Visualization of the birth of an optical vortex using diffraction from a triangular aperture.

The study and application of optical vortices have gained significant prominence over the last two decades. An interesting challenge remains the determination of the azimuthal index (topological charge) ℓ of an optical vortex beam for a range of applications. We explore the diffraction of such beams from a triangular aperture and observe that the form of the resultant diffraction pattern is dependent upon both the magnitude and sign of the azimuthal index and this is valid for both monochromatic and broadband light fields. For the first time we demonstrate that this behavior is related not only to the azimuthal index but crucially the Gouy phase component of the incident beam. In particular, we explore the far field diffraction pattern for incident fields incident upon a triangular aperture possessing non-integer values of the azimuthal index ℓ. Such fields have a complex vortex structure. We are able to infer the birth of a vortex which occurs at half-integer values of ℓ and explore its evolution by observations of the diffraction pattern. These results demonstrate the extended versatility of a triangular aperture for the study of optical vortices.

Optical eigenmodes; exploiting the quadratic nature of the energy flux and of scattering interactions.

We report a mathematically rigorous technique which facilitates the optimization of various optical properties of electromagnetic fields in free space and including scattering interactions. The technique exploits the linearity of electromagnetic fields along with the quadratic nature of the intensity to define specific Optical Eigenmodes (OEi) that are pertinent to the interaction considered. Key applications include the optimization of the size of a focused spot, the transmission through sub-wavelength apertures, and of the optical force acting on microparticles. We verify experimentally the OEi approach by minimising the size of a focused optical field using a superposition of Bessel beams.

Optical path clearing and enhanced transmission through colloidal suspensions.

We utilize advanced laser fields to clear a path through a dynamic turbid medium, a concept termed "Optical path clearing (OPC)." Particles are evacuated from a volume of the medium using the gradient and/or scattering forces due to an applied laser field with a suitably tailored spatial profile. Our studies encompass both an analytical model and proof-of-principle experiments where paths are cleared in dense bulk colloidal suspensions. Based on our results we suggest that high-performance and high efficiency OPC will be achieved by multiple-step clearing using dynamic laser fields based on Airy or inverted axicon beams.

Propagation characteristics of Airy beams: dependence upon spatial coherence and wavelength.

We generate a broadband "white light" Airy beam and characterize the dependence of the beam properties on wavelength. Experimental results are presented showing that the beam's deflection coefficient and its characteristic length are wavelength dependent. In contrast the aperture coefficient is not wavelength dependent. However, this coefficient depends on the spatial coherence of the beam. We model this behaviour theoretically by extending the Gaussian-Schell model to describe the effect of spatial coherence on the propagation of Airy beams. The experimental results are compared to the model and good agreement is observed.

Lattice dynamics of two-dimensional colloidal crystals subject to external light potentials.

By exposing two-dimensional crystals to tunable substrate potentials one can selectively manipulate the crystal's phonon band structure. We explore this idea and study the overdamped lattice dynamics of colloidal crystals subject to commensurate substrate potentials with sinusoidal modulations in up to two spatial directions. We furthermore show that the mean-square displacement of colloids in the crystal can be understood as the Laplace transform of the phonon spectrum and discuss how our results can best be verified experimentally.

Tailoring of phononic band structures in colloidal crystals.

We report an experimental study of the elastic properties of a two-dimensional (2D) colloidal crystal subjected to light-induced substrate potentials. In agreement with recent theoretical predictions [H. H. von Grünberg and J. Baumgartl, Phys. Rev. E 75, 051406 (2007).10.1103/PhysRevE.75.051406] the phonon band structure of such systems can be tuned depending on the symmetry and depth of the substrate potential. Calculations with binary crystals suggest that phononic band engineering can be also performed by variations of the pair potential and thus opens novel perspectives for the fabrication of phononic crystals with band gaps tunable by external fields.