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Maximizing the power conversion efficiency of solar cells plays a crucial role in upscaling solar energy production. Combining two or more solar cells with different bandgaps into a multi-junction tandem solar cells lowers thermalization losses and increases the power conversion efficiency. Whilst the best efficiencies have been achieved by vertically stacking solar cells, the fabrication process is technologically demanding and leads to high production costs. Novel photovoltaic materials such as organic photovoltaics allow solution processing, which enables the cost effective production of lateral multijunctions, where the single subcells are aligned side by side. To fully unlock their optimal performance, lateral tandems require careful light management, redirecting different spectral bands to the corresponding solar cell. So far, solar spectral splitters suffered from a strong angle dependency, which caused a degradation in performance at the slightest deviation from normal incidence. In this contribution, we reduce this limitation and achieve an enhancement in the conversion efficiency across a wide range of incident angles by inverse designing a solar spectral splitter comprised of two free-form microstructured surfaces on the top and bottom of a supporting glass substrate. Moreover, thanks to the versatility of our methodology, we can tailor the angle-dependent functionality of our device. As such, we also design devices that are optimized to provide enhanced performance at certain oblique angles, which correspond to different times of the day, e.g., when the unit price of energy is higher.

Optical metasurfaces are conventionally viewed as organized flat arrays of photonic or plasmonic nanoresonators, also called metaatoms. However, recent advancements in nanofabrication capabilities and design opportunities have led to the recognition of the advantages of incorporating disorder for specific optical functionalities. This review provides an overview of the principal theoretical, numerical, and experimental aspects concerning the exploration of disordered optical metasurfaces. It introduces fundamental concepts of light scattering by disordered metasurfaces and outlines theoretical and numerical methodologies for analyzing their optical behavior. Various fabrication techniques are discussed, highlighting the types of disorder they deliver and their achievable precision level. The review also explores critical applications of disordered optical metasurfaces, such as light manipulation in thin film materials and the design of structural colors and visual appearances. Finally, the article offers perspectives on the burgeoning future research in this field., Comment: review article: 40 pages, 15 figures

In optical imaging, achieving high resolution often comes at the expense of a shallow depth of field. This means that when using a standard microscope, any minor movement of the object along the optical axis can cause the image to become blurry. To address this issue, we exploit inverse design techniques to optimise a phase mask which, when inserted into a standard microscope, extends the depth of field by a factor of approximately four without compromising the microscope's resolution. Differentiable Fourier optics simulations allow us to rapidly iterate towards an optimised design in a hybrid fashion, starting with gradient-free Bayesian optimisation and proceeding to a local gradient-based optimisation. To fabricate the device, a commercial two-photon 3D laser nanoprinter is used, in combination with a two-step pre-compensation routine, providing high fabrication speed and much better than subwavelength accuracy. We find excellent agreement between our numerical predictions and the measurements upon integrating the phase mask into a microscope and optically characterising selected samples. The phase mask enables us to conduct simultaneous multiplane imaging of objects separated by distances that cannot be achieved with the original microscope.

This tutorial offers a comprehensive overview of photonic time crystals - artificial materials whose electromagnetic properties are periodically modulated in time at scales comparable to the oscillation period of light while remaining spatially uniform. Being the temporal analogs to traditional photonic crystals, photonic time crystals differ in that they exhibit momentum bandgaps instead of energy bandgaps. The energy is not conserved within momentum bandgaps, and eigenmodes with exponentially growing amplitudes exist in the momentum bandgap. Such properties make photonic time crystals a fascinating novel class of artificial materials from a basic science and applied perspective. This tutorial overviews the fundamental electromagnetic equations governing photonic time crystals and explores the groundbreaking physical phenomena they support. Based on these properties, we also oversee a diverse range of applications they unlock. Different material platforms suitable for creating photonic time crystals are discussed and compared. Furthermore, we elaborate on the connections between wave amplification in photonic time crystals and parametric amplification mechanisms in electrical circuits and nonlinear optics. The tutorial will be helpful for readers with physics or engineering backgrounds. It is designed to serve as an introductory guide for beginners and to establish a reference baseline reflecting the current understanding for researchers in the field., Comment: 94 pages, 38 figures

The use of coherent wave phenomena to enhance device performance is a cornerstone of modern optics. In juxtaposition to (locally) periodic metasurfaces, their disordered counterparts exhibit an interplay of destructive and constructive interferences occurring at the same spatial and spectral frequencies. This attribute provides disordered metasurfaces with a remarkable degree of flexibility, setting them apart from the constraints of periodic arrangements. Hereafter, we provide a concise overview of the cutting-edge developments and offer insights into the forthcoming research in this dynamic field.

