Superoscillatory diffraction-free beams

It is widely known that any beam with subwavelength characteristics will diffract very fast and these features will not propagate into the far field. This is due to the existence of evanescent waves, which diffract in the near field. By using the counter-intuitive effect of superoscillations [1] we show that it is possible to create a superoscillatory diffraction free beam by superimposing already known diffraction-free [2] solutions (Bessel beams for example) of Helmholtz equation. Such optical beams do not contain any evanescent waves and can propagate practically undistorted carrying these subwavelength features into the far field. Superoscillations have been recently studied and introduced to optics in the context of superresolution [3], and subwavelength focusing [4].

[1]  Mark R. Dennis,et al.  Natural superoscillations in monochromatic waves in D dimensions , 2009 .

[2]  Demetrios N. Christodoulides,et al.  Observation of accelerating Airy beams. , 2007 .

[3]  J. Durnin.  Exact solutions for nondiffracting beams. I. The scalar theory , 1987 .

[4]  M Mazilu,et al.  Optical eigenmodes; exploiting the quadratic nature of the energy flux and of scattering interactions. , 2010, Optics express.

[5]  Nikolay I Zheludev,et al.  Super-resolution without evanescent waves. , 2008, Nano letters.

[6]  Nikolay I. Zheludev,et al.  Optical super-resolution through super-oscillations , 2007 .

[7]  Nikolay I. Zheludev,et al.  Far field subwavelength focusing using optical eigenmodes , 2011 .

[8]  D. Christodoulides,et al.  Accelerating finite energy Airy beams. , 2007, Optics letters.

[9]  D. Christodoulides,et al.  Super-resolution via enhanced evanescent tunneling , 2011, CLEO: 2011 - Laser Science to Photonic Applications.

[10]  Sandu Popescu,et al.  Evolution of quantum superoscillations, and optical superresolution without evanescent waves , 2006 .

[11]  D. Pohl,et al.  Scanning near-field optical probe with ultrasmall spot size. , 1995, Optics letters.

[12]  Mark R. Dennis,et al.  Superoscillation in speckle patterns. , 2008, Optics letters.

[13]  Yonina C Eldar,et al.  Super-resolution and reconstruction of sparse sub-wavelength images. , 2009, Optics express.

[14]  P.J.S.G. Ferreira,et al.  Superoscillations: Faster Than the Nyquist Rate , 2006, IEEE Transactions on Signal Processing.

[15]  J. Gutiérrez-Vega,et al.  Alternative formulation for invariant optical fields: Mathieu beams. , 2000, Optics letters.

[16]  Miceli,et al.  Diffraction-free beams. , 1987, Physical review letters.

[17]  Jari Turunen,et al.  Propagation invariance and self-imaging in variable-coherence optics , 1991 .

[18]  George V Eleftheriades,et al.  Adaptation of Schelkunoff's Superdirective Antenna Theory for the Realization of Superoscillatory Antenna Arrays , 2010, IEEE Antennas and Wireless Propagation Letters.