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With his formal analysis in 1951, the physicist Pyotr Kapitza demonstrated that an inverted pendulum with an externally vibrating base can be stable in its upper position, thus overcoming the force of gravity. Kapitza's work is an example that an originally unstable system can become stable after a minor perturbation of its properties or initial conditions is applied. Inspired by his ideas, we show how non-Foster circuits can be stabilized with the application of external \textit{electrical vibration}, i.e., time modulations. Non-Foster circuits are highly appreciated in the engineering community since their bandwidth characteristics are not limited by passive-circuits bounds. Unfortunately, non-Foster circuits are usually unstable and they must be stabilized prior to operation. Here, we focus on the study of non-Foster $L(t)C$ circuits with time-varying inductors and time-invariant negative capacitors. We find an intrinsic connection between Kapitza's inverted pendulum and non-Foster $L(t)C$ resonators. Moreover, we show how positive time-varying modulations of $L(t)>0$ can overcome and stabilize non-Foster negative capacitances $C<0$. These findings open up an alternative manner of stabilizing electric circuits with the use of time modulations, and lay the groundwork for application of, what we coin \textit{Vibrational Electromagnetics}, in more complex media., Comment: 10 pages (7 pages main text, 3 pages supplementary materials), 4 figures

Here, we theoretically investigate the nonreciprocal response of an electrically biased graphene-coated dielectric fiber. By electrically biasing the graphene coating along the fiber axis, the dynamic conductivity of graphene exhibits a nonsymmetric response with respect to the longitudinal component of guided-mode wave vectors. Consequently, the guided waves propagating in two opposite directions may encounter distinct propagation features. In this work, the electromagnetic properties, such as modal dispersion and some field distributions are presented, and the strength of nonreciprocity is discussed for different parameters of graphene, such as its chemical potential and material loss. Furthermore, the influence of the radius of the fiber on the nonreciprocal response is investigated. We envision that such nonreciprocal optical fibers may find various potential applications in THz, microwave, and optical technologies., Comment: 8 pages, 2 figures

The concept of twistronics and moir\'e physics, which is present in twisted two-dimensional bilayer materials, has recently attracted growing attention in various fields of science and engineering such as condensed matter physics, nanophotonics, polaritonics and excitonics. The twist angle between the two layers has offered an additional degree of control over electron and photon interaction with such structures. Inspired by the photonic version of twistronics, here we introduce and investigate theoretically the temporal analogue of twistronics in anisotropic optical media. We study how a monochromatic electromagnetic plane wave propagating in a spatially unbounded, anisotropic medium undergoes major changes when the relative permittivity tensor of the medium is rapidly changed in time to create a new anisotropic medium that is the rotated version of the original medium. We consider both the elliptic and hyperbolic anisotropic scenarios. The propagation-angle-dependent forward (FW) and backward (BW) waves with their converted frequencies and relative amplitudes are obtained. To concentrate on the main features of this concept without getting into details of dispersion, in our work here we assume dispersionless and lossless material parameters. Our results reveal how frequency conversion is highly dependent on the direction of propagation of the original wave, rotation angle, and initial values of the material parameters, proposing another class of "magic angles" for such temporal twistronics., Comment: 11 pages, 3 figures

Photonic time interfaces, as the temporal analogue of spatial interfaces between two media, consist of a rapid change of the electromagnetic properties of a material (such as permittivity {\epsilon}, and permeability {\mu}) while the wave is present in the material. Here we exploit cascading of such time interfaces in spatially cascaded guided-wave structures such as slab waveguides and ring resonators by considering that the relative permittivity of the cladding of dielectric waveguides is rapidly changed at different moments of time from {\epsilon}clad_1 to {\epsilon}clad_2 , while the material of the core remains unchanged in time. It is shown how such time-dependent cladding can enable frequency conversion within the space-time dielectric ring resonator and slab waveguides due to an induced modification of the effective refractive index of the mode propagating within such photonic device. Cascaded frequency conversion is achieved in such cascaded space-time dielectric waveguides and ring resonators, showing how the combination of space and time interfaces can offer further opportunities for manipulation of light-matter interaction using four-dimensional (4D) photonic structures., Comment: 23 pages (17 pages main text and 6 pages supplementary materials), 9 figures (4 figure in main text and 5 figures in supplementary materials)