The realization of photonic time crystals is a major opportunity but also comes with significant challenges. The most pressing one, potentially, is the requirement for a substantial modulation strength in the material properties to create a noticeable momentum bandgap. Reaching that noticeable bandgap in optics is highly demanding with current, and possibly also future, material platforms since their modulation strength is small by tendency. Here, we demonstrate that by introducing temporal variations in a resonant material, the momentum bandgap can be drastically expanded with modulation strengths in reach with known low-loss materials and realistic laser pump powers. The resonance can emerge from an intrinsic material resonance or a suitably spatially structured material supporting a structural resonance. Our concept is validated for resonant bulk media and optical metasurfaces and paves the way toward the first experimental realizations of photonic time crystals., Comment: 9 pages, 5 figures

We provide a theoretical description of light scattering by a spherical particle whose permittivity is modulated in time at twice the frequency of the incident light. Such a particle acts as a finite-sized photonic time crystal and, despite its sub-wavelength spatial extent, can host optical parametric amplification. Conditions of parametric Mie resonances in the sphere are derived. We show that time-modulated materials provide a route to tailor directional light amplification, qualitatively different from that in scatterers made from a gain media. We design two characteristic time-modulated spheres that simultaneously exhibit light amplification and desired radiation patterns, including those with zero backward and/or vanishing forward scattering. The latter sphere provides an opportunity for creating shadow-free detectors of incident light., Comment: 8 pages, 4 figures

Designing objects with predefined optical properties is a task of fundamental importance for nanophotonics, and chirality is a prototypical example of such a property, with applications ranging from photochemistry to nonlinear photonics. A measure of electromagnetic chirality with a well-defined upper bound has recently been proposed. Here, we optimize the shape of silver helices at discrete frequencies ranging from the far infrared to the optical band. Gaussian process optimization, taking into account also shape derivative information of the helices scattering response, is used to maximize the electromagnetic chirality. We show that the theoretical designs achieve more than 90 percent of the upper bound of em-chirality for wavelenghts \SI{3}{\micro\meter} or larger, while their performance decreases towards the optical band. We fabricate and characterize helices for operation at \SI{800}{\nano\meter}, and identify some of the imperfections that affect the performance. Our work motivates further research both on the theoretical and fabrication sides to unlock potential applications of objects with large electromagnetic chirality at optical frequencies, such as helicity filtering glasses. We show that, at \SI{3}{\micro\meter}, a thin slab of randomly oriented helices can absorb 99 percent of the light of one helicity while absorbing only 9 percent of the opposite helicity.

Exploring the interaction of light with time-varying media is an intellectual challenge that, in addition to fundamental aspects, provides a pathway to multiple promising applications. Time modulation constitutes here a fundamental handle to control light on entirely different grounds. That holds particularly for complex systems simultaneously structured in space and time. However, a realistic description of time-varying materials requires considering their material dispersion. The combination thereof has barely been considered but is crucial since dispersion accompanies materials suitable for dynamic modulation. As a canonical scattering problem from which many general insights can be obtained, we develop and apply a self-consistent analytical theory of light scattering by a sphere made from a time-varying material exemplarily assumed to have a Lorentzian dispersion. We discuss the eigensolutions of Maxwell's equations in the bulk and present a dedicated Mie theory. The proposed theory is verified with full-wave simulations. We disclose effects such as energy transfer from the time-modulation subsystem to the electromagnetic field, amplifying carefully structured incident fields. Since many phenomena can be studied on analytical grounds with our formalism, it will be indispensable when exploring electromagnetic phenomena in time-varying and spatially structured finite objects of other geometries., Comment: 18 pages, 6 figures

We present an electromagnetic chirality measure for 2D arrays of subwavelength periodicities under normal illumination. The calculation of the measure uses only the complex reflection and transmission coefficients from the array. The measure allows the ordering of arrays according to their electromagnetic chirality, which further allows a quantitative comparison of different design strategies. The measure is upper bounded, and the extreme properties of objects with high values of electromagnetic chirality make them useful in both near- and far-field applications. We analyze the consequences that different possible symmetries of the array have on its electromagnetic chirality. We use the measure to study four different arrays. The results indicate the suitability of helices for building arrays of high electromagnetic chirality, and the low effectiveness of a substrate for breaking the transverse mirror symmetry.

