First-principles analysis of energy exchange in time-varying capacitors for energy trapping applications

Time-varying networks, consisting of lumped elements, such as resistors, capacitors, and inductors, actively modulated in time, have introduced a host of novel wave phenomena and witnessed a remarkable development during recent years. This paper investigates the scattering from a time varying capacitor and how such a load can be fully reflectionless when the capacitance is suitably modulated in time. We analytically derive the required temporal dependence of the capacitance and show how in contrast to other techniques it avoids extreme and negative values and, as a result, can be implemented in a feasible way, when the capacitor is charged with a DC voltage source. We also derive from first principles the energy balance of such a time-varying capacitor, proving that the energy of an incoming pulse is transferred to the modulation source. Our findings clarify scattering of waves from time-varying capacitors and open up a new way to matching of broadband pulses

Reconfigurable nonlinear optical element using tunable couplers and inverse-designed structure

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

Surface wave dispersion for anisotropic metasurfaces constituted by elliptical patches

This paper presents an effective approach for the derivation of the two-dimensional (2-D) frequency-wavenumber dispersion surface of anisotropic metasurfaces (MTSs) consisting of elliptical patches printed over a grounded slab. These MTSs are important in the design of leaky-wave antennas and transformation optics (TO) surface-wave based devices. The formulation resorts to an analytical expression of the currents excited on the element of the periodic texture to define a reduced spectral method of moments (MoM) procedure with only three basis functions. An exact compact formula, which links the MoM matrix to the homogenized equivalent anisotropic impedance of the MTS, is derived. The formulation presented here has been found accurate and useful for designing MTS antennas and TO devices

Dispersion Characteristics of Additive-Manufactured Metasurfaces

International audienceThis paper presents an efficient and accurate approach for the analysis of additive-manufactured metasurfaces (MTSs) consisting of dielectric posts grown on a grounded slab. The formulation is based conventional effective medium theory that allows modeling such MTSs as uniaxially anisotropic grounded slabs. This procedure can be used to effectively characterize the surface waves supported by additive-manufactured MTSs, as needed in the design of planar lenses and leaky-wave antennas

A Closed-Form Representation of Isofrequency Dispersion Curve and Group Velocity for Surface Waves Supported by Anisotropic and Spatially Dispersive Metasurfaces

A general closed-form representation is introduced for representing the isofrequency dispersion curve (IDC) of an anisotropic, spatially, and frequency dispersive metasurface (MTS) constituted by a dense periodic texture of metallic elements printed on a grounded substrate. The formulation is restricted to printed elements isolated from each other (namely, patches and not slots) whose geometry exhibits at least two axes of symmetry. The expression is valid for the dominant TM surface wave (SW) until the limit of the Floquet-Bloch (FB) region and generalizes our previous formulation to arbitrary direction of propagation. This generalization permits a closed-form representation of the IDCs and of the group velocity as a function of two parameters only; these are the equivalent quasi-static capacitances along the symmetry directions of the geometry. The limit of validity of the closed-form representation has been defined and the formulation has been tested by full-wave analysis. The present formulation simplifies the design of MTS antennas and flat transformation optics devices

Static-to-dynamic field conversion with time-varying media

International audienceWe 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 steplike 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

Flat Optics for Surface Waves

The name flat optics (FO) has been introduced in a recent paper by Capasso's group for denoting light-wave manipulations through a general type of penetrable or impenetrable metasurfaces (MTSs). There, the attention was focused on plane waves, whereas here we treat surface waves (SWs) excited on impenetrable impedance surfaces. Space variability of the boundary conditions imposes a deformation of the SW wavefront, which addresses the local wavector along not-rectilinear paths. The ray paths are subjected to an eikonal equation analogous to the one for geometrical optics (GO) rays in graded index materials. The basic relations among ray paths, ray velocity, and transport of energy for both isotropic and anisotropic boundary conditions are presented for the first time. This leads to an elegant formulation which allows for closed form analysis of flat operational devices (lenses or beam formers), giving a new guise to old concepts. It is shown that when an appropriate transformation is found, the ray paths can be conveniently controlled without the use of ray tracing, thus simplifying the problem and leading to a flat version of transformation optics, which is framed here in the general FO theory

A Fast and Accurate Method of Synthesizing X-Wave Launchers by Metallic Horns

International audienceThis paper presents a method for synthesizing metallic horns capable of radiating highly localized electromagnetic pulses, known as X-waves. The proposed method is based on a mode-matching framework for shaped horns. The aperture field distribution required to generate X-waves is synthesized by mode conversion. The near-field horns generated by this method are full-metal structures radiating X-waves in a wide range of frequencies with low dispersion. The obtained structures may be scaled to any frequency range, and they are particularly suited to millimeter and sub-millimeter wave applications. We validate the concept by presenting a horn capable of radiating X-waves over a 44% fractional bandwidth (FBW) with a 5 degrees dispersion of the axicon angle. Capabilities and limitations of this design procedure and the synthesized launchers are demonstrated, discussed, and compared with other state-of-the-art solutions