Generation of Optical Vortices with Strong Magnetic Fields for the Control of Nanoparticles*

Light can be spatially structured to enhance or reduce the interaction with particles. Optical vortices (OV) are a prominent example among structured beams, because of their possible new applications to materials science. An OV is a light field with phase singularities that carry orbital angular momentum, in addition to its spin angular momentum. Well-known examples of OVs with single phase singularities on the optical axis are Laguerre-Gauss and Bessel modes. Bessel beams are specially adequate for theoretical studies, because they are mathematically simple and represent paraxial as well as focused beams. We recently identified a large group of OV containing fields with varying degrees of relative strengths of electric (E) to magnetic (M) fields, parametrized by a real number γ. When γ = 0 the field at the optical axis (r = 0) has a constant E-field and a vanishing M-field. In contrast, for γ = 1 the M-field at r = 0 is constant and there is no E-field. A light beam of complex structure, such as an OV, can be decomposed into a superposition of plane waves. This modal decomposition or angular spectrum representation is useful to treat different problems, for example the propagation of structured light through interfaces using the well-known Fresnel coefficients. A γ = 1 field exhibits a dominant magnetic interaction with a particle placed at r = 0. This is magnetism at optical frequencies and it opens the way to more versatile control of particles. Here we show how a γ = 1 Bessel beam can be constructed as a superposition of plane waves. The decomposition allows us to explain how the beam can be generated in the lab using common optical elements. Furthermore, we clarify how one can measure, using an ion trap, the resulting γ = 1 beam emerging from the described optical system. Finally, we discuss possible uses of such a beam to the control of nanoparticles (e.g. quantum dots) or impurities (e.g. Eu3+).