A time interface (a rapid change of the constitutive parameters of a material in time), applied within an unbounded medium where a wave travels, can enable frequency conversion, and is considered the temporal analogue of a spatial interface between two materials. Here, we study light-matter interactions in four dimensions, 4D (space, x,y,z, and time, t), by exploring the implications of applying time interfaces not to the entire space where a wave travels, but to certain regions of space in order to create spatial interfaces in time. Different configurations such as induced perpendicular, parallel, and oblique spatial interfaces via a temporal interface are discussed. It is shown how such four-dimensional combinations of temporal and spatial interfaces can enable interesting features such as the 4D generalized Snell law and the temporal chirp, temporal lensing, and temporal routing of electromagnetic waves. Such exotic possibilities may provide new ways to manipulate light-matter interactions via a combination of temporal and spatial interfaces., Comment: 11 pages, 4 figures

We introduce a mechanism that can both hold and amplify electromagnetic waves by rapidly changing the permittivity of the medium during the wave travel from a positive to a dispersionless (i.e. non-Foster) negative value and then back again. The underlying physics behind this phenomenon is theoretically explored by considering a plane wave in an unbounded medium. Interestingly, we show that a rapid positive-to-negative temporal change of {\epsilon}(t) causes the propagation of the wave to stop (observed by a frozen phase in time) while the amplitude of the frozen field exponentially grows. Stepping the permittivity back to the original (or a new) positive value will cause the wave to thaw and resume propagation with the original (or the new) frequency, respectively. We numerically study the case of dipole radiation in such time-varying non-Foster structures. As a possible implementation, we propose a parallel plate waveguide platform loaded with time-dependent media emulating parallel lumped non-Foster negative capacitors. Such non-Foster time-varying structures may open new venues in controlling and manipulating wave-matter interaction., Comment: 51 pages (20 pages of main text and 31 pages of supplementary materials), 21 figures (6 figures in the main text and 15 figures in the supplementary materials)

Inverse-designed Silicon photonic metastructures offer an efficient platform to perform analog computations with electromagnetic waves. However, due to computational difficulties, scaling up these metastructures to handle a large number of data channels is not trivial. Furthermore, a typical inverse-design procedure utilizes a small computational domain and therefore tends to employ resonant features to achieve its objectives. This results in structures that are narrow-bandwidth and highly sensitive to fabrication errors. Here, we employ a 2D inverse-design method based on the effective index approximation with a low-index contrast constraint. This results in compact amorphous lens systems which are generally feed-forward and low-resonance. We designed and experimentally demonstrated a vector-matrix product for a 2 x 2 and a 3 x 3 matrix. We also designed a 10 x 10 matrix using the proposed 2D computational method. These examples demonstrate that these techniques have the potential to enable larger-scale wave-based analog computing platforms., Comment: 29 pages (including the main text and the supplementary materials), 10 figures (4 for the main text and 6 for supplementary materials)

The ability to perform mathematical computations using metastructures is an emergent paradigm that carries the potential of wave-based analog computing to the realm of near-speed-of-light, low-loss, compact devices. We theoretically introduce and experimentally verify the concept of a reconfigurable metastructure that performs analog complex mathematical computations using electromagnetic waves. Reconfigurable, RF-based components endow our device with the ability to perform stationary and non-stationary iterative algorithms. After demonstrating matrix inversion (stationary problem), we use the machine to tackle two major non-stationary problems: root finding with Newton's method and inverse design (constrained optimization) via the Lagrange multiplier method. The platform enables possible avenues for wave-based, analog computations for general linear algebraic problems and beyond in compact, ultrafast, and parallelized ways., Comment: 18 pages, 3 figures, supp material, 15 pages

In recent years, wave-based analog computing has been at the center of attention for providing ultra-fast and power-efficient signal processing enabled by wave propagation through artificially engineered structures. Building on these structures, various proposals have been put forward for performing computations with waves. Most of these proposals have been aimed at linear operations, such as vector-matrix multiplications. The weak and hardly controllable nonlinear response of electromagnetic materials imposes challenges in the design of wave-based structures for performing nonlinear operations. In the present work, first, by using the method of inverse design we propose a three-port device, which consists of a combination of linear and Kerr nonlinear materials, exhibiting the desired power-dependent transmission properties. Then, combining a proper arrangement of such devices with a collection of Mach-Zehnder interferometers (MZIs), we propose a reconfigurable nonlinear optical architecture capable of implementing a variety of nonlinear functions of the input signal. The proposed device may pave the way for wave-based reconfigurable nonlinear signal processing that can be combined with linear networks for full-fledged wave-based analog computing., Comment: 20 pages, 4 figures

