Rigorous electromagnetic test of super-oscillatory lens

Axial intensity distribution of a micro-Fresnel zone plate at an arbitrary numerical aperture

The axial focus number (the number of focal spots along the axial direction) and focus intensity of a micro-Fresnel zone plate (FZP) are analyzed from deep ultraviolet to infrared using the Fourier decomposition, the vectorial angular spectrum (VAS) theory, and the three-dimensional finite-difference time-domain (FDTD) method. For a low-numerical aperture (NA) micro-FZP (NA<0.1), there are multiple axial high-order foci, and the intensity of each focus decreases slowly. However, the intensity of each high-order focus decreases rapidly with NA increasing. For a relatively high-NA micro-FZP (NA>0.3), the axial high-order foci are suppressed and there is one single focus. A fast, precise, and cost-efficient additive manufacturing method, i.e. two-photon polymerization, is used to fabricate high-NA phase-type micro-FZPs. The experiment has validated the phenomenon of linear negative focal shift of a high-NA micro-FZP. This property can be particularly applied in precise measurement of micro-displacement, film thickness, micro/nano step height, and wavelength.

Sub-wavelength annular-slit-assisted superoscillatory lens for longitudinally-polarized super-resolution focusing

A binary metallic superoscillatory lens assisted with annular subwavelength slits is proposed, which generates a longitudinally-polarized super-resolution focal point. The annular slits are designed to selectively transmit radially-polarized light. Simulations using the finite element method show a 0.24 λ focal spot with 21.8 dB of polarization purity and only 0.342 dB reduction in efficiency compared to a standard superoscillatory lens.

Optimising superoscillatory spots for far-field super-resolution imaging

Optical superoscillatory imaging, allowing unlabelled far-field super-resolution, has in recent years become reality. Instruments have been built and their super-resolution imaging capabilities demonstrated. The question is no longer whether this can be done, but how well: what resolution is practically achievable? Numerous works have optimised various particular features of superoscillatory spots, but in order to probe the limits of superoscillatory imaging we need to simultaneously optimise all the important spot features: those that define the resolution of the system. We simultaneously optimise spot size and its intensity relative to the sidebands for various fields of view, giving a set of best compromises for use in different imaging scenarios. Our technique uses the circular prolate spheroidal wave functions as a basis set on the field of view, and the optimal combination of these, representing the optimal spot, is found using a multi-objective genetic algorithm. We then introduce a less computationally demanding approach suitable for real-time use in the laboratory which, crucially, allows independent control of spot size and field of view. Imaging simulations demonstrate the resolution achievable with these spots. We show a three-order-of-magnitude improvement in the efficiency of focusing to achieve the same resolution as previously reported results, or a 26 % increase in resolution for the same efficiency of focusing.

Controllable design of super-oscillatory lenses with multiple sub-diffraction-limit foci

The conventional multifocal optical elements cannot precisely control the focal number, spot size, as well as the energy distribution in between. Here, the binary amplitude-type super-oscillatory lens (SOL) is utilized, and a robust and universal optimization method based on the vectorial angular spectrum (VAS) theory and the genetic algorithm (GA) is proposed, aiming to achieve the required focusing performance with arbitrary number of foci in preset energy distribution. Several typical designs of multifocal SOLs are demonstrated. Verified by the finite-difference time-domain (FDTD) numerical simulation, the designed multifocal SOLs agree well with the specific requirements. Moreover, the full-width at half-maximum (FWHM) of the achieved focal spots is close to λ/3 for all the cases (λ being the operating wavelength), which successfully breaks the diffraction limit. In addition, the designed SOLs are partially insensitive to the incident polarization state, functioning very well for both the linear polarization and circular polarization. The optimization method presented provides a useful design strategy for realizing a multiple sub-diffraction-limit foci field of SOLs. This research can find its potentials in such fields as parallel particle trapping and high-resolution microscopy imaging.

Investigation of axial and transverse focal spot sizes of Fresnel zone plates

An axial spot size formula is given for a standard binary Fresnel zone plate (FZP) illuminated with a linearly polarized beam. The axial spot size, characterized by the full width at half-maximum (FWHM), can be accurately expressed by the Jiang-Wilson formula, viz., d_z=0.9λ₀/[η-(η²-NA²)^1/2], when the number of transparent annuli is no less than 3. λ₀ is the illumination light wavelength, η is the refractive index, and NA is the equivalent numerical aperture of a FZP. The transverse spot sizes are near linear with the radial width of the outmost annulus when the corresponding numerical aperture is not very large. This study is carried out based on vectorial angular spectrum theory and has been rigorously confirmed by the three-dimensional finite-difference time-domain method. This finding provides the theoretical basis for applying FZPs in a variety of applications, such as nanolithography, nanoscopy, and high-density data storage.

Electromagnetic exploration of far-field super-focusing nanostructured metasurfaces

Planar multi-annular nanostructured metasurfaces have provided a new way to realize far-field optical super-resolution focusing and nanoscopic imaging, due to the delicate interference of propagating waves diffracted from the metasurface mask. However, so far there are no proper methods that can be used to essentially interpret the super-focusing and nano-imaging mechanisms. This research proposes an electromagnetic methodology for the super-resolution investigation of nanostructured metasurfaces. We have physically modeled the polarization-dependent transmission effect of the subwavelength nanostructure and the vectorial imaging process of a high-numerical-aperture microscopic system. We have found theoretically and experimentally that the current design theories may produce imprecise results; the microscopic imaging experimental method can only detect transversely polarized electric field component and cannot map out three-dimensional total electric energy density distribution behind metasurfaces. This method will potentially be used in far-field nanoscopy, nanolithography, high-density optical storage, etc.