Introduction
We explore theoretically and experimentally the first creation of extended longitudinally optically bound chains of microparticles in one dimension. We use the geometry of two counterpropagating "nondifracting" light fields, so termed Bessel beams. Such beams suppressed the in fluence of the axial intensity profiles of the illuminating beams on the selforganisation process which then depended critically upon the interparticle interactions. Beam homogeneity and extended propagation allowed the creation of 200um long chains of organised microparticles and the first observation of multistability: short range multistability within a single chain and a longrange multi stability between several distinct chains. Our observations are supported by theoretical results of the coupled dipole method.
Experimental setup
High quality quasiBessel beam generated by roundtip axicon
We study theoretically and experimentally the spatial intensity distribution of the zeroorder Bessel beam formed by the axicon which possess a rounded tip. Such a tip generates a refracted beam that interferes with the quasiBessel beam created behind the axicon. In turn an undesired intensity modulation occurs that significantly disturbs the unique properties of the quasiBessel beam  namely the constant shape of the lateral intensity distribution and the slow variation of the onaxis beam intensity along the beam propagation. We show how the spatial filtration of the beam in the Fourier plane improves this spatial beam distribution and removes the undesired modulation. We use an efficient numerical method based on Hankel transformations to simulate the propagation of the beam behind the axicon and filter. We experimentally measure the intensity distribution of the beam in many lateral planes and subsequently reconstruct the spatial intensity distribution of the beam. Computed and measured beam distributions are compared and the obatind agreement is very good.
O. Brzobohaty, T. Cizmar, P. Zemanek: "High quality quasiBessel beam generated by roundtip axicon",
Optics Express 16, 1268812700, 2008,
ABSTRACT DOWNLOAD
 Axicon tip profile:
 Spatial filtration setup:

Coupled dipole method (CDM)
We modified the classical CDM algorithm for the purposes of the calculation of optical binding between two particles and especially we employed the existing symmetries in the problem to speed up the calculation. The CDM is based on the division of each object into sufficiently small domains. The volume of each domain is so small that the domain may be approximated by an induced radiating dipole.
 A sphere modeled by CDM :
 Cdm Theory:
V. Karasek, K. Dholakia, P. Zemanek: "Analysis of optical binding in one dimension",
Appl. Phys. B 84, 149156, 2006, DOWNLOAD
V. Karasek, O. Brzobohaty, P. Zemanek: "Longitudinal optical binding of several spherical particles studied by the coupled dipole method",
J. Opt. A 11, 034009, 2009, DOWNLOAD
Using CDM we model forces acting between particles for given geometrical configurations. By the dependence of the force on a chosen variable we acquire stable/multistable separations:
 Cdm calculated force acting on two and three particles:
 Cdm calculated force acting on five particles:
Results: comparison between CDM and experiment
In the experimental configuration described above we observed several formations of particles. We studied behaviour of polystyrene particles with two sizes which: 802nm and 1070nm. The shortrange formations for cases of two radii of Bessel beams are shown below:
V. Karasek, T. Cizmar, O. Brzobohaty, P. Zemanek, V. GarcesChavez, K. Dholakia: "Longrange onedimensional longitudinal optical binding",
Physical Review Letters 101, 143601:14, 2008,
ABSTRACT DOWNLOAD
 Cdm Vs. experiment  shortrange formations:
 Long formations:
Additional sources:
V. Karasek, P. Zemanek: "Analytical description of longitudinal optical binding of two nanoparticles",
J. Opt. A 9, S215S220, 2007, DOWNLOAD
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Last modification: 3 Feb 2009