S. López-Aguayo, Y. V. Kartashov, V.A. Vysloukh and L. Torner
Suppressing the diffraction of light beams is a holy grail in optics. Nondiffracting light patterns are widely used
in many applications where invariance of
the beam is desired, including trapping
of micro-objects and optical tweezing, 1
as well as in quantum2 and nonlinear
optics. 3 The patterns used to date correspond only to the known sets of simple
nondiffracting beams that are exact
solutions of Helmholtz equation governing propagation of light in uniform linear
media. They include periodic, Bessel,
Mathieu and parabolic beams. 4
However, each of these beams has
a particular topology, thereby affording specific applications. Thus, a task of
paramount importance is the formation
of quasi-nondiffracting beams with arbitrarily complex shapes and topologies, so
that they meet with the requirements of
each particular application.
This year we put forward a new strategy
that allows the formation of complex
light patterns that diffract extremely
slowly—thus, they may be considered nondiffracting over huge distances which are
dictated by the width of the beam angular
spectrum. 5 The amplitude of any truly
nondiffracting beam propagating along a
straight trajectory can be expressed in terms
of convolution of its angular spectrum
defined on an infinitely narrow ring in
the frequency space with an exponential
kernel function. 5 A broadening of the
angular spectrum allows for the generation of beams with arbitrarily complex
transverse shapes that remain quasi-nondiffracting as long as the width of their angular spectrum remains sufficiently small.
This technique affords the possibility to
distort otherwise rigorous nondiffracting
beams in a controllable manner, rendering them quasi-nondiffracting.
In particular, one can generate quasi-one-dimensional beams with stripes experiencing an abrupt bending in a desired
Intensity distributions in quasi-nondiffracting beams constructed via angular spectrum
engineering. Top row shows bent (a), curved (b), and stripe-like (c) beams. Middle row shows
truncated Mathieu (d), parabolic-cosine (e), and parabolic-Bessel (f) beams. Bottom row (g)-(i)
shows specific spiraling patterns.
part of the space (a), deformed patterns
featuring stripes that may periodically
curve in the transverse plane (b), or specific beams featuring several pronounced
stripes (c). The angular spectrum engineering also allows us to obtain patterns
featuring practically any combinations
of known harmonic, Bessel, Mathieu
or parabolic beams occupying different
arbitrary domains in the transverse plane
that propagate undistorted over considerable distances.
The figure above shows examples of
truncated Mathieu beams (d), combinations of parabolic and cosine beams (e), and
parabolic and Bessel beams (f). Importantly, the engineering of the angular
spectrum is a powerful tool that can be
used to generate beams that in principle
have no analogs among known nondiffracting beams. The illuminating
examples in the form of quasi-nondiffracting spiraling patterns are shown in
In summary, the concept allows
generating “on-demand” beams that are
nondiffracting for all practical purposes.
Such beam0s are expected to find important applications in several branches
of science that currently use nondiffracting light beams for the manipulation of
matter or light itself. t
;is work was partially supported by Fundacio
S. López-Aguayo, Y.V. Kartashov (
Yaroslav.Kartashfirstname.lastname@example.org) and L. Torner are with ICFO-Institut de
Ciencies Fotoniques, and Universitat Politecnica de
Catalunya, Mediterranean Technology, Barcelona,
Spain. S. López-Aguayo is also with the Photonics
and Mathematical Optics Group, Tecnólogico de
Monterrey, Monterrey, Mexico V.A. Vysloukh is with
the departamento de fisica y matematicas, Universidad de las Americas, Puebla, Mexico.
1. V. Garces-Chavez et al. Nature 419, 145 (2002).
2. I. Bloch. Nature Physics 1, 23 (2005).
3. J. W. Fleischer et al. Nature 422, 147 (2003).
4. M. Mazilu et al. Laser & Photon. Rev. 4, 529 (2010).
5. S. Lopez-Aguayo et al. Phys. Rev. Lett. 105, 013902