Doping a semiconductor with foreign atoms enables the control of its electrical and optical properties. We transplant the concept of doping to macroscopic photonics, demonstrating that two-dimensional dielectric particles immersed in a two-dimensional epsilon-near-zero medium act as dopants that modify the medium's effective permeability while keeping its effective permittivity near zero, independently of their positions within the host. The response of a large body can be tuned with a single impurity, including cases such as engineering perfect magnetic conductor and epsilon-and-mu-near-zero media with nonmagnetic constituents. This effect is experimentally demonstrated at microwave frequencies via the observation of geometry-independent tunneling. This methodology might provide a new pathway for engineering electromagnetic metamaterials and reconfigurable optical systems. Doping-the judicious inclusion of impurities into a material, with the aim of controlling the material's macroscopic parameters-has been essential in the development of the semiconductor industry (1). Arguably, the success of semiconductor devices lies largely in the possibility of engineering their electrical, optical, and/or magnetic properties with a relatively small number of randomly located impurities. For instance, tailoring the electrical conductivity via doping facilitated the development of diodes and transistors, which are the basis of microelectronics (2). Different doping mechanisms are also central to a number of optical and optoelectronic devices, including lasers, light-emitting diodes, and solar cells (3).In principle, the concepts behind doping could be transplanted to other structures, length scales, and, in general, fields of physics. This was successfully done, for instance, when applying doping principles from bulky semiconductors to nanocrystals or quantum dots (4). In our work, the concept of doping is applied to the fields of macroscopic photonics and electromagnetic metamaterials (5, 6) and, in particular, media with near-zero parameters (5, 7-9). However, the extrapolation is nontrivial. In fact, when a homogeneous host body, characterized by macroscopic material parameters such as relative permittivity e h and relative permeability m h , is filled with a macroscopic dopant (characterized by e d and m d ), this foreign body scatters the internal electromagnetic fields, and the response of the system in general differs from that of a homogeneous body with effective macroscopic parameters e eff and m eff .Traditionally, it is only in the long-wavelength regime that a body filled with impurities can be substituted with a homogenized body by using suitable effective-medium theories (EMTs) (10). Conventional EMTs apply usually under three conditions: The original body must contain a sufficiently large number of impurities, and both their size and separation must be much smaller than the wavelength of operation (10). Although these conditions are actually relaxed in advanced homogenization techniques (11, 12), these proce...
Metastructures hold the potential to bring a new twist to the field of spatial-domain optical analog computing: migrating from free-space and bulky systems into conceptually wavelength-sized elements. We introduce a metamaterial platform capable of solving integral equations using monochromatic electromagnetic fields. For an arbitrary wave as the input function to an equation associated with a prescribed integral operator, the solution of such an equation is generated as a complex-valued output electromagnetic field. Our approach is experimentally demonstrated at microwave frequencies through solving a generic integral equation and using a set of waveguides as the input and output to the designed metastructures. By exploiting subwavelength-scale light-matter interactions in a metamaterial platform, our wave-based, material-based analog computer may provide a route to achieve chip-scale, fast, and integrable computing elements.
The integration of radiofrequency electronic methodologies on micro- as well as nanoscale platforms is crucial for information processing and data-storage technologies. In electronics, radiofrequency signals are controlled and manipulated by 'lumped' circuit elements, such as resistors, inductors and capacitors. In earlier work, we theoretically proposed that optical nanostructures, when properly designed and judiciously arranged, could behave as nanoscale lumped circuit elements--but at optical frequencies. Here, for the first time we experimentally demonstrate a two-dimensional optical nanocircuit at mid-infrared wavelengths. With the guidance of circuit theory, we design and fabricate arrays of Si3N4 nanorods with specific deep subwavelength cross-sections, quantitatively evaluate their equivalent impedance as lumped circuit elements in the mid-infrared regime, and by Fourier transform infrared spectroscopy show that these nanostructures can indeed function as two-dimensional optical lumped circuit elements. We further show that the connections among nanocircuit elements, in particular whether they are in series or in parallel combination, can be controlled by the polarization of impinging optical signals, realizing the notion of 'stereo-circuitry' in metatronics-metamaterials-inspired optical circuitry.
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