Wave-based analog computing in the forms of inverse-designed metastructures and the meshes of Mach-Zehnder interferometers (MZI) have recently received considerable attention due to their capability in emulating linear operators, performing vector-matrix multiplication, inverting matrices, and solving integral and differential equations, via electromagnetic wave interaction and manipulation in such structures. Here, we combine these two platforms to propose a wave-based metadevice that can compute scattered fields in electromagnetic forward scattering problems. The proposed device consists of two sub-systems: a set of reconfigurable couplers with a proper feedback system and an inverse-designed inhomogeneous material block. The first sub-system computes the magnitude and phase of the dipole polarization induced in the scatterers when illuminated with a given incident wave (matrix inversion). The second sub-system computes the magnitude and phase of the scattered fields at given detection points (vector-matrix multiplication). We discuss the functionality of this metadevice, and through several examples, we theoretically evaluate its performance by comparing the simulation results of this device with full-wave numerical simulations and numerically evaluated matrix inversion. We also highlight that since the first section is reconfigurable, the proposed device can be used for different permittivity distributions of the scatterer and different incident excitations without changing the inverse-designed section. Our proposed device may provide a versatile platform for rapid computation in various scattering scenarios., Comment: Authors with equal contribution: Vahid Nikkhah and Dimitrios C. Tzarouchis

Casimir forces between charge-neutral bodies originate from quantum vacuum fluctuations of electromagnetic fields, which exhibit a critical dependence on material's electromagnetic properties. Over the years, in-situ modulation of material's optical properties has been enabled through various means and has been widely exploited in a plethora of applications such as electro-optical modulation, transient color generation, bio- or chemical sensing, etc. Yet Casimir force modulation has been hindered by difficulty in achieving high modulation signals due to the broadband nature of the Casimir interaction. Here we propose and investigate two configurations that allow for in-situ modulation of Casimir forces through electrical gating of a metal-insulator-semiconductor (MIS) junction comprised of transparent conductive oxide (TCO) materials. By switching the gate voltage on and off, a force modulation of > 400 pN is predicted due to substantive charge carrier accumulation in the TCO layer, which can be easily measured using state-of-the-art force measurement techniques in an atomic force microscope (AFM). We further examine the influence of the oxide layer thickness on the force modulation, suggesting the importance of the fine control of the oxide layer deposition. Our work provides a promising pathway for modulating the Casimir effect in-situ with experimentally measurable force contrast.

Performing analog computations with metastructures is an emerging wave-based paradigm for solving mathematical problems. For such devices, one major challenge is their reconfigurability, especially without the need for a priori mathematical computations or computationally-intensive optimization. Their equation-solving capabilities are applied only to matrices with special spectral (eigenvalue) distribution. Here we report the theory and design of wave-based metastructures using tunable elements capable of solving integral/differential equations in a fully-reconfigurable fashion. We consider two architectures: the Miller architecture, which requires the singular-value decomposition, and an alternative intuitive direct-complex-matrix (DCM) architecture introduced here, which does not require a priori mathematical decomposition. As examples, we demonstrate, using system-level simulation tools, the solutions of integral and differential equations. We then expand the matrix inverting capabilities of both architectures toward evaluating the generalized Moore-Penrose matrix inversion. Therefore, we provide evidence that metadevices can implement generalized matrix inversions and act as the basis for the gradient descent method for solutions to a wide variety of problems. Finally, a general upper bound of the solution convergence time reveals the rich potential that such metadevices can offer for stationary iterative schemes.

Epsilon-near-zero (ENZ) materials have been demonstrated to exhibit unique electromagnetic properties. Here we propose the concept of radiative energy bandgap for an ENZ nanoparticle coupled with a quantum emitter (QE). The radiative emission of the coupled QE-nanoparticle can be significantly suppressed around the ENZ frequency and substantially enhanced otherwise, yielding an effective energy bandgap for radiation. This suppression is effectively invariant with respect to the particle size and is therefore an intrinsic property of the ENZ material. Our concept also heralds an alternative pathway to quench the emission from a QE, which may find potential application in quantum information storage.

