Abstract

Using the history dependence of a dipolar glass hosted in a compositionally disordered lithium-enriched potassium tantalate niobate (KTN:Li) crystal, we demonstrate scale-free optical propagation at tunable temperatures. The operating equilibration temperature is determined by previous crystal spiralling in the temperature/cooling-rate phase space.

© 2012 Optical Society of America

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References

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  1. O. Firstenberg, P. London, M. Snuker, A. Ron, and N. Davidson, Nat. Phys. 5, 665 (2009).
    [CrossRef]
  2. E. DelRe, E. Spinozzi, A. J. Agranat, and C. Conti, Nat. Photon. 5, 39 (2011).
    [CrossRef]
  3. G. A. Samara, J. Phys. Condens. Matter 15, R367 (2003).
    [CrossRef]
  4. A. Bokov, J. Mater. Sci. 41, 31 (2006).
    [CrossRef]
  5. J. Parravicini, F. Di Mei, C. Conti, A. J. Agranat, and E. DelRe, Opt. Express 19, 24109 (2011).
    [CrossRef]
  6. V. Folli, E. DelRe, and C. Conti, Phys. Rev. Lett. 108, 033901 (2012).
    [CrossRef]
  7. The model breaks down for scales at which the space charge saturates. This is a sample-dependent limit associated with the acceptor density NA and the static εr. In typical KTN:Li samples, NA≃2·1018  cm−3, so that even in the critical regime with εr∼105, the model breaks down for beam widths l∼0.1  μm.
  8. C. Conti, A. J. Agranat, and E. DelRe, Phys. Rev. A 84, 043809 (2011).
    [CrossRef]
  9. F. Jona and G. Shirane, Ferroelectric Crystals (Dover, 1993).
  10. E. DelRe, M. Tamburrini, M. Segev, R. Della Pergola, and A. J. Agranat, Phys. Rev. Lett. 83, 1954 (1999).
    [CrossRef]
  11. W. Kleemann and R. Lindner, Ferroelectrics 199, 1 (1997).
    [CrossRef]
  12. L. Leuzzi and T. M. Nieuwenhuizen, Thermodynamics of the Glassy State (Taylor & Francis, 2008).
  13. S. Mossa and F. Sciortino, Phys. Rev. Lett. 92, 045504 (2004).
    [CrossRef]
  14. J. Parravicini, A. J. Agranat, C. Conti, and E. DelRe have prepared a manuscript to be called, “Kovacs and inverse Kovacs effect in the optical scale-free regime.”
  15. B. Crosignani, E. DelRe, P. Di Porto, and A. Degasperis, Opt. Lett. 23, 912 (1998).
    [CrossRef]
  16. B. Crosignani, A. Degasperis, E. DelRe, P. Di Porto, and A. J. Agranat, Phys. Rev. Lett. 82, 1664 (1999).
    [CrossRef]
  17. P. Ben Ishai, C. E. M. De Olivera, Y. Ryabov, Y. Feldman, and A. J. Agranat, Phys. Rev. B 70, 132104 (2004).
    [CrossRef]
  18. A. Gumennik, Y. Kurzweil-Segev, and A. J. Agranat, Opt. Mater. Express 1, 332 (2011).
    [CrossRef]
  19. The final equilibration temperature is held through small-amplitude rapid adjustments that are omitted in the S and R curves.
  20. E. DelRe, A. Ciattoni, and E. Palange, Phys. Rev. E 73, 017601 (2006).
    [CrossRef]

2012 (1)

V. Folli, E. DelRe, and C. Conti, Phys. Rev. Lett. 108, 033901 (2012).
[CrossRef]

2011 (4)

C. Conti, A. J. Agranat, and E. DelRe, Phys. Rev. A 84, 043809 (2011).
[CrossRef]

E. DelRe, E. Spinozzi, A. J. Agranat, and C. Conti, Nat. Photon. 5, 39 (2011).
[CrossRef]

J. Parravicini, F. Di Mei, C. Conti, A. J. Agranat, and E. DelRe, Opt. Express 19, 24109 (2011).
[CrossRef]

A. Gumennik, Y. Kurzweil-Segev, and A. J. Agranat, Opt. Mater. Express 1, 332 (2011).
[CrossRef]

2009 (1)

O. Firstenberg, P. London, M. Snuker, A. Ron, and N. Davidson, Nat. Phys. 5, 665 (2009).
[CrossRef]

2006 (2)

A. Bokov, J. Mater. Sci. 41, 31 (2006).
[CrossRef]

E. DelRe, A. Ciattoni, and E. Palange, Phys. Rev. E 73, 017601 (2006).
[CrossRef]

2004 (2)

