Abstract

We consider the nonlinear dynamics occurring when an optical beam couples to dielectric material polarization in an unbiased photorefractive crystal undergoing a ferroelectric phase transition. The polarization profile produced by the light-induced electric field is evaluated by means of the Landau–Ginzburg approach and is found to manifest new thermodynamical states with their own specific nonlinear optical effects. We show that a temperature TC, lower than the critical one, exists such that (a) if T>TC the optical beam experiences an increasing self-focusing for decreasing temperatures and (b) if T<TC the optical beam allows the existence of thermodynamically metastable states associated with an optical ultra-self-focusing effect.

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  1. D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 93, 083905 (2004).
    [CrossRef] [PubMed]
  2. A. D'Ercole, E. Palange, E. DelRe, A. Ciattoni, B. Crosignani, and A. J. Agranat, Appl. Phys. Lett. 85, 2679 (2004).
    [CrossRef]
  3. E. DelRe, M. Tamburrini, M. Segev, R. Della Pergola, and A. J. Agranat, Phys. Rev. Lett. 83, 1954 (1999).
    [CrossRef]
  4. M. E. Lines and A. M. Glass, Principles and Applications of Ferroelectrics and Related Materials (Claredon, 1977).
  5. S. Trillo and W. Torruellas, Spatial Solitons (Springer, 2001).
  6. A. Gordon and S. Dorfman, Phys. Rev. B 51, 9306 (1995).
    [CrossRef]
  7. L. Landau and E. Lifschitz, Electrodynamics of Continuous Media (Pergamon, 1984).
  8. B. Crosignani, A. Degasperis, E. DelRe, P. Di Porto, and A. J. Agranat, Phys. Rev. Lett. 82, 1644 (1999).
    [CrossRef]

2004 (2)

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 93, 083905 (2004).
[CrossRef] [PubMed]

A. D'Ercole, E. Palange, E. DelRe, A. Ciattoni, B. Crosignani, and A. J. Agranat, Appl. Phys. Lett. 85, 2679 (2004).
[CrossRef]

1999 (2)

E. DelRe, M. Tamburrini, M. Segev, R. Della Pergola, and A. J. Agranat, Phys. Rev. Lett. 83, 1954 (1999).
[CrossRef]

B. Crosignani, A. Degasperis, E. DelRe, P. Di Porto, and A. J. Agranat, Phys. Rev. Lett. 82, 1644 (1999).
[CrossRef]

1995 (1)

A. Gordon and S. Dorfman, Phys. Rev. B 51, 9306 (1995).
[CrossRef]

Agranat, A. J.

A. D'Ercole, E. Palange, E. DelRe, A. Ciattoni, B. Crosignani, and A. J. Agranat, Appl. Phys. Lett. 85, 2679 (2004).
[CrossRef]

E. DelRe, M. Tamburrini, M. Segev, R. Della Pergola, and A. J. Agranat, Phys. Rev. Lett. 83, 1954 (1999).
[CrossRef]

B. Crosignani, A. Degasperis, E. DelRe, P. Di Porto, and A. J. Agranat, Phys. Rev. Lett. 82, 1644 (1999).
[CrossRef]

Ciattoni, A.

A. D'Ercole, E. Palange, E. DelRe, A. Ciattoni, B. Crosignani, and A. J. Agranat, Appl. Phys. Lett. 85, 2679 (2004).
[CrossRef]

Crosignani, B.

A. D'Ercole, E. Palange, E. DelRe, A. Ciattoni, B. Crosignani, and A. J. Agranat, Appl. Phys. Lett. 85, 2679 (2004).
[CrossRef]

B. Crosignani, A. Degasperis, E. DelRe, P. Di Porto, and A. J. Agranat, Phys. Rev. Lett. 82, 1644 (1999).
[CrossRef]

Degasperis, A.

B. Crosignani, A. Degasperis, E. DelRe, P. Di Porto, and A. J. Agranat, Phys. Rev. Lett. 82, 1644 (1999).
[CrossRef]

Della Pergola, R.

E. DelRe, M. Tamburrini, M. Segev, R. Della Pergola, and A. J. Agranat, Phys. Rev. Lett. 83, 1954 (1999).
[CrossRef]

DelRe, E.

A. D'Ercole, E. Palange, E. DelRe, A. Ciattoni, B. Crosignani, and A. J. Agranat, Appl. Phys. Lett. 85, 2679 (2004).
[CrossRef]

E. DelRe, M. Tamburrini, M. Segev, R. Della Pergola, and A. J. Agranat, Phys. Rev. Lett. 83, 1954 (1999).
[CrossRef]

B. Crosignani, A. Degasperis, E. DelRe, P. Di Porto, and A. J. Agranat, Phys. Rev. Lett. 82, 1644 (1999).
[CrossRef]

D'Ercole, A.

A. D'Ercole, E. Palange, E. DelRe, A. Ciattoni, B. Crosignani, and A. J. Agranat, Appl. Phys. Lett. 85, 2679 (2004).
[CrossRef]

Di Porto, P.

B. Crosignani, A. Degasperis, E. DelRe, P. Di Porto, and A. J. Agranat, Phys. Rev. Lett. 82, 1644 (1999).
[CrossRef]

Dorfman, S.

