Polarization filtering induced by imaging systems: effect on image structure

Interferometric measurement of arbitrary propagating vector beams that are tightly focused

In this work, we demonstrate a simple setup to generate and measure arbitrary vector beams that are tightly focused. The vector beams are created with a spatial light modulator and focused with a microscope objective with an effective numerical aperture of 1.2. The transverse polarization components (E_x, E_y) of the tightly focused vector beams are measured with three-step interferometry. The axial component E_z is reconstructed using the transverse fields with Gauss's law. We measure beams with the following polarization states: circular, radial, azimuthal, spiral, flower, and spider web.

Experimental estimation of the longitudinal component of a highly focused electromagnetic field

The detection of the longitudinal component of a highly focused electromagnetic beam is not a simple task. Although in recent years several methods have been reported in the literature, this measure is still not routinely performed. This paper describes a method that allows us to estimate and visualize the longitudinal component of the field in a relatively simple way. First, we measure the transverse components of the focused field in several planes normal to the optical axis. Then, we determine the complex amplitude of the two transverse field components: the phase is obtained using a phase recovery algorithm, while the phase difference between the two components is determined from the Stokes parameters. Finally, the longitudinal component is estimated using the Gauss's theorem. Experimental results show an excellent agreement with theoretical predictions.

Visible achromatic super-oscillatory metasurfaces for sub-diffraction focusing

Conventional optical lenses enable precise foci but suffer from the diffraction limit due to the cutoff of spatial frequencies. Development of a super-oscillatory phenomenon offers an alternative approach to realize far-field sub-diffraction focusing. However, most super-oscillatory lenses exhibit a strong dependence on incident wavelengths, resulting in a narrow-band working frequency due to a fragile super-oscillatory field. Here, for the first time, achromatic super-oscillatory metasurfaces (ASOMs) are proposed to simultaneously steer optical fields at visible wavelengths of 473 nm, 532 nm and 632.8 nm and to achieve focusing at the same axial position with a resolution beyond the diffraction limit. These metasurface-based devices provide dispersionless phase profiles so that the material dispersion can be neglected in the optimization process. In addition, the design strategy can effectively circumvent the axial chromatic aberration observed in previously demonstrated metasurfaces. Constructed ASOMs are further verified numerically and simulated results for one ASOM with spot sizes of 0.706, 0.722 and 0.750 times the diffraction limit at the preset plane are consistent with the designs. Furthermore, benefiting from flexible and arbitrary phase modulations of the metasurface, the proposed method gives more freedom for a design of a super-oscillatory field and enables a lightweight, low-cost and compact optical element to replace the bulky doublet/triplet lens in a conventional optical system.

Superoscillation: from physics to optical applications

The resolution of conventional optical elements and systems has long been perceived to satisfy the classic Rayleigh criterion. Paramount efforts have been made to develop different types of superresolution techniques to achieve optical resolution down to several nanometres, such as by using evanescent waves, fluorescence labelling, and postprocessing. Superresolution imaging techniques, which are noncontact, far field and label free, are highly desirable but challenging to implement. The concept of superoscillation offers an alternative route to optical superresolution and enables the engineering of focal spots and point-spread functions of arbitrarily small size without theoretical limitations. This paper reviews recent developments in optical superoscillation technologies, design approaches, methods of characterizing superoscillatory optical fields, and applications in noncontact, far-field and label-free superresolution microscopy. This work may promote the wider adoption and application of optical superresolution across different wave types and application domains.

Sub-wavelength tight-focusing of terahertz waves by polarization-independent high-numerical-aperture dielectric metalens

A focusing device is one of the key elements for terahertz applications, including homeland security, medicine, industrial inspection, and other fields. Sub-wavelength tight-focusing of terahertz waves is attractive for microscopy and spectroscopy. Flat optical lenses based on metasurfaces have shown potential in diffraction-limit focusing and advantages of ultrathin thickness and lightweight for large-aperture optics. However previously reported THz metalenses suffered from either polarization-dependency or small numerical aperture (NA), which greatly limits their focusing performance. In this paper, to achieve high-NA and polarization-free operation, we proposed a polarization-independent dielectric metasurface with a sub-wavelength period of 0.4λ. A planar terahertz lens based on such metasurface was designed for a wavelength of λ = 118.8 μm with a focal length of 100λ, a radius of 300λ, and a high NA of 0.95, which was fabricated with a silicon-on-insulator wafer. The experimental results demonstrate a tight focal spot with sub-wavelength full widths at half-maxima of 0.45λ and 0.61λ in the x and y directions, respectively, on the focal plane. In the x direction, the size of 0.45λ is even smaller than the diffraction limit 0.526λ (0.5λ/NA). Such a metalens is favorable for sub-wavelength tight-focusing terahertz waves with different polarizations, due to its polarization independence. The metalens has potential applications in THz imaging, spectroscopy, information processing, and communications, among others.

