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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 24 — Nov. 19, 2012
  • pp: 27382–27387
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Rejuvenation in scale-free optics and enhanced diffraction cancellation life-time

J. Parravicini, C. Conti, A. J. Agranat, and E. DelRe  »View Author Affiliations


Optics Express, Vol. 20, Issue 24, pp. 27382-27387 (2012)
http://dx.doi.org/10.1364/OE.20.027382


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Abstract

We demonstrate rejuvenation in scale-free optical propagation. The phenomenon is caused by the non-ergodic relaxation of the dipolar glass that mediates the photorefractive nonlinearity in compositionally-disordered lithium-enriched potassium-tantalate-niobate (KTN:Li). We implement rejuvenation to halt aging in the dipolar glass and extend the duration of beam diffraction cancellation.

© 2012 OSA

1. Introduction

Supercooled photorefractive relaxors support a regime of undistorted beam propagation termed “scale-free optics” [1

1. E. DelRe, E. Spinozzi, A. J. Agranat, and C. Conti, “Scale-free optics and diffractionless waves in nanodisordered ferroelectrics,” Nat. Photonics 5, 39–42 (2011). [CrossRef]

7

7. V. Folli, E. DelRe, and C. Conti, “Beam instabilities in the scale-free regime,” Phys. Rev. Lett. 108, 033901 (2012). [CrossRef] [PubMed]

]. In distinction to linear waveguide modes [8

8. J. D. Jackson, Classical Electrodynamics, 3rd ed. (John Wiley & Sons, New York, 1999).

] and spatial solitons [9

9. Y. S. Kivshar and G. P. Agrawal, Optical Solitons (Academic Press, New York, 2003).

], this occurs without the scale-dependent constraints typical of linear and nonlinear diffraction compensation [1

1. E. DelRe, E. Spinozzi, A. J. Agranat, and C. Conti, “Scale-free optics and diffractionless waves in nanodisordered ferroelectrics,” Nat. Photonics 5, 39–42 (2011). [CrossRef]

], a diffraction cancellation that is reminiscent of effects observed in linear periodic systems [10

10. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999). [CrossRef]

, 11

11. H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85, 1863–1866 (2000). [CrossRef] [PubMed]

] and self-induced transparency [12

12. O. Firstenberg, P. London, M. Shuker, A. Ron, and N. Davidson, “Elimination, reversal and directional bias of optical diffraction,” Nat. Phys. 5, 665–668 (2009). [CrossRef]

]. Scale-free optics possesses considerable applicative potential because, in principle, it can greatly increase the resolution of image transmission [1

1. E. DelRe, E. Spinozzi, A. J. Agranat, and C. Conti, “Scale-free optics and diffractionless waves in nanodisordered ferroelectrics,” Nat. Photonics 5, 39–42 (2011). [CrossRef]

, 3

3. C. Conti, A. J. Agranat, and E. DelRe, “Subwavelength optical spatial solitons and three-dimensional localization in disordered ferroelectrics: Toward metamaterials of nonlinear origin,” Phys. Rev. A 84, 043809 (2011). [CrossRef]

, 7

7. V. Folli, E. DelRe, and C. Conti, “Beam instabilities in the scale-free regime,” Phys. Rev. Lett. 108, 033901 (2012). [CrossRef] [PubMed]

]. The effect emerges in lithium-enriched potassium-niobate-tantalate (KTN:Li) [13

13. A. J. Agranat, R. Hofmeister, and A. Yariv, “Characterization of a new photorefractive material: Kl−yLyT1−xNx,” Opt. Lett. 17, 713–715 (1992). [CrossRef] [PubMed]

], a photorefractive ferroelectric crystal with compositional disorder that manifest pronounced relaxor behavior [14

14. A. Bokov, “Recent progress in relaxor ferroelectrics with perovskite structure,” J. Mater. Sci. 41, 31–52 (2006). [CrossRef]

, 15

15. P. Ben Ishai, C. E. M. De Olivera, Y. Ryabov, Y. Feldman, and A. J. Agranat, “Glass-forming liquid kinetics manifested in a KTN:Cu crystal,” Phys. Rev. B 70, 132104 (2004). [CrossRef]

