Abstract

We report the simultaneous diffraction cancellation for beams of different wavelengths in out-of-equilibrium dipolar glass. The effect is supported by the photorefractive diffusive nonlinearity and scale-free optics, and can find application in imaging and microscopy.

© 2011 Optical Society of America

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References

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  1. E. DelRe, E. Spinozzi, A. J. Agranat, and C. Conti, “Scale-free optics and diffractionless waves in nanodisordered ferroelectrics,” Nat. Photon. 5, 39–42 (2011).
    [Crossref]
  2. C. Conti, A. J. Agranat, and E. DelRe, “Subwavelength optical spatial solitons and three-dimensional localization in disordered ferroelectrics: towards metamaterials of nonlinear origin,” Phys. Rev. A 84, 043809 (2011).
    [Crossref]
  3. D. Marcuse, Theory of Dielectric Optical Waveguides (Academic Press, New York, 1974).
  4. A. Yariv, Quantum Electronics, 3rd Edition (Wiley, New York, 1989).
  5. S. Trillo and W. Torruellas (eds.), Spatial solitons (Springer-Verlag, Berlin, 2001).
  6. D. Kip, C. Anastassiou, E. Eugenieva, D. Christodoulides, and M. Segev, “Transmission of images through highly nonlinear media by gradient-index lenses formed by incoherent solitons,” Opt. Lett. 26, 524–526 (2001).
    [Crossref]
  7. J. K. Yang, P. Zhang, M. Yoshihara, Y. Hu, and Z. G. Chen, “Image transmission using stable solitons of arbitrary shapes in photonic lattices,” Opt. Lett. 36, 772–774 (2011)
    [Crossref] [PubMed]
  8. 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]
  9. D. V. Dylov and J. W. Fleischer, “Nonlinear self-filtering of noisy images via dynamical stochastic resonance,” Nat. Photon. 4, 323–328 (2010)
    [Crossref]
  10. D. B. Murphy, Fundamentals of light microscopy and electronic imaging (Wiley, New York, 2001)
  11. 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]
  12. 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]
  13. E. DelRe, B. Crosignani, and P. Di Porto, “Photorefractive Solitons and Their Underlying Nonlocal Physics,” Prog. Optics 53, 153–200 (2009)
    [Crossref]
  14. G. Samara, “The relaxational properties of compositionally disordered ABO3 perovskites,” J. Phys.: Condens. Matter 15, R367–R411 (2003)
    [Crossref]
  15. A. A. Bokov and Z. -G. Ye, “Recent progress in relaxor ferroelectrics with perovskite structure,” J. Mater. Sci 41, 31–52 (2006)
    [Crossref]
  16. P. Ben Ishai, A. J. Agranat, and Y. Feldman, “Confinement kinetics in a KTN : Cu crystal: Experiment and theory,” Phys. Rev. B 73, 104104 (2006)
    [Crossref]

2011 (3)

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

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

J. K. Yang, P. Zhang, M. Yoshihara, Y. Hu, and Z. G. Chen, “Image transmission using stable solitons of arbitrary shapes in photonic lattices,” Opt. Lett. 36, 772–774 (2011)
[Crossref] [PubMed]

2010 (1)

D. V. Dylov and J. W. Fleischer, “Nonlinear self-filtering of noisy images via dynamical stochastic resonance,” Nat. Photon. 4, 323–328 (2010)
[Crossref]

2009 (2)

E. DelRe, B. Crosignani, and P. Di Porto, “Photorefractive Solitons and Their Underlying Nonlocal Physics,” Prog. Optics 53, 153–200 (2009)
[Crossref]

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]

2006 (2)

A. A. Bokov and Z. -G. Ye, “Recent progress in relaxor ferroelectrics with perovskite structure,” J. Mater. Sci 41, 31–52 (2006)
[Crossref]

P. Ben Ishai, A. J. Agranat, and Y. Feldman, “Confinement kinetics in a KTN : Cu crystal: Experiment and theory,” Phys. Rev. B 73, 104104 (2006)
[Crossref]

2003 (1)

G. Samara, “The relaxational properties of compositionally disordered ABO3 perovskites,” J. Phys.: Condens. Matter 15, R367–R411 (2003)
[Crossref]

2001 (1)

1999 (1)

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]

1998 (1)

Agranat, A. J.

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

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

P. Ben Ishai, A. J. Agranat, and Y. Feldman, “Confinement kinetics in a KTN : Cu crystal: Experiment and theory,” Phys. Rev. B 73, 104104 (2006)
[Crossref]

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]

Anastassiou, C.

Ben Ishai, P.

P. Ben Ishai, A. J. Agranat, and Y. Feldman, “Confinement kinetics in a KTN : Cu crystal: Experiment and theory,” Phys. Rev. B 73, 104104 (2006)
[Crossref]

Bokov, A. A.

A. A. Bokov and Z. -G. Ye, “Recent progress in relaxor ferroelectrics with perovskite structure,” J. Mater. Sci 41, 31–52 (2006)
[Crossref]

Chen, Z. G.

Christodoulides, D.

Conti, C.

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

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

Crosignani, B.

E. DelRe, B. Crosignani, and P. Di Porto, “Photorefractive Solitons and Their Underlying Nonlocal Physics,” Prog. Optics 53, 153–200 (2009)
[Crossref]

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]

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]

Davidson, N.

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]

Degasperis, A.

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]

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]

DelRe, E.