A. Gordon and S. Dorfman, Phys. Rev. B 51, 9306 (1995).
[CrossRef]

Glass, A. M.

M. E. Lines and A. M. Glass, Principles and Applications of Ferroelectrics and Related Materials (Claredon, 1977).

Gordon, A.

A. Gordon and S. Dorfman, Phys. Rev. B 51, 9306 (1995).
[CrossRef]

Hanna, B.

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 93, 083905 (2004).
[CrossRef] [PubMed]

Kivshar, Y. S.

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 93, 083905 (2004).
[CrossRef] [PubMed]

Krolikowski, W.

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 93, 083905 (2004).
[CrossRef] [PubMed]

Landau, L.

L. Landau and E. Lifschitz, Electrodynamics of Continuous Media (Pergamon, 1984).

Lifschitz, E.

L. Landau and E. Lifschitz, Electrodynamics of Continuous Media (Pergamon, 1984).

Lines, M. E.

M. E. Lines and A. M. Glass, Principles and Applications of Ferroelectrics and Related Materials (Claredon, 1977).

Neshev, D.

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 93, 083905 (2004).
[CrossRef] [PubMed]

Palange, E.

A. D'Ercole, E. Palange, E. DelRe, A. Ciattoni, B. Crosignani, and A. J. Agranat, Appl. Phys. Lett. 85, 2679 (2004).
[CrossRef]

Segev, M.

E. DelRe, M. Tamburrini, M. Segev, R. Della Pergola, and A. J. Agranat, Phys. Rev. Lett. 83, 1954 (1999).
[CrossRef]

Sukhorukov, A. A.

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 93, 083905 (2004).
[CrossRef] [PubMed]

Tamburrini, M.

E. DelRe, M. Tamburrini, M. Segev, R. Della Pergola, and A. J. Agranat, Phys. Rev. Lett. 83, 1954 (1999).
[CrossRef]

Torruellas, W.

S. Trillo and W. Torruellas, Spatial Solitons (Springer, 2001).

Trillo, S.

S. Trillo and W. Torruellas, Spatial Solitons (Springer, 2001).

Appl. Phys. Lett. (1)

A. D'Ercole, E. Palange, E. DelRe, A. Ciattoni, B. Crosignani, and A. J. Agranat, Appl. Phys. Lett. 85, 2679 (2004).
[CrossRef]

Phys. Rev. B (1)

A. Gordon and S. Dorfman, Phys. Rev. B 51, 9306 (1995).
[CrossRef]

Phys. Rev. Lett. (3)

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 93, 083905 (2004).
[CrossRef] [PubMed]

B. Crosignani, A. Degasperis, E. DelRe, P. Di Porto, and A. J. Agranat, Phys. Rev. Lett. 82, 1644 (1999).
[CrossRef]

E. DelRe, M. Tamburrini, M. Segev, R. Della Pergola, and A. J. Agranat, Phys. Rev. Lett. 83, 1954 (1999).
[CrossRef]

Other (3)

M. E. Lines and A. M. Glass, Principles and Applications of Ferroelectrics and Related Materials (Claredon, 1977).

S. Trillo and W. Torruellas, Spatial Solitons (Springer, 2001).

L. Landau and E. Lifschitz, Electrodynamics of Continuous Media (Pergamon, 1984).

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Figures (2)

Fig. 1
Fig. 1

(a) Thermodynamically stable (black and gray curves refer to ferroelectric and paraelectric phases, respectively) and (b) metastable polarization profile P ( x ) (gray curves) produced by the Gaussian profile A ( x , 0 ) = I 0 exp ( x 2 2 σ 2 ) for various temperatures close to the critical temperature T c . Here I 0 I b = 100 , σ = 10 μ m and, for the chosen KLTN sample, in SI units, a = 4.34 × 10 5 , B = 4 × 10 8 , and D = 5 × 10 6 .

Fig. 2
Fig. 2

Normalized intensity I I b of an optical beam with Gaussian boundary profile A ( x , 0 ) = I 0 exp ( x 2 2 σ 2 ) propagating through the crystal at (a) τ = 1.5 K (ferroelectric II regime with metastable polarization) and (b) τ = 0.2 K (paraelectric regime). (c) Intensity FWHM of the output beam produced by the above Gaussian profile after a propagation distance of 3000 μ m as a function of the temperature. Here I 0 I b = 100 , σ = 10 μ m and, for the chosen KLTN sample, in SI units, a = 4.34 × 10 5 , B = 4 × 10 8 , and D = 5 × 10 6 .

Equations (7)

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

P = ± P s + E 4 a τ ( τ < 0 ) , P = E 2 a τ ( τ > 0 ) ,
i A z + 1 2 k 2 A x 2 = k n 0 δ n A ,
E = K B T q x log [ 1 + | A ( x , z ) | 2 I b ] e ̂ x ,
i A z + 1 2 k 2 A x 2 = 1 2 k n 0 2 g eff P 2 A ,
G = G 0 + S L 2 L 2 d x [ D 2 ( P x ) 2 + a τ P 2 + B P 4 P E ]
D 2 P x 2 = ( 2 a τ + 4 B P 2 ) P E ,
( P x ) x = L 2 = ( P x ) x = L 2 = 0 ,

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