, in Nonlinear Guided Waves and Their Applications, Vol. 15 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), p. 157.

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Figures (13)

Fig. 1
Fig. 1

Theoretical plot of the existence curves (normalized soliton width versus the square root of the intensity ratio) for fundamental (a) bright and (b) dark photorefractive solitons. The points marked by filled circles correspond to conditions discussed in the text.

Fig. 2
Fig. 2

Experimental setup. Beams 1 and 2 are two soliton-forming beams made incoherent to each other. For bright-beam generation they are cylindrically focused directly onto the crystal input face. For dark-beam generation they are reflected from λ/2 step mirrors (M1 and M2) and then imaged onto the crystal input face.

Fig. 3
Fig. 3

Experimental results showing coupling–decoupling of a bright–bright soliton pair. Photographs are taken at (a) the input and (b)–(d) the output faces of the crystal: (b) diffraction output from the crystal, (c) coupled output when the pairing beam is present, and (d) decoupled output when the pairing beam is absent.

Fig. 4
Fig. 4

Numerical simulations corresponding to Figs. 3(c) and 3(d): (a) propagation of one of the bright beams from a coupled bright–bright soliton pair and (b) propagation of one of the bright beams when the pairing beam is absent.

Fig. 5
Fig. 5

Experimental results showing coupling–decoupling of a dark–dark soliton pair obtained in the region of low intensity ratio. Photographs are taken at (a) the input and (b)–(d) the output faces of the crystal: (b) diffraction output from the crystal, (c) coupled output when the pairing beam is present, and (d) decoupled output when the pairing beam is absent.

Fig. 6
Fig. 6

Numerical simulations corresponding to Figs. 5(c) and 5(d): (a) propagation of one of the dark beams from a coupled dark–dark soliton pair; (b) propagation of one of the dark beams when the pairing beam is absent, and (c) input (solid) and output (dashed) intensity profiles corresponding to (b).

Fig. 7
Fig. 7

Experimental results showing coupling–decoupling of a dark–bright soliton pair. Photographs are taken at (a) the input and (b)–(d) the output faces of the crystal: (b) diffraction output from the crystal, (c) coupled output when the pairing beam is present, and (d) decoupled output when the pairing beam is absent.

Fig. 8
Fig. 8

Numerical simulations corresponding to Figs. 7(c) and 7(d): (a), (b) propagation of the bright and dark components of a coupled soliton pair; (c), (d) corresponding propagation when the pairing component is absent.

Fig. 9
Fig. 9

Numerical simulations showing stable propagation of (a) a bright–bright and (b) a dark–dark soliton pair when the intensity of one of the components is perturbed by 20% at the input.

Fig. 10
Fig. 10

Experimental results showing output (a) dark and (b) bright components from an unstable dark–bright pair.

Fig. 11
Fig. 11

Numerical simulations showing unstable propagation of a dark–bright pair corresponding to Fig. 10: (a) the dark component and (b) the bright component.

Fig. 12
Fig. 12

Experimental results showing the master–slave relation in a dark–dark pair when the intensity of one of the components is much higher than that of the other. Photographs are taken at (a) the input and (b)–(d) the output faces of the crystal: (b) diffraction output, (c) output when both beams are present, and (d) output when the other beam is absent. Beam 1 is the weak beam, and beam 2 is the strong beam.

Fig. 13
Fig. 13

Numerical simulations corresponding to Fig. 12(d). Shown are (a) the strong beam and (b) the weak beam after removing the pairing beam.

Equations (12)

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z-i2k2x2-iknbΔn(Esc)Φ(x, z)=0,
z-i2k2x2-iknbΔn(Esc)Ψ(x, z)=0,
Δn(Esc)=-12nb3r33Esc.
Esc=E0I+IdI(x, z)+Id,
iUζ+12U2ξ2-β(1+ρ)U1+|U|2+|V|2=0,
iVζ+12V2ξ2-β(1+ρ)V1+|U|2+|V|2=0,
d2ydξ2-2µy-2β1+ry2y=0.
d2ydξ2-2µy-2β(1+ρ)1+ρy2y=0.
iuζ+12u2ξ2±(|u|2+|v|2)u=0,
ivζ+12v2ξ2±(|u|2+|v|2)v=0,
u(ζ, ξ)=tanh(aξ)exp(-iζ),
v(ζ, ξ)=1-a2 sech(aξ)exp[-i(1-a2/2)ζ],

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