]. At lower levels of Li content, the crystals (i.e., KLTN) support electroholography [16

16. N. Sapiens, A. Weissbrod, and A. J. Agranat, “Fast electroholographic switching,” Opt. Lett. 34, 353–355 (2009). [CrossRef] [PubMed]

] and optical spatial solitons [17

17. E. DelRe and M. Segev, “Self-focusing and solitons in photorefractive media” in Topics in Applied Physics vol. 114 (Springer, Berlin, 2009) pp. 547–572. [CrossRef]

]. When the relaxor is in a nonequilibrium state [1

1. E. DelRe, E. Spinozzi, A. J. Agranat, and C. Conti, “Scale-free optics and diffractionless waves in nanodisordered ferroelectrics,” Nat. Photonics 5, 39–42 (2011). [CrossRef]

, 4

4. J. Parravicini, C. Conti, A. J. Agranat, and E. DelRe, “Programming scale-free optics in disordered ferroelectrics,” Opt. Lett. 37, 2355–2357 (2012). [CrossRef] [PubMed]

6

6. J. Parravicini, A. J. Agranat, C. Conti, and E. DelRe, “Equalizing disordered ferroelectrics for diffraction cancellation,” Appl. Phys. Lett. 101, 111104 (2012). [CrossRef]

], i.e., when the hosted glass of polar nanoregions (PNRs) is rapidly cooled near the ferroelectric room-temperature Curie point TC [1

1. E. DelRe, E. Spinozzi, A. J. Agranat, and C. Conti, “Scale-free optics and diffractionless waves in nanodisordered ferroelectrics,” Nat. Photonics 5, 39–42 (2011). [CrossRef]

, 14

14. A. Bokov, “Recent progress in relaxor ferroelectrics with perovskite structure,” J. Mater. Sci. 41, 31–52 (2006). [CrossRef]

, 18

18. G. A. Samara, “The relaxational properties of compositionally disordered ABO3 perovskites,” J. Phys. Condens. Matter 15, R367 (2003). [CrossRef]

], the PNRs display an anomalously large static susceptibility which activates the scale-free optics [14

14. A. Bokov, “Recent progress in relaxor ferroelectrics with perovskite structure,” J. Mater. Sci. 41, 31–52 (2006). [CrossRef]

].

A key feature is that scale-free optics appears in an out-of-equilibrium phase and manifests aging [19

19. E. Donth, The Glass Transition (Springer-Verlag, Berlin & Heidelberg, 2001).

, 20

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

], a phenomenon that is well known also in other relaxor ferroelectrics [14

14. A. Bokov, “Recent progress in relaxor ferroelectrics with perovskite structure,” J. Mater. Sci. 41, 31–52 (2006). [CrossRef]

, 21

21. J. P. Bouchaud, P. Doussineau, T. de Lacerda-Arôso, and A. Levelut, “Frequency dependence of aging, rejuvenation and memory in a disordered ferroelectric,” Eur. Phys. J. B 21, 335–340 (2001). [CrossRef]

] as well as in a great variety of other systems, such as spin-glasses [22

22. K. Jonason, E. Vincent, J. Hamman, J. P. Bouchaud, and P. Nordblad, “Memory and chaos effect in spin glasses,” Phys. Rev. Lett. 81, 3243–3246 (1998). [CrossRef]

, 23

23. R. Mathieu, M. Hudl, and P. Nordblad, “Memory and rejuvenation in a spin glass,” Eur. Phys. Lett. 90, 67003 (2010). [CrossRef]

], polymers [24

24. S. Mossa and F. Sciortino, “Crossover (or Kovacs) effect in an aging molecular liquid,” Phys Rev. Lett. 92, 045504 (2004). [CrossRef] [PubMed]

], organic semiconductors [25

25. G. Parravicini, M. Campione, F. Marabelli, M. Moret, and A. Sassella, “Experimental assesment of nonergodicity in tetracene single crystals,” Phys. Rev. B 86, 024107 (2012). [CrossRef]

