Roadmap on Label-Free Super-Resolution Imaging.

Label-free super-resolution (LFSR) imaging relies on light-scattering processes in nanoscale objects without a need for fluorescent (FL) staining required in super-resolved FL microscopy. The objectives of this Roadmap are to present a comprehensive vision of the developments, the state-of-the-art in this field, and to discuss the resolution boundaries and hurdles which need to be overcome to break the classical diffraction limit of the LFSR imaging. The scope of this Roadmap spans from the advanced interference detection techniques, where the diffraction-limited lateral resolution is combined with unsurpassed axial and temporal resolution, to techniques with true lateral super-resolution capability which are based on understanding resolution as an information science problem, on using novel structured illumination, near-field scanning, and nonlinear optics approaches, and on designing superlenses based on nanoplasmonics, metamaterials, transformation optics, and microsphere-assisted approaches. To this end, this Roadmap brings under the same umbrella researchers from the physics and biomedical optics communities in which such studies have often been developing separately. The ultimate intent of this paper is to create a vision for the current and future developments of LFSR imaging based on its physical mechanisms and to create a great opening for the series of articles in this field.

Transforming Space with Non-Hermitian Dielectrics.

Coordinate transformations are a versatile tool to mold the flow of light, enabling a host of astonishing phenomena such as optical cloaking with metamaterials. Moving away from the usual restriction that links isotropic materials with conformal transformations, we show how nonconformal distortions of optical space are intimately connected to the complex refractive index distribution of an isotropic non-Hermitian medium. Remarkably, this insight can be used to circumvent the material requirement of working with refractive indices below unity, which limits the applications of transformation optics. We apply our approach to design a broadband unidirectional dielectric cloak, which relies on nonconformal coordinate transformations to tailor the non-Hermitian refractive index profile around a cloaked object. Our insights bridge the fields of two-dimensional transformation optics and non-Hermitian photonics.

The case for a Casimir cosmology.

The cosmological constant, also known as dark energy, was believed to be caused by vacuum fluctuations, but naive calculations give results in stark disagreement with fact. In the Casimir effect, vacuum fluctuations cause forces in dielectric media, which is very well described by Lifshitz theory. Recently, using the analogy between geometries and media, a cosmological constant of the correct order of magnitude was calculated with Lifshitz theory (Leonhardt 2019 Ann. Phys. (New York) 411, 167973. (doi:10.1016/j.aop.2019.167973)). This paper discusses the empirical evidence and the ideas behind the Lifshitz theory of the cosmological constant without requiring prior knowledge of cosmology and quantum field theory. This article is part of a discussion meeting issue 'The next generation of analogue gravity experiments'.

Boosting few-cycle soliton self-frequency shift using negative prechirp.

Soliton self-frequency shifting of light pulses in fibers is used for versatile tunable light sources. Few-cycle pulses of high soliton number offer unique advantages, in particular the rate of Raman frequency shift is extremely fast. However, their dynamics is complicated, which makes the optimization of the frequency shifting difficult and sometimes counter-intuitive. We performed a systematic experimental study of the effects of initial prechirp for different pulse energies (for two different fibers). We found that a negative prechirp around C=-0.75 is the most effective (C being the chirp parameter). With such prechirping we managed to cross the severe OH absorption bands of nonlinear photonic crystal fibers. The mechanism behind the effectiveness of the prechirp appears to be the power distribution between the products of soliton fission.

Observation of Stimulated Hawking Radiation in an Optical Analogue.

The theory of Hawking radiation can be tested in laboratory analogues of black holes. We use light pulses in nonlinear fiber optics to establish artificial event horizons. Each pulse generates a moving perturbation of the refractive index via the Kerr effect. Probe light perceives this as an event horizon when its group velocity, slowed down by the perturbation, matches the speed of the pulse. We have observed in our experiment that the probe stimulates Hawking radiation, which occurs in a regime of extreme nonlinear fiber optics where positive and negative frequencies mix.

Electronic zero-point fluctuation forces inside circuit components.

One of the most intriguing manifestations of quantum zero-point fluctuations are the van der Waals and Casimir forces, often associated with vacuum fluctuations of the electromagnetic field. We study generalized fluctuation potentials acting on internal degrees of freedom of components in electrical circuits. These electronic Casimir-like potentials are induced by the zero-point current fluctuations of any general conductive circuit. For realistic examples of an electromechanical capacitor and a superconducting qubit, our results reveal the possibility of tunable forces between the capacitor plates, or the level shifts of the qubit, respectively. Our analysis suggests an alternative route toward the exploration of Casimir-like fluctuation potentials, namely, by characterizing and measuring them as a function of parameters of the environment. These tunable potentials may be useful for future nanoelectromechanical and quantum technologies.

On cosmology in the laboratory.