As standard microelectronic technology approaches fundamental limitations in speed and power consumption, novel computing strategies are strongly needed. Analog optical computing enables processing large amounts of data at a negligible energy cost and high speeds. Based on these principles, ultrathin optical metasurfaces have been recently explored to process large images in real-time, in particular for edge detection. By incorporating feedback, it has also been recently shown that metamaterials can be tailored to solve complex mathematical problems in the analog domain, although these efforts have so far been limited to guided-wave systems and bulky setups. Here, we present an ultrathin Si metasurface-based platform for analog computing that is able to solve Fredholm integral equations of the second kind using free-space visible radiation. A Si-based metagrating was inverse-designed to implement the scattering matrix synthesizing a prescribed Kernel corresponding to the mathematical problem of interest. Next, a semi-transparent mirror was incorporated into the sample to provide adequate feedback and thus perform the required Neumann series, solving the corresponding equation in the analog domain at the speed of light. Visible wavelength operation enables a highly compact, ultrathin device that can be interrogated from free-space, implying high processing speeds and the possibility of on-chip integration.

We envision the use of an indium tin oxide (ITO) thin film as part of a bi-layered silicon-photonics subwavelength device to boost nonlinearity-assisted all-passive nonreciprocal behavior. The asymmetric p-polarized oblique excitation of a mode near the epsilon-near-zero (ENZ) frequency, with highly-confined and enhanced normal electric field component and large absorption, allows to harness ITO's strong ultrafast nonlinear response for the generation of a notable nonreciprocal performance in the two-port element. Though limited by loss, we find the device's optimal operational point and the maximum nonreciprocal transmittance ratio attainable vs. light intensity -- including an apparent upper bound slightly over 2 --, and we perform exhaustive numerical simulations considering nonlinear processes of both anharmonic and thermal nature that validate our predictions, including steady-state and pulsed-laser excitations., Comment: 12 pages (including 5 appendices), 9 figures (4 in the main text and 5 in the appendices)

Manipulation of wave-matter interactions in systems with loss and gain have opened new mechanisms to control wave propagation at will. Metamaterials and metasurfaces having spatially inhomogeneous loss and gain have been studied in the past few years by exploiting parity-time (PT) symmetry concepts inspired from quantum-physics. In this work we theoretically study the control of light-matter interactions in spatially unbounded metamaterials having a time-modulated permittivity whose imaginary part is temporally modulated to induce loss and gain, while the real part stays unchanged. We show both numerically and theoretically how such temporally modulated multistepped metamaterials with loss and gain can be equivalent to a temporal effective metamaterial having an effective permittivity modelled by a step function in time. Interestingly, it is shown how the amplitude of a monochromatic electromagnetic wave traveling inside such temporal metamaterials can experience spatiotemporal decay or amplification depending on the values of loss and gain added into the system, while its wavenumber is preserved. We envision that our findings may open new avenues in exploration of potential applications of temporal metamaterials in signal amplification and loss mitigation., Comment: 19 pages (14 pages of the main text and 5 pages of the supplementary materials}, 8 figures (4 figures in the main text and 4 figures in the supplementary materials)

In this Letter, we theoretically demonstrate that a uniform static electric field distribution can be partially converted to radiation fields when a portion of the medium undergoes a temporal change of its permittivity. An in-depth theoretical investigation of this phenomenon is developed for a dielectric block with a step-like temporal change located inside a waveguide charged with a DC voltage source. Closed analytical expressions are derived for the radiated electric and magnetic fields. The exchange of energy between the electrostatic and electromagnetic fields is discussed. The reconciliation between the seemingly contradictory temporal and spatial boundary conditions for the electric and magnetic fields at the interface of the time-varying dielectric block is analyzed and elucidated. Our findings may provide an alternative solution for generating electromagnetic radiation based on time-varying media., Comment: 36 pages (16 pages of main text and 20 pages of supplementary materials), 8 figures (4 figures in the main text and 4 figures in the supplementary materials)

