Photonic doping of epsilon-near-zero media

Abstract

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...

Electromagnetic Impurity-Immunity Induced by Parity-Time Symmetry

“…By applying such PT-symmetric metasurfaces to ENZ media, we can compensate for the divergent impedance contrast between the ENZ media and free space. More importantly and interestingly, with such PT-symmetric metasurfaces, we find that the original "doping" effect of impurities in ENZ media [4] is significantly suppressed, and the perfect transmission becomes immune to two-and threedimensional impurities of almost any material and shape.…”

“…The well-known divergent impedance mismatch of ENZ media can be removed by the EPs. More importantly, the original sensitivity of impurities in ENZ media, which can tune the transmission behavior from total transmission to total reflection [4,[12][13][14][15][16][17][18][19][20], can also be eliminated, leading to robust perfect transmission, irrespective of embedded impurities. In other words, the "doping" effect of ENZ media [4] is significantly suppressed, endowing the bulk system with the unprecedented property of impurity-immunity.…”

“…Previously, in the case of a connected defect such as a cylindrical wire of infinite length, without the PT-symmetric metasurfaces currently considered, it has been demonstrated that these impurities in ENZ media would lead to interesting doping effects, which can be used to tune the transmission behavior from total transmission to total reflection [4,[12][13][14][15][16][17][18][19][20]. We note that even the impedance-matched double-zero media (with both permittivity and permeability near zero) exhibit similar doping effects, resulting in impurity-dependent transmission properties [13,14].…”

“…Such extraordinary impurity-immunity effects for the infinite-sized impurities can actually be explained from the aspect of an effective medium by applying the doping theory [4]. In two dimensions, the ENZ medium with impurities embedded behaves as an effective medium with effective permittivity ε eff ≈ 0 and a tunable effective permeability μ eff .…”

“…Effective medium theories [1][2][3] have been developed to predict the modified bulk properties of electromagnetic media embedded with impurities in difference scenarios. Very recently, it has been observed that the bulk properties, as well as transmission behaviors of epsilon-near-zero (ENZ) media [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22], are very sensitive to embedded impurities. Based on this effect, a "doping" method has been proposed to control the impedance of ENZ media [4].…”