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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 24 — Nov. 21, 2011
  • pp: 24109–24114
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Diffraction cancellation over multiple wavelengths in photorefractive dipolar glasses

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


Optics Express, Vol. 19, Issue 24, pp. 24109-24114 (2011)
http://dx.doi.org/10.1364/OE.19.024109


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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 OSA

1. Introduction

A basic application of scale-free optics is in imaging or in microscopy, where nonlinearity is known to play a fundamental role [9

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]

]. However, in these systems the optical field typically has a large spectral content. In fluorescence microscopy, the optical image to be collected and transferred through the optical system is simply multi-colored [10

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

]. To date, all experiments into diffraction cancellation and scale-free optics have been limited to a single optical wavelength. The question lies open if and how diffraction cancellation can be achieve for colored images, that is, for optical fields composed of different wavelengths.

In this Letter we report the simultaneous cancellation of diffraction for a green λ1 = 532 nm and a red λ2 = 633 nm laser beam of same size and intensity. The phenomenon is supported by the scale-free diffusive nonlinearity [11

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]

13

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

] observed in a disordered photorefractive ferroelectric crystal [14

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

16

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]

], and emerges through the enhanced electro-optic response of polar nanoregions (PNR) that form when the crystal is supercooled close to its 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. Photon. 5, 39–42 (2011). [CrossRef]

, 2

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]

].

2. Model

3. Single-wavelength experiments

We carry out our experiments in Lithium-enriched potassium-lithium-tantalate niobate (KTN:Li), a crystal with complex dielectric behavior that has both relaxor-like response and strong photorefractive response induced by Cu impurities [1

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]

]. The crystal temperature is established by a current-controlled Peltier-junction, and two optical TEM00 beams, respectively from a doubled Nd-Yagg laser (λ1 = 532 nm) and a He-Ne laser (λ2 = 633 nm) are first expanded an focused down onto the input facet of the crystal. The two beams have independent optical paths and are recombined through a standard beam-splitter right before the crystal, so that both their size, intensity, polarization, and focusing can be fixed separately. In our basic experiment, we fix both beams to an approximately circular intensity distribution of equal intensity Full-Width-at-Half-Maximum (FWHM) Δx ≃ Δy ≃ 12 μm, and equal peak intensity of Ip1Ip2 ≃ 50 W/cm2, copropagating in parallel and with the same x linear polarization.

We first proceed to determine the conditions of supercooling that lead to scale-free propagation for the two wavelength beams separately.

In Fig. 1 we demonstrate that for a cooling rate of α1 ≃ 0.11°C/s (see the thermal cooling process in Fig. 1(d)) we observe the output intensity distribution to pass from the spread out shape caused by diffraction (Δx ≃ Δy ≃ 30μm, Fig. 1(a,b)) to the non-diffracting case (Fig. 1(c)), where the input beam size is held throughout the Lz = 3mm propagation in the sample (this being the threshold value of χPNR associated to the value of α1 for which L = L1 = λ1).

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.

Analogoulsy, in Fig. 2 we determine that scale-free propagation is observed for the red beam at α2 ≃ 0.13°C/s (see Fig. 2(d)), for which hence L = L2 = λ2. We note that the threshold cooling rates for the dipolar glass scale α1/α2 ≃ 0.84 ≃ λ1/λ2, as expected from the scale-free model, being that χPNRα (and LχPNR, see Eq. (5)).

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.

4. Dual-wavelength experiments

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).
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.

We note that to carry out the double wavelength experiments we have adopted techniques to allow the imaging of the two wavelength beams simultaneously at the output. Specifically, we adopted a slanted CCD scheme, by which a slight angle between the CCD detecting surface and the direction of propagation allows both the red and green beams to be focused simultaneously.

5. Discussion

Acknowledgments

We thank G.B. Parravicini for useful discussions, and M. Deen Islam, G. Bolle, F. Mancini, and A. Spaziani for mechanical and electronics support. Research was carried out through funding from the Italian Ministry of Research (MIUR) through the “Futuro in Ricerca” FIRB-grant PHOCOS - RBFR08E7VA and the PRIN grant n. 2009P3K72Z, through European Research Council ERC grant n. 201766 (COMPLEXLIGHT). Partial funding was received through the SMARTCONFOCAL and the TIRF project of the Regione Lazio (FILAS grant).

References and links

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]

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(160.2260) Materials : Ferroelectrics
(160.5320) Materials : Photorefractive materials
(190.0190) Nonlinear optics : Nonlinear optics

ToC Category:
Nonlinear Optics

History
Original Manuscript: September 16, 2011
Revised Manuscript: October 13, 2011
Manuscript Accepted: October 14, 2011
Published: November 10, 2011

Citation
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)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-24-24109


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References

  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. A84, 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. Optics53, 153–200 (2009) [CrossRef]
  14. G. Samara, “The relaxational properties of compositionally disordered ABO3 perovskites,” J. Phys.: Condens. Matter15, R367–R411 (2003) [CrossRef]
  15. A. A. Bokov and Z. -G. Ye, “Recent progress in relaxor ferroelectrics with perovskite structure,” J. Mater. Sci41, 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. B73, 104104 (2006) [CrossRef]

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