P. Ben Ishai, C. E. M. De Olivera, Y. Ryabov, Y. Feldman, and A. J. Agranat, Phys. Rev. B 70, 132104 (2004).
[CrossRef]

S. Mossa and F. Sciortino, Phys. Rev. Lett. 92, 045504 (2004).
[CrossRef]

2003 (1)

G. A. Samara, J. Phys. Condens. Matter 15, R367 (2003).
[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, 1664 (1999).
[CrossRef]

1998 (1)

1997 (1)

W. Kleemann and R. Lindner, Ferroelectrics 199, 1 (1997).
[CrossRef]

Agranat, A. J.

E. DelRe, E. Spinozzi, A. J. Agranat, and C. Conti, Nat. Photon. 5, 39 (2011).
[CrossRef]

J. Parravicini, F. Di Mei, C. Conti, A. J. Agranat, and E. DelRe, Opt. Express 19, 24109 (2011).
[CrossRef]

C. Conti, A. J. Agranat, and E. DelRe, Phys. Rev. A 84, 043809 (2011).
[CrossRef]

A. Gumennik, Y. Kurzweil-Segev, and A. J. Agranat, Opt. Mater. Express 1, 332 (2011).
[CrossRef]

P. Ben Ishai, C. E. M. De Olivera, Y. Ryabov, Y. Feldman, and A. J. Agranat, Phys. Rev. B 70, 132104 (2004).
[CrossRef]

B. Crosignani, A. Degasperis, E. DelRe, P. Di Porto, and A. J. Agranat, Phys. Rev. Lett. 82, 1664 (1999).
[CrossRef]

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

J. Parravicini, A. J. Agranat, C. Conti, and E. DelRe have prepared a manuscript to be called, “Kovacs and inverse Kovacs effect in the optical scale-free regime.”

Ben Ishai, P.

P. Ben Ishai, C. E. M. De Olivera, Y. Ryabov, Y. Feldman, and A. J. Agranat, Phys. Rev. B 70, 132104 (2004).
[CrossRef]

Bokov, A.

A. Bokov, J. Mater. Sci. 41, 31 (2006).
[CrossRef]

Ciattoni, A.

E. DelRe, A. Ciattoni, and E. Palange, Phys. Rev. E 73, 017601 (2006).
[CrossRef]

Conti, C.

V. Folli, E. DelRe, and C. Conti, Phys. Rev. Lett. 108, 033901 (2012).
[CrossRef]

C. Conti, A. J. Agranat, and E. DelRe, Phys. Rev. A 84, 043809 (2011).
[CrossRef]

J. Parravicini, F. Di Mei, C. Conti, A. J. Agranat, and E. DelRe, Opt. Express 19, 24109 (2011).
[CrossRef]

E. DelRe, E. Spinozzi, A. J. Agranat, and C. Conti, Nat. Photon. 5, 39 (2011).
[CrossRef]

J. Parravicini, A. J. Agranat, C. Conti, and E. DelRe have prepared a manuscript to be called, “Kovacs and inverse Kovacs effect in the optical scale-free regime.”

Crosignani, B.

B. Crosignani, A. Degasperis, E. DelRe, P. Di Porto, and A. J. Agranat, Phys. Rev. Lett. 82, 1664 (1999).
[CrossRef]

B. Crosignani, E. DelRe, P. Di Porto, and A. Degasperis, Opt. Lett. 23, 912 (1998).
[CrossRef]

Davidson, N.

O. Firstenberg, P. London, M. Snuker, A. Ron, and N. Davidson, Nat. Phys. 5, 665 (2009).
[CrossRef]

De Olivera, C. E. M.

P. Ben Ishai, C. E. M. De Olivera, Y. Ryabov, Y. Feldman, and A. J. Agranat, Phys. Rev. B 70, 132104 (2004).
[CrossRef]

Degasperis, A.

B. Crosignani, A. Degasperis, E. DelRe, P. Di Porto, and A. J. Agranat, Phys. Rev. Lett. 82, 1664 (1999).
[CrossRef]

B. Crosignani, E. DelRe, P. Di Porto, and A. Degasperis, Opt. Lett. 23, 912 (1998).
[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.