], superconductors [26

26. A. Gardchareon, R. Mathieu, P. E. Jonsson, and P. Nordblad, “Strong rejuvenation in chiral-glass superconductors,” Phys. Rev. B 67, 052505 (2003). [CrossRef]

], multiferroics [27

27. V. V. Shvartsman, S. Bedanta, P. Borisov, W. Kleemann, A. Trach, and P. M. Vilarinho, “(Sr, Mn)TiO(3): A magnetoelectric multiglass,” Phys. Rev. Lett. 101, 165704 (2008). [CrossRef] [PubMed]

] and soft matter optical nonlinearity [28

28. N. Gofraniha, C. Conti, and G. Ruocco, “Aging of the nonlinear optical susceptibility in doped colloidal suspensions,” Phys. Rev. B 75, 224203 (2007). [CrossRef]

30

30. C. Conti and E. DelRe, “Optical supercavitation in soft matter,” Phys. Rev. Lett. 105, 118301 (2010). [CrossRef] [PubMed]

]. Aging causes diffraction cancellation to persist only for a finite life-time which depends on the specific experimental conditions. The effect disappears as the glassy state of the PNRs relaxes [6

6. J. Parravicini, A. J. Agranat, C. Conti, and E. DelRe, “Equalizing disordered ferroelectrics for diffraction cancellation,” Appl. Phys. Lett. 101, 111104 (2012). [CrossRef]

]. Methods to forestall this relaxation and extend the life-time of scale-free optics appear crucial to its development into a practical high-resolution imaging technique.

Interestingly, in some systems that age, even after the physical parameters of the disordered system have been allowed to freely evolve and relax, the use of a specifically tailored thermal protocol T = T(t) can cause the “aged” parameters to be restored to the value they had before the relaxation: the system is said to be “rejuvenated” [31

31. P. Doussineau and A. Levelut, “Memory against temperature or electric field sweeps in potassium niobiotantalate crystals,” Eur. Phys. J. B 26, 13–21 (2002). [CrossRef]

]. In its basic realization, rejuvenation is achieved using the thermal trajectory T = T(t) illustrated in Fig. 1.

Fig. 1 Basic temperature variation protocol for rejuvenation experiments (as described e.g. in [21]): the sample is cooled at a constant rate from Tmax to an intermediate temperature Tpl below the (dynamic) glass transition temperature Td, where cooling is interrupted and an isothermal evolution takes place, for a given time interval (plateau); cooling then resumes down to Tmin and is immediately followed by a steady heating at an opposite rate from Tmin to Tmax.

As a manifestation of history-dependence, rejuvenation is, along with the so-called crossover effect, a consequence of the chaotic nature of the glassy phase [32

32. S. Sahoo, O. Petracic, W. Kleemann, P. Nordblad, S. Cardoso, and P. P. Freitas “Aging and memory in a superspin glass,” Phys. Rev. B 67, 214422 (2003). [CrossRef]

]. Most importantly, aging and rejuvenation is observed in the dielectric and susceptibility of relaxors ferroelectrics [21

21. J. P. Bouchaud, P. Doussineau, T. de Lacerda-Arôso, and A. Levelut, “Frequency dependence of aging, rejuvenation and memory in a disordered ferroelectric,” Eur. Phys. J. B 21, 335–340 (2001). [CrossRef]

, 23

23. R. Mathieu, M. Hudl, and P. Nordblad, “Memory and rejuvenation in a spin glass,” Eur. Phys. Lett. 90, 67003 (2010). [CrossRef]

, 31

31. P. Doussineau and A. Levelut, “Memory against temperature or electric field sweeps in potassium niobiotantalate crystals,” Eur. Phys. J. B 26, 13–21 (2002). [CrossRef]

].

In this work we harness rejuvenation of the dielectric susceptibility of the dipolar glass hosted in relaxor KTN:Li to achieve rejuvenation in the scale-free optical response. The effect is used to extend the life-time of the diffraction cancellation regime, increasing the time stability of the scale-free dynamics. Through rejuvenation, we are able to reverse the decay of the scale-free regime and lengthen the diffraction cancellation regime by more than three times (from an original time interval of 120 s to more than 400 s in our experiments).