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

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

E. DelRe, B. Crosignani, and P. Di Porto, “Photorefractive Solitons and Their Underlying Nonlocal Physics,” Prog. Optics 53, 153–200 (2009)
[Crossref]

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]

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]

Di Porto, P.

E. DelRe, B. Crosignani, and P. Di Porto, “Photorefractive Solitons and Their Underlying Nonlocal Physics,” Prog. Optics 53, 153–200 (2009)
[Crossref]

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]

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]

Dylov, D. V.

D. V. Dylov and J. W. Fleischer, “Nonlinear self-filtering of noisy images via dynamical stochastic resonance,” Nat. Photon. 4, 323–328 (2010)
[Crossref]

Eugenieva, E.

Feldman, Y.

P. Ben Ishai, A. J. Agranat, and Y. Feldman, “Confinement kinetics in a KTN : Cu crystal: Experiment and theory,” Phys. Rev. B 73, 104104 (2006)
[Crossref]

Firstenberg, O.

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]

Fleischer, J. W.

D. V. Dylov and J. W. Fleischer, “Nonlinear self-filtering of noisy images via dynamical stochastic resonance,” Nat. Photon. 4, 323–328 (2010)
[Crossref]

Hu, Y.

Kip, D.

London, P.

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]

Marcuse, D.

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic Press, New York, 1974).

Murphy, D. B.

D. B. Murphy, Fundamentals of light microscopy and electronic imaging (Wiley, New York, 2001)

Ron, A.

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]

Samara, G.

G. Samara, “The relaxational properties of compositionally disordered ABO3 perovskites,” J. Phys.: Condens. Matter 15, R367–R411 (2003)
[Crossref]

Segev, M.

Shuker, M.

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]

Spinozzi, E.

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

Yang, J. K.

Yariv, A.

A. Yariv, Quantum Electronics, 3rd Edition (Wiley, New York, 1989).

Ye, Z. -G.

A. A. Bokov and Z. -G. Ye, “Recent progress in relaxor ferroelectrics with perovskite structure,” J. Mater. Sci 41, 31–52 (2006)
[Crossref]

Yoshihara, M.

Zhang, P.

J. Mater. Sci (1)

A. A. Bokov and Z. -G. Ye, “Recent progress in relaxor ferroelectrics with perovskite structure,” J. Mater. Sci 41, 31–52 (2006)
[Crossref]

J. Phys.: Condens. Matter (1)

G. Samara, “The relaxational properties of compositionally disordered ABO3 perovskites,” J. Phys.: Condens. Matter 15, R367–R411 (2003)
[Crossref]

Nat. Photon. (2)

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

D. V. Dylov and J. W. Fleischer, “Nonlinear self-filtering of noisy images via dynamical stochastic resonance,” Nat. Photon. 4, 323–328 (2010)
[Crossref]

Nat. Phys. (1)

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]

Opt. Lett. (3)

Phys. Rev. A (1)

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

Phys. Rev. B (1)

P. Ben Ishai, A. J. Agranat, and Y. Feldman, “Confinement kinetics in a KTN : Cu crystal: Experiment and theory,” Phys. Rev. B 73, 104104 (2006)
[Crossref]

Phys. Rev. Lett. (1)

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]

Prog. Optics (1)

E. DelRe, B. Crosignani, and P. Di Porto, “Photorefractive Solitons and Their Underlying Nonlocal Physics,” Prog. Optics 53, 153–200 (2009)
[Crossref]

Other (4)

D. B. Murphy, Fundamentals of light microscopy and electronic imaging (Wiley, New York, 2001)

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic Press, New York, 1974).

A. Yariv, Quantum Electronics, 3rd Edition (Wiley, New York, 1989).

S. Trillo and W. Torruellas (eds.), Spatial solitons (Springer-Verlag, Berlin, 2001).

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Figures (4)

Fig. 1
Fig. 1 Green (λ = λ1) scale-free propagation and supercooling process. (a) Input intensity distribution, (b) output intensity distribution with no supercooling, (c) with the threshold supercooling α1. (d) Comparison between the supercooling (red line) and no supercooling (blue line) glass preparation (TC ≃ 14.5°C in our sample). The final dip in the temperature trajectory for the supercooling case is the standard overshooting of the temperature control circuit.

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Fig. 2
Fig. 2 Red (λ = λ2) scale-free propagation and supercooling process. (a) Input intensity distribution, (b) output intensity distribution with no supercooling, (c) with the threshold supercooling α2. (d) Comparison between the supercooling (red line) and no supercooling (blue line) glass preparation.

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Fig. 3
Fig. 3 Dual-wavelength beam self-trapping. (a) Output intensity distribution showing the two beams simultaneously trap to their input FWHM for α = 0.13°C/s. (b) Output diffraction intensity distribution in conditions of no supercooling (α ≃ 0).

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Fig. 4
Fig. 4 Intensity-independent of the achromatic effect. The output beam FWHM is seen to be independent of the peak intensity of the two beams. The intensity can be changed independently for the two beams, the effect is unchanged from that shown in Fig. 3.

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Equations (5)

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

Δ n i j = − 1 2 n 0 3 δ i j g P ⋅ P
E d = − k B T q ∇ I I
2 i k ∂ A ∂ z + ∇ ⊥ 2 A + 2 k 2 n 0 Δ n A = 0 ,
2 i k ∂ A ∂ z + ∇ ⊥ 2 A − L 2 4 λ 2 ( ∂ x I ) 2 + ( ∂ y I ) 2 I 2 A = 0 ,
L = 4 π n 0 2 ɛ 0 g χ P N R ( K B T / q ) .

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