V. Folli, E. DelRe, and C. Conti, Phys. Rev. Lett. 108, 033901 (2012).
[CrossRef]

J. Parravicini, F. Di Mei, C. Conti, A. J. Agranat, and E. DelRe, Opt. Express 19, 24109 (2011).
[CrossRef]

E. DelRe, E. Spinozzi, A. J. Agranat, and C. Conti, Nat. Photon. 5, 39 (2011).
[CrossRef]

C. Conti, A. J. Agranat, and E. DelRe, Phys. Rev. A 84, 043809 (2011).
[CrossRef]

E. DelRe, A. Ciattoni, and E. Palange, Phys. Rev. E 73, 017601 (2006).
[CrossRef]

B. Crosignani, A. Degasperis, E. DelRe, P. Di Porto, and A. J. Agranat, Phys. Rev. Lett. 82, 1664 (1999).
[CrossRef]

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

B. Crosignani, E. DelRe, P. Di Porto, and A. Degasperis, Opt. Lett. 23, 912 (1998).
[CrossRef]

J. Parravicini, A. J. Agranat, C. Conti, and E. DelRe have prepared a manuscript to be called, “Kovacs and inverse Kovacs effect in the optical scale-free regime.”

Di Mei, F.

Di Porto, P.

B. Crosignani, A. Degasperis, E. DelRe, P. Di Porto, and A. J. Agranat, Phys. Rev. Lett. 82, 1664 (1999).
[CrossRef]

B. Crosignani, E. DelRe, P. Di Porto, and A. Degasperis, Opt. Lett. 23, 912 (1998).
[CrossRef]

Feldman, Y.

P. Ben Ishai, C. E. M. De Olivera, Y. Ryabov, Y. Feldman, and A. J. Agranat, Phys. Rev. B 70, 132104 (2004).
[CrossRef]

Firstenberg, O.

O. Firstenberg, P. London, M. Snuker, A. Ron, and N. Davidson, Nat. Phys. 5, 665 (2009).
[CrossRef]

Folli, V.

V. Folli, E. DelRe, and C. Conti, Phys. Rev. Lett. 108, 033901 (2012).
[CrossRef]

Gumennik, A.

Jona, F.

F. Jona and G. Shirane, Ferroelectric Crystals (Dover, 1993).

Kleemann, W.

W. Kleemann and R. Lindner, Ferroelectrics 199, 1 (1997).
[CrossRef]

Kurzweil-Segev, Y.

Leuzzi, L.

L. Leuzzi and T. M. Nieuwenhuizen, Thermodynamics of the Glassy State (Taylor & Francis, 2008).

Lindner, R.

W. Kleemann and R. Lindner, Ferroelectrics 199, 1 (1997).
[CrossRef]

London, P.

O. Firstenberg, P. London, M. Snuker, A. Ron, and N. Davidson, Nat. Phys. 5, 665 (2009).
[CrossRef]

Mossa, S.

S. Mossa and F. Sciortino, Phys. Rev. Lett. 92, 045504 (2004).
[CrossRef]

Nieuwenhuizen, T. M.

L. Leuzzi and T. M. Nieuwenhuizen, Thermodynamics of the Glassy State (Taylor & Francis, 2008).

Palange, E.

E. DelRe, A. Ciattoni, and E. Palange, Phys. Rev. E 73, 017601 (2006).
[CrossRef]

Parravicini, J.

J. Parravicini, F. Di Mei, C. Conti, A. J. Agranat, and E. DelRe, Opt. Express 19, 24109 (2011).
[CrossRef]

J. Parravicini, A. J. Agranat, C. Conti, and E. DelRe have prepared a manuscript to be called, “Kovacs and inverse Kovacs effect in the optical scale-free regime.”

Ron, A.

O. Firstenberg, P. London, M. Snuker, A. Ron, and N. Davidson, Nat. Phys. 5, 665 (2009).
[CrossRef]

Ryabov, Y.

P. Ben Ishai, C. E. M. De Olivera, Y. Ryabov, Y. Feldman, and A. J. Agranat, Phys. Rev. B 70, 132104 (2004).
[CrossRef]

Samara, G. A.

G. A. Samara, J. Phys. Condens. Matter 15, R367 (2003).
[CrossRef]

Sciortino, F.

S. Mossa and F. Sciortino, Phys. Rev. Lett. 92, 045504 (2004).
[CrossRef]

Segev, M.

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

Shirane, G.

F. Jona and G. Shirane, Ferroelectric Crystals (Dover, 1993).

Snuker, M.

O. Firstenberg, P. London, M. Snuker, A. Ron, and N. Davidson, Nat. Phys. 5, 665 (2009).
[CrossRef]

Spinozzi, E.

E. DelRe, E. Spinozzi, A. J. Agranat, and C. Conti, Nat. Photon. 5, 39 (2011).
[CrossRef]

Tamburrini, M.