2. Methods

The scale-free optical regime exploits the diffusive nonlinearity of the photorefractive effect [33

33. B. Crosignani, E. DelRe, P. Di Porto, and A. Degasperis, “Self-focusing and self-trapping in unbiased centrosymmetric photorefractive media,” Opt. Lett. 23, 912–914 (1998). [CrossRef]

, 34

34. B. Crosignani, A. Degasperis, E. DelRe, P. Di Porto, and A. J. Agranat, “Nonlinear optical diffraction effects and solitons due to anisotropic charge-diffusion-based self-interaction,” Phys. Rev. Lett. 82, 1664–1667 (1999). [CrossRef]

]. The propagation of a beam in the z direction with wavelength λ is governed by [1

1. E. DelRe, E. Spinozzi, A. J. Agranat, and C. Conti, “Scale-free optics and diffractionless waves in nanodisordered ferroelectrics,” Nat. Photonics 5, 39–42 (2011). [CrossRef]

3

3. C. Conti, A. J. Agranat, and E. DelRe, “Subwavelength optical spatial solitons and three-dimensional localization in disordered ferroelectrics: Toward metamaterials of nonlinear origin,” Phys. Rev. A 84, 043809 (2011). [CrossRef]

]
2ikAz+2A(Lλ)2(I)24I2A=0
(1)
where k is the wave vector, I = |A|2 is the intensity of the field envelop A and the parameter L is defined by the relationship
L=4πn02ε0gχPNR(KBT/q).
(2)
Here g is the effective quadratic electro-optic coefficient, χPNR is the effective history-dependent low-frequency dielectric susceptibility of the dipolar glass (due to PNRs), KB the Boltzmann constant, T the crystal equilibration temperature (i.e. the temperature measured at a given istant) and q is the charge of the photoexcited carriers. The regime of diffraction cancellation is obtained when L = λ, so that for Gaussian beams diffraction ceases independently of beam size or intensity (scale-free regime).

To investigate the rejuvenation phenomenon in scale-free optics we employ a 6×3×2.5mm sample of KTN:Li doped with Cu [1

1. E. DelRe, E. Spinozzi, A. J. Agranat, and C. Conti, “Scale-free optics and diffractionless waves in nanodisordered ferroelectrics,” Nat. Photonics 5, 39–42 (2011). [CrossRef]

, 15

15. P. Ben Ishai, C. E. M. De Olivera, Y. Ryabov, Y. Feldman, and A. J. Agranat, “Glass-forming liquid kinetics manifested in a KTN:Cu crystal,” Phys. Rev. B 70, 132104 (2004). [CrossRef]

]. The optical setup is similar to that described in [1

1. E. DelRe, E. Spinozzi, A. J. Agranat, and C. Conti, “Scale-free optics and diffractionless waves in nanodisordered ferroelectrics,” Nat. Photonics 5, 39–42 (2011). [CrossRef]

]: a TEM00 x-polarized light beam from a He-Ne laser (λ = 632.8 nm) propagating in the z direction is focused onto the input facet of the sample. The intensity distribution of the beam at the output of the crystal is imaged and then recorded by a CCD camera. The peak intensity is Ip ≃ 7 W/cm2 and the input beam intensity distribution Full-Width-at-Half-Maximum (FWHM) Δrin = Δxin ≃ Δyin ≃ 11 μm. The temperature T is fixed by a computer-controlled Peltier-junction.

3. Results and discussion

Equations (1) and (2) predict a strong dependence of optical propagation on the static χPNR. The requirement of L = λ implies an unusually high value of χPNR ∼ 105, as observed only in proximity of TC. Furthermore, the crystal must be in a non-ergodic phase where PNRs form, so as to avoid critical opacity. In Fig. 2(a) we report the quasi-static dielectric response εr versus TTC (TC = 14.5°C) obtained from capacitance measurements at slow heating and cooling rates (|ΔTt| ≃ 0.01 °C/s) [5

5. E. DelRe, J. Parravicini, A. J. Agranat, and C. Conti, “Kovacs and inverse Kovacs effect in the optical scale-free regime” in Nonlinear Photonics, OSA Technical Digest (online) (Optical Society of America, 2012), paper NTu3D.6.

