Bessel beam does a twist

Research into newly discovered properties of optical traps has won a team from St. Andrew's University (St. Andrews, Scotland) the European Optics Prize for 2003. They share the award with their coworkers at INAOE (National Institute of Astronomy, Optics and Electronics; Puebla, Mexico). The group has shown that, in certain optical conditions, light beams can transfer angular momentum to trapped particles, making them rotate.¹

A beam in the sample plane of an optical trap has a quasi-Bessel transverse profile (left). The beam rotates a group of one 1-µm and four 5-µm spheres trapped in the inner ring of the beam, with frames taken at (from left-center to right) 0, 8, and 16 s.

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Optical traps use light to grab and hold minute objects in place. If a laser beam passes through a small particle and the light is refracted through the particle, the force involved in this change of light direction acts on the particle. If the refractive index is higher in the particle than what is around it, the net forces are such that the particle moves toward the most intense part of the laser beam, usually the center of the beam axis for a Gaussian beam. The particle becomes trapped in the focus of the beam. Creating forces large enough requires high-intensity gradients, so the beam must be focused down to a spot only a few microns in diameter. Diffraction of the beam from such a tight focus limits the size of the optical trap both across and along the beam, limiting the trapping potential.

Recent work with so-called Bessel beams has shown that they can get around the diffraction problem for optical trapping. Bessel beams are shaped by optical elements to have an amplitude proportional to a Bessel function; which appears as a bright spot surrounded by a set of concentric rings. An ideal Bessel beam would be diffraction free, but to achieve this it would also need to have an infinite number of rings, and so carry an infinite amount of power. Achievable quasi-Bessel beams, with a finite number of rings, are still useful because they have very low diffraction. They also have another useful property. Unlike a Gaussian beam, which is distorted after encountering a particle, a Bessel beam is able to reconstruct itself around an object. So, after trapping one set of particles, the beam is able to reform itself and trap another set.

The group at St. Andrews has demonstrated that a Bessel beam can be used to manipulate different types of particles both across and along the beam. The experiments were performed with a single Nd:YVO₄ (vanadate) laser at 1064 nm to create a Bessel beam with 19 rings around its central spot. The total power used was 700 mW, giving approximately 35 mW in the central spot.

Hollow spheres, which have a lower refractive index than the surrounding water in the sample cell, are repelled from regions of high light intensity and can be trapped in the dark circles of the beam, while solid particles are trapped in the bright areas.

The twisting effect relies on the angular momentum of the laser beam. "Each photon in the light beam can exert a tiny twist on small particles due to the 'spin' angular momentum of the photon," said group leader Kishan Dholakia. "This sort of effect has been studied for a long time. However, certain types of laser beam can exert additional twisting effects due to the way in which the light waves spiral in the beam. The wavefronts of the lightwaves in laser beams with this 'orbital' angular momentum are inclined to the direction of propagation, rather than being perpendicular to it as in a normal laser beam. The multiringed Bessel beam is interesting because certain types of this beam have these spiral wavefronts."

By moving the sample stage in the experiment, several spheres were loaded into the inner ring of a higher-order Bessel beam until its whole circumference was filled with spheres. This ring of spheres was found to rotate smoothly along the circumference of the inner ring (see photos). The sense of rotation can be reversed by inserting a Dove prism into the beam.

Not only will this newly discovered effect be useful, for example in cell sorters and microfluidic applications, but there is also some interesting fundamental physics to be investigated. "The rotation rate has a linear dependence on the orbital angular momentum content of the light beam,'' said Dholakia. "The measured rotation rates correspond to a transfer of about 1% of the Bessel beam's orbital angular momentum, which is consistent with calculations based on a transfer mechanism due to scattering. Our experiment opens up the prospect of further studies examining local angular-momentum density in different rings of the higher-order Bessel beam and looking at the variations predicted for different polarization states of such a beam."