Metamaterials and metasurfaces are designed by periodically arranged subwavelength geometries, allowing a tailored manipulation of the electromagnetic response of matter. Here, we exploit temporal variations of permittivity inside subwavelength geometries to propose the concept of spatiotemporal meta-atoms having time-dependent properties. We exploit isotropic-to-anisotropic temporal boundaries within spatially subwavelength regions where their permittivity is rapidly changed in time. In so doing, it is shown how resulting scattered waves travel in directions that are different from the direction of the impinging wave, and depend on the values of the chosen anisotropic permittivity tensor. To provide a full physical insight of their performance, multiple scenarios are studied numerically such as the effect of using different values of permittivity tensor, different geometries of the spatiotemporal meta-atom and time duration of the induced isotropic-to-anisotropic temporal boundary. The intrinsic asymmetric response of the proposed spatiotemporal meta-atoms is also studied demonstrating, both theoretically and numerically, its potential for an at-will manipulation of scattered waves in real time. These results may open new paradigms for controlling wave-matter interactions and may pave the way for the next generation of metamaterials and metasurfaces by unleashing their potential using four-dimensional (4D) unit cells., Comment: 17 pages, 6 figures

Breaking the reciprocity of electromagnetic interactions is of paramount importance in photonic and microwave technologies, as it enables unidirectional power flows and other unique electromagnetic phenomena. Here we explore a method to break the reciprocity of electromagnetic guided waves utilizing an electron beam with a constant velocity. By introducing an effective dynamic conductivity for the beam, we theoretically demonstrate how nonreciprocal guided waves and a one-way propagating regime can be achieved through the interaction of swift electrons with electromagnetic waves in two-dimensional (2D) parallel-plate and three-dimensional (3D) circular-cylindrical waveguides. Unlike the conventional electron beam structures such as traveling wave tubes and electron accelerators, here the goal is neither to generate and/or amplify the wave nor to accelerate electrons. Instead, we study the salient features of nonreciprocity and unidirectionality of guided waves in such structures. The relevant electromagnetic properties such as the modal dispersion, the field distributions, the operating frequency range, and the nonreciprocity strength and its dependence on the electron velocity and number density are presented and discussed. Moreover, we compare the dispersion characteristics of waves in such structures with some electric-current-based scenarios in materials reported earlier. This broadband tunable magnet-free method offers a unique opportunity to have a switchable strong nonreciprocal response in optoelectronics, nanophotonics, and THz systems., Comment: 26 pages (including the supplementary materials), 7 figures (including 3 figures in the supplementary materials)

We study the problem of a temporal discontinuity in the permittivity of an unbounded medium with Lorentzian dispersion. More specifically, we tackle the situation in which a monochromatic plane wave forward-travelling in a (generally lossy) Lorentzian-like medium scatters from the temporal "half-space interface" that results from an abrupt temporal change in its plasma frequency (while keeping its resonance frequency constant). In order to achieve momentum preservation across the temporal discontinuity, we show how, unlike in the well-known problem of a nondispersive discontinuity, the second-order nature of the dielectric function now gives rise to two shifted frequencies. As a consequence, whereas in the nondispersive scenario the continuity of the electric displacement D and the magnetic induction B suffice to find the amplitude of the new forward and backward wave, we now need two extra temporal boundary conditions. That is, two forward and two backward plane waves are now instantaneously generated in response to a forward-only plane wave. We also include a transmission-line equivalent with lumped circuit elements that describes the dispersive time-discontinuous scenario under consideration., Comment: 13 pages (including four appendices), 9 figures (including 2 figures in the appendix section)

Controlling amplitude, phase and polarization of electromagnetic waves is key for a full manipulation of wave-matter interactions. The Brewster angle is one of the important features in this context. Here, we exploit metamaterial concepts with a time-modulated permittivity to propose the temporal equivalent of the spatial Brewster angle, a concept we call temporal Brewster angle. We consider temporal boundaries (as the temporal equivalent of the spatial boundaries between two media) by rapidly changing the permittivity of the medium, where a wave travels, from isotropic to an anisotropic permittivity tensor. It is theoretically shown that when the incidence angle coincides with that of the temporal Brewster angle a forward (temporal transmission) wave is produced while the backward (temporal reflection) is eliminated. We provide a closed-form analytical expression of the temporal Brewster angle and demonstrate its performance both theoretically and numerically. Our findings may provide a fresh view on how to control electromagnetic wave propagation and wave-matter interactions in real time using temporal metamaterials., Comment: 12 pages, 4 figures