, 6

6. J. Parravicini, A. J. Agranat, C. Conti, and E. DelRe, “Equalizing disordered ferroelectrics for diffraction cancellation,” Appl. Phys. Lett. 101, 111104 (2012). [CrossRef]

]. The marked hysteresis in εr(TTC) (shaded region in Fig. 2(a)) signals the glassy non-ergodic phase near TC, where the formation of PNRs takes place, and the dynamic glass transition temperature Td ≃ 18.2°C is identified with the breakdown of the Curie-Weiss law (Fig. 2(b)) [14

14. A. Bokov, “Recent progress in relaxor ferroelectrics with perovskite structure,” J. Mater. Sci. 41, 31–52 (2006). [CrossRef]

, 20

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

].

Fig. 2 (a) Identification of the region where dielectric response is dominated by PNRs. KTN:Li static dielectric constant εr for slow cooling (red curve) and slow heating (blue curve) as a function of temperature (TC = 14.5 °C). The regions of paraelectric (PE) and ferroelectric (FE) behavior are unable to support scale-free propagation. The glassy region where PNRs can support scale-free propagation is indicated with the shading, where marked thermal hysteresis is detected. (b) 1/εr vs. (TTC) plot identifying Td ≃ 18.2°C as the dynamic glass transition temperature when the mean-field Curie-Weiss law (dotted line) breaks down [14, 20].

In order to follow the trend of diffraction cancellation as a function of time we introduce the dimensionless parameter S
S=ΔrdΔrΔrdΔrin
(3)
where Δrd is the FWHM of the exiting Gaussian beam due to the standard linear diffraction, Δrin is the FWHM of the Gaussian beam at the input facet of the crystal and Δr is the FWHM of the exiting beam measured as a function of time during the experiment. S = Sr) allows us to pinpoint the occurrence of scale-free regime, because it varies continuously from 0, i.e., for standard linear diffraction (L = 0, Δr = Δrd), to 1, when diffraction is fully cancelled (L = λ, Δr = Δrin).

Figure 3 reports optical rejuvenation of diffraction cancellation. Figure 3(a) shows the thermal protocol to activate scale-free propagation used and the resulting S(t). The sample is cooled at a constant rate α = ΔTt ≃ −0.13 °C/s below TC and then heated at −α up to an equilibration temperature of T = 16.8 °C which is maintained constant.

Fig. 3 Optical rejuvenation. (a) Standard thermal protocol T = T(t) to activate scale-free propagation with the corresponding trend of diffraction cancellation S as a function of time; (b) rejuvenation thermal protocol and stabilization of S to its maximum value for a ΔT ≃ 3.5°C pulse activated when S ≃ 0.85 ; (c) rejuvenation for a ΔT ≃ 2.5°C pulse activated when S ≃ 0.86; and (d) absence of rejuvenation for a ΔT ≃ 3.5°C activated when S ≃ 0.73.

At t = 0 diffraction is linear (S = 0); after a transient of ≃ 130 s it comes to a complete deletion (S ≃ 1, Lλ). This regime is maintained for 100–150 s. Then it suffers aging, and relaxes to the original diffractive regime (S → 0).

Figure 3(b) reports the thermal protocol and S(t) for a rejuvenation process. The sample is cooled at a constant rate α ≃ −0.13 °C/s below TC and then heated at −α up to an equilibration temperature T = 16.8 °C and kept at that T. The scale-free regime arises as in Fig. 3(a) at t ≃ 130 s and remains steady for a time interval of about 110 s, when it begins to relax and disappear, with a time scale of tens of seconds. At t ≃ 300 s, S has decreased by 15%. A rejuvenation pulse is thus applied (a cooling at the rate α, followed by heating at −α) up to an equilibration temperature of 17.6 °C. The beam stops to broaden and focuses again: at t = 370 s diffraction cancellation is fully restored. The rejuvenation depends on the amplitude and time position of the thermal pulse, as shown in Fig. 3(c) and (d). Specifically, a thermal pulse with an amplitude less than ΔT ≃ 2°C and activated after the beam has decayed to below S ≃ 0.75 fails to produce a rejuvenation back to S ≃ 1. We note that, in distinction to the basic standard rejuvenation protocols of Fig. 1, our protocol has a “hump” before the plateau, necessary to activate the scale-free regime [5

5. E. DelRe, J. Parravicini, A. J. Agranat, and C. Conti, “Kovacs and inverse Kovacs effect in the optical scale-free regime” in Nonlinear Photonics, OSA Technical Digest (online) (Optical Society of America, 2012), paper NTu3D.6.

