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Scale-Free optics

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Nonlinear Photonics and Novel Optical Phenomena

Part of the book series: Springer Series in Optical Sciences ((SSOS,volume 170))

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Abstract

The most fascinating images and patterns emerge when light diffracts from minute structures [1]. Even the image of an otherwise featureless hole produces enthralling ripples that spread out to invest space and form what is known as an Airy pattern. It is a basic fact that diffraction becomes dominant when the size of the feature becomes micrometric, and the transmitted wave has an angular spread Δθ that depends on the size of the aperture d measured in units of the optical wavelength λ, i.e., Δθ ≃ λ/d. From a practical perspective, diffraction represents a major obstacle to imaging of finer details, and a great research effort is continuously exerted to overcome it. In fact, diffraction spreads the optical wave and blurs the spatial information encoded in the optical beam. Consider an image composed of separate pixels of characteristic size d and spacing l.

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References

  1. M. Born, E. Wolf, A. Bhatia, Principles of Optics (Cambridge University Press, Cambridge, 1999)

    Google Scholar 

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

    Google Scholar 

  3. A. Yariv, Quantum Electronics, 3rd edn. (Wiley, New York, 1988)

    Google Scholar 

  4. P.G. Drazin, R.S. Johnson, Solitons: An Introduction (Cambridge University Press, Cambridge, 1989)

    Book  MATH  Google Scholar 

  5. Y.S. Kivshar, G.P. Agrawal, Optical Solitons (Academic Press, San Diego, 2003)

    Google Scholar 

  6. M. Segev, B. Crosignani, A. Yariv, B. Fischer, Spatial solitons in photorefractive media. Phys. Rev. Lett. 68, 923–926 (1992)

    Article  ADS  Google Scholar 

  7. M. Segev, G.I. Stegeman, Self-trapping of optical beams: spatial solitons. Phys. Today 51, 43–48 (1998)

    Article  Google Scholar 

  8. E. DelRe, M. Segev, Self-focusing and Solitons in Photorefractive Media, in Topics in Applied Physics, vol. 114 (Springer, Berlin, 2009), pp 547–572

    Google Scholar 

  9. E. DelRe, M. Tamburrini, M. Segev, R. Della Pergola, A.J. Agranat, Spontaneous self-trapping of optical beams in metastable paraelectric crystals. Phys. Rev. Lett. 83, 1954–1957 (1999)

    Article  ADS  Google Scholar 

  10. E.A. Ultanir, D. Michaelis, F. Lederer, G.I. Stegeman, Stable spatial solitons in semiconductor optical amplifiers. Opt. Lett. 28, 251–253 (2003)

    Article  ADS  Google Scholar 

  11. W.E. Torruellas et al., Observation of two-dimensional spatial solitary waves in a quadratic medium. Phys. Rev. Lett. 74, 5036–5039 (1995)

    Article  ADS  Google Scholar 

  12. P.J. Reece, E.M. Wright, K. Dholakia, Experimental observation of modulation instability and optical spatial soliton arrays in soft condensed matter. Phys. Rev. Lett. 98, 203902 (2007)

    Article  ADS  Google Scholar 

  13. C. Conti, M. Peccianti, G. Assanto, Observation of optical spatial solitons in a highly nonlocal medium. Phys. Rev. Lett. 92, 113902 (2004)

    Article  ADS  Google Scholar 

  14. J.W. Fleischer, M. Segev, N.K. Efremidis, D.N. Christodoulides, Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices. Nature 422, 147–150 (2003)

    Article  ADS  Google Scholar 

  15. C. Conti, G. Ruocco, S. Trillo, Optical spatial solitons in soft matter. Phys. Rev. Lett. 95, 183902 (2005)

    Article  ADS  Google Scholar 

  16. S. Trillo, W. Torruealls (eds.), Spatial Solitons (Springer, Berlin, 2001)

    Google Scholar 

  17. A.D. Boardman, A.P. Sukhorukov (eds.), Soliton Driven Photonics (Kluwer Academic, Dordrecht, 2001)

    Google Scholar 

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

    Article  ADS  Google Scholar 

  19. A.A. Bokov, Z.-G. Ye, Recent progress in relaxor ferroelectrics with perovskite structure. J. Mater. Sci. 41, 31–52 (2006)

    Article  ADS  Google Scholar 

  20. E. Dagotto, Complexity in strongly correlated electronic systems. Science 309, 257–262 (2005)

    Article  ADS  Google Scholar 

  21. N. Ghofraniha, C. Conti, G. Ruocco, F. Zamponi, Time-dependent nonlinear optical susceptibility of an out-of-equilibrium soft material. Phys. Rev. Lett. 102, 038303 (2009)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  23. P.B. Ishai, C.E.M. de Oliveira, Y. Ryabov, Y. Feldman, A.J. Agranat, Glassforming liquid kinetics manifested in a KTN:Cu crystal. Phys. Rev. B 70, 132104 (2004)

    Article  ADS  Google Scholar 

  24. A. Agranat, R. Hofmeister, A. Yariv, Characterization of a new photorefractive material: KLTN. Opt. Lett. 17, 713–715 (1992)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  26. E. DelRe, J. Parravicini, G. Parravicini, A.J. Agranat, C. Conti, Wavelength-insensitive negative optical permittivity without nanofrabrication in transparent nonlinear dipolar glasses under extreme frustration, submitted to Physical Review Letters (2012)

    Google Scholar 

  27. J. Parravicini, F. Di Mei, C. Conti, A.J. Agranat, and E. DelRe, Diffraction cancellation over multiple wavelengths in photorefractive dipolar glasses. Opt. Exp. 19, 24109 (2011)

    ADS  Google Scholar 

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

    Article  Google Scholar 

  29. A. Bitman, N. Sapiens, L. Secundo, A.J. Agranat, G. Bartal, M. Segev, Opt. Lett. 31, 2849 (2006)

    Article  ADS  Google Scholar 

  30. Y. Xu, Ferroelectric Materials and Their Applications (North-Holland, Amsterdam, 1991)

    Google Scholar 

  31. V. Folli, E. DelRe, C. Conti, Beam Instabilities in the Scale Free Regime. Phys. Rev. Lett. 108, 033901 (2012)

    Article  ADS  Google Scholar 

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Acknowledgments

This contribution is based on work carried out with Prof. Aharon J. Agranat of the Applied Physics Department at the Hebrew University of Jerusalem, and with Elisa Spinozzi, now at the University of Rome La Sapienza. The research leading to these results has received funding from the Italian Ministry of Research (MIUR) through the “Futuro in Ricerca” FIRB-grant PHOCOS—RBFR08E7VA, and from the European Research Council under the European Community’s SeventhFramework Program (FP7/2007-2013)/ERC Grant Agreement No. 201766. Partial funding was received through the SMARTCONFOCAL project of the Regione Lazio.

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DelRe, E., Conti, C. (2012). Scale-Free optics. In: Chen, Z., Morandotti, R. (eds) Nonlinear Photonics and Novel Optical Phenomena. Springer Series in Optical Sciences, vol 170. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-3538-9_8

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