Metasurfaces are artificially structured thin films with unusual properties on demand. Different from metamaterials, the metasurfaces change the electromagnetic waves mainly by exploiting the boundary conditions, rather than the constitutive pa-rameters in three dimensional (3D) spaces. Despite the intrinsic similarities in the operational principles, there is not a universal theory available for the understanding and design of metasurface-based devices. In this article, we propose the concept of metasurface waves (M-waves) and provide a general theory to describe the principles of them. Most importantly, it is shown that the M-waves share some fundamental properties such as extremely short wavelength, abrupt phase change and strong chromatic dispersion, which make them different from traditional bulk waves. It is shown that these properties can enable many important applications such as subwavelength imaging and lithography, planar optical devices, broadband anti-reflection, absorption and polarization conversion. Our results demonstrated unambiguously that traditional laws of diffraction, refraction, reflection and absorption should be revised by using the novel properties of M-waves. The theory provided here may pave the way for the design of new electromagnetic devices and further improvement of metasurfaces. The exotic properties of metasurfaces may also form the foundations for two new sub-disciplines called “subwavelength surface electromagnetics” and “subwavelength electromagnetics”.

Principles of electromagnetic waves in metasurfaces

An imaging arrangement and method for extended the depth of focus are provided. The imaging arrangement comprises an imaging lens having a certain affective aperture, and an optical element associated with said imaging lens. The optical element is configured as a phase-affecting, non-diffractive optical element defining a spatially low frequency phase transition. The optical element and the imaging lens define a predetermined pattern formed by spaced-apart substantially optically transparent features of different optical properties. Position of at least one phase transition region of the optical element within the imaging lens plane is determined by at least a dimension of said affective aperture.

Optical method and system for extended depth of focus

Superoscillations are band-limited functions with the counterintuitive property that they can vary arbitrarily faster than their fastest Fourier component, over arbitrarily long intervals. Modern studies originated in quantum theory, but there were anticipations in radar and optics. The mathematical understanding—still being explored—recognises that functions are extremely small where they superoscillate; this has implications for information theory. Applications to optical vortices, sub-wavelength microscopy and related areas of nanoscience are now moving from the theoretical and the demonstrative to the practical. This Roadmap surveys all these areas, providing background, current research, and anticipating future developments.

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Roadmap on superoscillations

Focusing properties of annular binary phase filters

We demonstrate a metamaterial superlens: a planar array of discrete subwavelength metamolecules with individual scattering characteristics tailored to vary spatially to create subdiﬀraction superoscillatory focus of, in principle, arbitrary shape and size. Metamaterial free-space lenses with previously unattainable eﬀective numerical apertures – as high as 1.52 – and foci as small as 0.33λ in size are demonstrated. Super-resolution imaging with such lenses is experimentally veriﬁed breaking the conventional diﬀraction limit of resolution and exhibiting resolution close to the size of the focus. Our approach will enable far-ﬁeld label-free super-resolution nonalgorithmic microscopies at harmless levels of intensity, including imaging inside cells, nanostructures, and silicon chips, without impregnating them with ﬂuorescent materials.

/pdf/far-field-superoscillatory-metamaterial-superlens-3b1cv9s62b.pdf

Far-field superoscillatory metamaterial superlens

We present a procedure for designing rotationally symmetric pupil-plane masks to control the three-dimensional light-intensity distribution near focus. Our method is based on the use of a series of figures of merit that are properly defined to describe the effect of general complex pupil functions. As a practical implementation, we have applied our method to obtain superresolving continuous smoothly varying phase-only filters. The advantages of these kinds of filters are that they do not produce energy absorption and they are easy to build with a phase-controlling device such as a deformable mirror. Results of comparisons between the performance of our method and that of other phase-filter designs are provided.

Design of superresolving continuous phase filters.

A novel procedure to design axial and transverse superresolving pupil filters for the 4Pi-confocal microscope is presented. The method is based on the use of a series of figures of merit developed to describe the effect of inserting two identical filters in the two arms of the illumination path of the microscope. As a practical implementation, we have applied our method to obtain superresolving continuous phase-only filters. Different resolution-improving phase functions are shown for the transverse and the axial direction. These filters provided axial gain up to 1.3 and transverse gain up to 1.4 without an increase in sidelobes.

Transverse or axial superresolution in a 4Pi-confocal microscope by phase-only filters.

We present a procedure for attaining resolution beyond the diffraction limit in ground-based telescopes. This procedure is based on the use of rotationally symmetric pupil plane filters that can be easily implemented in dynamic optical devices such as a deformable mirror of an adaptive-optics system. We show that a successful application of the technique requires partial compensation for atmospheric distortion by adaptive optics. Consequently, we derive the required level of compensation as a function of the atmospheric conditions. Finally, our results are checked using simulated data.

Superresolution in compensated telescopes.

The appearance of commercial spatial light modulators (SLM) opens new ways for teaching some optical phenomena. There are possible applications in a great variety of fields: interferometry, diffraction theory, simulation and compensation of random media, Fourier Optics, etc. In this paper, we propose the use of low cost liquid crystals displays (LCDs) as SLMs to perform some interesting optical experiments. The liquid crystal SLMs are extracted from a commercial video projector. This is one of the cheapest ways to obtain a SLM. For phase modulation, it requires the calibration of the system, because the manufacturers do not provide the physical specifications of the LCDs. This work is quite instructive since many different aspects are involved in the calibration process. Finally, we show an experiment using this setup, which demonstrates that the proposed SLM is an easy-to-use and flexible tool to show some well-known optical phenomena.

https://www.spiedigitallibrary.org/conference-proceedings-of-spie/4588/0000/Teaching-optics-with-a-spatial-light-modulator/10.1117/12.468709.pdf

Daniel M. de Juana

Papers

Design of superresolving continuous phase filters.

Focusing properties of annular binary phase filters

Transverse or axial superresolution in a 4Pi-confocal microscope by phase-only filters.

Superresolution in compensated telescopes.

Teaching optics with a spatial light modulator