, 6

6. J. Parravicini, A. J. Agranat, C. Conti, and E. DelRe, “Equalizing disordered ferroelectrics for diffraction cancellation,” Appl. Phys. Lett. 101, 111104 (2012). [CrossRef]

]. For comparison, in Figs. 4(a) and 4(b) we report the transverse intensity distribution of the beam in the two conditions of respectively the standard scale-free formation of Fig. 3(a) and the rejuvenation protocol of Fig. 3(b). Even though the time dynamics depend on the specific value of the input intensity, as is known to occur for all photorefractive phenomena, the rejuvenated beam is observed to consistently reach the maximum value S ≃ 1 irrespective of the actual value of Ip in the range of 3–20 W/cm2, as compatible with scale-free propagation [1

1. E. DelRe, E. Spinozzi, A. J. Agranat, and C. Conti, “Scale-free optics and diffractionless waves in nanodisordered ferroelectrics,” Nat. Photonics 5, 39–42 (2011). [CrossRef]

].

Fig. 4 Intensity distribution at the output facet of the crystal for standard (a) and rejuvenating (b) thermal protocols, as in respectively Figs. 3(a)–(b) and 3(e)–(f).

The causal relationship between the details of the protocol and its effect on glassy state is still a matter of study [20

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

]: we are here interested in demonstrating the possibility of activating an optical rejuvenation effect harnessing the nonequilibrium features of the material.

4. Conclusions

In conclusion, we have demonstrated how rejuvenation can be observed in a disordered ferroelectric and used to stabilize scale-free propagation. The phenomenon involves the glassy nature of dielectric polar-nano-regions inside the crystal. Results are a direct evidence of how optics can make use of out-of-equilibrium solid-state mechanisms.

Acknowledgments

We thank G.B. Parravicini for dielectric measurements and M. Deen Islam for technical assistance. This work was supported by funding from the Firb grant PHOCOS-RBFR08E7VA of the Italian Ministry of Research, from the E.R.C. under the European Community 7th Framework Program (FP7/2007–2013)/ERC grant agreement no.201766, from SmartConfocal project of the Regione Lazio and from the Prin project no.2009P3K72Z. A.J.A. acknowledges the support of the P. Brojde Center for Innovative Engineering.

References and links

1.

E. DelRe, E. Spinozzi, A. J. Agranat, and C. Conti, “Scale-free optics and diffractionless waves in nanodisordered ferroelectrics,” Nat. Photonics 5, 39–42 (2011). [CrossRef]

2.

J. Parravicini, F. Di Mei, C. Conti, A. J. Agranat, and E. DelRe, “Diffraction cancellation over multiple wavelengths in photorefractive dipolar glasses,” Opt. Express 19, 24109–24114 (2011). [CrossRef] [PubMed]

3.

C. Conti, A. J. Agranat, and E. DelRe, “Subwavelength optical spatial solitons and three-dimensional localization in disordered ferroelectrics: Toward metamaterials of nonlinear origin,” Phys. Rev. A 84, 043809 (2011). [CrossRef]

4.

J. Parravicini, C. Conti, A. J. Agranat, and E. DelRe, “Programming scale-free optics in disordered ferroelectrics,” Opt. Lett. 37, 2355–2357 (2012). [CrossRef] [PubMed]

5.

E. DelRe, J. Parravicini, A. J. Agranat, and C. Conti, “Kovacs and inverse Kovacs effect in the optical scale-free regime” in Nonlinear Photonics, OSA Technical Digest (online) (Optical Society of America, 2012), paper NTu3D.6.

6.