We present a Bloch modes' based Green's function scattering formalism for cost efficient forward modelling of disordered binary surface textures. The usage of Bloch modes of an unperturbed reference ordered system as ansatz allows our formalism to address surface scattering beyond the shallow amplitude regime. The main advantage of our formalism is the possibility to utilize a small amount of plane waves to represent the assumed Bloch modes thereby reducing computational costs, while still allowing one to estimate the scattering response to all channels accessible by the disordered system. Benchmarking calculations discussed in the paper demonstrate how the usage of our Bloch modes ansatz provides an excellent estimate of the scattering response over an important regime of disorder. As an example of our method's strength, we examine an electrically decoupled binary light trapping texture and demonstrate how introducing disorder may improve light incoupling into the considered solar cell structure., Comment: 12 pages, 9 figures, submitted to PRB

Numerical simulation of complex optical structures enables their optimization with respect to specific objectives. Often, optimization is done by multiple successive parameter scans, which are time consuming and computationally expensive. We employ here Bayesian optimization with Gaussian processes in order to automatize and speed up the optimization process. As a toy example, we demonstrate optimization of the shape of a free-form reflective meta surface such that it diffracts light into a specific diffraction order. For this example, we compare the performance of six different Bayesian optimization approaches with various acquisition functions and various kernels of the Gaussian process., Comment: Proceedings article, SPIE conference "Digital Optical Technologies 2017"

The exact suppression of backscattering from rotationally symmetric objects requires dual symmetric materials where ${\epsilon_r} = {\mu_r}$. This prevents their design at many frequency bands, including the optical one, because magnetic materials are not available. Electromagnetically small non-magnetic spheres of large permittivity offer an alternative. They can be tailored to exhibit balanced electric and magnetic dipole polarizabilities, which result in approximate zero backscattering. In this case, the effect is inherently narrowband. Here, we put forward a different alternative that allows broadband functionality: Electromagnetically large spheres made from low permittivity materials. The effect occurs in a parameter regime that approaches the trivial ${\epsilon_r} \to {\mu_r} =1$ case, where approximate duality is met in a weakly wavelength dependence fashion. Despite the low permittivity, the overall scattering response of the spheres is still significant. Radiation patterns from these spheres are shown to be highly directive across an octave spanning band. The effect is analytically and numerically shown using the Mie coefficients., Comment: 6 Figures

Micro-sized spheres can focus light into subwavelength spatial domains: a phenomena called photonic nanojet. Even though well studied in three-dimensional (3D) configurations, only a few attempts have been reported to observe similar phenomena in two-dimensional (2D) systems. This, however, is important to take advantage of photonic nanojets in integrated optical systems. Usually, surface plasmon polaritons are suggested for this purpose, but they suffer notoriously from the rather low propagation lengths due to intrinsic absorption. Here, we solve this problem and explore, theoretically, numerically, and experimentally, the use of Bloch surface waves sustained by a suitably structured all-dielectric media to enable subwavelength focusing in an integrated planar optical system. Since only a low index contrast can be achieved while relying on Bloch surface waves, we perceive a new functional element that allows a tight focusing and the observation of a photonic nanojet on top of the surface. We experimentally demonstrate a spot size of 0.66{\lambda} in the effective medium. Our approach paves the way to 2D all-dielectric photonic chips for nano-particle manipulation in fluidic devices and sensing applications.