In transformation optics, ideas from general relativity have been put to practical use for engineering problems. This article asks the question how this debt can be repaid. In discussing a series of recent laboratory experiments, it shows how insights from wave phenomena shed light on the quantum physics of the event horizon.

Integral method for the calculation of Hawking radiation in dispersive media. I. Symmetric asymptotics.

Hawking radiation has become experimentally testable thanks to the many analog systems which mimic the effects of the event horizon on wave propagation. These systems are typically dominated by dispersion and give rise to a numerically soluble and stable ordinary differential equation only if the rest-frame dispersion relation Ω^{2}(k) is a polynomial of relatively low degree. Here we present a new method for the calculation of wave scattering in a one-dimensional medium of arbitrary dispersion. It views the wave equation as an integral equation in Fourier space, which can be solved using standard and efficient numerical techniques.

Cloaked electromagnetic, acoustic, and quantum amplifiers via transformation optics.

The advent of transformation optics and metamaterials has made possible devices producing extreme effects on wave propagation. Here we describe a class of invisible reservoirs and amplifiers for waves, which we refer to as Schrödinger hats. The unifying mathematical principle on which these are based admits such devices for any time harmonic waves modeled by either the Helmholtz or Schrödinger equation, e.g., polarized waves in electromagnetism, acoustical waves and matter waves in quantum mechanics. Schrödinger hats occupy one part of a parameter-space continuum of wave-manipulating structures which also contains standard transformation optics based cloaks, resonant cloaks and cloaked sensors. Possible applications include near-field quantum microscopy.

Engineering antenna radiation patterns via quasi-conformal mappings.

We use a combination of conformal and quasi-conformal mappings to engineer isotropic electromagnetic devices that modify the omnidirectional radiation pattern of a point source. For TE waves, the designed devices are also non-magnetic. The flexibility offered by the proposed method is much higher than that achieved with conformal mappings. As a result, it is shown that complex radiation patterns can be achieved, which can combine high directivity in a desired number of arbitrary directions and isotropic radiation in other specified angular ranges. In addition, this technique enables us to control the power radiated in each direction to a certain extent. The obtained results are valid for any part of the spectrum. The potential of this method is illustrated with some examples. Finally, we study the frequency dependence of the considered devices and propose a practical dielectric implementation.

Luneburg lens in silicon photonics.

The Luneburg lens is an aberration-free lens that focuses light from all directions equally well. We fabricated and tested a Luneburg lens in silicon photonics. Such fully-integrated lenses may become the building blocks of compact Fourier optics on chips. Furthermore, our fabrication technique is sufficiently versatile for making perfect imaging devices on silicon platforms.

An omnidirectional retroreflector based on the transmutation of dielectric singularities.

Transformation optics is a concept used in some metamaterials to guide light on a predetermined path. In this approach, the materials implement coordinate transformations on electromagnetic waves to create the illusion that the waves are propagating through a virtual space. Transforming space by appropriately designed materials makes devices possible that have been deemed impossible. In particular, transformation optics has led to the demonstration of invisibility cloaking for microwaves, surface plasmons and infrared light. Here, on the basis of transformation optics, we implement a microwave device that would normally require a dielectric singularity, an infinity in the refractive index. To fabricate such a device, we transmute a dielectric singularity in virtual space into a mere topological defect in a real metamaterial. In particular, we demonstrate an omnidirectional retroreflector, a device for faithfully reflecting images and for creating high visibility from all directions. Our method is robust, potentially broadband and could also be applied to visible light using similar techniques.

Broadband invisibility by non-Euclidean cloaking.

Invisibility and negative refraction are both applications of transformation optics where the material of a device performs a coordinate transformation for electromagnetic fields. The device creates the illusion that light propagates through empty flat space, whereas in physical space, light is bent around a hidden interior or seems to run backward in space or time. All of the previous proposals for invisibility require materials with extreme properties. Here we show that transformation optics of a curved, non-Euclidean space (such as the surface of a virtual sphere) relax these requirements and can lead to invisibility in a broad band of the spectrum.

The case for artificial black holes.

The event horizon is predicted to generate particles from the quantum vacuum, an effect that bridges three areas of physics--general relativity, quantum mechanics and thermodynamics. The quantum radiation of real black holes is too feeble to be detectable, but black-hole analogues may probe several aspects of quantum black holes. In this paper, we explain in simple terms some of the motivations behind the study of artificial black holes.

Fiber-optical analog of the event horizon.

The physics at the event horizon resembles the behavior of waves in moving media. Horizons are formed where the local speed of the medium exceeds the wave velocity. We used ultrashort pulses in microstructured optical fibers to demonstrate the formation of an artificial event horizon in optics. We observed a classical optical effect: the blue-shifting of light at a white-hole horizon. We also showed by theoretical calculations that such a system is capable of probing the quantum effects of horizons, in particular Hawking radiation.