J. Parravicini, A. J. Agranat, C. Conti, and E. DelRe, “Equalizing disordered ferroelectrics for diffraction cancellation,” Appl. Phys. Lett. 101, 111104 (2012). [CrossRef]

7.

V. Folli, E. DelRe, and C. Conti, “Beam instabilities in the scale-free regime,” Phys. Rev. Lett. 108, 033901 (2012). [CrossRef] [PubMed]

8.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (John Wiley & Sons, New York, 1999).

9.

Y. S. Kivshar and G. P. Agrawal, Optical Solitons (Academic Press, New York, 2003).

10.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999). [CrossRef]

11.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85, 1863–1866 (2000). [CrossRef] [PubMed]

12.

O. Firstenberg, P. London, M. Shuker, A. Ron, and N. Davidson, “Elimination, reversal and directional bias of optical diffraction,” Nat. Phys. 5, 665–668 (2009). [CrossRef]

13.

A. J. Agranat, R. Hofmeister, and A. Yariv, “Characterization of a new photorefractive material: Kl−yLyT1−xNx,” Opt. Lett. 17, 713–715 (1992). [CrossRef] [PubMed]

14.

A. Bokov, “Recent progress in relaxor ferroelectrics with perovskite structure,” J. Mater. Sci. 41, 31–52 (2006). [CrossRef]

15.

P. Ben Ishai, C. E. M. De Olivera, Y. Ryabov, Y. Feldman, and A. J. Agranat, “Glass-forming liquid kinetics manifested in a KTN:Cu crystal,” Phys. Rev. B 70, 132104 (2004). [CrossRef]

16.

N. Sapiens, A. Weissbrod, and A. J. Agranat, “Fast electroholographic switching,” Opt. Lett. 34, 353–355 (2009). [CrossRef] [PubMed]

17.

E. DelRe and M. Segev, “Self-focusing and solitons in photorefractive media” in Topics in Applied Physics vol. 114 (Springer, Berlin, 2009) pp. 547–572. [CrossRef]

18.

G. A. Samara, “The relaxational properties of compositionally disordered ABO3 perovskites,” J. Phys. Condens. Matter 15, R367 (2003). [CrossRef]

19.

E. Donth, The Glass Transition (Springer-Verlag, Berlin & Heidelberg, 2001).

20.

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

21.

J. P. Bouchaud, P. Doussineau, T. de Lacerda-Arôso, and A. Levelut, “Frequency dependence of aging, rejuvenation and memory in a disordered ferroelectric,” Eur. Phys. J. B 21, 335–340 (2001). [CrossRef]

22.

K. Jonason, E. Vincent, J. Hamman, J. P. Bouchaud, and P. Nordblad, “Memory and chaos effect in spin glasses,” Phys. Rev. Lett. 81, 3243–3246 (1998). [CrossRef]

23.

R. Mathieu, M. Hudl, and P. Nordblad, “Memory and rejuvenation in a spin glass,” Eur. Phys. Lett. 90, 67003 (2010). [CrossRef]

24.

S. Mossa and F. Sciortino, “Crossover (or Kovacs) effect in an aging molecular liquid,” Phys Rev. Lett. 92, 045504 (2004). [CrossRef] [PubMed]

25.

G. Parravicini, M. Campione, F. Marabelli, M. Moret, and A. Sassella, “Experimental assesment of nonergodicity in tetracene single crystals,” Phys. Rev. B 86, 024107 (2012). [CrossRef]

26.

A. Gardchareon, R. Mathieu, P. E. Jonsson, and P. Nordblad, “Strong rejuvenation in chiral-glass superconductors,” Phys. Rev. B 67, 052505 (2003). [CrossRef]

27.

V. V. Shvartsman, S. Bedanta, P. Borisov, W. Kleemann, A. Trach, and P. M. Vilarinho, “(Sr, Mn)TiO(3): A magnetoelectric multiglass,” Phys. Rev. Lett. 101, 165704 (2008). [CrossRef] [PubMed]

28.

N. Gofraniha, C. Conti, and G. Ruocco, “Aging of the nonlinear optical susceptibility in doped colloidal suspensions,” Phys. Rev. B 75, 224203 (2007). [CrossRef]

29.