We propose a novel scheme to normalize scattering modes of the electromagnetic field. By relying on analytical solutions for Maxwell's equations in the homogenous medium outside the scatterer, we derive normalization conditions that only depend on the electromagnetic field on the surface of a sphere containing the scatterer. We pay special attention to the important cases of plane wave illumination and illumination with a multipolar field, for which an explicit and easy to use normalization condition is derived. We demonstrate the versatility of our method by normalizing scattering modes of some selected metallic and dielectric scatterers of different geometries in the context of different application scenarios. Since every quantum mechanical treatment of light-matter interaction requires the proper normalization of electromagnetic fields, we deem our proposed normalization scheme broadly applicable independent of the scatterer involved., Comment: 16 pages, 5 figures

The multipole expansion is a key tool in the study of light-matter interactions. All the information about the radiation of and coupling to electromagnetic fields of a given charge-density distribution is condensed into few numbers: The multipole moments of the source. These numbers are frequently computed with expressions obtained after the long-wavelength approximation. Here, we derive exact expressions for the multipole moments of dynamic sources that resemble in their simplicity their approximate counterparts. We validate our new expressions against analytical results for a spherical source, and then use them to calculate the induced moments for some selected sources with a non-trivial shape. The comparison of the results to those obtained with approximate expressions shows a considerable disagreement even for sources of subwavelength size. Our expressions are relevant for any scientific area dealing with the interaction between the electromagnetic field and material systems., Comment: 21 pages, 3 figures

Patterned graphene, as an atomically thin layer, supports localized surface plasmon-polaritons (LSPPs) at mid-infrared or far-infrared frequencies. This provides a pronounced optical force/torque in addition to large optical cross sections and will make it an ideal candidate for optical manipulation. Here, we study the optical force and torque exerted by a linearly polarized plane wave on circular and oval graphene flakes. Whereas the torque vanishes for circular flakes, the finite torque allows rotating and orienting oval flakes relative to the electric field polarization. Depending on the wavelength, the alignment is either perpendicular or parallel. In our contribution, we rely on full-wave numerical simulation but also on an analytical model that treats the graphene flakes in dipole approximation. The presented results reveal a good level of control on the spatial alignment of graphene flakes subjected to far-infrared illumination., Comment: Copyright 2016 Optical Society of America. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modifications of the content of this paper are prohibited. Online abstract link

Aperture based scanning near field optical microscopes are important instruments to study light at the nanoscale and to understand the optical functionality of photonic nanostructures. In general, a detected image is affected by both, the transverse electric and magnetic field components of light. The discrimination of the individual field components is challenging, as these four field components are contained within two signals in the case of a polarization-resolved measurement. Here, we develop a methodology to solve the inverse imaging problem and to retrieve the vectorial field components from polarization- and phase-resolved measurements. Our methodology relies on the discussion of the image formation process in aperture based scanning near field optical microscopes. On this basis, we are also able to explain how the relative contributions of the electric and magnetic field components within detected images depend on the probe geometry, its material composition, and the illumination wavelength. This allows to design probes that are dominantly sensitive either to the electric or magnetic field components of light.

In a recent comment arxiv:1310.1503 Miller et al. noted that a cloak we previously presented (Scientific Reports 3, 2328) that exploits a scattering cancellation technique to render an optically small dielectric particle invisible suffers from increased extinction. According to Miller et al. this disqualifies the terminology of a cloak. We concur with the crux of the comment but wish to stress that we never claimed nor suggested a reduction in extinction. A scattering cancellation cloak cancels scattering. The issue, therefore, seems to be whether the structure should be called a cloak or not. We understand a cloaked object as an object that is not perceived by an external observer. We argue that optically small particles are much easier seen in a scattering configuration whereas it is difficult to perceive them in extinction; providing justification to the terminology as used., Comment: This is a reply to a comment published in arxiv:1310.1503

In this paper, we will introduce THz graphene antennas that strongly enhance the emission rate of quantum systems at specific frequencies. The tunability of these antennas can be used to selectively enhance individual spectral features. We will show as an example that any weak transition in the spectrum of coronene can become the dominant contribution. This selective and tunable enhancement establishes a new class of graphene-based THz devices, which will find applications in sensors, novel light sources, spectroscopy, and quantum communication devices.