Planar Diffractive Lenses: Fundamentals, Functionalities, and Applications

Traditional objective lenses in modern microscopy, based on the refraction of light, are restricted by the Rayleigh diffraction limit. The existing methods to overcome this limit can be categorized into near-field (e.g., scanning near-field optical microscopy, superlens, microsphere lens) and far-field (e.g., stimulated emission depletion microscopy, photoactivated localization microscopy, stochastic optical reconstruction microscopy) approaches. However, they either operate in the challenging near-field mode or there is the need to label samples in biology. Recently, through manipulation of the diffraction of light with binary masks or gradient metasurfaces, some miniaturized and planar lenses have been reported with intriguing functionalities such as ultrahigh numerical aperture, large depth of focus, and subdiffraction-limit focusing in far-field, which provides a viable solution for the label-free superresolution imaging. Here, the recent advances in planar diffractive lenses (PDLs) are reviewed from a united theoretical account on diffraction-based focusing optics, and the underlying physics of nanofocusing via constructive or destructive interference is revealed. Various approaches of realizing PDLs are introduced in terms of their unique performances and interpreted by using optical aberration theory. Furthermore, a detailed tutorial about applying these planar lenses in nanoimaging is provided, followed by an outlook regarding future development toward practical applications.

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.

Synthesis of light needles with tunable length and nearly constant irradiance

We introduce a new method for producing optical needles with tunable length and almost constant irradiance based on the evaluation of the on-axis power content of the light distribution at the focal area. According to theoretical considerations, we propose an adaptive modulating continuous function that presents a large derivative and a zero value jump at the entrance pupil of the focusing system. This distribution is displayed on liquid crystal devices using holographic techniques. In this way, a polarized input beam is shaped and subsequently focused using a high numerical aperture (NA) objective lens. As a result, needles with variable length and nearly constant irradiance are produced using conventional optics components. This procedure is experimentally demonstrated obtaining a 53λ-long and 0.8λ-wide needle.

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.

Quantum super-oscillation of a single photon

Super-oscillation is a counterintuitive phenomenon describing localized fast variations of functions and fields that happen at frequencies higher than the highest Fourier component of their spectra. The physical implications of this effect have been studied in information theory and optics of classical fields, and have been used in super-resolution imaging. As a general phenomenon of wave dynamics, super-oscillations have also been predicted to exist in quantum wavefunctions. Here we report the experimental demonstration of super-oscillatory behavior of a single-quantum object, a photon. The super-oscillatory behavior is demonstrated by tight localization of the photon wavefunction after focusing with an appropriately designed slit mask to create an interference pattern with a sub-diffraction hotspot (~0.45 λ). Such quantum super-oscillation can be used for low-intensity far-field super-resolution imaging techniques even down to single-photon counting regime, which would be of interest to quantum physics and non-invasive and label-free biological studies.

Controllable design of super-oscillatory planar lenses for sub-diffraction-limit optical needles

Sub-diffraction-limit optical needle can be created by a binary amplitude mask through tailoring the interference of diffraction beams. In this paper, a controllable design of super-oscillatory planar lenses to create sub-diffraction-limit optical needles with the tunable focal length and depth of focus (DOF) is presented. As a high-quality optical needle is influenced by various factors, we first propose a multi-objective and multi-constraint optimization model compromising all the main factors to achieve a needle with the prescribed characteristics. The optimizing procedure is self-designed using the Matlab programming language based on the genetic algorithm (GA) and fast Hankel transform algorithm. Numerical simulations show that the optical needles' properties can be controlled accurately. The optimized results are further validated by the theoretical calculation with the Rayleigh-Sommerfeld integral. The sub-diffraction-limit optical needles can be used in wide fields such as optical nanofabrication, super-resolution imaging, particle acceleration and high-density optical data storage.