N. Gofraniha, C. Conti, G. Ruocco, and F. Zamponi, “Time-dependent nonlinear optical susceptibility of an out-of-equilibrium soft material,” Phys. Rev. Lett. 102, 038303 (2009). [CrossRef]

30.

C. Conti and E. DelRe, “Optical supercavitation in soft matter,” Phys. Rev. Lett. 105, 118301 (2010). [CrossRef] [PubMed]

31.

P. Doussineau and A. Levelut, “Memory against temperature or electric field sweeps in potassium niobiotantalate crystals,” Eur. Phys. J. B 26, 13–21 (2002). [CrossRef]

32.

S. Sahoo, O. Petracic, W. Kleemann, P. Nordblad, S. Cardoso, and P. P. Freitas “Aging and memory in a superspin glass,” Phys. Rev. B 67, 214422 (2003). [CrossRef]

33.

B. Crosignani, E. DelRe, P. Di Porto, and A. Degasperis, “Self-focusing and self-trapping in unbiased centrosymmetric photorefractive media,” Opt. Lett. 23, 912–914 (1998). [CrossRef]

34.

B. Crosignani, A. Degasperis, E. DelRe, P. Di Porto, and A. J. Agranat, “Nonlinear optical diffraction effects and solitons due to anisotropic charge-diffusion-based self-interaction,” Phys. Rev. Lett. 82, 1664–1667 (1999). [CrossRef]

OCIS Codes
(160.2750) Materials : Glass and other amorphous materials
(190.4400) Nonlinear optics : Nonlinear optics, materials
(190.5330) Nonlinear optics : Photorefractive optics

ToC Category:
Materials

History
Original Manuscript: September 5, 2012
Revised Manuscript: October 20, 2012
Manuscript Accepted: October 20, 2012
Published: November 19, 2012

Virtual Issues
Nonlinear Photonics (2012) Optics Express

Citation
J. Parravicini, C. Conti, A. J. Agranat, and E. DelRe, "Rejuvenation in scale-free optics and enhanced diffraction cancellation life-time," Opt. Express 20, 27382-27387 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-24-27382


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References

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  27. V. V. Shvartsman, S. Bedanta, P. Borisov, W. Kleemann, A. Trach, and P. M. Vilarinho, “(Sr, Mn)TiO(3): A magnetoelectric multiglass,” Phys. Rev. Lett.101, 165704 (2008). [CrossRef] [PubMed]
  28. N. Gofraniha, C. Conti, and G. Ruocco, “Aging of the nonlinear optical susceptibility in doped colloidal suspensions,” Phys. Rev. B75, 224203 (2007). [CrossRef]
  29. N. Gofraniha, C. Conti, G. Ruocco, and F. Zamponi, “Time-dependent nonlinear optical susceptibility of an out-of-equilibrium soft material,” Phys. Rev. Lett.102, 038303 (2009). [CrossRef]
  30. C. Conti and E. DelRe, “Optical supercavitation in soft matter,” Phys. Rev. Lett.105, 118301 (2010). [CrossRef] [PubMed]
  31. P. Doussineau and A. Levelut, “Memory against temperature or electric field sweeps in potassium niobiotantalate crystals,” Eur. Phys. J. B26, 13–21 (2002). [CrossRef]
  32. S. Sahoo, O. Petracic, W. Kleemann, P. Nordblad, S. Cardoso, and P. P. Freitas “Aging and memory in a superspin glass,” Phys. Rev. B67, 214422 (2003). [CrossRef]
  33. B. Crosignani, E. DelRe, P. Di Porto, and A. Degasperis, “Self-focusing and self-trapping in unbiased centrosymmetric photorefractive media,” Opt. Lett.23, 912–914 (1998). [CrossRef]
  34. B. Crosignani, A. Degasperis, E. DelRe, P. Di Porto, and A. J. Agranat, “Nonlinear optical diffraction effects and solitons due to anisotropic charge-diffusion-based self-interaction,” Phys. Rev. Lett.82, 1664–1667 (1999). [CrossRef]

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