Realising superoscillations: A review of mathematical tools and their application

Superoscillations are making a growing impact on an ever-increasing number of real-world applications, as early theoretical analysis has evolved into wide experimental realisation. This is particularly true in optics: the first application area to have extensively embraced superoscillations, with much recent growth. This review provides a tool for anyone planning to expand the boundaries in an application where superoscillations have already been used, or to apply superoscillations to a new application. By reviewing the mathematical methods for constructing superoscillations, including their considerations and capabilities, we lay out the options for anyone wanting to construct a device that uses superoscillations. Superoscillations have inherent trade-offs: as the size of spot reduces, its relative intensity decreases as high-energy sidebands appear. Different methods provide solutions for optimising different aspects of these trade-offs, to suit different purposes. Despite numerous technological ways of realising superoscillations, the mathematical methods can be categorised into three approaches: direct design of superoscillatory functions, design of pupil filters and design of superoscillatory lenses. This categorisation, based on mathematical methods, is used to highlight the transferability of methods between applications. It also highlights areas for future theoretical development to enable the scientific and technological boundaries to be pushed even further in real-world applications

Enhanced two-point resolution using optical eigenmode optimized pupil functions

Pupil filters have the capability to arbitrarily narrow the central lobe of a focal spot. We decompose the focal field of a confocal-like imaging system into optical eigenmodes to determine optimized pupil functions, that deliver superresolving scanning spots. As a consequence of this process, intensity is redistributed from the central lobe into side lobes restricting the field of view (FOV). The optical eigenmode method offers a powerful way to determine optimized pupil functions. We carry out a comprehensive study to investigate the relationship between the size of the central lobe, its intensity, and the FOV with the use of a dual display spatial light modulator. The experiments show good agreement with theoretical predictions and numerical simulations. Utilizing an optimized sub-diffraction focal spot for confocal-like scanning imaging, we experimentally demonstrate an improvement of the two-point resolution of the imaging system

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. (C) 2011 Optical Society of America</p

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. (C) 2011 Optical Society of America</p

Optical super-oscillations: sub-wavelength light focusing and super-resolution imaging

Optical super-oscillations, first predicted in 1952 and observed in 2007, offer a promising route to optical super-resolution imaging and show potential for manufacturing with light and data-storage applications such as direct optical recording and heat assisted magnetic recording. We review the history and basic physics behind the phenomenon of super-oscillation and its application in optics. We overview recent results in creating optical super-oscillations using binary masks, spatial light modulators and planar metamaterial masks. We also investigate the limits and competitiveness of super-oscillatory imaging.<br/