Experimental solution for scattered imaging of the interference of plasmonic and photonic mode waves launched by metal nano-slits

Using an L-shaped metal nanoslit to generate waves of the pure photonic and plasmonic modes simultaneously, we perform an experimental solution for the scattered imaging of the interference of the two waves. From the fringe data of interference, the amplitudes and the wavevector components of the two waves are obtained. The initial phases of the two waves are obtained from the phase map reconstructed with the interference of the scattered image and the reference wave in the interferometer. The difference in the wavevector components gives rise to an additional phase delay. We introduce the scattering theory under Kirchhoff's approximation to metal slit regime and explain the wavevector difference reasonably. The solution of the quantities is a comprehensive reflection of excitation, scattering and interference of the two waves. By decomposing the polarized incident field with respect to the slit element, the scattered image produced by slit of arbitrary shape can be solved with the nanoscale Huygens-Fresnel principle. This is demonstrated by the experimental intensity pattern and phase map produced by a ring-slit and its consistency with the calculated results.

Planar super-oscillatory lens for sub-diffraction optical needles at violet wavelengths

Planar optical lenses are fundamental elements of miniaturized photonic devices. However, conventional planar optical lenses are constrained by the diffraction limit in the optical far-field due to the band-limited wavevectors supported by free-space and loss of high-spatial-frequency evanescent components. As inspired by Einstein's radiation ‘needle stick', electromagnetic energy can be delivered into an arbitrarily small solid angle. Such sub-diffraction optical needles have been numerically investigated using diffractive optical elements (DOEs) together with specially polarized optical beams, but experimental demonstration is extremely difficult due to the bulky size of DOEs and the required alignment precision. Planar super-oscillatory lenses (SOLs) were proposed to overcome these constraints and demonstrated that sub-diffraction focal spots can actually be formed without any evanescent waves, making far-field, label-free super-resolution imaging possible. Here we extend the super-oscillation concept into the vectorial-field regime to work with circularly polarized light, and experimentally demonstrate, for the first time, a circularly polarized optical needle with sub-diffraction transverse spot size (0.45λ) and axial long depth of focus (DOF) of 15λ using a planar SOL at a violet wavelength of 405 nm. This sub-diffraction circularly polarized optical needle has potential applications in circular dichroism spectroscopy, super-resolution imaging, high-density optical storage, heat-assisted magnetic recording, nano-manufacturing and nano-metrology.

Near field phase mapping exploiting intrinsic oscillations of aperture NSOM probe

An innovative, simple, compact and low cost approach for phase mapping based on the intrinsic modulation of an aperture Near Field Scanning Optical Microscope probe is analyzed and experimentally demonstrated. Several nanoscale silicon waveguides are phase-mapped using this approach, and the different modes of propagation are obtained via Fourier analysis. The obtained measured results are in good agreement with the effective indexes of the modes calculated by electromagnetic simulations. Owing to its simplicity and effectiveness, the demonstrated system is a potential candidate for integration with current near field systems for the characterization of nanophotonic components and devices.

Light microscopy with doughnut modes: a concept to detect, characterize, and manipulate individual nanoobjects

Higher order laser modes, mainly called doughnut modes (DMs) have use in many different branches of research, such as, bio-imaging, material science, single-molecule microscopy, and spectroscopy. The main reason of their increasing importance is that recently, the techniques to generate well-defined DMs have been refined or rediscovered. Although their potential is still not fully utilized, their specifically polarized field distribution gives rise to a wide field of applications. They are contributing to complete our fundamental knowledge of the optical properties of single emitting species, such as molecules, nanoparticles, or quantum dots, offering insight into the three-dimensional dipole or particle orientation in space. The perfect zero intensity in the focus center qualifies some DMs for stimulated emission depletion (STED) microscopy. For the same reason, they have been suggested for trapping and tweezing applications.

Demonstration of an elliptical plasmonic lens illuminated with radially-like polarized field

We demonstrate an elliptically symmetric plasmonic lens that is illuminated by a radially-like polarization field. This illumination function is TM polarized with regard to the plasmonic lens, ensuring optimum coupling of the incident light into surface plasmons polaritons. The structure is analyzed theoretically by using the Green function approach, and a finite difference time domain simulation. Both approaches provide similar results. Specifically we calculate and experimentally measure the field distribution on the surface and a few microns above it. The results show strong dependency of the electric field distribution on the eccentricity of the elliptic structure and the illumination wavelength. The interference of surface plasmons generates a structured pattern consisting of distinct peaks distributed inside the ellipse with locations that are wavelength dependent. This pattern can be used in several applications including structured illumination microscopy, particles beam trapping and sensing.