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

Ferroelectrics (1)

W. Kleemann and R. Lindner, Ferroelectrics 199, 1 (1997).
[CrossRef]

J. Mater. Sci. (1)

A. Bokov, J. Mater. Sci. 41, 31 (2006).
[CrossRef]

J. Phys. Condens. Matter (1)

G. A. Samara, J. Phys. Condens. Matter 15, R367 (2003).
[CrossRef]

Nat. Photon. (1)

E. DelRe, E. Spinozzi, A. J. Agranat, and C. Conti, Nat. Photon. 5, 39 (2011).
[CrossRef]

Nat. Phys. (1)

O. Firstenberg, P. London, M. Snuker, A. Ron, and N. Davidson, Nat. Phys. 5, 665 (2009).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Opt. Mater. Express (1)

Phys. Rev. A (1)

C. Conti, A. J. Agranat, and E. DelRe, Phys. Rev. A 84, 043809 (2011).
[CrossRef]

Phys. Rev. B (1)

P. Ben Ishai, C. E. M. De Olivera, Y. Ryabov, Y. Feldman, and A. J. Agranat, Phys. Rev. B 70, 132104 (2004).
[CrossRef]

Phys. Rev. E (1)

E. DelRe, A. Ciattoni, and E. Palange, Phys. Rev. E 73, 017601 (2006).
[CrossRef]

Phys. Rev. Lett. (4)

V. Folli, E. DelRe, and C. Conti, Phys. Rev. Lett. 108, 033901 (2012).
[CrossRef]

B. Crosignani, A. Degasperis, E. DelRe, P. Di Porto, and A. J. Agranat, Phys. Rev. Lett. 82, 1664 (1999).
[CrossRef]

S. Mossa and F. Sciortino, Phys. Rev. Lett. 92, 045504 (2004).
[CrossRef]

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

Other (5)

L. Leuzzi and T. M. Nieuwenhuizen, Thermodynamics of the Glassy State (Taylor & Francis, 2008).

J. Parravicini, A. J. Agranat, C. Conti, and E. DelRe have prepared a manuscript to be called, “Kovacs and inverse Kovacs effect in the optical scale-free regime.”

The model breaks down for scales at which the space charge saturates. This is a sample-dependent limit associated with the acceptor density NA and the static εr. In typical KTN:Li samples, NA≃2·1018  cm−3, so that even in the critical regime with εr∼105, the model breaks down for beam widths l∼0.1  μm.

F. Jona and G. Shirane, Ferroelectric Crystals (Dover, 1993).

The final equilibration temperature is held through small-amplitude rapid adjustments that are omitted in the S and R curves.

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Figures (3)

Fig. 1.
Fig. 1.

(a) KTN:Li static dielectric constant εr for slow cooling (red curve) and slow heating (green curve) as a function of T, (b) representation of the parameter plane (TTC,α) of the sample preparation. Both regions of paraelectric and ferroelectric behavior, which are unable to support scale-free propagation through rapid cooling, are indicated, together with the glassy region (dashed curve indicates the approximate phase separation). The shaded region indicates the range of hysteresis, while the “GLASSY” region indicates the temperature/cooling-rate range where standard constant α preparation (rapid cooling) can give rise to Lλ (see text). The red (R) and blue (S) curves represent respectively the rapid-cooling (α=constant) and the spiralling trajectories with initial (Ti=24.5°C) and final (Tf=16.8°C, dot-dashed line) temperatures that refer to the experimental data in Fig. 2.

Fig. 2.
Fig. 2.

Intensity distributions and x and y profiles of the beam in the conditions of rapid cooling (R) and spiraling (S) of Fig. 1(b). (a) Input facet of the sample (ΔxΔy12μm), (b) output facet after the rapid-cooling process (curve R, L/λ1), (c) output facet after the spiraling thermal trajectory (curve S, L=λ). Note that (b) manifests a quasi-linear diffraction (ΔxΔy33μm), while the intensity profile in (c) is devoid of spreading (ΔxΔy12μm).

Fig. 3.
Fig. 3.

Programming scale-free response at temperatures TTC. Top right: Representation in the (TTC,α)=(TTC,T˙) parameter plane of the different conditions of scale-free optics reported. Activation, testified by the diffraction-free output intensity distribution (top) reported in the series of images S15, is achieved through spiraling thermal trajectories (bottom). Programmed temperatures: T14.8°C (S1), 15.7 °C (S2), 16.8 °C (S3), 17.7 °C (S4), 18.7 °C (S5). In the parameter plane representation, α is the mean value along the trajectory. The points lie in a temperature range of more than 4 °C.

Equations (1)

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neff=n0/(1(L/λ)2),

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