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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
M. Born, E. Wolf, A. Bhatia, Principles of Optics (Cambridge University Press, Cambridge, 1999)
D. Marcuse, Theory of Dielectric Optical Waveguides (Academic Press, New York, 1974)
A. Yariv, Quantum Electronics, 3rd edn. (Wiley, New York, 1988)
P.G. Drazin, R.S. Johnson, Solitons: An Introduction (Cambridge University Press, Cambridge, 1989)
Y.S. Kivshar, G.P. Agrawal, Optical Solitons (Academic Press, San Diego, 2003)
M. Segev, B. Crosignani, A. Yariv, B. Fischer, Spatial solitons in photorefractive media. Phys. Rev. Lett. 68, 923–926 (1992)
M. Segev, G.I. Stegeman, Self-trapping of optical beams: spatial solitons. Phys. Today 51, 43–48 (1998)
E. DelRe, M. Segev, Self-focusing and Solitons in Photorefractive Media, in Topics in Applied Physics, vol. 114 (Springer, Berlin, 2009), pp 547–572
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)
E.A. Ultanir, D. Michaelis, F. Lederer, G.I. Stegeman, Stable spatial solitons in semiconductor optical amplifiers. Opt. Lett. 28, 251–253 (2003)
W.E. Torruellas et al., Observation of two-dimensional spatial solitary waves in a quadratic medium. Phys. Rev. Lett. 74, 5036–5039 (1995)
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)
C. Conti, M. Peccianti, G. Assanto, Observation of optical spatial solitons in a highly nonlocal medium. Phys. Rev. Lett. 92, 113902 (2004)
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)
C. Conti, G. Ruocco, S. Trillo, Optical spatial solitons in soft matter. Phys. Rev. Lett. 95, 183902 (2005)
S. Trillo, W. Torruealls (eds.), Spatial Solitons (Springer, Berlin, 2001)
A.D. Boardman, A.P. Sukhorukov (eds.), Soliton Driven Photonics (Kluwer Academic, Dordrecht, 2001)
E. DelRe, E. Spinozzi, A.J. Agranat, C. Conti, Scale-free optics and diffractionless waves in nanodisordered ferroelectrics. Nat. Photon. 5, 39–42 (2011)
A.A. Bokov, Z.-G. Ye, Recent progress in relaxor ferroelectrics with perovskite structure. J. Mater. Sci. 41, 31–52 (2006)
E. Dagotto, Complexity in strongly correlated electronic systems. Science 309, 257–262 (2005)
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)
B. Crosignani, A. Degasperis, E. DelRe, P. Di Porto, A.J. Agranat, Phys. Rev. Lett. 82, 1664 (1999)
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)
A. Agranat, R. Hofmeister, A. Yariv, Characterization of a new photorefractive material: KLTN. Opt. Lett. 17, 713–715 (1992)
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)
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)
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)
O. Firstenberg, P. London, M. Shuker, A. Ron, N. Davidson, Elimination, reversal and directional bias of optical diffraction. Nat. Phys. 5, 665–668 (2009)
A. Bitman, N. Sapiens, L. Secundo, A.J. Agranat, G. Bartal, M. Segev, Opt. Lett. 31, 2849 (2006)
Y. Xu, Ferroelectric Materials and Their Applications (North-Holland, Amsterdam, 1991)
V. Folli, E. DelRe, C. Conti, Beam Instabilities in the Scale Free Regime. Phys. Rev. Lett. 108, 033901 (2012)
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.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer Science+Business Media New York
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-1-4614-3538-9_8
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-3537-2
Online ISBN: 978-1-4614-3538-9
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)