Full vectorial imaging of electromagnetic light at subwavelength scale

We propose a concept of near-field imaging for the complete experimental description of the structure of light in three dimensions around nanodevices. It is based on a near-field microscope able to simultaneously map the distributions of two orthogonal electric-field components at the sample surface. From a single 2D acquisition of these two components, the complementary electric and magnetic field lines and Poynting vector distributions are reconstructed in a volume beneath the sample using rigorous numerical methods. The experimental analysis of localized electric and magnetic optical effects as well as energy flows at the subwavelength scale becomes possible. This work paves the way toward the development of a complete electromagnetic diagnostic of nano-optical devices and metamaterials.

Polarization-dependent extraction properties of bare fiber probes

Despite their modest spatial resolution, uncoated tapered fiber probes are now widely used by the nano-optics community for mapping, with scanning near-field optical microscopy (SNOM), the nonradiative fields at the surface of optical and plasmonic microstructures and nanostructures. Given the significant complexity of the vectorial optical phenomena associated with subwavelength structures, the correct interpretation of SNOM acquisitions requires a complete and accurate understanding of the intrinsic image-formation procedure. In this theoretical study, we show that the SNOM imaging process with uncoated tapered fiber probes is highly polarization dependent and that the dominant effect is, surprisingly, the choice of optical fiber from which the tapered probe was fabricated. We demonstrate that although a tapered monomode fiber is unable to collect the component of the vector electric field parallel to the tip axis, a tapered multimode fiber can successfully collect all the three field components. However, we show that the signal from the longitudinal field component is collected only 10% as efficiently as the signal from the two transverse field components.

Demonstration of nanofocusing by the use of plasmonic lens illuminated with radially polarized light

We experimentally demonstrate the focusing of surface plasmon polaritons by a plasmonic lens illuminated with radially polarized light. The field distribution is characterized by near-field scanning optical microscope. A sharp focal spot corresponding to a zero-order Bessel function is observed. For comparison, the plasmonic lens is also measured with linearly polarized light illumination, resulting in two separated lobes. Finally, we verify that the focal spot maintains its width along the optical axis of the plasmonic lens. The results demonstrate the advantage of using radially polarized light for nanofocusing applications involving surface plasmon polaritons.

Smallest lithographic marks generated by optical focusing systems

We show that the combination of Bessel beams and photosensitive materials exhibiting polarization filtering properties allows one to reach the smallest mark that can be lithographically generated by focusing systems. This property is of interest in current optical data storage techniques.

Conical optics: the solution to confine light

We compare the performances in terms of confinement and depth of field of spherical and conical optics. It turns out that, if the spherical optics is adapted to the usual parallel imaging, conical optics seems to be the optimized solution for systems based on scanning (sequential imaging). It is shown that the optimized confinement capability of conical optics is due to the ability of conical components to generate a single Bessel beam with high efficiency. The calculations are based on Weyl formulas.

Selective coupling of HE11 and TM01 modes into microfabricated fully metal-coated quartz probes

We report computational and experimental investigations on injection and transmission of light in microfabricated fully Aluminum-coated quartz probes. In particular, we show that a selective coupling of either the HE(11) or the TM(01) mode can be carried out by injecting focused linearly or radially polarized beams into the probe. Optical fields, emitted by the probe after a controlled injection, are characterized in intensity and phase with the help of an interferometric technique. With the help of near-field measurement, we finally demonstrate that a longitudinally polarized spot localized at the tip apex is actually produced when the TM(01) mode is coupled into the probe.

Optical properties of microfabricated fully-metal-coated near-field probes in collection mode

A study of the optical properties of microfabricated, fully-metal-coated quartz probes collecting longitudinal and transverse optical fields is presented. The measurements are performed by raster scanning the focal plane of an objective, focusing azimuthally and radially polarized beams by use of two metal-coated quartz probes with different metal coatings. A quantitative estimation of the collection efficiencies and spatial resolutions in imaging both longitudinal and transverse fields is made. Longitudinally polarized fields are collected with a resolution approximately 1.5 times higher as compared with transversely polarized fields, and this behavior is almost independent of the roughness of the probe's metal coating. Moreover, the coating roughness is a critical parameter in the relative collection efficiency of the two field orientations.