In the search for improved computational capabilities, conventional microelectronic computers are facing various problems arising from the miniaturization and concentration of active electronics devices (1-2). Therefore, researchers have been exploring several paths for the next generation of computing platforms, which could exploit various physical phenomena for solving mathematical problems at higher speeds and larger capacities. Among others, physical systems described by waves, such as photonic and quantum devices, have been utilized to compute the solution of mathematical problems (1-18). However, previous devices have not fully exploited the linearity of the wave equation, which as we show here, allows for the simultaneous parallel solution of several independent mathematical problems within the same device. In this Letter, we demonstrate, theoretically and experimentally, that a transmissive cavity filled with a judiciously tailored dielectric distribution and embedded in a multi-frequency feedback loop can calculate the solutions of an arbitrary number of mathematical problems simultaneously. We design, build, and test a computing structure at microwave frequencies that solves two independent integral equations with any two arbitrary inputs. We offer another design that can invert four arbitrary 5x5 matrices, confirming its functionality with numerical simulations. We believe our results presented here can provide "coincident computing" and pave the way for the design of low-power, ultrafast, parallel photonic analog computing devices for sensing and signal processing in embedded computing applications., Comment: 15 pages (including supplementary materials), 3 figures

We investigate, theoretically and numerically, the dependence of a material's nonlinear-optical response on the linear relative electric permittivity $\epsilon$ and magnetic permeability $\mu$. The conversion efficiency of low-order harmonic-generation processes, as well as the increase rate of Kerr-effect nonlinear phase shift and nonlinear losses from two-photon absorption (TPA), are seen to increase with decreasing $\epsilon$ and/or increasing $\mu$. We also discuss the rationale and physical insights behind this nonlinear response, particularly its enhancement in $\epsilon$-near-zero (ENZ) media. This behavior is consistent with the experimental observation of intriguingly high effective nonlinear refractive index in degenerate semiconductors such as indium tin oxide [\textit{Alam et al., Science 352 (795), 2016}] (where the nonlinearity is attributed to a modification of the energy distribution of conduction-band electrons due to laser-induced electron heating) and aluminum zinc oxide [\textit{Caspani et al., Phys. Rev. Lett. 116 (233901), 2016}] at frequencies with vanishing real part of the linear permittivity. Such strong nonlinear response can pave the way for a new paradigm in nonlinear optics with much higher conversion efficiencies and therefore better miniaturization capabilities and power requirements for next-generation integrated nanophotonics., Comment: 10 pages, 8 figures

We explore the mathematical theory to rigorously describe the response of media with linear time-varying, generally dispersive, electromagnetic constitutive parameters. We show that even when the temporal inhomogeneity takes place on a time scale comparable or shorter than the driving fields' time period, one can still define a physically meaningful time-varying dispersion. Accordingly, a generalized set of Kramers-Kronig relations is investigated to link the real and imaginary parts of the time-varying frequency-dispersive spectra characterizing the medium's constitutive response. Among others, we study the case of a Lorentzian dielectric response with time-varying volumetric density of polarizable atoms and present the varying circuital equivalents of the governing differential equation, which in turn allow us to use the notion of generalized time-varying impedances/admittances of a time-dependent resistor, inductor and capacitor., Comment: 16 pages, 5 figures, 3 appendices

Epsilon-near-zero (ENZ) media disclose the peculiarities of electrodynamics in the limit of infinite wavelength but non-zero frequency for experiments and applications. Theory suggests that wave interaction with obstacles and disturbances dramatically changes in this domain. To investigate the optics of those effects we fabricated a nanostructured 2D optical ENZ multilayer waveguide that is probed with wavelength-tuned laser light via a nanoscale wave launch configuration. In this experimental framework we directly optically measure wave propagation and diffraction in a realistic system with the level and scale of imperfection that is typical in nanooptics. As we scan the wavelength from 1.0 $\mu$m to 1.7 $\mu$m, we approach the ENZ regime, and observe the interference pattern of a micro-scale Young's double slit to steeply diverge. By evaluating multiple diffraction orders we experimentally determine the effective refractive index $n_{eff}$ and its zero-crossing as an intrinsic measured reference, which is in agreement with theoretical predictions. We further verify that the double-slit and specifically placed scattering objects become gradually invisible when approaching the ENZ regime. We also observe that light-matter-interaction intensifies towards ENZ and quantify how speckle noise, caused by tiny random imperfections, increasingly dominates the optical response and blue-shifts the cut-off frequency., Comment: 24 pages manuscript with 4 figures and 40 pages supplementary information with 27 figures