We investigate experimentally and theoretically the third harmonic generated by a double-layer fishnet metamaterial. To unambiguously disclose most notably the influence of the magnetic resonance, the generated third harmonic was measured as a function of the angle of incidence. It is shown experimentally and numerically that when the magnetic resonance is excited by pump beam, the angular dependence of the third harmonic signal has a local maximum at an incidence angle of {\theta} \simeq 20{\deg}. This maximum is shown to be a fingerprint of the antisymmetric distribution of currents in the gold layers. An analytical model based on the nonlinear dynamics of the electrons inside the gold shows excellent agreement with experimental and numerical results. This clearly indicates the difference in the third harmonic angular pattern at electric and magnetic resonances of the metamaterial., Comment: 7 pages, 5 figures

We experimentally demonstrate a three-dimensional chiral optical metamaterial that exhibits an asymmetric transmission for forwardly and backwardly propagating linearly polarized light. The observation of this novel effect requires a metamaterial composed of three-dimensional chiral metaatoms without any rotational symmetry. Our analysis is supported by a systematic investigation of the transmission matrices for arbitrarily complex, lossy media that allows deriving a simple criterion for asymmetric transmission in an arbitrary polarization base. Contrary to physical intuition, in general the polarization eigenstates in such three-dimensional and low-symmetry metamaterials do not obey fxed relations and the associated transmission matrices cannot be symmetrized.

We introduce a technique to decompose the scattered near field of two-dimensional arbitrary metaatoms into its multipole contributions. To this end we expand the scattered field upon plane wave illumination into cylindrical harmonics as known from Mie theory. By relating these cylin- drical harmonics to the field radiated by Cartesian multipoles, the contribution of the lowest order electric and magnetic multipoles can be identified. Revealing these multipoles is essential for the design of metamaterials because they largely determine the character of light propagation. In par- ticular, having this information at hand it is straightforward to distinguish between effects that result either from the arrangement of the metaatoms or from their particular design.

We report that rhomb-shaped metal nanoantenna arrays support multiple plasmonic resonances, making them favorable bio-sensing substrates. Besides the two localized plasmonic dipole modes associated with the two principle axes of the rhombi, the sample supports an additional grating-induced surface plasmon polariton resonance. The plasmonic properties of all modes are carefully studied by far-field measurements together with numerical and analytical calculations. The sample is then applied to surface-enhanced Raman scattering measurements. It is shown to be highly efficient since two plasmonic resonances of the structure were simultaneously tuned to coincide with the excitation and the emission wave- length in the SERS experiment. The analysis is completed by measuring the impact of the polarization angle on the SERS signal., Comment: 13 pages, 5 figures

We present an analytical model which permits the calculation of effective material parameters for planar metamaterials consisting of arbitrary unit cells (metaatoms) formed by a set of straight wire sections of potentially different shape. The model takes advantage of resonant electric dipole oscillations in the wires and their mutual coupling. The pertinent form of the metaatom determines the actual coupling features. This procedure represents a kind of building block model for quite different metaatoms. Based on the parameters describing the individual dipole oscillations and their mutual coupling the entire effective metamaterial tensor can be determined. By knowing these parameters for a certain metaatom it can be systematically modified to create the desired features. Performing such modifications effective material properties as well as the far field intensities remain predictable. As an example the model is applied to reveal the occurrence of optical activity if the split ring resonator metaatom is modified to L- or S-shaped metaatoms., Comment: 5 figures, 1 table

We show for the first time that a planar metamaterial, an array of coupled metal split-ring resonators with a unit cell lacking mirror symmetry, exhibits asymmetric transmission of terahertz radiation (0.25-2.5 THz) propagating through it in opposite directions. This intriguing effect, that is compatible with Lorentz reciprocity and time-reversal, depends on a directional difference in conversion efficiency of the incident circularly polarized wave into one of opposite handedness, that is only possible in lossy low-symmetry planar chiral metamaterials. We show that asymmetric transmission is linked to excitation of enantiomerically sensitive plasmons, these are induced charge-field excitations that depend on the mutual handedness of incident wave and metamaterial pattern. Various bands of positive, negative and zero phase and group velocities have been identified indicating the opportunity to develop polarization sensitive negative index and slow light media based on such metamaterials., Comment: 5 pages, 6 figures (various minor improvements throughout)

Nanostructured metamaterials, especially arrays of metallic nanoparticles which sustain the excitation of localized plasmon polaritons, provide excellent opportunities to mold the flow of light in the linear regime. We suggest a metamaterial structure whose properties are determined not only by its inner geometry but also by its entire shape. We call this structure a \emph{metamaterial nanotip}. We evaluate the potential of this nanotip to control the size and the location of the field enhancement. Two-dimensional implementations of this metamaterial nanotip were comprehensively numerically simulated and confirm the expected, physically distinct regimes of operation., Comment: 4 pages, 4 figures